Eureka Math Grade 5 Answer Key | Engage NY Math 5th Grade Answer Key Solutions

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EngageNY Math Grade 5 Answer Key | Eureka Math 5th Grade Answers Key PDF Free Download

Eureka Grade 5 Mathematics Module 1 to Module 6 Lesson-wise Answer key PDF links are provided online to access and download for free of cost. After downloading the Engage NY Math Fifth Grade Solutions Pdf , you can practice more with the help of Mid Module and End Module Assessments, Practice Tools. These resources boost up your confidence and identify your level of preparation and areas your lagging. So, download the Eureka Math Grade 5 Answer Keys for all modules and ace up your preparation.

  • Eureka Math Grade 5 Module 1 Answer Key
  • Eureka Math Grade 5 Module 2 Answer Key
  • Eureka Math Grade 5 Module 3 Answer Key
  • Eureka Math Grade 5 Module 4 Answer Key
  • Eureka Math Grade 5 Module 5 Answer Key
  • Eureka Math Grade 5 Module 6 Answer Key

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Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)

Looking for video lessons that will help you in your Common Core Grade 5 Math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Grade 5 students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. The Lesson Plans and Worksheets are divided into six modules.

Related Pages Common Core Math Resources, Lesson Plans And Worksheets Common Core Math Video Lessons, Math Worksheets and Games for Grade 5 Common Core Math Video Lessons, Math Worksheets and Games for all grades

Grade 5 Homework, Lesson Plans And Worksheets

Module 1 Topics and Objectives

Standard: 5.NBT.1, 5.NBT.2, 5.MD.1
Days: 4





: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths. ( )

: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths. ( )

: Use exponents to name place value units and explain patterns in the placement of the decimal point. ( )

: Use exponents to denote powers of 10 with application to metric conversions. ( )

Standard: 5.NBT.3
Days: 2



: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning. ( )

: Compare decimal fractions to the thousandths using like units and express comparisons with >, <, =. ( )

Standard: 5.NBT.4
Days: 2



, : Round a given decimal to any place using place value understanding and the vertical number line. ( ) ( )
: Topics A-C (assessment ½ day, return ½ day, remediation or further applications 1 day)

Standard: 5.NBT.2, 5.NBT.3, 5.NBT.7
Days: 2



: Add decimals using place value strategies and relate those strategies to a written method. ( )

: Subtract decimals using place value strategies and relate those strategies to a written method. ( )

Standard: 5.NBT.1, 5.NBT.3, 5.NBT.7
Days: 2



: Multiply a decimal fraction by single-digit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the reasoning used. ( )

: Multiply a decimal fraction by single-digit whole numbers, including using estimation to confirm the placement of the decimal point. ( )

Standard: 5.NBT.3, 5.NBT.7
Days: 4



: Divide decimals by single-digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method. ( )

: Divide decimals with a remainder using place value understanding and relate to a written method. ( )

: Divide decimals using place value understanding including remainders in the smallest unit. ( )

: Solve word problems using decimal operations. ( )
: Topics A-F (assessment ½ day, return ½ day, remediation or further applications 1 day)
Module 2 Topics and Objectives

Standard: 5.NBT.1, 5.NBT.2, 5.OA.1
Days: 2





: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties. ( )

: Estimate multi-digit products by rounding factors to a basic fact and using place value patterns. ( )

Standard: 5.OA.1, 5.OA.2, 5.NBT.5
Days: 7



: Write and interpret numerical expressions and compare expressions using a visual model. ( )

: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication. ( )

: Connect visual models and the distributive property to partial products of the standard algorithm without renaming. ( )

:Connect area diagrams and the distributive property to partial products of the standard algorithm without renaming. ( )

: Connect area diagrams and the distributive property to partial products of the standard algorithm with renaming. ( )

: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product. ( )

: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems. ( )

Standard: 5.NBT.7, 5.OA.1, 5.OA.2, 5.NBT.1
Days: 3



: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products. ( )

: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal. ( )

: Reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation. ( )

Standard: 5.NBT.7, 5.NBT.7, 5.MD.1
Days: 3



: Use whole number multiplication to express equivalent measurements. ( )

: Use decimal multiplication to express equivalent measurements. ( )

: Solve two-step word problems involving measurement and multi-digit multiplication. ( )
: Topics A-D (assessment ½ day, return ½ day, remediation or further applications 2 days)

Standard: 5.NBT.1, 5.NBT.2, 5.NBT.6
Days: 3



: Use patterns for multi-digit whole number division. ( )

, : Use basic facts to approximate quotients with two-digit divisors. ( ) ( )

Standard: 5.NBT.6
Days: 5



: Divide two- and three-digit dividends by multiples of 10 with single-digit quotients and make connections to a written method. ( )

: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients and make connections to a written method. ( )

: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients and make connections to a written method. ( )

, : Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value. ( ) ( )

Standard: 5.NBT.2, 5.NBT.7
Days: 4



: Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method. ( )

: Use basic facts to approximate decimal quotients with two-digit divisors, reasoning about the placement of the decimal point. ( )

, : Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. ( ) ( )

Standard: 5.NBT.6, 5.NBT.7
Days: 2



, : Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown. ( ) ( )
: Topics A-H (assessment ½ day, return ½ day, remediation or further application 2 days)
Module 3 Topics and Objectives

Standard: 5.NF.1, 5.NF.3
Days: 2





: Make equivalent fractions with the number line, the area model, and numbers. ( )

: Make equivalent fractions with sums of fractions with like denominators. ( )

Standard: 5.NF.1, 5.NF.2
Days: 5



: Add fractions with unlike units using the strategy of creating equivalent fractions. ( )

: Add fractions with sums between 1 and 2. ( )

: Subtract fractions with unlike units using the strategy of creating equivalent fractions. ( )

: Subtract fractions from numbers between 1 and 2. ( )

: Solve two-step word problems. ( )
: Topics A-B (assessment ½ day, return ½ day, remediation or further applications 2 day)

Standard: 5.NF.1, 5.NF.2
Days: 5



: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies. ( )

: Add fractions making like units numerically. ( )

: Add fractions with sums greater than 2. ( )

: Subtract fractions making like units numerically. ( )

: Subtract fractions greater than or equal to one ( )

Standard: 5.NF.1, 5.NF.2
Days: 4



: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations. ( )

: Strategize to solve multi-term problems. ( )

: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers. ( )

: Explore part to whole relationships. ( )
: Topics C-D (assessment ½ day, return ½ day, remediation or further applications 2 day)
Module 4 Topics and Objectives

Standard: 5.MD.2
Days: 1





: Measure and compare pencil lengths to the nearest 1/2, 1/4, and 1/8 of an inch, and analyze the data through line plots. ( )

Standard: 5.NF.3
Days: 4



, : Interpret a fraction as division. ( )( )

: Use tape diagrams to model fractions as division. ( )

: Solve word problems involving the division of whole numbers with answers in the form of fractions or whole numbers. ( )


Standard: 5.NF.4a
Days: 4



: Relate fractions as division to fraction of a set. ( )

: Multiply any whole number by a fraction using tape diagrams. ( )

: Relate fraction of a set to the repeated addition interpretation of fraction multiplication. ( )

: Find a fraction of a measurement, and solve word problems. ( )

Standard: 5.OA.1, 5.OA.2, 5.NF.4a, 5.NF.6
Days: 3



: Compare and evaluate expressions with parentheses. ( )

, : Solve and create fraction word problems involving addition, subtraction, and multiplication. ( )
: Topics A-D (assessment ½ day, return ½ day, remediation or further applications 1 day)

Standard: 5.NBT.7, 5.NBT.4a, 5.NF.6, 5.MD.1
Days: 8



: Multiply unit fractions by unit fractions. (

: Multiply unit fractions by non-unit fractions. ( )

: Multiply non-unit fractions by non-unit fractions. ( )

: Solve word problems using tape diagrams and fraction-by-fraction multiplication. ( )

, : Relate decimal and fraction multiplication. ( )

: Convert measures involving whole numbers, and solve multi-step word problems. ( )

: Convert mixed unit measurements, and solve multi-step word problems. ( )

Standard: 5.NF.5, 5.NF.6
Days: 4



: Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1. ( )

, : Compare the size of the product to the size of the factors. ( )

: Solve word problems using fraction and decimal multiplication. ( )

Standard: 5.OA.1, 5.NBT.7, 5.NF.7
Days: 7



: Divide a whole number by a unit fraction. ( )

: Divide a unit fraction by a whole number. ( )

: Solve problems involving fraction division. ( )

: Write equations and word problems corresponding to tape and number line diagrams. ( )

: Connect division by a unit fraction to division by 1 tenth and 1 hundredth. ( )

, : Divide decimal dividends by non-unit decimal divisors. ( )( )

Standard: 5.OA.1, 5.OA.2
Days: 2



: Interpret and evaluate numerical expressions including the language of scaling and fraction division. ( )

: Create story contexts for numerical expressions and tape diagrams, and solve word problems. ( )
: Topics A-H (assessment ½ day, return ½ day, remediation or further applications 2 days)
Module 5 Topics and Objectives

Standard: 5.MD.3, 5.MD.4
Days: 3





: Explore volume by building with and counting unit cubes. ( )

: Find the volume of a right rectangular prism by packing with cubic units and counting.( )

: Compose and decompose right rectangular prisms using layers. ( )

Standard: 5.MD.3, 5.MD.5
Days: 6



: Use multiplication to calculate volume. ( )

: Use multiplication to connect volume as with volume as . ( )

: Find the total volume of solid figures composed of two non-overlapping rectangular prisms. ( )

: Solve word problems involving the volume of rectangular prisms with whole number edge lengths. ( )

, : Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters. ( )
: Topics A-B (assessment 1 day, return ½ day, remediation or further applications ½ day)

Standard: 5.NF.4b, 5.NF.6
Days: 6



: Find the area of rectangles with whole-by-mixed and whole-by-fractional number side lengths by tiling, record by drawing, and relate to fraction multiplication. ( )

: Find the area of rectangles with mixed-by-mixed and fraction-by-fraction side lengths by tiling, record by drawing, and relate to fraction multiplication. ( )

: Measure to find the area of rectangles with fractional side lengths. ( )

: Multiply mixed number factors, and relate to the distributive property and the area model. ( )

, : Solve real world problems involving area of figures with fractional side lengths using visual models and/or equations. ( ) ( )

Standard: 5.G.3, 5.G.4
Days: 6



: Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes. ( )

: Draw parallelograms to clarify their attributes, and define parallelograms based on those attributes. ( )

: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes. ( )

: Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes. ( )

: Classify two-dimensional figures in a hierarchy based on properties. ( )

: Draw and identify varied two-dimensional figures from given attributes. ( )
: Topics A-D (assessment 1 day, return ½ day, remediation or further applications ½ day)
Module 6 Topics and Objectives

Standard: 5.G.1
Days: 6





: Construct a coordinate system on a line. ( )

: Construct a coordinate system on a plane. ( )

, : Name points using coordinate pairs, and use the coordinate pairs to plot points. ( )

, : Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes. ( )( )

Standard: 5.OA.2, 5.OA.3, 5.G.1
Days: 6



: Plot points, use them to draw lines in the plane, and describe patterns within the coordinate pairs. ( )

: Generate a number pattern from a given rule, and plot the points. ( )

: Generate two number patterns from given rules, plot the points, and analyze the patterns. ( )

: Compare the lines and patterns generated by addition rules and multiplication rules. ( )

: Analyze number patterns created from mixed operations. ( )

: Create a rule to generate a number pattern, and plot the points.( )
: Topics A-B (assessment 1 day, return 1 day, remediation or further applications 1 day)

Standard: 5.G.1, 5.G.2
Days: 5



: Construct parallel line segments on a rectangular grid. ( )

: Construct parallel line segments, and analyze relationships of the coordinate pairs. ( )

: Construct perpendicular line segments on a rectangular grid. ( )

: Construct perpendicular line segments, and analyze relationships of the coordinate pairs. ( )

: Draw symmetric figures using distance and angle measure from the line of symmetry. ( )

Standard: 5.OA.3, 5.G.2
Days: 3



: Draw symmetric figures on the coordinate plane. ( )

: Plot data on line graphs and analyze trends.( )

: Use coordinate systems to solve real world problems. ( )
: Topics A-D (assessment 1 day, return 1 day, remediation or further applications 1 day)

Standard: 5.NF.2, 5.NF.3, 5.NF.6, 5.NF.7c, 5.MD.1, 5.MD.5, 5.G.2
Days: 5



, , , , : Make sense of complex, multi-step problems and persevere in solving them. Share and critique peer solutions. ( )

Days: 9



, : Solidify writing and interpreting numerical expressions. ( )

: Solidify fluency with Grade 5 skills.

, : Solidify the vocabulary of geometry. ( )

: Explore the Fibonacci sequence.

: Explore patterns in saving money. ( )

, : Design and construct boxes to house materials for summer use. ( )

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Eureka Math Grade 5 Module 6 Lesson 5 Answer Key

Engage ny eureka math 5th grade module 6 lesson 5 answer key, eureka math grade 5 module 6 lesson 5 problem set answer key.

Engage NY Math Grade 5 Module 6 Lesson 5 Problem Set Answer Key 1

Question 3. For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the x-axis? Circle your answer(s). Without plotting them, explain how you know. a. (1.4, 2.2) and (4.1, 2.4) b. (3, 9) and (8, 9) c. (1\(\frac{1}{4}\), 2) and (1\(\frac{1}{4}\), 8) Answer: Option b Explanation : To form a parallel line to x -axis, the y-coordinates should be same for all x-coordinates. so in option c we have same y -coordinates b. (3, 9) and (8, 9).

Question 4. For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the y-axis? Circle your answer(s). Then, give 2 other coordinate pairs that would also fall on this line. a. (4, 12) and (6, 12) b. (\(\frac{3}{5}\), 2\(\frac{3}{5}\)) and (\(\frac{1}{5}\), 3 \(\frac{1}{5}\)) c. (0.8, 1.9) and (0.8, 2.3) Answer: Option c Explanation : To form a parallel line to y -axis, the x-coordinates should be same for all y-coordinates. so in option a we have same y -coordinates (0.8, 1.9) and (0.8, 2.3) The 2 Other coordinate pairs that would also fall on this line are (0.8, 2) and (0.8, 2.1)

Question 5. Write the coordinate pairs of 3 points that can be connected to construct a line that is 5\(\frac{1}{2}\) units to the right of and parallel to the y-axis. a. ________________ b. ________________ c. ________________ Answer: A (5\(\frac{1}{2}\) ,\(\frac{1}{2}\)) B (5\(\frac{1}{2}\), 2\(\frac{1}{2}\)) C (5\(\frac{1}{2}\), 3) Explanation : To form a parallel line to y -axis, the x-coordinates should be same for all y-coordinates.

Question 6. Write the coordinate pairs of 3 points that lie on the x-axis. a. ________________ b. ________________ c. ________________ Answer: A ( 3, 0 ) B ( 5, 0) C ( 7, 0) Explanation : To lie 3 points on x – axis y coordinates should be 0 . then any point with different x-coordinates lie on x-axis.

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-5-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-5-Problem-Set-Answer-Key-Question-7

Eureka Math Grade 5 Module 6 Lesson 5 Exit Ticket Answer Key

Eureka Math 5th Grade Module 6 Lesson 5 Exit Ticket Answer Key 1

Question 2. Which axis is parallel to line l? Which axis is perpendicular to line l? Answer: y – axis is parallel to line l x – axis is perpendicular to line l

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-5-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-5-Exit-Ticket-Answer-Key-Question-3

Question 4. Give the coordinates of each point below. A: ___________ B: ___________ C: ___________ D: ___________ Answer: A : ( 4, 6 ) B: ( 4, 3 ) C: ( 4, 5 ) D: ( 4, 4 )

Question 5. Give the coordinates of another point that falls on line l with a y-coordinate greater than 20. Answer: ( 4, 22 ) Explanation : All the x- coordinates are the same it is parallel line to y – axis and given y – coordinate should be greater than 20 so, (4, 22) .

Eureka Math Grade 5 Module 6 Lesson 5 Homework Answer Key

Eureka Math Grade 5 Module 6 Lesson 5 Homework Answer Key 1

Question 3. For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the x-axis? Circle your answer(s). Without plotting them, explain how you know. a. (3.2, 7) and (5, 7) b. (8, 8.4) and (8, 8.8) c. (6\(\frac{1}{2}\), 12) and (6.2, 11) Answer: a. (3.2, 7) and (5, 7) Explanation : To form a parallel line to x -axis, the y-coordinates should be same for all x-coordinates. In  option a. (3.2, 7) and (5, 7) we have same x – coordinate .

Question 4. For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the y-axis? Circle your answer(s). Then, give 2 other coordinate pairs that would also fall on this line. a. (3.2, 8.5) and (3.2, 24) b. (13\(\frac{1}{2}\), 4\(\frac{2}{3}\)) and (13\(\frac{1}{3}\), 7) c. (2.9, 5.4) and (7.2, 5.4) Answer: a. (3.2, 8.5) and (3.2, 24) Explanation : To form a parallel line to y -axis, the x-coordinates should be same for all y-coordinates. In Option a. (3.2, 8.5) and (3.2, 24) we have same x-coordinates .

Question 5. Write the coordinate pairs of 3 points that can be connected to construct a line that is 5\(\frac{1}{2}\) units to the right of and parallel to the y-axis. a. ________________ b. ________________ c. ________________ Answer: A ( 5\(\frac{1}{2}\), 2\(\frac{1}{2}\) ) B ( 5\(\frac{1}{2}\), 5\(\frac{1}{2}\)) C ( 5\(\frac{1}{2}\), 4) Explanation : To form a parallel line to y -axis, the x-coordinates should be same for all y-coordinates.

Question 6. Write the coordinate pairs of 3 points that lie on the y-axis. a. ________________ b. ________________ c. ________________ Answer: A ( 0, 2 ) B ( 0, 4) C ( 0, 6) Explanation : The 3 points that lie on the y-axis means x-coordinate should be 0 then all the points lie on y-axis .

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-5-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-5-Homework-Answer-Key-Question-7

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