Transformations as Functions

Match each coordinate rule to a description of its resulting transformation.

\((x,y) \rightarrow (x+3,y)\)

\((x,y) \rightarrow (2x,2y)\)

\((x,y) \rightarrow (x,y+4)\)

\((x,y) \rightarrow (x,y-4)\)

\((x,y) \rightarrow (x-3,y+4)\)

Translate by the directed line segment from \((0,0)\) to \((0,4)\) .

Translate by the directed line segment from \((0,0)\) to \((3,0)\) .

Dilate using the origin as the center and a scale factor of 2.

Translate by the directed line segment from \((0,0)\) to \((0,\text-4)\) .

Translate by the directed line segment from \((0,0)\) to \((\text-3,4)\) .

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  • Draw the image of triangle \(ABC\) under the transformation \((x,y) \rightarrow (x-4,y+1)\) . Label the result \(T\) .
  • Draw the image of triangle \(ABC\) under the transformation \((x,y) \rightarrow (\text- x,y)\) . Label the result \(R\) .

Expand image

Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.

  • \((x,y) \rightarrow (x-2,y-3)\)
  • \((x,y) \rightarrow (2x,3y)\)
  • \((x,y) \rightarrow (3x,3y)\)
  • \((x,y) \rightarrow (2-x,y)\)

Reflect triangle \(ABC\) over the line \(x=0\) . Call this new triangle \(A’B’C’\) . Then reflect triangle \(A’B’C’\) over the line \(y=0\) . Call the resulting triangle \(A''B''C''\) .

Which single transformation takes \(ABC\) to \(A''B''C''\) ?

Translate triangle \(ABC\) by the directed line segment from \((1,1)\) to \((\text-2,1)\) .

Reflect triangle \(ABC\) across the line \(y=\text-x\) .

Rotate triangle \(ABC\) counterclockwise using the origin as the center by 180 degrees.

Dilate triangle \(ABC\) using the origin as the center and a scale factor of 2.

Reflect triangle \(ABC\) over the line \(y=2\) .

Translate the image by the directed line segment from \((0,0)\) to \((3,2)\) .

What are the coordinates of the vertices in the final image?

The density of water is 1 gram per cm 3 . An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. Will a cylindrical log with radius 0.4 meters, height 5 meters, and mass 1,950 kilograms sink or float? Explain your reasoning.

These 3 congruent square pyramids can be assembled into a cube with side length 3 feet. What is the volume of each pyramid?

1 cubic foot

3 cubic feet

9 cubic feet

27 cubic feet

Reflect square  \(ABCD\) across line \(CD\) . What is the ratio of the length of segment  \(AA'\)  to the length of segment \(AD\) ? Explain or show your reasoning.

Math Expressions Answer Key

Math Expressions Grade 4 Unit 6 Lesson 2 Answer Key Fractions That Add to One

Solve the questions in Math Expressions Grade 4 Homework and Remembering Answer Key Unit 6 Lesson 2 Answer Key Fractions That Add to One to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-4-unit-6-lesson-2-answer-key/

Math Expressions Common Core Grade 4 Unit 6 Lesson 2 Answer Key Fractions That Add to One

Math Expressions Grade 4 Unit 6 Lesson 2 Homework

Name the fraction of the shape that is shaded and the fraction of the shape that is not shaded. Then, write an equation that shows how the two fractions make one whole.

Unit 6 Lesson 2 Fractions That Add To One Grade 4 Math Expressions

Write the fraction that will complete each equation.

Question 4. 1 = \(\frac{3}{3}\) = \(\frac{1}{3}\) + __________ Answer: 1 = \(\frac{3}{3}\) = \(\frac{1}{3}\) + \(\frac{2}{3}\)

Question 5. 1 = \(\frac{8}{8}\) = \(\frac{3}{8}\) + ____________ Answer: 1 = \(\frac{8}{8}\) = \(\frac{3}{8}\) + \(\frac{5}{8}\)

Question 6. 1 = \(\frac{4}{4}\) = \(\frac{2}{4}\) + ____________ Answer: 1 = \(\frac{4}{4}\) = \(\frac{2}{4}\) + \(\frac{2}{4}\)

Question 7. 1 = \(\frac{10}{10}\) = \(\frac{7}{10}\) + ____________ Answer: 1 = \(\frac{10}{10}\) = \(\frac{7}{10}\) + \(\frac{3}{10}\)

Question 8. 1 = \(\frac{6}{6}\) = \(\frac{5}{6}\) + _____________ Answer: 1 = \(\frac{6}{6}\) = \(\frac{5}{6}\) + \(\frac{1}{6}\)

Question 9. 1 = \(\frac{9}{9}\) = \(\frac{8}{9}\) + ______________ Answer: 1 = \(\frac{9}{9}\) = \(\frac{8}{9}\) + \(\frac{1}{9}\)

Question 10. 1 = \(\frac{7}{7}\) = \(\frac{4}{7}\) + ______________ Answer: 1 = \(\frac{7}{7}\) = \(\frac{4}{7}\) + \(\frac{3}{7}\)

Question 11. 1 = \(\frac{12}{12}\) = \(\frac{9}{12}\) + _____________ Answer: 1 = \(\frac{12}{12}\) = \(\frac{9}{12}\) + \(\frac{3}{12}\)

Solve. Show your work.

Question 12. Kim drank \(\frac{1}{3}\) of a carton of milk. Joan drank \(\frac{1}{4}\) of a carton of milk. Who drank more milk? Answer: Kim drank more milk.

Explanation: Quantity of a carton of milk Kim drank = \(\frac{1}{3}\) = 0.33. Quantity of a carton of milk Joan drank = \(\frac{1}{4}\) = 0.25.

Question 13. Maria read \(\frac{1}{8}\) of a story. Darren read \(\frac{1}{7}\) of the same story. Who read less of the story? Answer: Maria read less of the story.

Explanation: Quantity of a story Maria read = \(\frac{1}{8}\) = 0.125. Quantity of a story Darren read = \(\frac{1}{7}\) = 0.143.

Math Expressions Grade 4 Unit 6 Lesson 2 Remembering

Write = or ≠ to make each statement true.

Math Expressions Common Core Grade 4 Unit 6 Lesson 2 Answer Key 4

Explanation: 25 + 25 = 50.

Explanation: 17 + 3 = 20. 30 – 10 = 20.

Explanation: 9 + 8 = 17. 8 + 9 = 17.

Explanation: 31. 23 + 9 = 32.

Explanation: 3 + 1 + 12 = 4 + 12 =  16. 15.

Explanation: 40 – 22 = 18. 18.

Solve each equation.

Question 7. 8 ÷ b = 2 b = ________ Answer: b = 4.

Explanation: 8 ÷ b = 2 => b = 8 ÷ 2 => b = 4.

Question 8. j ÷ 6 = 7 j = _________ Answer: j = 42.

Explanation: j ÷ 6 = 7 => j = 7 × 6 => j = 42.

Question 9. k = 5 × 3 k = ___________ Answer: k = 15.

Explanation: k = 5 × 3 => k = 15.

Question 10. q × 10 = 90 q = _________ Answer: q = 9.

Explanation: q × 10 = 90 => q = 90 ÷ 10 => q = 9.

Question 11. 12 × r = 36 r = ___________ Answer: r = 3.

Explanation: 12 × r = 36 => r = 36 ÷ 12 => r = 3.

Question 12. a = 7 × 8 a = ___________ Answer: a = 56.

Explanation: a = 7 × 8 => a = 56.

Write each fraction as a sum of unit fractions.

Question 13. \(\frac{4}{6}\) = _________________ Answer: \(\frac{4}{6}\) = \(\frac{2}{6}\) + \(\frac{2}{6}\)

Question 14. \(\frac{6}{8}\) = _________________ Answer: \(\frac{6}{8}\) = \(\frac{2}{8}\) + \(\frac{4}{8}\)

Question 15. Stretch Your Thinking Margaret and June both made a pumpkin pie of the same size. Each cut her pie into equal pieces. Margaret’s whole pie can be represented by the fraction \(\frac{8}{8}\). June’s whole pie can be represented by the fraction \(\frac{6}{6}\). What is different about the two pies? If Margaret and June each eat 1 piece of their own pie, who will eat more? Explain how you know. Answer: Two pies are cut into different size pieces. June eats more.

Explanation; Margaret’s whole pie = \(\frac{8}{8}\). June’s whole pie = \(\frac{6}{6}\). Margaret eats 1 piece = \(\frac{1}{8}\) = 0.125. June eats 1 piece = \(\frac{1}{6}\) = 0.167.

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Go Math Answer Key

Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8

Go Math Answer Key:  HMH Go Math Answer Key for Grade K, 1, 2, 3, 4, 5, 6, 7, and 8 are provided helps students to have learning targets and achieve success at chapter and lesson level and makes learning visible.

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Go Math Grade K Answer Key

  • Chapter 1 Represent, Count, and Write Numbers 0 to 5
  • Chapter 2 Compare Numbers to 5
  • Chapter 3 Represent, Count, and Write Numbers 6 to 9
  • Chapter 4 Represent and Compare Numbers to 10
  • Chapter 5 Addition
  • Chapter 6 Subtraction
  • Chapter 7 Represent, Count, and Write 11 to 19
  • Chapter 8 Represent, Count, and Write 20 and Beyond
  • Chapter 9 Identify and Describe Two-Dimensional Shapes
  • Chapter 10 Identify and Describe Three-Dimensional Shapes
  • Chapter 11 Measurement
  • Chapter 12 Classify and Sort Data
  • Chapter 1 Addition Concepts
  • Chapter 2 Subtraction Concepts
  • Chapter 3 Addition Strategies
  • Chapter 4 Subtraction Strategies
  • Chapter 5 Addition and Subtraction Relationships
  • Chapter 6 Count and Model Numbers
  • Chapter 7 Compare Numbers
  • Chapter 8 Two-Digit Addition and Subtraction
  • Chapter 9 Measurement
  • Chapter 10 Represent Data
  • Chapter 11 Three-Dimensional Geometry
  • Chapter 12 Two-Dimensional Geometry
  • Chapter 1 Number Concepts
  • Chapter 2 Numbers to 1,000
  • Chapter 3 Basic Facts and Relationships
  • Chapter 4 2-Digit Addition
  • Chapter 5 2-Digit Subtraction
  • Chapter 6 3-Digit Addition and Subtraction
  • Chapter 7 Money and Time
  • Chapter 8 Length in Customary Units
  • Chapter 9 Length in Metric Units
  • Chapter 10 Data
  • Chapter 11 Geometry and Fraction Concepts

Grade 3 HMH Go Math – Answer Keys

  • Chapter 1: Addition and Subtraction within 1,000
  • Chapter 2: Represent and Interpret Data
  • Chapter 3: Understand Multiplication
  • Chapter 4: Multiplication Facts and Strategies
  • Chapter 5: Use Multiplication Facts
  • Chapter 6: Understand Division
  • Chapter 7: Division Facts and Strategies
  • Chapter 8: Understand Fractions
  • Chapter 9: Compare Fractions
  • Chapter 10: Time, Length, Liquid Volume, and Mass
  • Chapter 11: Perimeter and Area
  • Chapter 12:Two-Dimensional Shapes

Grade 3 HMH Go Math – Extra Practice Questions and Answers

  • Chapter 1: Addition and Subtraction within 1,000 Extra Practice
  • Chapter 2: Represent and Interpret Data Extra Practice
  • Chapter 3: Understand Multiplication Extra Practice
  • Chapter 4: Multiplication Facts and Strategies Extra Practice
  • Chapter 5: Use Multiplication Facts Extra Practice
  • Chapter 6: Understand Division Extra Practice
  • Chapter 7: Division Facts and Strategies Extra Practice
  • Chapter 8: Understand Fractions Extra Practice
  • Chapter 9: Compare Fractions Extra Practice
  • Chapter 10: Time, Length, Liquid Volume, and Mass Extra Practice
  • Chapter 11: Perimeter and Area Extra Practice
  • Chapter 12: Two-Dimensional Shapes Extra Practice

Common Core Grade 4 HMH Go Math – Answer Keys

  • Chapter 1 Place Value, Addition, and Subtraction to One Million
  • Chapter 2 Multiply by 1-Digit Numbers
  • Chapter 3 Multiply 2-Digit Numbers
  • Chapter 4 Divide by 1-Digit Numbers
  • Chapter 5 Factors, Multiples, and Patterns
  • Chapter 6 Fraction Equivalence and Comparison
  • Chapter 7 Add and Subtract Fractions
  • Chapter 8 Multiply Fractions by Whole Numbers
  • Chapter 9 Relate Fractions and Decimals
  • Chapter 10 Two-Dimensional Figures
  • Chapter 11 Angles
  • Chapter 12Relative Sizes of Measurement Units
  • Chapter 13 Algebra: Perimeter and Area

Grade 4 Homework Practice FL.

Common Core – Grade 4 – Practice Book

  • Chapter 1 Place Value, Addition, and Subtraction to One Million  (Pages 1- 20)
  • Chapter 2 Multiply by 1-Digit Numbers  (Pages 21 – 47)
  • Chapter 3 Multiply 2-Digit Numbers  (Pages 49- 65)
  • Chapter 4 Divide by 1-Digit Numbers  (Pages 67 – 93)
  • Chapter 5 Factors, Multiples, and Patterns  (Pages 95 – 109)
  • Chapter 6 Fraction Equivalence and Comparison  (Pages 111 – 129)
  • Chapter 7 Add and Subtract Fractions  (Pages 131 – 153)
  • Chapter 8 Multiply Fractions by Whole Numbers  (Pages 155- 167)
  • Chapter 9 Relate Fractions and Decimals  (Pages 169- 185)
  • Chapter 10 Two-Dimensional Figures  (Pages 187- 204)
  • Chapter 11 Angles  (Pages 205- 217)
  • Chapter 12 Relative Sizes of Measurement Units  (Pages 219- 244)
  • Chapter 13 Algebra: Perimeter and Area  (Pages 245- 258)

Grade 4 Homework FL. – Answer Keys

  • Chapter 2 Multiply by 1-Digit Numbers Review/Test
  • Chapter 3 Multiply 2-Digit Numbers Review/Test
  • Chapter 4 Divide by 1-Digit Numbers Review/Test
  • Chapter 5 Factors, Multiples, and Patterns Review/Test
  • Chapter 6 Fraction Equivalence and Comparison Review/Test
  • Chapter 7 Add and Subtract Fractions Review/Test
  • Chapter 8 Multiply Fractions by Whole Numbers Review/Test
  • Chapter 9 Relate Fractions and Decimals Review/Test
  • Chapter 10 Two-Dimensional Figures Review/Test
  • Chapter 11 Angles Review/Test
  • Chapter 12 Relative Sizes of Measurement Units Review/Test
  • Chapter 13 Algebra: Perimeter and Area Review/Test
  • Chapter 1: Place Value, Multiplication, and Expressions
  • Chapter 2: Divide Whole Numbers
  • Chapter 3: Add and Subtract Decimals
  • Chapter 4: Multiply Decimals
  • Chapter 5: Divide Decimals
  • Chapter 6: Add and Subtract Fractions with Unlike Denominators
  • Chapter 7: Multiply Fractions
  • Chapter 8: Divide Fractions
  • Chapter 9: Algebra: Patterns and Graphing
  • Chapter 10: Convert Units of Measure
  • Chapter 11: Geometry and Volume
  • Chapter 1: Divide Multi-Digit Numbers
  • Chapter 2: Fractions and Decimals
  • Chapter 3: Understand Positive and Negative Numbers
  • Chapter 4: Model Ratios
  • Chapter 5: Model Percents
  • Chapter 6: Convert Units of Length
  • Chapter 7: Exponents
  • Chapter 8: Solutions of Equations
  • Chapter 9: Independent and Dependent Variables
  • Chapter 10: Area of Parallelograms
  • Chapter 11: Surface Area and Volume
  • Chapter 12: Data Displays and Measures of Center
  • Chapter 13: Variability and Data Distributions

Go Math Answer Key for Grade 7

  • Chapter 1: Adding and Subtracting Integers
  • Chapter 2: Multiplying and Dividing Integers
  • Chapter 3: Rational Numbers
  • Chapter 4: Rates and Proportionality
  • Chapter 5: Percent Increase and Decrease
  • Chapter 6: Algebraic Expressions
  • Chapter 7: Writing and Solving One-Step Inequalities
  • Chapter 8: Modeling Geometric Figures
  • Chapter 9: Circumference, Area, and Volume
  • Chapter 10: Random Samples and Populations
  • Chapter 11: Analyzing and Comparing Data
  • Chapter 12: Experimental Probability
  • Chapter 13: Theoretical Probability and Simulations
  • Chapter 1 Real Numbers
  • Chapter 2 Exponents and Scientific Notation
  • Chapter 3 Proportional Relationships
  • Chapter 4 Nonproportional Relationships
  • Chapter 5 Writing Linear Equations
  • Chapter 6 Functions
  • Chapter 7 Solving Linear Equations
  • Chapter 8 Solving Systems of Linear Equations
  • Chapter 9 Transformations and Congruence
  • Chapter 10 Transformations and Similarity
  • Chapter 11 Angle Relationships in Parallel Lines and Triangles
  • Chapter 12 The Pythagorean Theorem
  • Chapter 13 Volume
  • Chapter 14 Scatter Plots
  • Chapter 15 Two-Way Tables

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