1 Breakout 6 Connecting our Learning with Different Representations of Fractions Deb Wines MaryLou Kestell

Birthday Buddies Join the people who have the same birthday month as you Split into pairs Pick up a 0 – 4 number line and some markers 22

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 nning/ 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 Fun Cathy Fosnot; Contexts for Learning Mathematics Read the story problem to the group 8

Details – 26 mile race There are markers every 12 th 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 7 th marker Mark ran to the 5 th water station How many miles did they run and how much further did they run compared to last year? 9

Details – 36 km race There are markers every twelfth 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 seventh marker Mark ran to the fifth water station How many kilometres did they run and how much further did they run compared to last year? 10

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

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