Multiplying and Dividing Fractions Grade 5, CCSSM

Critical Area of 5th Grade CCSSM “Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense.” Yes, we are multiplying and dividing fractions in 5th grade!

Laura had $240. She spent 5/8 of it. How much money did she have left? On a recent international test, only 25 % of U.S. eighth graders answered correctly… Laura had $240. She spent 5/8 of it. How much money did she have left? Solved this problem correctly. A recent report from the US Dept of Education 2008 fount that “learning fractions is pervasive and an obstacle to further progress in mathematics..Yet.. Go to next slide..

Rectangle, 8 equal parts, shaded 5 of the 8 Number line, 240, cut in half (120), cut each half into 4ths (30), shaded 5/8 8 circles (sets), 30 in each circle, crossed out 5 circles

Laura had $240. She spent 5/8 of it. How much money did she have left? How much is 1/8 of $240? If she spent 5/8, how many eighths are left? Is the important question: How many 1/8 are in 3/8? OR How many 1/8 are in 3/8? Solved this problem correctly. A recent report from the US Dept of Education 2008 fount that “learning fractions is pervasive and an obstacle to further progress in mathematics..Yet.. Go to next slide..

Unpacking the DPI Grade 5 Common Core Unit Multiplying and Dividing fractions

Indirect Instruction Engage- opening Explore- task Explain- discussion of the task, share student work, AVOID lecture Elaborate- follow up task or activity Evaluate- formative and summative assessment Intervention- during Elaborate

Lesson 1 Essential Question How are you decomposing and composing fractions?

How much ice cream was served? We served 4 boxes that had 12 ice cream cones each.  4 6 40 400  We had box of 12 ice cream cones. We served ½ a box. 6 12 24 We had ½ a container of ice cream and ½ of what was in the container was scooped out. How much of the whole container was scooped out? 1 container ½ of the container ¼ of the container

Lesson 1 Show on number line

Relational Understandings n groups of 1/n equals a whole E.g.- 4 groups of ¼ equals a whole (4th grade) The multiplicative relationship between a part and a whole The whole can be broken apart into unit fractions The unit fractions can be put back together to make the whole

How are 2 groups of 2/3 the same as 4 groups of 1/3? Use the number line model AND the region model to justify that 2 x 2/3 = 4 x 1/3 ?

Essential Question Lesson 2 What patterns do you notice in the products when we multiply whole numbers and fractions? How are the products related to the factors in the problems?

Stephen and Raul were looking at how their class was doing on the recycling drive. They noticed that they were 1⁄2 way to their goal of 60 cans.

Mr. Chandler has asked each class to try to reach a goal of 20 cans by the end of the week. One fifth grade class collected ¾ of their goal. How many cans have they collected? How many do they still need?

What was the first tick mark? Compare this to kids folding paper to get fourths?

Number line What should the start and end numbers be on our number line? How should we partition our number line? What fractions can we use to notate our number line?

Number line

Number line How many cans do we need to collect to meet our goal? What is half of our goal? What is ¼ of our goal?

Number line How many cans do we need to collect to meet our goal? What is half of our goal? What is ¼ of our goal? 5 10 ? 20

¾ of 20 ¾ * 20 (3*20)/4 (20/4) * 3

Lesson 4: Tiling The Art Room How do the lengths of a rectangle (array) correspond to the total area of the rectangle?

The Lance Elementary School asked the fifth grade students to help the art teacher design some tile murals for the new art room. A mural will have 3⁄4 of the design as red tiles and 1⁄2 of those red tiles will have flowers on them. How much of the entire design will have flowers on them? Use a picture or number line to support your answer.

Building on what we know… ½ of ¾ =

Comparing Murals The students decided to create a tile arrangement with geometric shapes. 1/5 of the tiles will be triangles. 1⁄2 of the triangle tiles will be painted blue. What part of this mural will be blue triangles? The students decided to create a tile arrangement with geometric shapes. 2/5 of the tiles will be triangles. 1⁄2 of the triangle tiles will be painted blue. What part of this mural will be blue triangles? What is the relationship between the amount of blue triangles in the two murals?

We are NOT… Teaching algorithms…. “Just multiply top by top and bottom by bottom.”

What do students’ know? There is 1/2 of a bag of potato chips in the classroom. Each student gets 1/5 of the chips. How much of a bag does each student get? Explain how you know. Sarah said, “I know that 1/2 x 5 equals five halves which is 2 and a half. That makes sense since two halves is a whole and I had 5 halves.

Find a new group of friends In Grade 3, students now find fractions of wholes (e.g., 1/3 of 24). Is this work (1/2 of 3/4) much more difficult- why or why not? Where does partitioning from earlier grades come into play with this mathematical work? Knowing your students- are your 5th grade students ready for this type of work?

¾ is equal to 6/8. took half of 6/8 = 3/8

Lesson 5: Relay Race Warm-up A relay race is 3/4 of a mile. Two students run the entire relay race but run different lengths of the race. Part 1: Find three pairs of possible lengths that each student could have run. Support your answer with a number line.

Relay Race How did you show your work?

Relay Race Part 2: One student ran two-thirds of the relay. How much of a mile did they run?

Relay Race

Third part of the unit Shifts from fractions of a fraction (1/2 of 3/4) to the idea of sharing and dividing fractional parts...

Equal Sharing Problems From 5th CCSS: If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? (5.NF.3) Draw a picture to support your answer. Discuss how you would solve this problem. What type of reasoning would support your strategy?

Equal Sharing 5.NF.3- Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). 6 brownies shared among 2 people. How many brownies does each person get? 6 brownies shared among 4 people. How many brownies does each person get? Show each with a picture. What is division?

End of the Unit: Fifth Grade at the Spring Carnival During the carnival, Ms. Garcia notices that there 5 bags of balloons. She wants to give 1⁄3 a bag of balloons to some of the volunteers. How many volunteers can she give 1⁄3 a bag to? 9/20/2018 • page 44

Balloon Task What representations did you use? Region or number line? Does it matter?

Division of Fractions 5 ÷ ⅓ = ? 9/20/2018 • page 46

Division of Fractions 5 ÷ ⅓ = 9/20/2018 • page 47

5 ÷ ⅓ = Division of Fractions 4 5 6 7 8 9 1 2 3 13 14 15 10 11 12 9/20/2018 • page 48

Let’s unpack… 5.NF.7b. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. If you get stuck use 2 in place of (1/5)!

4 ÷ (1/5) How do we think about this?

4 ÷ (1/5) 4 “things” Dividing those “things” into portions that are 1/5 of a “thing” How many “servings?” 4 pizzas. Each student gets 1/5 of a piece of pizza. How many students get pizza?

More from 5.NF.7b 5.NF.7b. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. 20 students are eating. Each eats 1/5 of a pizza. How much pizza gets eaten?

2 ÷ (1/4) Create a story context and draw a visual fraction model.

Task Exploration Six tasks on the sheet from this unit Listen for directions…

Our role as facilitators… This year- how do we support teachers? Thinking ahead- what foundations are essential for this work?

Share cartoon. How many of you have heard “Don’t ask me Share cartoon. How many of you have heard “Don’t ask me. I don’t do math.” How about “I don’t do read.”

Questions 9/20/2018 • page 57