Transcript Considering multiple items as one thing

Ratios & Proportional
Relationships for All
Pamela Weber Harris
@pwharris
pamelawharris.com
[email protected]
Math is
figure-outable!
0.26 x 24
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270 18
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Counting Strategies
Additive Thinking
Multiplicative
Thinking
Proportional
Reasoning
Algebraic Reasoning
Unitizing
• Considering multiple
items as one thing
Counting Rack
Rekenrek
Counting
Additive
Counting Rack
Rekenrek
Counting Rack
Rekenrek
Consider the
Multiplication and
Division Algorithms
11 x 12
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132 ... Um, I knew 10 x 12 = 120, and um, then I just
add 12 because 1 x 12 = 12 and um I just add 12 to
120 and I got 132.
I didn’t ask you if you know
it, I asked you what it is.
What do you know...
and figure it out from there!
How to Build Multiplicative &
Proportional Reasoning at the Same
Time?
• Good, rich contexts
• Mini-lesson: Problem Strings
Proble 2 x 274 x 278 x 2710 x
279 x 275 x 27100 x
m
2799 x 27
324/27
Strings
405/27
Graph it
What kind of relation?
•Open:
•packs sticks.tns
•Enter the values in lists
•Enter
the equation in
f (x) 
1
•What questions could
•you ask?
2 x 3.24 x 3.28 x 3.210 x 3.29 x 3
x 3.2
15 x 3.2100 x 3.299 x 3.2
44.8/3.2
323.2/3.2
313.6/3.2
480/3.2
Proble
m
Strings
CC
PB
2
4
Proble
m
Strings
8
10
9
6
5
3
400
450
456
18
25
Proble
m
Strings
25 x 361/4 x 360.25 x
360.26 x 360.24 x
360.25 x 24 0.75 x
240.76 x 24
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Math is Figure-outable
• Look to most efficient strategies and
build proportional reasoning at the same
time
• Teachers build own numeracy
• It’s about relationships:
-
Among numbers to solve problems
Between teachers and students to
build young mathematicians
Ratios & Proportional
Relationships for All
Pamela Weber Harris
@pwharris
pamelawharris.com
[email protected]