Math Myths and Misconceptions - Los Angeles Unified School ......1. Math Myths and Misconceptions. A...
Transcript of Math Myths and Misconceptions - Los Angeles Unified School ......1. Math Myths and Misconceptions. A...
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Math Myths and Misconceptions
A Series on Preventing and Repairing Student Misconceptions
in Mathematics
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Preventing Misconceptions
Session 4b
Strategies for Learning the Basic Addition Facts
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Basic Addition Facts
There are strategies for learning the “basic facts” which will
develop a child’s conceptual understanding of addition.
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Basic Addition Facts
One could memorize all the basic facts by rote, but pattern-
based and number sense strategies build a stronger foundation for higher level
mathematics.
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Basic Addition Facts
When using pattern-based and number sense strategies, we
don’t necessarily “march through” the basic facts in
numerical order.
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Basic Addition Facts
Rather, we build on foundational prerequisite skills and develop “hooks” on which children are
able to hang their understandings.
(see Module 4a)
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Basic Addition Facts
Let’s begin!
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Basic Addition Facts
Start with adding 1, 2, and doubles
Adding 1: 3+1 5+1 9+1Adding 2: 4+2 7+2 8+2Doubles: 3+3 4+4 6+6
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Basic Addition Facts
Start with adding 1, 2, and doubles
These three facts groups have already been learned visually,
orally, and aurally through adding 1 more, 2 more, and doubling
numbers from 0 to 9(see Module 4a)
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Basic Addition Facts
Adding 0 (zero)
This is the additive identity property.
In the additive identity property, the sum of the number and zero yields the same
number.
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Basic Addition Facts
So far we’ve worked on these 58 addition facts just through the prerequisite skillsprerequisite skills:
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Basic Addition Facts
Adding 9Adding 9Say one less than the other
addend and “teen”This strategy is based on the prerequisite
learning of taking one less from any number.
(see Module 4a)
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Basic Addition Facts
Adding 9Adding 9Say one less than the other
addend and “teen”99 + 7 = 6 “teen”5 + 99 = 4 “teen”
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Basic Addition Facts
Including the 99’’ss, we’ve now worked through these addition facts:
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Basic Addition Facts
Adding 8Adding 8Say two less than the other
addend and “teen”This strategy is based on the prerequisite
learning of taking two less from any number.
(see Module 4a)
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Basic Addition Facts
Adding 8Adding 8Say two less than the other
addend and “teen”88 + 7 = 5 “teen”*5 + 88 = 3 “teen”*
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Basic Addition Facts
Including the 88’’ss, we’ve now worked through these addition facts:
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Basic Addition Facts
Uphill / Downhill NeighborsUphill / Downhill NeighborsDouble one addend then add
one more or take one lessThis strategy is based on the prerequisite learning of doubling a number and taking
one more or one less from a number.(see Module 4a)
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Basic Addition Facts
As shown here, 3 + 43 + 4 can be though of as:
33 doubled plus 1 (if we take the “downhill” neighbor: 3)
or, 44 doubled minus 1 (if we take the “uphill” neighbor: 4)
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Basic Addition Facts
The other neighbors,44 and 5555 and 6666 and 77
can be solved using the same strategy
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Basic Addition Facts
We’ve now dealt with most of the addition facts:
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Basic Addition Facts
The Final 6The Final 65+3 6+3 6+4 7+3 7+4 7+5
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Basic Addition Facts
The Final 6The Final 6
5+3 6+3 6+4 7+3 7+4 7+5
Chose one fact to memorize to “unlock” the other five
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Basic Addition Facts
The Final 6The Final 6
5+3 6+3 6+4 7+3 7+4 7+5
Chose one fact to memorize to “unlock” the other five, for example:
6 + 4 = 10
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Basic Addition Facts
The Final 6The Final 6
5+3 6+3 6+4 7+3 7+4 7+5
6 + 4 = 106 + 3 = 10 – 1
3 is one less than 4
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Basic Addition Facts
The Final 6The Final 6
5+3 6+3 6+4 7+3 7+4 7+5
6 + 4 = 105 + 3 = 10 – 2
5 is one less than 63 is one less than 4
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Basic Addition Facts
The Final 6The Final 6
5+3 6+3 6+4 7+3 7+4 7+5
6 + 4 = 107 + 3 = 10
7 is one more than 63 is one less than 4
No change—just like adding 0
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Basic Addition Facts
The Final 6The Final 6
5+3 6+3 6+4 7+3 7+4 7+5
6 + 4 = 107 + 4 = 10 + 1
7 is one more than 6
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Basic Addition Facts
The Final 6The Final 6
5+3 6+3 6+4 7+3 7+4 7+5
6 + 4 = 107 + 5 = 10 + 2
7 is one more than 65 is one more than 4
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Basic Addition Facts
We’ve now dealt with all the addition facts: