Idea Transcript
What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
THE WHAT, WHY, AND HOW OF NUMBER BONDS AND BAR MODELS
Melissa Salvatori Math Professional Development Specialist
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What, Why, and How of Number Bonds and Bar Models
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What, Why, and How of Number Bonds and Bar Models
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TEN FRAME Concrete
Pictorial
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What, Why, and How of Number Bonds and Bar Models
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NUMBER BOND
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NUMBER BONDS (continued) 15
5
1
3
5
5
5
5 + 5 + 5 = 15 or 5 x 3 = 15
2y + 4 = 12
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What, Why, and How of Number Bonds and Bar Models
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PARTPARTWHOLE
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What, Why, and How of Number Bonds and Bar Models
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ADDITION and SUBTRACTION BAR MODEL (aka TAPE DIAGRAM)
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What, Why, and How of Number Bonds and Bar Models
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What, Why, and How of Number Bonds and Bar Models
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Another way of seeing subtraction....
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What, Why, and How of Number Bonds and Bar Models
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MULTIPLICATION BAR MODEL (aka TAPE DIAGRAM)
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What, Why, and How of Number Bonds and Bar Models
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DIVISION BAR MODEL (aka TAPE DIAGRAM) Known number of groups.
How many in each group is known.
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What, Why, and How of Number Bonds and Bar Models
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COMPARISON BAR MODEL (aka TAPE DIAGRAM)
55 + 12 = ?
300 126 = ?
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What, Why, and How of Number Bonds and Bar Models
B
B A
}
A
April 02, 2016
}
A + B
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What, Why, and How of Number Bonds and Bar Models
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COMPARISON BAR MODEL (aka TAPE DIAGRAM) Can be used for multiple comparisons.
Adam Brad Charles
Brad has 3 times the amount of cards as Adam does. Charles has 9 less cards than Brad. Adam has 11 cards. How many do they have in total?
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
Brad has 3 times the amount of cards as Adam does. Charles has 9 less cards than Brad. Adam has 11 cards. How many do they have in total?
Adam
11
Brad Charles
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What, Why, and How of Number Bonds and Bar Models
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Brad has 3 times the amount of cards as Adam does. Charles has 9 less cards than Brad. Adam has 11 cards. How many do they have in total?
Adam Brad
11 11
11
11
Charles
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
Brad has 3 times the amount of cards as Adam does. Charles has 9 less cards than Brad. Adam has 11 cards. How many do they have in total?
Adam Brad Charles
11 11
11
11
24
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
Brad has 3 times the amount of cards as Adam does. Charles has 9 less cards than Brad. Adam has 11 cards. How many do they have in total?
Adam Brad Charles
11 11
11
24
11
}
68 total
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What, Why, and How of Number Bonds and Bar Models
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Using Models with Fractions
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UNIT FRACTION
Bar
Figure
Number Line
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What, Why, and How of Number Bonds and Bar Models
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FRACTION EQUIVALENCY
Bar
Figure
Number Line
1 3 5 15
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What, Why, and How of Number Bonds and Bar Models
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COMPARE/ORDER FRACTIONS Bar
3 4
<
7 8
Number Line
Figure
5 6
<
3 4
1 4
least to greatest: 5 7 1 3 8 8 2 8
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What, Why, and How of Number Bonds and Bar Models
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ADDING/SUBTRACTING FRACTIONS (can use any figure or a number line)
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What, Why, and How of Number Bonds and Bar Models
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FRACTION MULTIPLICATION (can use any type of figure)
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What, Why, and How of Number Bonds and Bar Models
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FRACTION MULTIPLICATION: Area Model "of "
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FRACTION MULTIPLICATION: Number Line
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What, Why, and How of Number Bonds and Bar Models
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FRACTIONS AND DIVISION
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What, Why, and How of Number Bonds and Bar Models
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FRACTIONS AND DIVISION
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What, Why, and How of Number Bonds and Bar Models
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FRACTIONS AND DIVISION: Common Denominator Area Model
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DIVIDING FRACTIONS: NUMBER LINE
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FRACTIONS OF A SET
2 What is of 49? 7
7 7 7 7 7 7 7
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12 12 12 12
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12 x 7 $84
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12 12 12 12
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12 12 12
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"The Toolkit"
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What is 64 + 18? Number Bond
PartPartWhole Mat
64 18
64
Bar Model
64
18
18
How will we find the sum?
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What, Why, and How of Number Bonds and Bar Models
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What is 64 + 18?
Counting on: 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82 Counting on with 10: "18 is equal to a 10 plus an 8. So 10 more than 64 is 74, then 75, 76, 77, 78, 79, 80, 81, 82"
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What, Why, and How of Number Bonds and Bar Models
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What is 64 + 18? Using a number line:
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What is 64 + 18? Using a benchmark value:
18 is 2 fewer than 20. So 64 + 20 = 84, and 2 fewer than 84 is 82. So 64 + 18 = 82
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What, Why, and How of Number Bonds and Bar Models
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What is 64 + 18? Partial Sums: "64 is 6 tens and 4 ones. 18 is 1 ten and 8 ones. So I have 7 tens and 12 ones. 70 + 12 equals 82"
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What, Why, and How of Number Bonds and Bar Models
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What is 64 + 18? Base 10 Blocks:
https://wwwk6.thinkcentral.com/content/hsp/math/mathinfocus/common/itools_pri_9780547673851 _/basetenblocks.html
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What, Why, and How of Number Bonds and Bar Models
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What is 64 + 18? Decomposition: "64 is 6 away from 70. So if I take 6 from the 18, I am left with 12. So I can do 70 + 12 = 82."
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What is 64 + 18? Standard Algorithm: 1 6 4 + 1 8 8 2
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We expose our students to a variety of methods so that they are able to expand their personal "toolkit." When it comes to execution, they can choose which "tool" to use.
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