1

Breakout 6Connecting our Learning with Different Representations of

Fractions

Deb WinesMaryLou Kestell

Ordering and Comparing Fractions• Order the following fractions on your

number line:

1/2, 3/4, 5/6, 3 3/4,

8/4, 16/4, 15/5, 3 3/3,

2/6, 1 1/2, 1 5/10, 2/1

3

Gallery Walk / Discussion

4

Video Preview• In what ways does the problem unpack key

understandings about fractions?• In what ways does the problem allow ALL students

(including those with specific LDs) access to the mathematics?

• What do you notice about the teacher’s questioning?

• What do you notice about student representations and dialogue?

5

• LNS The Three Part Lesson in Mathematics;

Supporting Student Learning– Part 2 During– Part 3 After

http://resources.curriculum.org/secretariat/coplanning/

In The Classroom

6

Discussion• In what ways does the problem unpack key

understandings about fractions?• In what ways does the problem allow ALL students

(including those with specific LDs) access to the mathematics?

• What do you notice about the teacher’s questioning?

• What do you notice about student representations and dialogue?

7

Running for FunCathy Fosnot; Contexts for Learning Mathematics

• Read the story problem to the group

8

Details – 26 mile race• There are markers every 12th of the route’s total length

• There are 8 water stations equally spaced along the way and the last is at the finish line

• Last year Rachel and Mark both ran 1/2 of the route

• This year Rachel knows she ran 7/12 of the route because she counted the markers and stopped at the 7th marker

• Mark ran to the 5th water station

• How many miles did they run and how much further did they run compared to last year?

9

Gallery Walk Solutions

• Any new mathematical learning to share?

11

Consolidation

Brainstorm at your tables• What mathematics did we engage in as

we solved this problem?• What strategies surfaced in this problem?• How did the solutions lead to emergent

thinking about multiplication and division of fractions?

12

Discussion Questions

• Why is a number line an effective model for this problem?

• What other models did you notice in the gallery walk?

13

Discussion Questions con’t…

• Would you engage students in a contextual problem that leads to multiplicative thinking as related to fractions and to considering division of fractions prior to teaching algorithms for these operations? – Why or why not?

14

Hidden Slide

15

Notes from Cathy!

Hidden Slide – Possible Strategies

16

Hidden Slide – Possible Strategies

17

Hidden Slide

18

Hidden Slide

19