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
April 02, 2016
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
TEN FRAME
Concrete
Pictorial
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
NUMBER BOND
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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
April 02, 2016
PART­PART­WHOLE
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
ADDITION and SUBTRACTION BAR MODEL
(aka TAPE DIAGRAM)
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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
Another way of seeing subtraction....
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
MULTIPLICATION BAR MODEL
(aka TAPE DIAGRAM)
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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
April 02, 2016
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
April 02, 2016
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
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
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
April 02, 2016
Using Models
with Fractions
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
UNIT FRACTION
Bar
Figure
Number Line
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
FRACTION EQUIVALENCY
Bar
Figure
Number Line
1
3
5
15
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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
April 02, 2016
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
April 02, 2016
FRACTION MULTIPLICATION
(can use any type of figure)
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
FRACTION MULTIPLICATION: Area Model
"of "
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
FRACTION MULTIPLICATION: Number Line
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
FRACTIONS AND DIVISION
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
FRACTIONS AND DIVISION
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
FRACTIONS AND DIVISION: Common Denominator Area Model
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
DIVIDING FRACTIONS: NUMBER LINE
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
FRACTIONS OF A SET
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What is of 49?
7
7 7 7 7 7 7 7
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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12 12 12 12
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What, Why, and How of Number Bonds and Bar Models
12 x 7
$84
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12 12 12 12
April 02, 2016
12 12 12
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
"The Toolkit"
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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
April 02, 2016
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
April 02, 2016
What is 64 + 18?
Using a number line:
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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
April 02, 2016
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
April 02, 2016
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
April 02, 2016
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, Why, and How of Number Bonds and Bar Models
April 02, 2016
What is 64 + 18?
Standard Algorithm:
1
6 4
+ 1 8 8 2
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What, Why, and How of Number Bonds and Bar Models
April 02, 2016
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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