5th Grade Fraction Operations Part 2 2015-11-13 www.njctl.org - PDF document

Slide 1 / 130 Slide 2 / 130 5th Grade Fraction Operations Part 2 2015-11-13 www.njctl.org Slide 3 / 130 Slide 4 / 130 Table of Contents click on the topic to go to that section · Multiplying Fractions · Multiplying Fractions and Whole Numbers Multiplying · Multiplying with Mixed Numbers · Interpreting Multiplication of Fractions Fractions Area of fractional side length rectangles · · Dividing Unit Fractions by Whole Numbers · Dividing Whole Numbers by Unit Fractions Return to Line Plots with Fractional Data · Table of Contents Slide 5 / 130 Slide 6 / 130 Folding Shading You can use folding to show a fractional part of a You can use shading to find a fractional part fraction. (You will need a set of Fraction Pieces.) of another fraction. 1 1 Here is how to find of 1 1 Here is how to find of 2 3 3 4 1 1. Use the fraction piece. 1. Divide your whole into fourths. 3 2. Fold it in half. 1 2. Shade a third of 4 3. Compare the folded part with the other fraction 3. What fractional part of the whole did you pieces to find a piece that matches. shade? click to reveal Slide over bar below 1 1 1 to show equality. 1 of is 2 3 6 click 12

Slide 7 / 130 Slide 8 / 130 Multiplying Fractions Problem is from: Multiplication describes events when equal groups of things are combined together. Click for link for commentary For example, 3 groups of 4 apples and solution. can be abbreviated using the number sentence 3 x 4 = ?. Multiplication number sentences should be read as, "What is (variable) groups of (variable) things?" The variable can be a whole number, a rational number, or any expression that represents either a number of groups, or the number of items in a group. We will be working with variables that are fractions. Read this number sentence aloud using the phrase, "What is (variable) groups of (variable) things?" 1 2 x = 3 5 Slide 9 / 130 Slide 10 / 130 Multiplying Using Area Models Review from Decimal Computation Unit Using an Area Model to Multiply Decimals Multiplication of two factors can be illustrated using an array called How can we turn this model showing 2 x 3 into an area model. When you make an array, each factor represents either the vertical or horizontal dimension of a square or a a model showing 2 x 3.5? rectangle. 3 .5 3 2 Click 4 How many square tiles is it now? With the above example, a rectangle can be constructed with 3 units on one side of the array, and 4 units on the other side. The What number sentence represents the number of square tiles? resulting three by four rectangle contains 12 square units. The result can be read, "12 is 3 groups of 4". What if we add another row? What number sentence will represent the number of square tiles? Slide 11 / 130 Slide 12 / 130 Lets label this model. Rectangle Model (Click to remove boxes) The array or area model is also very effective when illustrating 2 3 tenths multiplication of two fractions. When multiplying 1/2 x 5/4, the question can be read, "What is 1/2 of 5/4?" or "What is 1/2 of a group of 5/4?" 4 6 tenths Lets show a group of 5/4. 2 ? ? Review from Decimal Computation Unit 8 tenths 4 tenths ? Now, lets show 1/2 of that. 4 12 hundredths What are these? 0.8 What is the sum? 0.6 + 0.12 5.52 5/8 Click

Slide 13 / 130 Slide 14 / 130 Interactive Area Model Multiplying Using the Algorithm Use the interactive model to show 1/2 of 5/4. 1. Use the arrow keys to section off one dimension of a whole into 2 To multiply fractions, multiply the numerators, and parts, and the other dimension into 4 parts. then multiply the denominators. A 2 by 4 array is a rectangle with 8 units making up a whole group. Make sure you simplify your answer! 2. Using the slider bar, highlight 1/2 on the side divided into 2 parts, and highlight 5/4 on the side divided into 4 parts. The intersection of these shaded parts represents the answer to the question, "What is 1/2 of 5/4?" The answer can be read, "5/8 is 4 x 3 = 4 x 3 = 12 = 3 1/2 of 5/4." 5 4 5 x 4 20 5 Sketch an area model to check your answer. (Click for interactive site) Slide 15 / 130 Slide 16 / 130 Multiply 1 Examples 1 x 2 = Sketch an area model to check your answer. 5 3 click to reveal 7 x 2 = 7 x 2 = 14 11 9 11 x 9 99 click to reveal 3 x 4 = 3 x 4 = 12 = 1 8 9 8 x 9 72 6 click to reveal ( ) 8 6 = 8(6) = 48 = 24 14 7 14(7) 98 49 Slide 17 / 130 Slide 18 / 130 2 3 2 x 3 5 x 4 = = 3 7 8 7

Slide 19 / 130 Slide 20 / 130 4 5 ( ) ( ) 4 3 2 5 = = 11 6 9 8 Slide 21 / 130 Slide 22 / 130 Internet Link for More Practice Problem is from: 5.NF Drinking Juice Click for link for commentary and solution. Alisa had 1/2 a liter of juice in a bottle. She drank 3/4 of the juice that was in the bottle. How many liters did she drink? Slide 23 / 130 Slide 24 / 130 6 At Cliffords’s school, of the students wanted to learn 7 A bridge span is of a mile long. Workers have repainted about the new science museum that was just built. This of it. How much has been repainted? month, of the students were able to go see it. What fraction of students were able to go see it right away?

Slide 25 / 130 Slide 26 / 130 Problem is from: 5.NF Running to School Click for link for commentary and solution. 8 The distance between Rosa's house and her school is mile. She ran of the way to school. How many miles did she run? Slide 27 / 130 Slide 28 / 130 Slide 29 / 130 Slide 30 / 130

Slide 31 / 130 Slide 32 / 130 Slide 33 / 130 Slide 34 / 130 14 Solve the problem. Simplify prior to multiplying if you can. 15 Solve the problem. Simplify prior to multiplying if you can. Slide 35 / 130 Slide 36 / 130 16 Solve the problem. Simplify prior to multiplying if you can. 17 Solve the problem. Simplify prior to multiplying if you can.

Slide 37 / 130 Slide 38 / 130 19 Solve. 18 Solve the problem. Simplify prior to multiplying if you can. From PARCC EOY sample test #25 Slide 39 / 130 Slide 40 / 130 Problem is from: 5.NF Connor and Makayla Discuss Multiplication Click for link for commentary and solution. Multiplying Fractions and Whole Numbers Return to Table of Contents Slide 41 / 130 Slide 42 / 130 Whole Number times a Fraction To multiply fractions with whole numbers, write the 20 whole number as a fraction (over 1) then multiply the x 1 5 x 1 5 = two fractions. W rite your answer in simplest form. 2 1 2 4 6 4 6 = 6 x 4 = 24 x 6 2 = x 2 2 True = = 9 1 9 1 x 9 9 9 3 False 2 Alternate Method 6 6 4 4 = 8 2 2 x = x = of canceling 3 components 1 9 1 9 3 3 5 ( ) 5 ( ) 3 3 7 21 7 4 1 = = = 1 5 5

Slide 43 / 130 Slide 44 / 130 21 22 x 4 x 8 3 12 7 9 1 5 96 12 32 A C A C 7 9 21 3 12 3 5 11 1 10 2 B D B D 7 7 3 3 Slide 45 / 130 Slide 46 / 130 23 On Wednesday morning, of Sue’s classmates put 24 Of the 49 kids on the campout, wanted to go to bed right blueberries on their cereal. If there are 27 students in after the sing-along around the fire. How many kids wanted Sue’s class, how many put blueberries on their cereal? to go to bed right away? Slide 47 / 130 Slide 48 / 130 Multiplying Mixed Numbers To multiply fractions with mixed numbers, write the mixed numbers as an improper fractions, then multiply the two fractions. Multiplying with Make sure you write your answer in simplest form. Mixed Numbers 3 1 7 3 11 = 11 x 7 = 77 2 5 9 x = x = 4 2 4 2 4 x 2 8 8 Return to Table of ( Contents ) 1 ( ) 1 5 4 5 1 20 6 2 = = = 3 3 3 3

Slide 49 / 130 Slide 50 / 130 25 26 3 1 6 3 1 1 2 8 5 x x = 8 8 4 2 True 1 44 44 A C 2 False 88 1 40 B D 2 2 Slide 51 / 130 Slide 52 / 130 Problem is from: 5.NF Half of a Recipe 27 ( ) ( 3 ) 5 2 5 Click for link for commentary and solution. 8 5 3 1 20 15 C A Kendra is making 1/2 of a recipe. The full recipe calls for 8 4 3 1/4 cup of flour. How many cups of flour should Kendra use? 1 1 19 18 D B 8 8 Slide 53 / 130 Slide 54 / 130 28 A boat was traveling 12 miles each hour. At that rate, 29 Riding her bike, Terry averages 9 miles per hour. At how many miles would it travel in 1 hours? that speed, how far could she go in 2 hours?

Slide 55 / 130 Slide 56 / 130 Interpreting Multiplication Interpreting You can determine the relative size of the product of a multiplication problem without actually multiplying. Multiplication of Fractions Return to Table of Contents Slide 57 / 130 Slide 58 / 130 Interpreting Multiplication 30 Which of the following product(s) are greater than 700,000? When you multiply a given number by a fraction greater than 1, it will result in a product greater than the given number. A Examples: B C D Slide 59 / 130 Slide 60 / 130 Interpreting Multiplication 31 Which of the following product(s) are greater than 876? When you multiply a given number by a fraction less than 1, it A will result in a product smaller than the given number. Examples: B C D