## Classroom Management

Classroom ideas, classroom community, teaching word problems in 2nd grade.

If you’re looking for a better way to teach word problems, and more importantly, want your students to be more successful in solving word problems, I’m here to help. Teaching word problems in 2nd grade doesn’t have to be a challenge.

## Why is teaching word problems in 2nd grade so hard?

When I first started teaching, I taught my students to use keywords, underline and circle, highlight and box…and yet, it didn’t help. They still didn’t know when to add and when to subtract.

And, my students didn’t understand or perform any better.

It didn’t help that I wasn’t consistently teaching or letting my students practice solving word problems.

Word problems have always been a source of contention for my students no matter what grade I taught (1st, 2nd, and 4th), and have always been something I’ve taught haphazardly as part of an adopted math curriculum.

Most math curriculums offer the following:

- 1 or 2 word problems at the end of each lesson, but don’t actually offer a way to teach students how to solve word problems
- 1 chapter on “problem solving”

And seriously, neither of those is helpful.

I wanted my students to get daily, strategic word problem practice.

And guess what? When I started teaching word problems in 2nd grade in a consistent, strategic way, my students were less frustrated, and much more proficient word problem solvers.

## So, what’s the solution?

Now, I follow a 4-day teaching plan, and assess on day 5.

I no longer teach key words or underlining, circling, highlighting, and/or boxing…instead, I teach my students to look for patterns in how word problems are structured…word problem situations.

In addition, I dedicate 5-10 minutes each day for word problem teaching and practicing.

## How do I know what to teach?

I start with the standard.

Honestly, no matter what I’m teaching this is where I start. I need to know exactly what the expectation is, so then I can help my students master it.

The Common Core standard for 2nd grade says:

CCSS.MATH.CONTENT.2.OA.A.1

- Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

While many states no longer use the term “Common Core” many of their adopted standards are the same, or at least similar.

MAFS.2.OA.1.1 (Florida Standards)

- Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

## So here’s what 2nd graders need to be able to solve:

- Addition/Subtraction within 100
- One-Step & Two-Step
- Put Together

When you look at what 2nd graders are supposed to do, it’s no wonder teaching word problems is so difficult, not to mention students actually getting the hang of them.

## How I teach word problems in 2nd grade:

At the beginning of the year, students are introduced to our word problem routine after the first couple of weeks of school.

I explain that word problems are like stories we have to read, and understand what’s going on in the story. We call these word problem situations.

Then, I teach students that there are 4 things they should always do when they solve a word problem:

- Write a Number Sentence
- I explain to students that I can’t hop inside their brains to see what they’re thinking, and if I don’t know what they’re thinking, I can’t help them become better word problem solvers.
- Students can draw a picture, use a fact family, base 10 blocks, and/or the standard algorithm.
- I look to see that the student has the correct answer.
- For example, instead of just saying “4,” my students write, “Cheyenne has 4 dogs.” This is important to connect math and writing, but also helps students check to see if their answer actually answers the question asked in the word problem.

Launching the word problem routine is all about modeling and routine. It doesn’t take long for students to get the hang of it.

I’ve done the hard work for you – I have 2nd grade word problems for the entire year, ready for you!

## What’s the 2nd grade word problem routine?

On Mondays, I introduce the word problem situation. I find it helpful to have students “act out” the situation. Use the example on the situation poster/anchor chart to show students the pattern. (I teach students that the underlined portions of the number sentence are pieces we know, while the square represents the unknown.)

Model and solve the practice word problem, and provide feedback to students.

For the next 3 days, we model and solve a word problem that has the same situation as Monday. So we’re not skipping around. This is very systematic.

Finally, on Fridays, students complete 2 word problems on their own following the same situation we’ve used all week.

For differentiation or extension, students can write a word problem on the back of their assessment that follows the same situation they learned that week. This is such a great way to see if students really understand the situation we learned that week.

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## Teaching 2nd Grade Word Problems

Teaching word problems.

Word problems was one of the biggest units I taught in 2 nd grade, and I know firsthand that teaching word problems to 2nd graders can be challenging. But as challenging as it can be, it is also extremely important. Word problems are a key skill for students and should be taught and reviewed throughout the entire year.

Before we talk about teaching 2nd grade word problems, let’s look at where students should be when they enter 2nd grade and how to handle below level students.

## What First Graders Should Know

Students entering the 2nd grade should have the following skills:

- Solve word problems up to 20 using addition and subtraction;
- Types of word problems: adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions.

At the beginning of the year, it’s beneficial to evaluate students’ understanding of adding and subtracting to 20. If they can add and subtract to 20 fluently, then move on to numbers 20-50. If there are a large group of students who still struggle, take some time to review the 1st-grade word problem standard 1.OA.A.1.

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

The only difference between the 1 st and 2 nd grade standards is that 1 st grade solves up to 20, while 2 nd grade solves up to 100. So if you do need to review 1 st grade standards, you’re still covering the practical concepts of the standard, just within a limited number range.

How much time you spend on review will depend on the levels of your students. If your students need it, it is helpful to allocate the entire first cycle of teaching word problems to review, which would put this at about two weeks. That may seem like a lot of time to review, but keep in mind that during this time you are teaching students about the different types of word problems and the problem-solving process. Working with numbers under 20 makes the computation more manageable and allows students to focus on learning the types of problems and the problem-solving process.

## Teaching 2nd Grade Word Problems: Day 1

Preparing for the lesson:.

- Create a poster to model a word problem. You can use my poster word problems from my 2 nd Grade Word Problem packet, or you can write your own.
- Print and laminate the Problem-Solving Process posters. Attach them to a ribbon and hang them in a convenient place where all students can see them. Make sure you can easily access the poster or move it for the lessons.
- Begin creating a “Types of Word Problems” poster. For day 1, you should include “Adding To” word problems. You will add skills to this poster as you introduce them to the students.
- Prepare one group word problem posters for each group for the students to use during group work. You can write your own problems or print one of the “adding to” poster problems in my word problem packet . A great way to engage your students is to write word problems with their names. I’ve also made my word problem packet editable, so you can type your class list and the problems will autogenerate with your class list!

## Opening the Lesson:

1) introduce the standard.

Introduce the standard. Tell students that you are starting by reviewing word problems they learned in first grade. Today students will work on “Adding to” word problems. “Adding to” problems mean you start with a number of something, and more gets added to your group.

## 2) Introduce the Problem

Show the word problem poster. Explain that you are going to show them how to solve this problem.

- Show the problem-solving process poster. Point to the first step. Explain that first, we need to read the problem and visualize it. Then model the skill by reading the problem and then explaining the picture you see in your mind.
- “Sweet Delights had 33 strawberry cupcakes. They baked 6 more. How many strawberry cupcakes does Sweet Delights have now?”
- I am imagining a cupcake shop with trays of cupcakes on the counter. They have a tray with 33 cupcakes, which is 3 rows of 10 and 1 row of 3. Next, I am imagining the baker coming out with 6 more strawberry cupcakes and adding them to the row of 3.
- Now I have visualized the problem (point to the first step on the process chart).

## 3) Retell for Comprehension

Next, I am going to retell the problem.

- Cover up the problem with your hands and retell the story to your class. Ask, “Did I get the gist of the problem?”

## 4) Identify Key Words

Now that I have retold the problem, I know I comprehend it, so I am ready to circle and underline key words. Model circling the numbers in the problem and underlining the key words.

- “Sweet Delights had (33) strawberry cupcakes. They baked (6) more . How many strawberry cupcakes does Sweet Delights have now ?”
- Check! I have circled and underlined the key words and numbers that will help me solve the problem.

## 5) Solving Strategy

Next, I am going to solve the problem using a strategy. For this problem, I am going to draw a picture.

- Draw a cupcake tray with 3 rows of ten circles and one row of 3 circles using a black marker.
- “I have the 33 cupcakes Sweet Delights started off with. Now, I am going to add 6 more.” Draw 6 pink circles on the tray.
- Now I have all of the strawberry cupcakes, so to answer the question “How many strawberry cupcakes does Sweet Delights have now?” I am going to count all of the cupcakes. I have 39 cupcakes.

*Note* In the beginning of 2 nd grade, drawing pictures and diagrams to solve problems is an appropriate method for solving problems. As students learn the problem-solving process, numbers will get more difficult and students should move to more efficient strategies.

## 6) Write Equation

Now that I have solved the problem, I am going to write an equation.

- This was an “adding to” problem, so I know this is an addition equation.

______ + _______ = ________

- Sweet Delights started with 33 strawberry cupcakes, so I know that is going to be the first number in my equation.
- Then, they added 6 more strawberry cupcakes, so I know that is going to be my second number.
- I know that after they added 6 cupcakes, they had a total of 39 strawberry cupcakes, so 39 is what comes after the equal sign.

## 7) Label Answer

The next step says to label my answer.

- What does 39 mean? Are there 39 puppies? Or 39 children? Maybe 39 pencils? No, it means 39 strawberry cupcakes.

## 8) Check Work

Now that I have my answer, you probably think I’m done, right? No! Math is awesome because we know there is often a right or wrong answer. There are lots of chances for making mistakes, but if we check our work, we will be much more confident we didn’t make a mistake.

- Model how to check your work by using a different strategy. The strategy could be using manipulatives, doing another picture, or counting on your fingers. After you’ve modeled checking your work, put a big check next to the answer to show this step is complete.

## Group Work:

Now students will have a chance to try the problem-solving steps with an “adding to” problem in their groups. They will make their own poster with their groups showing all of their work. Students love to work on chart paper or large construction paper.

(Note: It is important to set expectations for group work, including all students participate and help each other. When the teacher comes over to ask a question, all group members should be able to answer.)

As each group works on their problem, rotate to ask questions to check for understanding. If students make mistakes, don’t tell them directly. Instead, expect students to “catch it” when they check their work. After students have completed all of the steps, review their poster and allow them to go over their work in markers, so it stands out. Then, I select one group to share with the class how they solved the problem.

## Independent Work:

Next, students work independently on one of the 2nd grade word problems from my word problem packet . Pull students who are struggling into quick one on ones. Reteaching in small groups can also be effective, but it is usually sufficient to have students work independently while you monitor and ask questions to guide them in the right direction. Don’t forget that the goal is to get them to be more independent!

Right before the end of the work period, walk around the room one more time to observe students working. Select one student who has followed the steps and gotten the correct answer to share how they solved the problem. (Note: At the beginning of the unit I liked to purposefully select students who “get it”, but as the unit progresses, I think it is important to have students share who may have skipped a step or gotten the wrong answer.

At the beginning of this unit, I would only give students 1-2 problems to practice each day. This is of the utmost importance. Less is more because the goal is to get students to master the problem-solving process. Giving students too many problems early on can overwhelm their learning process and put too much focus on getting answers just to get it done.

Start by collecting all independent work. Then have the selected student share how they solved the problem. Initially, it is important to have the student share the whole process, but as the unit and year continue and students have mastered the process, you can shorten this by having a student share one step they did.

To ensure students have mastered the problem solving strategy, I always gave a short quiz on the last day or before beginning the next strategy. My word problem packet also includes short, 2 question quizzes so ensure your students are on track.

## Building on Word Problem Skills:

Continue this routine each day, going through a different type of story problem. Here is a sample schedule:

Adding to, taking from, putting together, and taking apart problems tend to be easier for students to grasp, because they have the most exposure to these. Comparing, unknown, and multistep problems are much more challenging, so you may need a few days to focus on these.

After teaching all of the typse of problems, I assess students on 2.OA.A.1 with the number range I taught. You can find assessments for 20-50, 50-100, and 100-1,000 in word problem packet .

## The Big Picture:

While teaching 2nd grade word problems throughout the year, use this same process to build on student’s problem-solving skills.

When students are learning to add and subtract to 100, do another unit on problem-solving with numbers to 100. When students are learning to add and subtract to 1,000, you can expand on the skills and do a problem-solving unit with numbers to 1,000, despite the standard only going to 100.

Other thoughts

- While teaching 2nd grade word problems, I place a strong emphasis on the problem-solving process. As students begin to understand the steps and develop their problem solving skills, it is important to give them flexibility. Everyone’s brain works differently, and we may do some steps in a different order. For example, it may make more sense for some students to write their equation before they solve the problem, but others may need to work the problem out first. Some students may circle key words while they read the problem because this helps them comprehend. Remember to remain flexible with students and don’t be afraid to suggest different approaches to help them grasp the concepts.

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## 3 Reads Strategy to Problem Solve

Problem solving strategies in math are not always as easy as they seem. Many times, students read a mathematical problem and have no idea what to do from there. I’m often asked how to teach word problems. Word problems especially tend to give students the most trouble because they oftentimes require multiple steps in order to solve. They also require reading and comprehension skills. Although there are multiple problem solving strategies in math, one of my favorite ways to break down these steps is to use the 3 reads strategy for problem solving. Read on to learn how it works!

## How to Implement the 3 Reads Strategy

In order for the 3 reads strategy to be successful, it’s important that you introduce it to your students by explaining the various steps and the goal of each step. Just like the strategy says, let your students know that you will be reading the math problem 3 times. Each time you read the word problem, you will be looking for different pieces of information each time. This is a much different approach than other problem solving strategies in math, but it is highly effective.

You can watch a break down of the 3 reads strategy in my YouTube video below.

## First Read: What is the problem about?

Teacher reads the problem stem out loud only.

The most important concept for your students to understand is that with the first read, they will NOT be able to see the math problem. The teacher will read the question orally while your students listen carefully. They will begin to think about what the problem is about.

I always provide an opportunity after the first read for my students to turn and talk with their shoulder partner about what they just heard.

Overall, the main objective of this step is for students to get a general, brief overview of the word problem. Do not worry if your students don’t pick up on the small details yet. We will work on that in the next step.

## 3 Reads Strategy Anchor Chart

During the first read, I like to guide students with this 3 reads strategy anchor chart. This will help you visually represent the various pieces of information you’re looking for during the reads and help guide your students’ thinking.

## Second Read: What are the quantities (numbers) & units?

Teacher displays the math problem and tells students to focus on the numbers within the problem..

Throughout the second read of the 3 reads strategy, students will now be given the first opportunity to see what the math problem looks like. You can share it on your whiteboard or under your document camera. Sometimes I would print the problem on a piece of paper and have it face down on my students’ desks. During this step they would be allowed to flip the paper over and look at the problem.

In the course of the second read, I also like to have the whole class participate in a choral read of the math problem. Since this is the first time they are actually seeing the problem, it can be helpful to read it aloud together. One of the key factors for this step is to inform students that there are always quantities or numbers that need to be counted within mathematical problems.

## 3 Reads Strategy Interactive Notebook Activity

Students can use this interactive notebook activity to break down the 3 reads problem solving strategy in math. You can have students cover the word problem during the first read or have them glue it to the top of their page during the 2nd read.

They can lift the flap and record their thoughts about what the problem is about. They will use this activity to guide their thinking through all of the reads. This goes along perfectly with the whole class 3 reads strategy anchor chart.

## Third Read: What are the possible math questions you could ask about this problem?

Teacher chooses one student to read the question one last time..

As this student is reading the question for the final time, it’s crucial for your class to think about any math questions they can come up with about the problem. I always like to use this step to ask my students, “Can we come up with multiple questions that we can ask about this problem?”

You will notice that you may have to do a little extra digging to really get students thinking during this step. Sometimes probing a few extra questions is necessary so that your class can think more critically and still stay on track. List all the possible questions that your students come up with and decide which one you want to tackle together.

## How To Teach Word Problems

You can have this FREE 3 Reads Strategy problem solving template sent straight to your inbox to use with your own students. All you need to do is fill out the form below. I recommend using your home email address because school spam filters like to block these emails sometimes.

After you’ve done the 3 reads strategy for problem solving a few times as a whole group, give students the opportunity to try it on their own with a partner. Working on problem solving strategies in math is one of the best ways to set students up for success!

If you’re looking for resources where you can incorporate this strategy, be sure to check out my problem solving units ! You can find examples of word problems comparing part-part whole-whole unknown as well as comparing difference unknowns !

You can also check out my problem solving strategies in math posters to help your students break down what to look for when solving word problems.

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## 4 Tips for Solving 2nd Grade Math Word Problems

Last Updated on August 31, 2021 by Thinkster

Math word problems are challenging for students at any age, but particularly for second graders who have barely mastered their reading skills. Becoming proficient in math word problems is crucial in 2nd grade because it sets children up for success in the grades to come. Fortunately, math word problems at this age are less complex than the ones they will see in later years, so you can implement the following common strategies to help your child become an expert . Here are some tips to help with these math problems.

## 1. Read the problem aloud

Because students this age read at varied levels, not every second-grader will fully understand a word problem on his first pass through. Reading the problem aloud can be quite helpful, especially with a child who hasn’t completely mastered reading. Of course, there will be times when a student won’t be allowed to speak (for example, during tests), but when at home working on word problems, encourage your child to read the story aloud and actually hear what the problem is asking. And for tests, even mouthing the words silently will give a student a better mental image of the problem.

## 2. Circle the numbers

Ultimately, every word problem will include the numbers necessary to arrive at an answer. Students should circle these numbers so they are easier to find during the solving process. If a number is spelled out, kids can circle the words and write the numeral above or near it so she is just dealing with digits. Once she devises a strategy to solve the problem, the numbers are already standing out for her to insert into whichever operation she’s using.

## 3. Look for keywords

Certain words give clues to what operation is being asked for, and second-grade math word problems are no exception. For example, total, sum, together , and how many all suggest addition; difference, how many more, take away , and fewer all point to subtraction. As your child learns these keywords and spots them in word problems, she will be able to arrive at a solution strategy more quickly.

## 4. Draw it out

If the structure and information of a word problem are too confusing, illustrating the problem in her own terms may help your child figure out the math and come up with an answer. Bar graphs, pie charts, tally marks, or whatever works for a particular student can do wonders toward solving a word problem. Even just writing out the numbers from the text again can help establish her own space and parameters that will make a solution easier to reach.

Do 2nd grade math word problems confuse your child? Check out our Thinkster math worksheets for some extra practice to help your child master math word problems .

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## How to help a 2nd grader with math

The top 10 tips to help your 2nd grader progress in math while boosting their confidence and making learning enjoyable along the way!

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Published July 18, 2023

- Key takeaways
- Lack of sleep, low motivation, or a disconnect between school and home learning can contribute to math struggles in second graders
- Unleash your 2nd grader’s joy of math through engaging activities, real-world connections, and a positive mindset.
- Math apps are a smart and affordable option (plus, they’re enjoyable!) instead of hiring a private tutor for your second-grade child.

## Table of contents

- 10 ways to help with math
- FAQs about math help

Is your second grader facing challenges with math? Lack of sleep, decreased motivation, or a disconnect between school and home learning can contribute to their struggles. As parents, it’s important to understand the 2nd grade math curriculum and identify specific areas where your child needs assistance. In this article, we’ll provide you with ten effective strategies to support your 2nd grader in overcoming math challenges and achieving success. Let’s unlock your child’s math potential together.

## 10 ways to help your 2nd grader with math

Math help for 2nd graders is simpler than you think. It just takes time, patience, and a bit of creativity. Take a look at our recommendations for second-grade math help and try them out with your child this week.

## 1. Boost confidence through encouragement

Celebrate your child’s efforts and achievements in math, emphasizing progress rather than focusing solely on correct answers. Let them know that making mistakes in math is how you grow and it is okay to need 2nd grade math help.

## 2. Make math fun with engaging activities

Explore math beyond textbooks by incorporating fun activities like math games , puzzles, and real-life math challenges. Find interactive math resources, both online and offline, that align with your child’s interests. Math apps , math scavenger hunts , and and 2nd grade math practice problems are all great tools to help weave math into your child’s day to day.

## 3. Practice math at home

Set aside regular time for math practice at home. Work together on math problems, utilize flashcards, or engage in math-related projects that involve hands-on learning and problem-solving.

## 4. Foster a positive attitude

When wondering how to help a 2nd grader with math , show enthusiasm for math and highlight its relevance in everyday life. Encourage a growth mindset, where mistakes are opportunities for learning and improvement.

## 5. Set achievable math goals

Math help for 2nd graders includes setting realistic math goals, such as mastering identifying new shapes or improving on greater than and less than skills. Break down the goals into smaller milestones to celebrate progress along the way.

## 6. Connect math to real-life scenarios

Demonstrate how math is in everyday situations, such as counting the money they earned from doing chores, measuring how much water it takes to make lemonade, or practicing telling time when they wake up and go to sleep.

## 7. Encourage math dialogue

Engage your child in math discussions by asking open-ended questions and encouraging them to explain their thoughts. This promotes critical thinking and strengthens their understanding of math concepts.

## 8. Collaborate with teachers

Stay in touch with your child’s math teacher to understand the second grade math curriculum and identify areas where your child may need additional support. Collaborate on strategies to reinforce learning at home.

## 9. Celebrate progress and effort

Recognize and reward your child’s progress and effort in math. Focus on the process rather than just the outcome. Use positive reinforcement, such as praise, small rewards, or a special math-related outing to motivate them.

## 10. Try a math app

Introduce your child to DoodleMath, an app for math help that offers personalized math lessons tailored to their learning needs. It provides a scaffolded approach, gradually introducing concepts and building a solid math foundation.

## Math apps vs tutoring

Your child may need more support than just your encouragement in the subject. While private tutoring is a wonderful option, the popularity of personalized math practice apps is growing. Both options have unique strengths when choosing the best option for your child.

Math apps offer convenience and accessibility, allowing kids to dive into math anytime and anywhere. The interactivity and fun features of these apps make learning math an engaging adventure.

However, it’s essential to remember that tutoring offers something special too. Tutors can cater to a child’s specific needs via hands-on instruction. Keep in mind, one to two tutoring sessions can cost you the same amount as a full-year subscription to a math app like Doodle.

Ultimately, the decision between math apps and tutoring depends on what works best for your child and their learning style.

## FAQs about 2nd-grade math help

We know helping a second grader with math can be hard so we’ve provided a few frequently asked questions many parents have when their child needs help with math.

To help your 2nd grader with math, encourage them to practice basic math facts regularly, use manipulatives for hands-on learning, incorporate math into daily activities, and engage in math games and puzzles for problem-solving practice.

In 2nd grade math, students should have a solid understanding of addition and subtraction, counting up to 1000, comparing two- and three-digit numbers, place value, solving simple word problems, recognizing geometric shapes, working with money, and measuring length, weight, and time.

To develop number sense, allow your child to work with numbers in various contexts. Please encourage them to count objects, estimate quantities, and compare numbers. Practice skip counting by twos, fives, and tens to strengthen their understanding of number patterns. Engage them in number talks, where they can discuss strategies and reasoning behind their mathematical thinking.

The recommended time for a 2nd grader to practice math at home can vary. It is generally recommended to spend10-15 minutes per day on math practice. This duration allows for consistent reinforcement of concepts without overwhelming the child. However, every child is unique so you can adjust the time based on your child’s attention span and learning needs. Maintaining a balance between practice and ensuring that math learning remains enjoyable for them is crucial.

To help your child with word problems, encourage them to read the problem carefully, underline key information, and identify the mathematical operations involved. Encourage them to visualize the problem using drawings or manipulatives. Guide them to break down the problem into smaller steps and check their answers for reasonableness.

Lesson credits

Michelle Griczika

Michelle Griczika is a seasoned educator and experienced freelance writer. Her years teaching first and fifth grades coupled with her double certification in elementary and early childhood education lend depth to her understanding of diverse learning stages. Michelle enjoys running in her free time and undertaking home projects.

MIchelle Griczika

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## 2nd Grade Common Core Resources

These tasks are grade-level formative performance assessment tasks aligned to the Common Core State Standards for Mathematics. Some have accompanying scoring rubrics and discussion of student work samples. Others, such as the Dana Center Early Mathematics Tasks, connect to children’s literature.

You may download and use these tasks for professional development purposes without modifying the tasks.

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Inside Problem Solving Got Your Number (2.OA.B.2) Squirreling It Away (2.OA.1) Performance Assessment Tasks Incredible Equations (2.OA.2) Pam's Shopping Trip (2.OA.3) Dana Center Early Math Tasks One Hungry Monster, the Eleventh Hour (Series) (2.OA.1)

Inside Problem Solving Got Your Number (2.NBT.A.1, 2.NBT.A.4, 2.NBT.B.5) Miles of Tiles (2.NBT.B.5) Performance Assessment Tasks Apple Farm Field Trip (2.NBT.5, 2.NBT.6) Carol's Numbers (2.NBT.) Peanuts and Ducks (2.NBT.5, 2.NBT.7) Pocket Money (2.NBT.5, 2.NBT.6) Sheep and Ducks (2.NBT.5) Dana Center Early Math Tasks One Hungry Monster, the Eleventh Hour (Series) (2.NBT.1, 2.NBT.3, 2.NBT.8, 2.NBT.9)

Inside Problem Solving Courtney’s Collection (2.MD.C.8) Digging Dinosaurs (2.MD.C.8) Through the Grapevine (2.MD.D.9, 2.MD.D.10) Dana Center Early Math Tasks One Hungry Monster, the Eleventh Hour (Series) (2.MD.6)

Inside Problem Solving Part and Whole (2.G.A.3) Piece it Together (2.G.A.1) The Shape of Things (2.G.A.1) What’s Your Angle (2.G.A.1) Performance Assessment Tasks Don's Shapes (2.G.1) Half and Half (2.G.2, 2.G.3)

## Related Lessons

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## 2nd Grade Math - ¿Como Se Suma? How Do We Add?

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## Real World Problem Solving in Second Grade Mathematics

Introduction.

Edgewood Magnet School in New Haven, Connecticut is an arts magnet school, integrating the arts across the curriculum. Students in this environment are encouraged to use the strategies of observation, interpretation, and analysis to increase their thinking skills in every subject. With that mission, both teachers and students use unique and exciting approaches to “the basics” and work together to ensure that all learners are included.

For most second graders, the beginning of the year is a time for refreshing knowledge and skills from first grade. The summer away from direct instruction and opportunities for practice and guidance sometimes means a loss of solid understanding of learned concepts in mathematics. This three- to four-week unit is designed to review and build new understanding of one-step word problem solving using addition and subtraction as students develop skills and strategies they will use all year. The students, through a series of mathematical scenarios, will use the problem types identified in Table 1 of the Common Core Mathematics Glossary which covers addition and subtraction. 1

The Common Core concentrates on a clear set of math skills and concepts. Students learn concepts in an organized way during the school year as well as across grades. The standards encourage students to solve real-world problems. 2

The Common Core calls for greater focus in mathematics. Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom. This means focusing sharply on the major work of each grade, which for grades Kindergarten through second grade includes concepts, skills, and problem solving related to addition and subtraction.

The New Haven Public School district uses the Math in Focus Singapore Approach, a Common Core-based curriculum for students from Kindergarten to Fifth Grade. The student books and workbooks follow an instructional pathway that includes learning concepts and skills through visual lessons and teacher instruction for understanding the how and why; consolidating concepts and skills through practice, activities and math journals for deep math understanding, hands-on work in pairs and in small groups; and, applying concepts and skills through extensive problem solving practice and challenges to build real world problem solvers. 3

This approach embeds problem solving throughout each lesson and encourages frequent practice in both computation and problem solving. The word problems appear throughout each chapter and progress from 1-step to 2-step to multi-step. Each chapter concludes with a challenging problem or set of problems that require students to solve some non-routine questions. To solve these problems, the students need to draw on their deep prior knowledge as well as recently acquired concepts and skills, combining problem solving strategies with critical thinking skills, including classifying, comparing, sequencing, identifying parts and whole, identifying patterns and relationships, induction and deduction and spatial visualization.

The second grade text begins with numbers to 1000. Students begin by expressing numbers in standard form (231), expanded form (200 + 30 + 1), and word form (two hundred thirty-one). This is accompanied by concrete representations via base ten blocks, and, for two digit numbers and a few three digit numbers, representation by trains of rods, of lengths 1, 10 and 100. This initial chapter also includes sequencing numbers and comparing using greater than and less than terminology, and then moving right into addition and subtraction of two- and three-digits numbers. Here the take-away should be, if you have more hundreds, the tens and ones don’t make any/much difference; and if you have the same number of hundreds, but more tens, then the ones don’t make any/much difference. Most of my students (if not all) struggle from the start! They do not seem to have a solid foundation of understanding numbers to 100 or the concept of place value in general. This unit is designed to get ahead of the frustration that the students feel when pushed too quickly before they have a firm understanding of principles of place value and the properties of operations.

This unit launches the school year with 1-step addition and subtraction problems of all types using numbers to 10. The goal is to spend time practicing basic computations with numbers that student can work comfortably with before jumping right into the district curriculum. Once there is a level of understanding with these problem sets (numbers to 10), students will move on to solving 1-step problems using teen numbers and then onto numbers to 100. Most of the curriculum problems at the start of the year require addition and subtraction of 3-digit numbers. Some students will move quickly through the problem sets with numbers to 100 and will be ready to work with the regular curriculum.

For the duration of the unit, the focus will be steadily on solving and later constructing a collection of word problems that provide robust and balanced practice. Problems sets will be based on a scenario which will provide the substance of the story. Each scenario will allow us to extract several problems, changing the numbers and ensuring each set of numbers makes a reasonable problem. This idea looks like the following: John has 8 crayons in his box. He shares 3 with Sam. How many crayons does John have left in the box? John has some crayons in his box. He shares 3 with Sam. John has 5 crayons left in his box. How many crayons did John start with? John has 5 crayons. Sam has 2 fewer than John. How many crayons does Sam have? John and Sam are sharing crayons. John has 5 and Sam has 3. How many crayons do the friends have together? The two students participate in several crayon-sharing stories that use the same set of numbers but in slightly different situations. Some situations are more obvious and direct while others take more thinking. It is important to provide opportunities for students to work with and solve the different problem types that can be created from one set of numbers. 4

## Background: Problem Types

The taxonomy of addition and subtraction problem types as identified in the Common Core State Standards of Mathematics Glossary is a framework that sorts one-step problems into three broad classes: change , comparison , and part-part-whole . Each of the three classes is then separated further into a total of 14 problem types sorted out as follows: change , in which some quantity is either added to or taken away from another quantity over time; comparison , in which one amount is described as more or less than another amount; and part-part-whole , in which an amount is made up of two parts. 5

Within the group of change problems, there are two subgroups: change-increase , in which a quantity is added to an initial amount and change-decrease , in which a quantity is taken from an initial amount. We might recognize these subgroups more familiarly as “add to” or “take from.” Additionally within each of these subgroups, there are three possible unknown quantities. One scenario to show change-increase : 2 kittens were playing with some yarn. 3 more kittens join them. Now there are 5 kittens playing with the yarn. Using these quantities, the unknown might be the result (2 + 3 = ?), an unknown quantity of change (2 + ? = 5) or an unknown initial amount (? + 3 = 5). In the change-decrease subgroup, there are again three possible unknowns. A scenario for this example: 5 birds are sitting on the branch. 2 fly away. Now there are 3 birds sitting on the branch. Here again the students might solve for the final amount (5 – 2 = ?), the amount of change (5 - ? = 3), or the initial amount (? – 2 = 3). This gives in all six types of change problems.

Similarly comparison problems can also be categorized into two subgroups: comparison-more , in which one quantity is described as more or greater than another, and comparison-less, in which one quantity is described as less or fewer than another. Here again, each of these two subgroups has three possible unknowns, for a total of 6 types. Sam has 6 marbles. James has 8 marbles. James has 2 more marbles than Sam. The unknown quantity may be the lesser amount (? + 2 = 8), an unknown greater amount

(6 + 2 = ?), or the unknown difference (8 – 6 = ?) one quantity that is more and one that is less. Using this same scenario for a set of comparison-less problems, the language need to change from “more than” to “less than.” Here is a way to present this set with the language adjustment: Sam has 6 marbles. James has 8 marbles. Sam has 2 fewer marbles than James.

Part-part-whole problems are a set of two quantities, the parts that, when put together, make up a whole quantity. This problem type seems very like to change category but in this problem type there is no change over time. The two parts play equivalent roles, which allow for only two possible unknown categories: either a part is unknown or the whole is the unknown. There are 4 large dogs and 3 small dogs. There are 7 dogs in all. One of the parts may be unknown (4 + ? = 7 or ? + 3 = 7) or the unknown may be the size of the whole (4 + 3 = ?). Since the parts are interchangeable, there are only 2 types in this class of problems.

The following chart sort these classes and categories into the framework. Located in Appendix A of this unit is a set of example problems illustrating each of these 14 types.

## The Scenarios of the Problems

For second graders, life at school is a large part of their world. Most of my students arrived at Edgewood for their Kindergarten year and stayed through First Grade making the year in second grade essentially their third year at the same school. They are comfortable in the building and know many of the other students. They will become the active players in the math stories that I, and we together, will construct. Activities that occur in the classroom, in the cafeteria, on the playground, and on the bus seem to be recognizable situations that will help with the basic understanding of context.

Additionally, there are opportunities for students to incorporate the topics and learning that occur in the other subjects, such as science, social studies, literacy, art, music and, in our school, dance and drama. One example might be to create set of story problems centered on the life cycle of the butterfly, a unit of study each year in second grade. With the common knowledge the students will be obtaining, this content could become the scenarios for word problems. An example might be: Seven caterpillars climbed up the branch and formed their chrysalises. Later that day, three more caterpillars climbed up the branch and formed their chrysalises. How many chrysalises are hanging from the branch? Similarly, using the characters in a book read together as a class could provide the characters in a new set of problems. Curious George had a bunch of bananas. He ate 4 of them. Now he has 3. How many bananas did Curious George begin with? The use of common or thematic content will not only connect all the thinking and practicing, it will provide tangible and real situations. With an established scenario, students will work with a set of numbers, determining the unknown within each of problems types.

## Creating the Problems

A question that is frequently answered with a guess is “What should we do to answer the question to solve the word problem?” The fundamental understanding of what is being asked is not apparent to the students, making the solution inaccessible. Most first graders entering second grade have a basic understanding when the story (problem) is categorized as final unknown or whole unknown , but most other components of the taxonomy are unfamiliar to them or just too difficult to decode. To begin to help them with their thinking, they will use concrete models, such as themselves (2 children are sitting at the reading table, 4 more join them) acting out scenarios. Many basic materials in the classroom – pencils, notebooks, folders, crayons – can be used to create and design scenarios, with each type of problem represented.

## Solving the Problems

Following the overall plan of the Singapore Math program, the students will solve problems using the concrete, pictorial and abstract approach. Because this is a standard approach in our district mathematics instruction throughout the year, the students will begin with this set of strategies to solve problem sets.

Word problems are written as stories and scenarios making language a consideration in crafting the problems for the beginning second graders. Word problems are as much about language and reading as they are about math. If the story is not understandable, how can students begin the know what to do with the numbers they’ve been given and the question they’ve been asked? Thus, words and vocabulary need to be appropriate and useful for the variety of reading levels of the incoming students. The structure of word problems should be understandable and clear, accessible in language as well as numbers. Also, the language, especially the words that express the relationship between the quantities involved, should be discussed to ensure that it is familiar to all students.

This is a clear integration of Language Arts and Mathematics and a method in which students can connect math to the real world, in this case, through the activities they engage in at school. Reading skills and computation skills come together with even the simplest of word problems.

## Structure of Problem Collection

The content introduction over the duration of this unit includes a certain sequencing and scaffolding to guide students through the 14 problem types. To begin the unit, students will only be working with numbers to 10. This is an important starting place to ensure that understanding is occurring. Most of my second graders are capable with addition and subtraction to 10, but are not so comfortable with the word problem language. So first, students will be challenged more by the language than the arithmetic. Students will practice figuring out what exactly the problems are asking with problems that they are familiar with before moving on to a new step. Practicing all the problem types will improve and increase strategies and confidence!

With addition and subtraction within 10 mastered, the next phase of the unit moves to numbers to 20. The key is to continue with scenarios that are obvious and repeated as new numbers are introduced. An example of this transition would be these parallel problems:

6 students got on the bus at the first stop. 3 students got on the bus at the second stop. After the second stop, how many students are on the bus? ( change-increase, final unknown)

Some students got on the bus at the first stop. 3 students got on the bus at the second stop. Now there are 9 students on the bus. How many students got on at the first stop? ( change-increase, initial unknown)

These now become:

11 students got on the bus at the first stop. 7 students got on the bus at the second stop. After the second stop, how many students are on the bus? ( change-increase, final unknown)

Some students got on the bus at the first stop. 7 students got on the bus at the second stop. Now there are 18 students on the bus. How many students got on at the first stop? ( change-increase, initial unknown)

When working with numbers to 20, it is essential that students understand that the “teen” numbers (11-19) are really 10 and some ones. Students should work with numbers within 20, creating equations using their knowledge and skill of making a ten first. In the case of 7 + 6, making a new ten looks like this:

7 + 6 = 7 + 3 + 3 = 10 + 3 = 13

Because 7 needs a 3 to make ten, and 6 is composed of 3 + 3, this equation shows the progression of making 10 and some more. Practicing this method using two ten frames demonstrates the process concretely. In the example above, students use the ten-frames to show 7 and 6 separately. To make the new 10, students will move 3 from the 6, which now shows 10 and 3 more or 13.

As mentioned earlier, it is obvious that the most accessible problem types for students entering the second grade are the change-increase or change-decrease, result unknown and part-part-whole, whole unknown. The general go-to strategy for solving a word problem seems to be to just take the two numbers you see and add them together, or maybe subtract, but often the students are just unsure. It seems that these are the most practiced problem types, which leaves students without balanced experience with all 14 types and ultimately without some strategies to employ as they problem-solve. Students need to see a broad range of problems to gain a strong understanding of how addition and subtraction are used and how they are related to each other. The notion of example sufficiency means students should be exposed to a wide array of examples to provide well-rounded practice with the concept. 6

## Teaching Strategies

The approaches for this curriculum unit vary to reflect the learning styles of all students.

The general format is based on the workshop model. The concepts and skills are taught through a series of mini-lessons focused on the objective with the following methods used throughout:

Experiential Learning: Most young students need to begin with hands-on learning. Using concrete models to work out math stories allows students to see the problem and manipulate the pieces as the story progresses. This type of learning is an important first step.

Differentiated Instruction: Lessons and activities will be targeted to maximize learning. The students will use a variety of approaches, working sometimes individually and sometimes in small groups, determined by the complexity of the work. Some students will move more quickly as they master skills and some will need more opportunities for practice.

Cooperative Learning: The students will be given opportunities to work as cooperative groups to create math stories to present to the class. This strategy will allow students to work collaboratively taking on various roles necessary to complete the work, with a focus on success for all.

## Classroom Activities

Activity 1: sequenced problem types – problems to 10.

The introduction (and review) portion of the unit covers all problem types but in a sequenced manner. The objective is for students to read and interpret a word problem with guided instruction followed by independent practice. Because of the many problem types, this part will take several days of review and practice before students are comfortable beginning to write their own sets of problems. Based on student need and pace of understanding, I expect this section to be a four- to six-day set of lessons, more if needed.

The sequence is as follows: part-part-whole ; change-increase and change-decrease ; and finally, compare-greater and compare-fewer . The following introductory sessions are designed as a whole group activity, with students either at their desks or gathered on the rug close to the board or easel. The whole group portion should be 20 minutes at most. At the close of each session, I will give students between 5 and 10 similar problems to solve. More capable students can begin to generate their own problems during the independent work time.

Beginning with the fundamentals provides a good opportunity to get to know students’ skills which is helpful in preparing differentiated work and creating groups,

In this lesson, students will interpret real world problems and with the help of manipulatives and pictures, solve part-part-whole stories using addition and subtraction.

6 girls are playing

3 boys are playing with them.

How many children are playing in all?

Begin the story with the whole unknown as in this example. This type of story is perfect for students to act out right in the classroom. Write the story on the board or chart paper and have students volunteer as actors. Once the students have solved the problem, write the math sentence to show what happened: 6 + 3 = 9 students. Explain that the 2 parts (boys and girls) have made a whole (children). With the students still in acting position, present a new approach to this scenario:

9 students are playing.

6 of them are girls.

How many boys are playing?

With this visual example, students should see right away how many. The important concept to demonstrate is that the parts can be determined when the whole and one part are known, in this case 9 is known as the whole and 6 as one part. Again, write the math sentence to show this calculation: 6 + ? = 9 and include the strategy of starting with the whole to determine the missing part as a subtraction sentence 9 – 6 = 3. Practicing both approaches to the solution will help students connect addition and subtraction and recognize how they are used together.

Since this lesson requires students to read story problems, I will pair fluent readers with those who are less fluent, provide counters for those who want them, and allow partners to work together to solve and problems and share the strategies that they used.

I will use two more examples, like the ones below, to demonstrate, remembering to write the word problem on the board as well as the math sentence. I will also reword the problems to have the part as the unknown.

Hannah has 5 red markers.

She has 3 blue markers

How many markers does Hannah have in all?

7 students are drawing with crayons.

2 students are drawing with colored pencils.

How many students are drawing?

Continuing with this same idea, the next set of problem types includes change-increase and change-decrease . Although part-part-whole is language that students can adopt and use while discussing their work, the change-increase and change decrease language is a bit trickier. The use of the word change is more appropriate for students to demonstrate that some amount has been either added or subtracted from an initial amount.

Introduce the word problem below which is an example of the unknown result in the change-increase category.

Jason had 8 “caught being good” stickers on his chart at the beginning of the day.

During the school day, he earned 2 more stickers.

How many stickers does Jason have on his chart at the end of the day?

Student can solve the problem as written and, using the same scenario, challenge them to create the change-unknown and initial unknown story. One example might be:

Jason had some “caught being good” stickers on his chart at the

beginning of the day.

At the end of the day, he has 10 stickers.

How many stickers did Jason have at the beginning of the day?

This is an oral activity, with me writing the adjusted version across the board, placing the math sentence underneath. It is important to allow students to work on composing the problem so they can begin the see the relationship between the problems and what the problems are asking.

The goal is for students to understand and not just solve. I can informally assess during the discussion of rewriting the text of the word problem, with more formal assessment later in the unit.

The next category to introduce is the change-decrease problem types. Following the same format as before, I will introduce the result unknown, change unknown and then initial unknown.

Crystal collected 7 leaves for her project.

2 leaves blew away in the breeze.

How many leaves does Crystal have left for her project?

Again, the goal is for students to understand and not just solve.

The third broad class, compare, is more difficult for my 2 nd grade students. This requires the text of the word problems to be very straight-forward. Students should not get tangled up when they are learning to take the data from the problem. Remember that using the exact terminology is not the goal, but rather understanding what the problem is asking. Here are three ways I will present a scenario that shows the problem types comparison-more , and three ways to show comparison-less. Students need to be exposed to and have opportunities to practice all types. Of course, not all of these examples should be used at one time. As I write the problems out on chart paper and post them in the classroom, the students can begin to see and do their own comparing and contrasting as one scenario is explained in different ways. The use of the words “more” and “fewer” should be highlighted and explained as the problem set is introduced and worked on. My role here is to let the students begin to notice the subtle differences in the wording and how it changes the thinking. Simpler is better to start with!

Throughout these introductory sessions, the students and I will brainstorm scenarios that can eventually be used in own word problems. Ideas should generate from school activities and materials, guiding students to think of what students can actually use for manipulatives or, as in the first scenario, be able to act out to solve. By keeping a list of ideas on chart paper as reference material, students won’t struggle with vocabulary or appropriate scenarios; they will be on to the task of crafting their problems. This list will prepare the students for the second part of the unit.

## Activity 2: Classroom / school scenarios

As stated earlier, words and vocabulary should be accessible to students and not a challenge or hurdle. The goal is to get to the thinking of the stories and plugging in the information that was gathered during the brainstorming session. To begin this portion, review the charts and add more if students have new ideas. It may be helpful for the purposes of composing word problems to have the information in categories, such as these:

Materials We Use

Classes We Attend

Activities at School

Classmate’s Names

I will create groups of two or three students to have them write problems of their own to share with the class. Since this lesson requires students to read and write story problems, again, fluent readers and writers with those who are less fluent, provide counters for those who want them, and allow partners to work together to solve and problems and share the strategies that they used.

The goal during this period of time is to challenge students to write the same problem but try it another way, choose a different type as they tell the story. The timing for the student groups to work together will be during arrival time as morning work and during the math workshop portion of math instruction time. This will allow students to work as much as 30 minutes per day with their partners to create some math stories.

I will stress that it is important to keep their collection together as much of their work will become part of the workbook they will create at the end of this unit. Folders and math journals can be helpful, or my collecting the work-in-progress daily is another option.

## Activity 3: Science Scenarios

The first unit in 2 nd grade science is investigation and research on the life cycle of the butterfly. Students receive caterpillars at the start of the semester and observe and record the changes the caterpillar’s life. The work that the students do during their science lessons can become the information and scenarios they can use for crafting word problems.

Using all different problem types, we will write several together as a class. This is an additional opportunity to integrate math very specifically into our science research and work. It is important for students to recognize that, although their learning has been compartmentalized into subject areas, it is essentially impossible to separate it all out into categories. So this portion of the unit uses math, science and reading to help students learn about the life cycle of a butterfly (and other animals as well).

Students will create problem sets that use their daily experiences tracking their caterpillars. Each student has 2-3 caterpillars to observe and record information on, which can become the start of word problems. Examples to start: If Table 3 has 8 caterpillars and 2 caterpillars join that group, how many caterpillars are being observed at Table 3? Here are 28 students in the class. Each student need one cup of caterpillar food. There are 30 cups of caterpillar food. How many more cups of food are there than students?

There are often students who have great interest in other areas of science. This is an area to encourage if students are excited about sharing their knowledge. Some students will be more inclined to use the unit of study going on in class, but throughout the literacy portion of the day, students are exposed to a great deal of non-fiction, or informational text, that could certainly enrich our science word problems.

Throughout the duration of the science unit, students will continue to write word problems of various types to eventually include in our final project, the workbook. These problems can be written during the morning work session, during math workshop, and at the end of science class. By the end of the unit, each student should have two problems to add to the Science chapter of the workbook.

## Activity 4: Creation of Workbook / Publishing Celebration

The goal of this portion of the unit is to sort the word problems into “chapters” and create a workbook to share at the Publication Celebration. Chapters will be titled by subject or category, depending on student choice and teacher suggestion. Ideas include Beginning Stories, Classroom Activities, Playground Fun, Science & Math, and Social Studies Connections. Let students be creative with titles!

Students will submit their work which will include at least one word problem for each chapter. They must also submit the solutions to their problems so that they can be included in an answer key. Each chapter will have at least 25 problems, with examples of all types and with varying levels of difficulty. Word problems can either be typed or hand-written for the final workbook, depending on what the students decide as a class. One workbook per student will need to be copied and bound in some manner for the Celebration.

Two weeks before the Publication Celebration, students will create an invitation to give to their family and friends, inviting them to come for a “Celebration of Problem Solving.” Parents and other VIP guests will spend some time working on word problems, moving around the room, visiting many students. The students will share their own specific work with the guests (the word problems they themselves created) and “help” their visitors figure out the answers.

Each student will have a “Comments” sheet for guests to sign and leave comments on their experience working with the student. I will encourage visitors to stop to talk with each student or as many as they can during their visit.

Additionally, this is an opportunity to have some students work as editors and publishers. Creating the workbook will require review and assembly time and these tasks can be delegated and shared by the students who are interested.

Common Core State Standards for Mathematics,

http://www.corestandards.org/the-standards/mathematics.

Fong, Ho Kheong. Math in Focus Singapore Math by Marshall Cavendish . Final ed. Singapore: Marshall Cavendish Education, 2015.

Fuson, Karen C. Math Expressions . 2011 ed. Orlando, FL: Houghton Mifflin Harcourt ;, 2011.

Howe, Roger. Three Pillars of First Grade Mathematics and Beyond

Howe, Roger, The Most Important Thing for Your Child to Learn about Arithmetic

Howe, Roger and Harold Reiter, The Five Stages of Place Value

Ma, L. Knowing and Teaching Elementary Mathematics , Erlbaum Associates, Mahwah, NJ, 1999.

The Moscow Puzzles: 359 Mathematical Recreations . New York: Dover Publications, 1992.

Polya, George. How to Solve It: A New Aspect of Mathematical Method . New Princeton Science Library ed., 2014.

## Appendix A: Problem Set

Change Increase / Result Unknown

7 students are in the classroom. 2 more students join them. How many students are in the classroom now?

Change Increase / Change Unknown

7 students are in the classroom. Some more students join them. Then there were 9 students. How many students join the first 7?

Change Increase / Initial Unknown

Some students are in the classroom. 2 more students joined them. Then there were 9 students. How many students were in the classroom at the beginning?

Change Decrease / Result Unknown

9 students were in the classroom. 2 students went home. How many students are in the classroom now?

Change Decrease / Change Unknown

9 students were in the classroom. Some students went home. Now there are 7 students. How many students went home?

Change Decrease / Initial Unknown

Some students were in the classroom. 2 students went home. Then there were 7 students in the classroom. How many students were in the classroom in the beginning?

Compare More / Difference Unknown

Sam has 10 French fries. Emily has 6 French fries. How many more does Sam have than Emily?

Compare More / Greater Unknown

Sam has 4 more French fries than Emily. Emily has 6 French fries. How many French fries does Sam have?

Compare More / Smaller Unknown

Sam has 4 more French fries than Emily. Sam has 10 French fries. How many French fries does Emily have?

Compare Fewer / Difference Unknown

Sam has 10 French fries. Emily has 6 French fries. How many fewer does Emily have than Sam?

Compare Fewer / Smaller Unknown

Emily has 4 fewer French fries than Sam. Sam has 10 French fries. How many French fries doe Emily have?

Compare Fewer / Greater Unknown

Emily has 4 fewer French fries than Sam. Emily has 6 French fries. How many French fries does Sam have?

Part-Part-Whole / Whole Unknown

Sam has 4 cookies for lunch. He has 2 more for dinner. How many cookies does Sam have?

Sam ate 6 cookies today. He had 4 of them for lunch. How many did he have for dinner?

## Appendix B – Implementing Common Core Standards

This unit integrates, quite naturally, literacy and math. Both reading and writing are essential parts of the students’ ability to solve word problems involving both addition and subtraction.

Students will work most specifically toward the Common Core State Standard in Mathematics, 2.OA.A.1 which states that second graders should, by the end of the year, be able to “represent and solve problems involving addition and subtraction within 100 to solve one- step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. During this unit students will begin solving and crafting word problems with numbers to 10, advance to numbers to 20 and continue on to the 100’s and up to 1000 as they master place value concepts.

This unit also addresses the Language Arts Common Core State Standards of Reading Informational Text, RI.2.1, in which students work on locating key ideas and details by asking and answering such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. Throughout this unit on word problems, students will be working asking these questions as they determine what information the math story is providing. As they begin to write their own word problems, they will need to consider these questions to craft a meaningful story for the text of their problem.

- Common Core State Standards for Mathematics, http://www.corestandards.org/the-standards/mathematics.
- Common Core State Standards for Mathematics
- Ho Kheong Fong, Math in Focus Singapore Math by Marshall Cavendish , 8.
- Roger Howe, Three Pillars of First Grade Mathematics and Beyond, 2 .
- Roger Howe, Three Pillars of First Grade Mathematics and Beyond, 1 . Common Core State Standards for Mathematics
- Roger Howe, Three Pillars of First Grade Mathematics and Beyond, 2

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## Teaching 2nd Grade Mental Math: Expanding and Applying Number Facts

Jodie lopez.

Second grade mental math will continue to consolidate and build on number facts learned in earlier years. As children enter 2nd grade math they should already have some secure mental math skills which they can apply to simple math problems.

Understanding of place value becomes increasingly important as 2nd grade students are expecting to manipulate bigger numbers in mental math and apply their known number bond facts to more complex problems involving 3 digit numbers.

2nd grade children will continue using two of the four number operations – addition and subtraction– and applying them, including working out which operation to use in missing number/operation problems.

## What the curriculum says about 2nd grade mental math

Recommended mental math skills to teach in 2nd grade, the importance of mental math skills in 2nd grade problem solving, 2nd grade mental math challenges, 2nd grade mental math resources .

According to the Common Core State Standards, students will “…use their understanding of addition to develop fluency with addition and subtraction within 100.

They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.”

Students should be taught to add and subtract numbers mentally, including: a three-digit number and ones; a three-digit number and tens; and a three-digit number and hundreds.

They will also be learning more multiplication tables. Some of these multiplication facts will also start to be used in division and an understanding of basic fractions.

Children should be able to answer the following 2nd grade mental math questions:

- Fluently add and subtract within 20
- All sums of two one-digit numbers
- Addition and subtraction of multiples of 10 where the answer is between 0 and 100 (e.g. 70 + 30 = 100, 20 + 40 = 60)
- Double and halves of multiples of 10 to 100 (e.g. double 60 = 120)

## 2nd grade mental math: place value

Understanding place value in elementary is vital and helps children to really understand numbers and mathematical facts.

For some children it may take a while for the understanding to “click” into place and manipulatives can help a lot with this. Our place value accordion , for example, is free to download, easy for children to make for themselves and effective in demonstrating place value.

Teaching resources such as these can help to visualize the numbers in multiple ways and this will support children of all abilities when it comes to the rapid recall needed when applying to problem solving.

Place value games can also be used to revisit the topic without it seeming like a chore. Repetition is an effective way of making sure knowledge is embedded.

## 2nd grade mental math: addition and subtraction

Addition and subtraction happens naturally for children to an extent as they will learn even as toddlers that they want “more” i.e. one more sweet after dinner. They also learn what happens when toys are “taken away” from them.

In kindergarten and 1st grade they will have built on these rudimentary understandings of the principles of addition and subtraction to apply this to multiple contexts.

In 2nd grade they will be introduced to more formal written methods, for adding to 3 digit numbers, for example, so their mental math strategies will also help them when checking their answers.

## 2nd grade mental math: fractions, percentages and decimals

Fractions in elementary usually start with physical objects. You may use Cuisenaire rods to show how one 10 is split into 10 equal parts. Early examples may also include cutting paper plates into fractions, to mimic cutting a pizza or cake.

It is vital that they understand the importance of equal sharing – and for this sharing of a cake is a good example. While students are not formally introduced to fractions until 3rd grade, students will partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths.

Children do not yet need to tackle decimals and percentages but a solid understanding of fractions in 2nd grade will help them to more quickly understand how this later relates to decimals and percentages.

Formal mental math tests may not be used a lot yet in all schools. However, concepts learned in 2nd grade math will form the foundation for the end of elementary school math tests, as well as prepare children for middle school math expectations.

In 2nd grade, students are tackling 2-step math word problems and applying their mental math skills to help to solve them. Mental math will help them to a) answer questions quickly and b) show them how those mental math skills apply to real life situations.

Without the math understanding and solid skills children may struggle to understand what the problem is asking of them. If they lack, for example, the knowledge of multiplication tables and how that relates to division, then they may struggle to answer a question which asks them to share sweets between friends. They will also find it harder to check that their answer is accurate.

In 2nd grade any mental math challenges should aim to build on, and extend the secured number facts across addition and subtraction. However, we should bear in mind that children may not be fluent readers yet and must therefore make sure that reading level does not impede their progression in math.

Including visuals such as pictures, or using manipulatives such as base 10 or Cuisenaire rods, will help to ensure no child is hindered in math by their reading skills. Consider verbal challenges given during whole class carpet sessions, or as part of working with a group.

In 2nd grade you will hope to see children noticing patterns and making links in their learning. Math challenges with number sequences are great for helping them with multiplication tables in third grade, as well as known numbers bonds.

As a quick start to each math lesson, put a sequence on the board with a missing number and they can start to solve that as they get settled in for the lesson. Ask them to suggest what the missing number is and ask other children to check if they are right, and test out the “theory” of their answer – this also starts to embed the methods of checking and proving their mathematical reasoning.

As they get confident you can start to increase the difficulty of the sequence and leave more than 1 number missing. You might also want to experiment with shape sequences, and then move to have shapes with different shaded fractions to increase difficulty.

Math activities and games may also form part of your repertoire of math challenges to test and encourage recall of known facts. Quizzes which are more “fun” versions of mental math tests can also help to give the right level of challenge, although you may wish to consider the level of support available if giving the same quiz to the whole class.

Third Space Learning provides a wide variety of math resources, including mental math worksheets, mental math games , test questions and question powerpoints for every grade level.

A plethora of free teaching resources are also available. Check out some of our most popular resources and expand your class’ mental math skills:

- 150 Mental Math Questions
- 10 Minute Math Number Facts
- Math Challenges At Elementary

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade – 3rd grade – 4th grade – 5th grade – 6th grade – 7th grade – 8th grade Why not learn more about how it works ?

The content in this article was originally written by an EdTech consultant and multi-award-winning former primary teacher Jodie Lopez and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

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How to teach word problems: strategies for elementary teachers.

If you are looking for tips and ideas for how to teach word problems to your elementary students, then you’ve found the right place! We know that teaching elementary students how to solve word problems is important for math concept and skill application, but it sure can feel like a daunting charge without knowing about the different types, the best practices for teaching them, and common misconceptions to plan in advance for, as well as having the resources you need. All this information will make you feel confident about how to teach addition, subtraction, multiplication, and division word problems! Teaching students how to solve word problems will be so much easier!

This blog post will address the following questions:

- What is a word problem?
- What is a multi-step word problem?
- Why are elementary math word problems important?
- Why are math word problems so hard for elementary students?
- What are the types of word problems?
- How do I teach math word problems in a systematic way?
- What are the best elementary math word problem strategies I can teach my students and what are some tips for how to teach math word problems strategies?
- Do you have any helpful tips for how to teach word problems?
- What are the common mistakes I should look for that my students may make?
- How do I address my students’ common misconceptions surrounding elementary math word problems?

## What is a Word Problem?

A word problem is a math situation that calls for an equation to be solved. Students must apply their critical thinking skills to determine how to solve the problem. Word problems give students the opportunity to practice turning situations into numbers. This is critical as students progress in their education, as well as in their day-to-day life. By teaching students how to solve word problems in a strategic way, you are setting them up for future success!

## What is a Multi-Step Word Problem?

A multi-step word problem , also known as a two-step word problem or two-step equation word problem, is a math situation that involves more than one equation having to be answered in order to solve the ultimate question. This requires students to apply their problem solving skills to determine which operation or operations to use to tackle the problem and find the necessary information. In some cases, the situation may call for mixed operations, and in others the operations will be the same. Multi-step word problems offer students the opportunity to practice the skill of applying different math concepts with a given problem.

## Why are Word Problems Important in Math?

Word problems are essential in math because they give students the opportunity to apply what they have learned to a real life situation. In addition, it facilitates students in developing their higher order thinking and critical thinking skills, creativity, positive mindset toward persevering while problem solving, and confidence in their math abilities. Word problems are an effective tool for teachers to determine whether or not students understand and can apply the concepts and skills they learned to a real life situation.

## Why do Students Struggle with Math Word Problems?

Knowing why students have trouble with word problems will help you better understand how to teach them. The reason why math word problems are difficult for your students is because of a few different reasons. First, students need to be able to fluently read and comprehend the text. Second, they need to be able to identify which operations and steps are needed to find the answer. Finally, they need to be able to accurately calculate the answer. If you have students who struggle with reading or English is their second language (ESL), they may not be able to accurately show what they know and can do because of language and literacy barriers. In these cases, it is appropriate to read the text aloud to them or have it translated into their native language for assignments and assessments.

## Types of Word Problems

Knowing the different types of word problems will help you better understand how to teach math word problems. Read below to learn about the four types of basic one-step addition and subtraction word problems, the subcategories within each of them, and specific examples for all of them. Two-step equation word problems can encompass two of the same type or two separate types (also known as mixed operation word problems).

This type of word problem involves an action that increases the original amount. There are three kinds: Result unknown, change unknown, and initial quantity unknown.

## Result Unknown

Example : There were 7 kids swimming in the pool. 3 more kids jumped in. How many kids are in the pool now? (7 + 3 = ?)

## Change Unknown

Example : There were 8 kids swimming in the pool. More kids jumped in. Now there are 15 kids in the pool. How many kids jumped in? (8 + ? = 15)

## Initial Quantity Unknown

Example : There were kids swimming in the pool. 2 kids jumped in. Now there are 6 kids in the pool. How many kids were swimming in the pool at first? (? + 2 = 6)

## 2. Separate

This type of word problem involves an action that decreases the original amount. There are three kinds: Result unknown, change unknown, and initial quantity unknown.

Example: There were 12 kids swimming in the pool. 6 of the kids got out of the pool. How many kids are in the pool now? (12 – 6 = ?)

Example: There were 9 kids swimming in the pool. Some of the kids got out of the pool. Now there are 4 kids in the pool. How many kids got out of the pool? (9 – ? = 4)

Example: There were kids swimming in the pool. 3 of the kids got out of the pool. Now there are 2 kids in the pool. How many kids were in the pool at first? (? – 3 = 2)

## 3. Part-Part-Whole

This type of word problem does not involve an action like the join and separate types. Instead, it is about defining relationships among a whole and two parts. There are two kinds: result unknown and part unknown.

Example: There are 5 boys and 9 girls swimming in the pool. How many kids are in the pool? (5 + 9 = ?)

## Part Unknown

Example: There are 12 kids swimming in the pool. 8 of them are girls and the rest of them are boys. How many boys are swimming in the pool? (8 + ? = 12)

This type of word problem does not involve an action or relationship like the three other types. Instead, it is about comparing two different unrelated items. There are two kinds: Difference unknown and quantity unknown.

## Difference Unknown

Example: There are 2 kids in the pool. There are 7 kids in the yard. How many more kids are in the yard than in the pool? (2 + ? = 7 or 7 – 2 = ?)

## Quantity Unknown

Example 1: There are 5 kids in the pool. There are 3 fewer kids playing in the yard. How many kids are playing in the yard? (5 – 3 = ?)

Example 2: There are 2 kids in the pool. There are 10 more kids playing in the yard than in the pool. How many kids are playing in the yard? (2 + 10 = ?)

## How to Solve Word Problems in 5 Easy Steps

Here are 5 steps that will help you teach word problems to your 1st, 2nd, 3rd, 4th or 5th grade students:

- Read the problem.
- Read the problem a second time and make meaning of it by visualizing, drawing pictures, and highlighting important information (numbers, phrases, and questions).
- Plan how you will solve the problem by organizing information in a graphic organizer and writing down equations and formulas that you will need to solve.
- Implement the plan and determine answer.
- Reflect on your answer and determine if it is reasonable. If not, check your work and start back at step one if needed. If the answer is reasonable, check your answer and be prepared to explain how you solved it and why you chose the strategies you did.

## 5 Math Word Problem Strategies

Here are 5 strategies for how to teach elementary word problems:

Understand the math situation and what the question is asking by picturing what you read in your head while you are reading.

## Draw Pictures

Make meaning of what the word problem is asking by drawing a picture of the math situation.

## Make Models

Use math tools like base-ten blocks to model what is happening in the math situation.

## Highlight Important Information

Underline or highlight important numbers, phrases, and questions.

## Engage in Word Study

Look for key words and phrases like “less” or “in all.” Check out this blog post if you are interested in learning more about math word problem keywords and their limitations.

## 10 Tips for Teaching Students How to Solve Math Word Problems

Here are 10 tips for how to teach math word problems:

- Model a positive attitude toward word problems and math.
- Embody a growth mindset.
- Model! Provide plenty of direct instruction.
- Give lots of opportunities to practice.
- Explicitly teach strategies and post anchor charts so students can access them and remember prior learning.
- Celebrate the strategies and process rather than the correct answer.
- Encourage students to continue persevering when they get stuck.
- Invite students to act as peer tutors.
- Provide opportunities for students to write their own word problems.
- Engage in whole-group discussions when solving word problems as a class.

## Common Misconceptions and Errors When Students Learn How to Solve Math Word Problems

Here are 5 common misconceptions or errors elementary students have or make surrounding math word problems:

## 1. Use the Incorrect Operation

Elementary students often apply the incorrect operations because they pull the numbers from a word problem and add them without considering what the question is asking them or they misunderstand what the problem is asking. Early in their experience with word problems, this strategy may work most of the time; however, its effectiveness will cease as the math gets more complex. It is important to instruct students to develop and apply problem-solving strategies.

Although helpful in determining the meaning, elementary students rely solely on key words and phrases in a word problem to determine what operation is being called for. Again, this may be an effective strategy early on in their math career, but it should not be the only strategy students use to determine what their plan of attack is.

## 2. Get Stuck in a Fixed Mindset

Some elementary students give up before starting a word problem because they think all word problems are too hard. It is essential to instill a positive mindset towards math in students. The best way to do that is through modeling. If you portray an excitement for math, many of your students will share that same feeling.

## 3. Struggle with Reading Skills Component

For first and second graders (as well as struggling readers and ESL students), it is common for students to decode the text incorrectly. Along the same lines, some elementary students think they can’t solve word problems because they do not know how to read yet. The purpose of word problems is not to assess whether a child can read or not. Instead, the purpose is to assess their critical thinking and problem-solving skills. As a result, it is appropriate to read word problems to elementary students.

## 4. Calculate Incorrectly

You’ll find instances where students will understand what the question is asking, but they will calculate the addends or the subtrahend from the minuend incorrectly. This type of error is important to note when analyzing student responses because it gives you valuable information for when you plan your instruction.

## 5. Encode Response Incorrectly

Another error that is important to note when analyzing student responses is when you find that they encode their solution in writing incorrectly. This means they understand what the problem is asking, they solve the operations correctly, document their work meticulously, but then write the incorrect answer on the line.

## How to Address Common Misconceptions Surrounding Math Word Problems

You might be wondering, “What can I do in response to some of these misconceptions and errors?” After collecting and analyzing the data, forming groups based on the results, and planning differentiated instruction, you may want to consider trying out these prompts:

- Can you reread the question aloud to me?
- What is the question asking us to do?
- How can we represent the information and question?
- Can we represent the information and question with an equation?
- What is our first step?
- What is our next step?
- Can you think of any strategies we use to help us solve?
- How did you find your answer?
- Can you walk me through how you found your answer step by step?
- What do we need to remember when recording our answer?

Now that you have all these tips and ideas for how to teach word problems, we would love for you to try these word problem resources with your students. They offer students opportunities to practice solving word problems after having learned how to solve word problems. You can download word problem worksheets specific to your grade level (along with lots of other math freebies) in our free printable math resources bundle using this link: free printable math activities for elementary teachers .

Check out my monthly word problem resources !

- 1st Grade Word Problems
- 2nd Grade Word Problems
- 3rd Grade Word Problems
- 4th Grade Word Problems
- 5th Grade Word Problems

- Read more about: ELEMENTARY TEACHING , MATH

## You might also like these posts...

Gardening reading comprehension activities for 2nd, 3rd, and 4th grade, arbor day reading comprehension activities for 2nd, 3rd, and 4th grade, easter reading comprehension activities for 2nd, 3rd, and 4th grade.

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## Math Problem Solving Strategies

How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem? For me, the answer is too many to count. Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for . There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!

## 1. C.U.B.E.S.

C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work.

- Why I like it: Gives students a very specific ‘what to do.’
- Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem. None of the steps emphasize reading the problem but maybe that is a given.

## 2. R.U.N.S.

R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence.

- Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence. This is a great strategy to teach when you are tackling various types of problems.
- Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

## 3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

- Why I like it: I love that there is a check step in this problem solving strategy. Students having to defend the reasonableness of their answer is essential for students’ number sense.
- Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

## 4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

Here is the strategy that I adopted a few years ago. It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

- Know: This will help students find the important information.
- Need to Know: This will force students to reread the question and write down what they are trying to solve for.
- Organize: I think this would be a great place for teachers to emphasize drawing a model or picture.
- Work: Students show their calculations here.
- Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

## Ideas for Promoting Showing Your Work

- White boards are a helpful resource that make (extra) writing engaging!
- Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
- Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.

## Show Work Digitally

Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work.

If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more.

Students who plan succeed at a higher rate than students who do not plan. Do you have a go to problem solving strategy that you teach your students?

Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.

## Problem Solving Posters (Represent It! Bulletin Board)

Check out these related products from my shop.

## Reader Interactions

18 comments.

October 4, 2017 at 7:55 pm

As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!

October 4, 2017 at 8:59 pm

Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!

December 15, 2017 at 7:57 am

Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:

1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.

This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.

October 5, 2017 at 6:27 am

Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)

I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….

October 5, 2017 at 9:46 am

Great idea! Thanks so much for sharing with our readers!

October 8, 2017 at 6:51 pm

LOVE this idea! Will definitely use it this year! Thank you!

December 18, 2019 at 7:48 am

I would love an anchor chart for RUBY

October 15, 2017 at 11:05 am

I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.

April 20, 2018 at 7:36 am

I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.

June 22, 2018 at 12:19 pm

That’s brilliant! Thank you for sharing!

May 31, 2018 at 12:15 pm

Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?

June 22, 2018 at 10:46 am

Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.

July 28, 2018 at 6:53 pm

I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.

February 3, 2019 at 3:56 pm

This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.

March 7, 2019 at 6:59 am

Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution

September 2, 2019 at 11:18 am

Going off of your idea, Natalie, how about the following?

K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)

I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.

March 16, 2020 at 4:44 pm

I’m doing this one. Love it. Thank you!!

September 17, 2019 at 7:14 am

Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.

I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!

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## 2nd Grade Addition Strategies Learning Resources

Strengthen your child's addition strategies skills with interactive educational resources for addition strategies for 2nd graders online. These learning resources include fun games and worksheets with eye-catching visuals and characters. Get started to help your 2nd grader master this concept by engaging their critical thinking.

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## Addition Strategies within 20

## Compose Numbers within 5 Game

Take a look at how to compose numbers within 5 with this addition game.

## Count on using a Number Line Game

Take a deep dive into the world of math by learning to count on using a number line.

## One More or One Less within 20: Horizontal Addition and Subtraction Worksheet

Dive into this fun-filled printable worksheet by finding one more or one less within 20.

## One More or One Less within 20: Vertical Addition and Subtraction Worksheet

This downloadable worksheet is designed to practice finding one more or one less within 20.

## Addition Strategies within 100

## Word Problems to Add Multiples of 10 Game

Learn to solve word problems to add multiples of 10.

## Word Problems to Add Tens to a 2-digit number Game

Make math learning fun by solving word problems to add tens to a 2-digit number.

## Find 1 More or 1 Less Worksheet

Put your skills to the test by practicing to find 1 more or 1 less.

## Find 10 More or 10 Less Worksheet

Make math practice a joyride by solving problems to find 10 more or 10 less.

## Addition Strategies within 1000

## Add Multiples of 100 in Unit Form Game

Enjoy the marvel of math-multiverse by exploring how to add multiples of 100 in unit form.

## Add Multiples of 100 Using Base-10 Blocks Game

Enjoy the marvel of mathematics by exploring how to add multiples of 100 using base-10 blocks.

## Making Multiple of 100 to Find the Sum Worksheet

Pack your math practice time with fun by making multiples of 100 to find the sum.

## Simplify and Add Worksheet

Reinforce math concepts by practicing to simplify and add.

## All Addition Strategies Resources

## Complete the Statements Using Addition Sentence Worksheet

Print this worksheet to complete the statements using addition sentences like a math legend!

## Solve Word Problems on Add to Scenarios Game

Ask your little one to solve word problems on "Add to" scenarios to play this game.

## Add 3-Digit and 1-Digit Numbers Using Place Value Worksheet

Focus on core math skills by solving to add 3-digit and 1-digit numbers using place values.

## Anchor 5 Worksheet

Use this printable Anchor 5 worksheet to strengthen your math skills.

## Solve Word Problems on Put together Scenarios Game

Practice the superpower of addition by learning to solve word problems on "Put together" scenarios.

## Represent and Add Number using Place Value Chart Worksheet

Assess your math skills by representing and adding numbers using the place value chart.

## Add and Mark the Sum on the Number Line Game

Have your own math-themed party by learning how to add and mark the sum on the number line.

## Anchor 10 Worksheet

Pack your math practice time with fun by solving this Anchor 10 worksheet.

## Find More & Less Worksheet

Solidify your math skills by practicing to find 'More' & 'Less'.

## Solve Word Problems with Add to Scenarios Game

Shine bright in the math world by learning how to solve word problems with "Add to" scenarios.

## Use Count On to Add Game

Shine bright in the math world by learning how to use "Count On" to add.

## Addition of 3-Digit and 1-Digit Numbers Worksheet

Learn addition at the speed of lightning by practicing addition of 3-digit and 1-digit numbers.

## Anchor 5 & 10 Worksheet

Put your skills to the test by practicing this Anchor 5 & 10 worksheet.

## Solve Word Problems with Put Together Scenarios Game

Ask your little one to solve word problems with "Put Together" scenarios.

## Complete More or Less Sentences Worksheet

Pack your math practice time with fun by completing 'more' or 'less' sentences.

## Addition of 3-Digit and 2-Digit Numbers Worksheet

Put your skills to the test by practicing addition of 3-digit and 2-digit numbers.

## Find the Missing Addends Game

Learn to solve math problems by finding the missing addends.

## Make the Numbers from 5 and 10 Worksheet

Help your child revise subtraction by solving to make the numbers from 5 and 10.

## Add or Subtract Multiples of 10 Worksheet

Learners must add or subtract multiples of 10 to enhance their math skills.

## Use Count On to Add and Find Related Facts Game

Sharpen your addition skills by using count on to add and find the related facts.

## Adding Two 3-Digit Numbers Worksheet

In this worksheet, learners will get to add two 3-digit numbers.

## Represent Numbers Using Anchor 5, 10 and 20 Worksheet

Reinforce math concepts by practicing to represent numbers using anchor 5, 10 and 20.

## Add Numbers by Making 10 Game

Enjoy the marvel of math-multiverse by exploring how to add numbers by making 10.

## Add Multiples of 100 Using Place Value Chart Game

Ask your little one to add multiples of 100 using the place value chart to play this game.

## Add & Subtract Multiples of 10 Worksheet

Solidify your math skills by practicing to add & subtract multiples of 10.

## Addition Using Place Value Chart Worksheet

Be on your way to become a mathematician by practicing addition using a place value chart.

## Make 10 to Add Game

Kids must make 10 to add.

## Add Multiples of 100 Game

Learn to solve real world problems through our 'Add Multiples of 100' game.

## Add with 10: Horizontal Addition Worksheet

Reveal the secrets of math wizardry by practicing to add with 10.

## Add & Subtract Ones & 2-Digit Numbers Worksheet

Learners must add & subtract ones & 2-digit numbers to enhance their math skills.

## Add the Numbers by Making a 10 Game

Use your addition skills to add the numbers by making a 10.

## Adding Multiples of 100 Game

Help your child take flight by learning how to add multiples of 100.

## Find the Sum Using Place Value Chart Worksheet

Help your child revise number sense by solving to find the sum using a place value chart.

## Add with 10: Vertical Addition Worksheet

Reinforce math concepts by practicing to add with 10.

## Add 1-Digit Numbers Game

Enjoy the marvel of mathematics by exploring how to add 1-digit numbers.

## Solve by Adding Multiples of 100 Game

Take a deep dive into the world of math through solving by adding multiples of 100.

## Add Using Place Value Cards With Regrouping Worksheet

Make math practice a joyride by solving problems to add using place value cards with regrouping.

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## Iowa Academic Standards

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Browse required Iowa Academic Standards by subject and grade.

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Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

More word problems resources Second Grade Math Word Problems In second grade, students focus on one-step problems, covering a range of topics. At this stage the majority of word problems students are tackling will have one-step, but they may also start to be introduced to simple two-step word problems.

There are many different strategies to teach students to solve 2nd grade math word problems. Try one, some, or all of the strategies listed to reach learners of all levels and abilities. 1. Identify Key Words for Each Operation In every 2nd grade math word problem, there is an important keyword.

entry point or a way to start the task. Second Grade students also develop a foundation for problem solving strategies and become independently proficient on using those strategies to solve new tasks. In Second Grade, students' work continues to use concrete manipulatives and pictorial representations as well as mental mathematics.

2nd grade 8 units · 75 skills. Unit 1 Add and subtract within 20. Unit 2 Place value. Unit 3 Add and subtract within 100. Unit 4 Add and subtract within 1,000. Unit 5 Money and time. Unit 6 Measurement. Unit 7 Data. Unit 8 Geometry.

Solve word problems up to 20 using addition and subtraction; Types of word problems: adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions. At the beginning of the year, it's beneficial to evaluate students' understanding of adding and subtracting to 20.

Teacher Professional Development 3 Reads Strategy to Problem Solve Problem solving strategies in math are not always as easy as they seem. Many times, students read a mathematical problem and have no idea what to do from there. I'm often asked how to teach word problems.

1. Read the problem aloud Because students this age read at varied levels, not every second-grader will fully understand a word problem on his first pass through. Reading the problem aloud can be quite helpful, especially with a child who hasn't completely mastered reading.

Second graders practice problem solving strategies. In this problem solving instructional activity, 2nd graders use strategies such as guess and check, acting out, drawing pictures and looking for patterns to solve problems. Students work in groups to solve problems using buttons. Students make lists of attributes and compare with other groups.

I want my students to find an answer that corresponds to the problem. In this lesson, the students and I are working on understanding the language of word problems, using the specific words as clues to the mathematical operations embedded in the problem. I use examples of student work to uncover misconceptions and errors and help support the ...

Use manipulatives, number grids, tally marks, mental arithmetic, paper & pencil, and calculators to solve problems involving the addition and subtraction of 2-digit whole numbers; describe the strategies used; calculate and compare values of coin and bill combinations. Make Reasonable Estimates. Computational estimation.

Numberless word problems are a great way to get your 2nd grade students to use their critical thinking skills to determine the operation needed to solve a word problem, rather than just guessing. These numberless word problems now have a digital distance learning option.

Try for free DoodleMath For schools For families US UK US Log in Try for free How to help a 2nd grader with math The top 10 tips to help your 2nd grader progress in math while boosting their confidence and making learning enjoyable along the way! Author Michelle Griczika Published July 18, 2023 Key takeaways

Quick reference: What are these tools? Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Measurement and Data (MD) Geometry (G) These tasks are grade-level formative performance assessment tasks aligned to the Common Core State Standards for Mathematics.

Objectives. The Common Core concentrates on a clear set of math skills and concepts. Students learn concepts in an organized way during the school year as well as across grades. The standards encourage students to solve real-world problems. 2. The Common Core calls for greater focus in mathematics.

Children should be able to answer the following 2nd grade mental math questions: Fluently add and subtract within 20. All sums of two one-digit numbers. Addition and subtraction of multiples of 10 where the answer is between 0 and 100 (e.g. 70 + 30 = 100, 20 + 40 = 60) Double and halves of multiples of 10 to 100 (e.g. double 60 = 120)

Teaching students how to solve word problems will be so much easier! This blog post will address the following questions: What is a word problem? What is a multi-step word problem? Why are elementary math word problems important? Why are math word problems so hard for elementary students? What are the types of word problems?

Grade 2 Problem Solving Strategies Marvin solved the equation below: 14 + 25 = 39 Which of these equations could be used to check Marvin's answer? 25 + 39 = 65 14 + 39 = 53 64 - 25 = 39 39 - 14 = 25 Grade 2 Problem Solving Strategies How would the inverse operation of addition be used to solve this equation? P + 62 = 100 100 - 62 = P 62 - 100 = P

5 2nd Grade Addition and Subtraction Word Problems Learning Resources View all 68 resources Addition and Subtraction Word Problems Addition Word Problems on Finding the Total Game Learn to solve addition word problems on finding the total. 2 3 2.OA.1 VIEW DETAILS Addition and Subtraction Word Problems

This is a great strategy to teach when you are tackling various types of problems. Why I don't like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time. 3. U.P.S. CHECK. U.P.S. Check stands for understand, plan, solve, and check.

These word problems games for 2nd grade will help students implement various mathematical strategies and operations to solve interesting math problems. Keep your child entertained while learning with these fun games for 2nd graders. Personalized Learning. Fun Rewards.

Explore essential '2nd Grade Subtraction Strategies' using our curriculum-aligned learning resources. Master subtraction techniques effectively. Start for free! Parents. Educators ... Make math practice a joyride by solving problems to find 10 more or 10 less. K 1 2 3. VIEW DETAILS. Subtraction Strategies within 1000 View all 22 resources.

2nd Grade Addition Strategies Learning Resources. Strengthen your child's addition strategies skills with interactive educational resources for addition strategies for 2nd graders online. These learning resources include fun games and worksheets with eye-catching visuals and characters. Get started to help your 2nd grader master this concept by ...

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