4.NF.4 NUMBER & OPERATIONS - FRACTIONS

CLUSTER: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.4 STANDARDS a.Understand Fractions as Multiples of Unit Fractions b.Understand Fractions as Multiples of Unit Fractions c.Multiply Fractions by Whole Numbers in Word Problems

4NF.4 A - UNDERSTAND FRACTIONS AS MULTIPLES OF UNIT FRACTIONS Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). (4.NF footnote: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.)

PROBLEM 1: Each day Debbie reads ⅛ of her new book. Which number sentence best represents the fraction of her book that Debbie has read after 7 days? A.1/8 × 1/7 = 1/56 B.1/8 × 1/7 = 7/8 C.1/8 × 7 = 1/56 D.1/8× 7 = 7/8

PROBLEM 2: Which multiplication sentence can be used to calculate the total shaded area shown in the model below? A. 4 x ⅛ B. 8 x ¼ C. 4 x ⅙ D. 6 x ¼

4 x ⅜ PROBLEM 3: WRITE AN EXPRESSION TO SHOW:

4 x ⅓ = PROBLEM 4: TRUE OR FALSE??

PROBLEM 5: For each of the expressions below, circle either “Less than 1” or “Greater than 1” to show whether the expression is less than or greater than 1.

4NF.4 B - UNDERSTAND MULTIPLICATION OF FRACTIONS BY WHOLE NUMBERS Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) (4.NF footnote: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.)

PROBLEM 1: Which expression is equivalent to 6 × ⅔ ? A. 12 × ½ B. 12 × ⅓ C. 6 × ⅓ D. 3 × ⅔

PROBLEM 2: True or False? =

PROBLEM 3: Kara wrote an expression that has a value of 12/5. For parts (a)-(c), circle YES or NO to indicate whether each expression has a value of 12/5. YES or NO (a) 12 × ⅕ YES or NO (b) 12 × 5/5 YES or NO (c) 3 × ⅘

PROBLEM 4: Rewrite: 3 x 6/8 as the product of a unit fraction and a whole number. Solve. Rewrite: 4 x 2/3 as the product of a unit fraction and a whole number. Solve

4NF.4 C - MULTIPLY FRACTIONS BY WHOLE NUMBERS IN WORD PROBLEMS Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? (4.NF footnote: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.)

PROBLEM 1: Jasmine makes 6 purses. She uses ¾ yard of cloth to make each purse. What is the total amount of cloth, in yards, Jasmine uses to make all 6 purses?

What is the ? 5 x ?= PROBLEM 2:

PROBLEM 3: In a relay race, each runner runs ½ of a lap. If there are 4 team members, how long is the race altogether? A. ⅛ lap B. 1 lap C. 2 laps D. 4½ laps

PROBLEM 4: A builder planned to build houses. Each house will be built on ⅚ of an acre. How much land will be needed for 7 houses? Show your work.