Elementary Mathematics

5th Grade Unit 4 Overview and Standards


Use these links to access resources for this unit.


 Before You Begin this Unit…   Unit at a Glance

The work in this unit builds on the work from 4th grade where students added and subtracted fractions with like denominators. Although students have not yet studied percents (nor is it an elementary standard), this unit introduces the concepts of fractions, decimals and percents together. Learning about them simultaneously helps students make connections between the different forms and builds number sense about rational numbers. It also helps them judge the reasonableness of solutions because they can use equivalencies to catch computational errors.

This unit highlights the relationship among fractions, decimals, and percents. Students add, subtract and compare rational numbers using 10 X 10 grids, equivalency strips, clocks and number lines. Emphasis is also placed on comparing fractions to landmark numbers such as 0, ½ and 1. In fifth grade, students find a common denominator by finding the product of both denominators. This process should come after students have used visual fraction models (area models, number lines, etc.) to build understanding before moving into the standard algorithm described in the standard. Students should apply their understanding of equivalent fractions and their ability to rewrite fractions in an equivalent form to find common denominators.

Suggested Dates:
October 9th- December 12th

Estimated Duration: 42 days

Investigation 1:  4 Lessons (combine 1.3 and 1.4)

Investigation 2:  5 Lessons (combine 2.5 and 2.6)

Investigation 3:  10 Lessons

Investigation 4:  10 Lessons

After you complete Investigation 4, use these 6
DPI Multiplying and Dividing Fractions lessons to extend learning.

After you complete the DPI lessons, complete the following2 lessons for MD.2!  

In addition to the 2 lessons for MD.2, it's suggested you use the 2 lessons from Unit 9 on line plots, 1.1 and 1.5A

*Note: Fraction work will continue throughout the rest of the year and be incorporated with other concepts

 Standards Addressed in the Unit

Link to CCSS Unpacking Document- Updated Sept. '15 (look at pages 30-43)

5NF1  Use equivalent fractions as a strategy to add and subtract fractions.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5NF2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. . For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

5NF4a-b Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

  1. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
  2. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5NF5a-b Interpret multiplication as scaling (resizing), by:

  1. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  2. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5NF6  Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

  1. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

  1. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
  2. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

For example, how much chocolate will each person get if 3 people share ½ lb of chocolate equally?  How many 1/3-cup servings are 2 cups of raisins?