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Proportional Reasoning: What it Is and Isn’t
plenary 1
getting acquainted
percents in random order
• neighbour to guess which percent is which
•percent of your daily calorie intake that is snacks
•percent of your life that you’ve been a teacher/consultant/etc.
• percent of your staff that is under 28.
Estimate.
past two camps•focus on big ideas
in algebraic thinking and proportional reasoning
•focus on using open questions and parallel tasks for DI and richer mathematics classrooms
and now
•2011----
•focus more on how to respond to student thinking in these areas
big ideas
•on the wiki and in the program booklet
how long?
• three different ways to compare their lengths.
•Which is better?
175 cm 90 cm
SPINNING COLOURS
•Work with a partner.
•Create a spinner where you are likely to spin 3 more reds than blues in 10 spins.
•How many more reds than blues are you likely to spin in 15 spins?
mixing colours
•Jane
•Lianne
•same shade?
•Explain.
2 cans 3 cans
2 cans
1
2
1
23 cans
proportional reasoning
•deliberate use of multiplicative relationships to compare and to predict
additive approach
shapes 6 + 6+6triangles 4 + 4 +4
potential problem
shapes
6 14
triangles
4 12
between thinking
4
6
?
12=
within thinking
4
8
?
12=
unitizing
cross-muliplying
4
6 21
?=
4
This lunch is Papa Bear’s.
Draw a sandwich that would be just right for
Baby Bear.
How does the picture show that 4/5 is less than 9/10?
How does the picture show that 4/5 is less than 9/10?