NYS COMMON CORE MATHEMATICS …

1 Lesson 1 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 1: Decompose fractions as a sum of unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. Name Date 1. Draw a number bond, and write the number sentence to match each tape diagram. The first one is donefor b. c. d. e. f. 1 1 1 1 1= 13 + 13 + 131 11313131 2015 Great Minds. Lesson 1 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 1: Decompose fractions as a sum of unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License.

2 G. h. 2. Draw and label tape diagrams to model each 16+16+16+16+16+16b. 45 = 15 + 25 +15c. = 3 + 3 + 1 d. 11 = + 1 + 3 1 1 2015 Great Minds. Lesson 1 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 1: Decompose fractions as a sum of unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. e. 121 = 61 + 41 +21 f. 1512 = 12 + 312 + + 23 =1+1 + 1 + 3 2015 Great Minds. Lesson 2 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Name Date 1: Draw and shade a tape diagram of the given 2: Record the decomposition as a sum of unit 3: Record the decomposition of the fraction two more ways.

3 (The first one has been done for you.)a. 5 b. 1 c. 3258 = 28 + 28 + 1858 = 28 + 18 + 18 + 181 58 = 18 + 18 + 18 + 18 + 18 Lesson 2: Decompose fractions as a sum of unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. 2015 Great Minds. Lesson 2 Problem Set NYS COMMON core MATHEMATICS curriculum 45 1: Draw and shade a tape diagram of the given 2: Record the decomposition of the fraction in three different ways using number b. 53c. 2: Decompose fractions as a sum of unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License.

4 2015 Great Minds. Lesson 3 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Name Date 1. Decompose each fraction modeled by a tape diagram as a sum of unit fractions. Write the equivalentmultiplication sentence. The first one has been done for 34=14 + 14 + 1434= 3 14b. c. d. e. 1 1 1 1 1 Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. 2015 Great Minds. Lesson 3 Problem Set NYS COMMON core MATHEMATICS curriculum 45 2. Write the following fractions greater than 1 as the sum of two b.

5 3. Draw a tape diagram, and record the given fraction s decomposition into unit fractions as a 45b. 5 c. d. 4e. 6 1 1 Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. 2015 Great Minds. Lesson 4 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. Name Date 1.

6 The total length of each tape diagram represents 1. Decompose the shaded unit fractions as the sum ofsmaller unit fractions in at least two different ways. The first one has been done for b. c. d. 12= 14 + 141212= 1 + 1 + 1 + 1 121313 2015 Great Minds. Lesson 4 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. total length of each tape diagram represents 1. Decompose the shaded fractions as the sum ofsmaller unit fractions in at least two different b.

7 3. Draw and label tape diagrams to prove the following statements. The first one has been done for 25=41 b. 26=412 2015 Great Minds. Lesson 4 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. c. 34=6 d. 34= 124. Show that 12is equivalent to4 using a tape diagram and a number sentence. 5. Show that 23is equivalent to 6 using a tape diagram and a number Show that 46is equivalent to 12 using a tape diagram and a number sentence.

8 2015 Great Minds. Lesson 5 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 5: Decompose unit fractions using area models to show equivalence. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. Name Date 1. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the modelto give the shaded area as both a sum of unit fractions and as a multiplication 2 rows b. 2 rowsc. 4 rows14 = 214 = 18+=14 = 2 = 2015 Great Minds. Lesson 5 Problem Set NYS COMMON core MATHEMATICS curriculum 45 Lesson 5: Decompose unit fractions using area models to show equivalence.

9 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. 2. Draw area models to show the decompositions represented by the number sentences below. Representthe decomposition as a sum of unit fractions and as a multiplication 12 = 36 b. 12= 48c. 12= 510d. 13= 26e. 13= 412f. 14= 3123. Explain why 112+112+112is the same as14. 2015 Great Minds. NYS COMMON core MATHEMATICS curriculum 45 Lesson 6 Problem Set Name Date rectangle represents 1. Draw horizontal lines to decompose each rectangle into the fractional unitsas indicated. Use the model to give the shaded area as a sum and as a product of unit fractions.

10 Useparentheses to show the relationship between the number sentences. The first one has been partiallydone for = 43+3= 16+16 + 16+16 =4 16+16 + 16+16 = 2 + 2 =423=4 =4 Lesson 6: Decompose fractions using area models to show equivalence. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike Unported License. 2015 Great Minds. NYS COMMON core MATHEMATICS curriculum 45 Lesson 6 Problem Set area models to show the decompositions represented by the number sentences below. Expresseach as a sum and product of unit fractions. Use parentheses to show the relationship between thenumber 35=61 b.