Adding and Subtracting Fractions and Mixed Numbers 

OVERVIEW  
6 Days  Adding and subtracting fractions


5.NF.1. 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.)  **See Resources submitted with Unit Plan**  VOCABULARY*Simplify
*common denominators *unlike denominators *fraction *equivalent *reduce *mixed number *improper fraction *numerator 
7 Days  Fractions and real world situations 

5.NF.2. 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.  **See Resources submitted with Unit Plan**  VOCABULARY*unlike denominators
*benchmark fractions *estimation *fraction *equivalent *reduce *mixed number *improper fraction

2 Days 
Review and QUIZ 
Multiplying Fractions and Mixed Numbers 

OVERVIEW  
1 Day  Fractions 

5.NF.3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?  **See Resources submitted with Unit Plan**  VOCABULARY*Numerator
*Denominator *Division *Quotient 
3 Days  Multiplying fractions and whole numbers 

5.NF.4a. 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. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)  **See Resources submitted with Unit Plan**  VOCABULARY*part of
*area *tiling *unit fraction

1 Day  Area of rectangles with fractional side lengths 

5.NF.4b. 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.  **See Resources submitted with Unit Plan**  VOCABULARY*Tiling
*unit square *equivalence

1 Day  Size of products 

5.NF.5a. 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.  **See Resources submitted with Unit Plan**

VOCABULARY*Product
*Factor *improper fraction *mixed number

1 Day  Size of products 

5.NF.5b. 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.  **See Resources submitted with Unit Plan**  VOCABULARY*Product
*Factor *equivalent fraction

1 Day  Multiplying fractions and mixed numbers 

5.NF.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

**See Resources submitted with Unit Plan**  VOCABULARY*Fractions
*mixed number *visual models

1 Day 
Quiz 
Dividing Fractions and Mixed Numbers 

OVERVIEW  
1 Day  Division of unit fractions and whole numbers 

5.NF.7a. Interpret division of a unit fraction by a nonzero 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.  **See Resources submitted with Unit Plan**

VOCABULARY*unit fraction
*whole number *divide *estimation *quotients *lowest terms

2 Days  Division of unit fractions and whole numbers or unit fractions 

5.NF.7b. 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.  **See Resources submitted with Unit Plan**

VOCABULARY*unit fraction
*whole number *divide *estimation *quotients *lowest terms *numerator *denominator

1 Day  Division of unit fractions and whole numbers 

5.NF.7c.Solve real world problems involving division of unit fractions by nonzero 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 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins?  **See Resources submitted with Unit Plan**  VOCABULARY*unit fraction
*whole number *divide *estimation *quotients *lowest terms *numerator denominator 
1 Day 
Quiz 