1. Multiplying and Dividing
5th Grade Fractions
Multiplying and Dividing

2. Closest Estimate
5 x ⅞ =
What thinking did you use to determine the answer? How is multiplication helping you with this? What is it about multiplication in general that is helping you with this?
there is something here about “times as many” that is helping me to reason about how many wholes I might have after multiplying. The fact that the fraction is almost a whole supports thinking as well.

3. What comes to mind when you think about multiplication?
I am looking for those terms, phrases that we always say when teaching multiplication. “this times that or this by that or this many groups of that. I want to use this as a way to make sense of what it means to multiply fractions.

4. Fraction Multiplication
For the two situations below, draw a picture and create a story.
a. 12 x ¼ b. ¼ x 12
Remember my and Amy’s stories and how we had two different drawings or ways of picturing what these expressions meant to us. It would be beneficial to think here about how our pictures match the story and/or our solution path.

5. Fraction Multiplication
a. 12 x ¼ b. ¼ x 12
How would your pictorial representations change if the ¼ above were changed to a 4?
This slide is great for highlighting what happens when we multiply fractions. What would happen to the context when the number changes to 4? How does this illustrate what multiplying fractions is all about.? 4 times bigger and smaller.

6. The Bike Race A Bicycle race is 480 miles long.
Amy rode ⅙ of the race.
Use a strip of paper to show how many miles Amy rode.
What does it look like when students struggle? what does it mean and what would you do? (see chapter 1 examples)

7. Writing Equations Read CC. p. 33 and 34.
How are students introduced to writing equations?
Equations muddy the water for children. We have to gauge what the students understand about the concept and not expose them to the ideas before they are ready or know how to and be willing to ease up to an easier idea to be able to go forward. Use the translating symbols activity from Putting the practice into action to bring to life the challenges of translating the action that symbols imply.

8. The Over-Achiever
The swimming pool is 16 meters long. Kaneka swam 1 ½ times the length of the swimming pool.
Did she swim more or less than 16 meters?
How many meters did Kaneka swim?
Poster a solution path for issue with content and reasoning.

9. Mental Multiplication
Luisa explains 3 ½ x 2
What understanding is Luisa calling upon to make sense of this problem? What makes you say this?
What understanding are these students bringing from whole numbers to approach this new situation?
Click Computing Mentally; Louisa
Where do we see something from the “multiplication chart” we generated at the beginning of

10. Mental Multiplication
Watch Jada explain 3 ½ x 2
Thoughts?

11. Create a Representation
⅓ x ¼

12. How Much Brownie do You Get?
There was ¼ of a brownie left on the table. You got ⅓ of it.
What portion of the brownie did you get?
What part of the whole brownie did you get?

13. Area Representation
Your school owns a piece of land that has an area of 1 square mile.
¾ of the land is reserved for students to use. The students decide that ½ of their land should be saved to make a playground.
What fraction of the school land is reserved for a playground?

14. Considering Division
What comes to mind when you think about division?

15. Think about 8÷2 draw a picture
Picturing Division
Think about 8÷2 draw a picture
of this expression and based on your picture write a short context to go with your picture.

16. Picturing Division Now think about 8 ÷ ½
What is your picture for this? Try repeating the same steps as above and reflect on how your mental images are the same or different from before.

17. Did Your Picture Change?
What if the expression was ½ ÷ 8? This time consider a situation that would result in this expression.
- Record a context for this expression
When you have a context try drawing a picture of this expression and reflect on how your thinking shifts for this exercise.
Your thinking shifts so automatically that you may barely notice it. This minor shift makes a big difference when making sense of fractions. Please post your thinking for 8÷ ½ and ½ ÷ 8 using an interactive whiteboard app. (showme, educreations, explain everything, or something else). Facilitators: Please feel free to questions to Kaneka or Amy as you have a need.

18. Gardening Anyone?
Land is reserved for gardening at The Perfect Elementary School. See the details below regarding how the land is to be planted:
Grade 5 gets ½ the land
Grades 2-4 each get a ¼ of what is left
Kindergarten and First have to share evenly the remaining portion

19. Here if you need me