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Eureka Math Grade 5 Module 4 Lesson 8 Answer Key
Engage ny eureka math 5th grade module 4 lesson 8 answer key, eureka math grade 5 module 4 lesson 8 problem set answer key.
Question 1. Laura and Sean find the product of \(\frac{2}{3}\) × 4 using different methods. Laura: It’s 2 thirds of 4. \(\frac{2}{3}\) × 4 = \(\frac{4}{3}\) + \(\frac{4}{3}\) = 2 × \(\frac{4}{3}\) = \(\frac{8}{3}\)
Sean: It’s 4 groups of 2 thirds. \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = 4 × \(\frac{2}{3}\) = \(\frac{8}{3}\) Use words, pictures, or numbers to compare their methods in the space below. Answer: Laura: 2/3 * 4 = 4/3 + 4/3 = 2*4/3 = 8/3 Sean: 2/3 + 2/3 + 2/3 + 2/3 = 4 * 2/3 = 8/3 Both methods are correct. 2/3 *4 is 2 thirds of 4, and it will also have the same product as the 4 groups of 2 thirds.
Question 2. Rewrite the following addition expressions as fractions as shown in the example. Example: \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = (\(\frac{4 × 2}{3}\)) = \(\frac{8}{3}\) a. \(\frac{7}{4}\) + \(\frac{7}{4}\) + \(\frac{7}{4}\) = Answer: 21/4
Explanation: The addition expression for the fraction given is : 7/4 + 7/4 + 7/4 = (3 × 7)/4 = 21/4
b. \(\frac{14}{5}\) + \(\frac{14}{5}\) = Answer: 28/5
Explanation: The addition expression for the fraction given is : 14/5 + 14/5 = (2×14)/5 = 28/5
c. \(\frac{4}{7}\) + \(\frac{4}{7}\) + \(\frac{4}{7}\) = Answer: 12/7
Explanation: 4/7 +4/7 +4/7 = (3×4)/7 = 12/7
b. \(\frac{3}{5}\) × 10 10 × \(\frac{3}{5}\) Answer: 6
Explanation: 3 ×10/5 = 3 × 2 = 6 10 × 3/5 = (10×3)/5 = 30/5 = 6
a. 14 × \(\frac{3}{7}\) 14 × \(\frac{3}{7}\) Answer: 6
Explanation: (14×3)/7 = (7×2×3)/7 = (7×6)/7 = 6 (14 × 3)/7 = (2×3)/1 = 6
b. \(\frac{3}{4}\) × 36 \(\frac{3}{4}\) ×36 Answer: 27
Explanation: (3×36)/4 = (3×4×9)/4 = (4×27)/4 = 27 (3×36)/4 = (3×9) = (3×9) = 27
c. 30 × \(\frac{13}{10}\) 30 × \(\frac{13}{10}\) Answer: 39
Explanation: (30×13)/10 = (10×3×13)/10 = (10×39)/10 = 39 (30 ×13)/10 = (3×13)/1 = 39
d. \(\frac{9}{8}\) ×32 \(\frac{9}{8}\) × 32 Answer: 36
Explanation: (9×32)/8 = (9×4×8)/8 = (36×8)/8 = 36 (9×32)/8 = (9×32)/8 = (9×4)/1 = 36
Question 5. Solve each problem any way you choose. a. \(\frac{1}{2}\) × 60 \(\frac{1}{2}\) minute = __________ seconds Answer: 30seconds
Explanation: The answer and the procedure are explained clearly in the below steps. 1 minute = 60 seconds (1×60)/2 = (1×30)/1 = 30
b. \(\frac{3}{4}\) × 60 \(\frac{3}{4}\) hour = __________ minutes Answer: 45 minutes
Explanation: The answer and the procedure are explained clearly in the below steps. 1 hour = 60 minutes (3×60)/4 = (3×15)/1 = 45
c. \(\frac{3}{10}\) × 1,000 \(\frac{3}{10}\) kilogram = __________ grams” Answer: 300 grams
Explanation: The answer and the procedure are explained clearly in the below steps. 1 kilogram = 1000 grams (3×1000)/1 = 300
d. \(\frac{4}{5}\) × 100 \(\frac{4}{5}\) meter = __________ centimeters Answer: 80 centimeters
Explanation: The answer and the procedure are explained clearly in the below steps. 1 meter (4×100)/5 = (4×20)/1 = 80
Eureka Math Grade 5 Module 4 Lesson 8 Exit Ticket Answer Key
a. \(\frac{2}{3}\) × 15 \(\frac{2}{3}\) × 15 Answer: 10
Explanation: By solving the given question in two methods we could get the same answer i.e 10. The Explanation is given below. 2/3 × 15 = (2 ×15)/3 = 30/3 = 10 2/3 ×15 = (2×15)/3 = (2×5) = 10
b. \(\frac{5}{4}\) × 12 \(\frac{5}{4}\) × 12 Answer: 15
Explanation: By solving the given question in two methods we could get the same answer i.e 15. The process for the question is done below. 5/4 × 12 = (5×12)/4 = (60)/4 =15 5/4 ×12 = ( 5×12)/4 = (5×3) =15
Eureka Math Grade 5 Module 4 Lesson 8 Homework Answer Key
Question 1. Rewrite the following expressions as shown in the example. Example: \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) + \(\frac{2}{3}\) = (\(\frac{4 × 2}{3}\)) = \(\frac{8}{3}\)
a. \(\frac{5}{3}\) + \(\frac{5}{3}\) + \(\frac{5}{3}\) Answer: 5
Explanation: (\(\frac{3 × 5}{3}\)) = \(\frac{15}{3}\) =5
b. \(\frac{13}{5}\) + \(\frac{13}{5}\) Answer: \(\frac{26}{5}\)
Explanation: (\(\frac{2 × 13}{5}\)) = \(\frac{26}{5}\)
c. \(\frac{9}{4}\) + \(\frac{9}{4}\) + \(\frac{9}{4}\) Answer: \(\frac{27}{4}\)
Expalanation: (\(\frac{3 × 9}{4}\)) = \(\frac{27}{4}\)
a. \(\frac{3}{4}\) × 16 \(\frac{3}{4}\) × 16 Answer: 12
Explanation: (\(\frac{3 × 16}{4}\)) = \(\frac{48}{4}\) = 12 (\(\frac{3 × 16}{4}\)) = \(\frac{3 × 4}{1}\) = 12
b. \(\frac{4}{3}\) × 12 \(\frac{4}{3}\) × 12 Answer: 16
Explanation: (\(\frac{4 × 12}{3}\)) = \(\frac{48}{3}\) = 16 (\(\frac{4 × 12}{3}\)) = \(\frac{4 × 12}{1}\) = 16
c. 40 × \(\frac{11}{10}\) 40 × \(\frac{11}{10}\) Answer: 44
Explanation: (\(\frac{40 × 11}{10}\)) = \(\frac{440}{10}\) = 44 (\(\frac{40× 11}{10}\)) = \(\frac{4 × 11}{1}\) = \(\frac{44}{1}\) = 44
d. \(\frac{7}{6}\) × 36 \(\frac{7}{6}\)× 36 Answer: 42
Explanation: (\(\frac{7 × 36}{6}\)) = \(\frac{252}{6}\) = 42 (\(\frac{7 × 36}{6}\)) = \(\frac{7 × 6}{1}\) = 42
e. 24 × \(\frac{5}{8}\) 24 × \(\frac{5}{8}\) Answer: 15
Explanation: (\(\frac{24 × 5}{8}\)) = \(\frac{126}{8}\) = 15 (\(\frac{24 × 5}{8}\)) = \(\frac{3 × 5}{1}\) = 15
f. 18 × \(\frac{5}{12}\) 18 × \(\frac{5}{12}\) Answer: 7 1/2
Explanation: (\(\frac{18 × 5}{12}\)) = \(\frac{90}{12}\) = 7 6/12 = 7 1/2 (\(\frac{18 × 5}{12}\)) = \(\frac{3 × 5 }{2}\) = \(\frac{15}{2}\)= 7 1/2
g. \(\frac{10}{9}\) × 21 \(\frac{10}{9}\) × 21 Answer: 23 3/9 = 23 1/3
Explanation: (\(\frac{10 × 21}{9}\)) = \(\frac{210}{9}\) = 23 3/9 = 23 1/3 (\(\frac{10 × 21}{9}\)) = \(\frac{10 × 7}{3}\) = \(\frac{70}{3}\) = 23 1/3
Question 3. Solve each problem any way you choose.
a. \(\frac{1}{3}\) × 60 \(\frac{1}{3}\) minute = _________ seconds Answer: 20 seconds
Explanation: (\(\frac{1 × 60}{3}\)) = \(\frac{60}{3\) = 20
b. \(\frac{4}{5}\) × 60 \(\frac{4}{5}\) hour = _________ minutes Answer: 48 minutes
Explanation: (\(\frac{4 × 60}{5}\)) = \(\frac{48}{1\) = 48
c. \(\frac{7}{10}\) × 1000 \(\frac{7}{10}\) kilogram = _________ grams Answer: 700 grams
Explanation: (\(\frac{7 × 1000}{10}\)) = \(\frac{700}{1\) = 700
d. \(\frac{3}{5}\)× 100 \(\frac{3}{5}\) meter = _________ centimeters Answer: 60 centimeres
Explanation: (\(\frac{3 × 100}{5}\)) = \(\frac{60}{1\) = 60
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Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)
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
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.
Grade 5 Homework, Lesson Plans And Worksheets
Printable Common Core Worksheets for 5th Grade
| 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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