what, why, and how of number bonds and bar …...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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April 02, 2016
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
THE WHAT, WHY, AND HOW OF NUMBER BONDS AND BAR MODELS
Melissa SalvatoriMath Professional Development Specialist
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April 02, 2016
TEN FRAMEPictorialConcrete
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NUMBER BOND
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2y + 4 = 12
15
5 5 5
513
NUMBER BONDS (continued)
5 + 5 + 5 = 15 or 5 x 3 = 15
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April 02, 2016
PARTPARTWHOLE
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April 02, 2016
ADDITION and SUBTRACTION BAR MODEL
(aka TAPE DIAGRAM)
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
Another way of seeing subtraction....
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April 02, 2016
MULTIPLICATION BAR MODEL(aka TAPE DIAGRAM)
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
DIVISION BAR MODEL(aka TAPE DIAGRAM)
Known number of groups. How many in each groupis known.
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COMPARISON BAR MODEL(aka TAPE DIAGRAM)
55 + 12 = ? 300 126 = ?
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April 02, 2016
A
BB A} }A + B
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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?
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
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?
11
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
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?
11
11 1111
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
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?
11
11 1111
24
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
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?
11
11 1111
24
68 total}
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April 02, 2016
Using Modelswith Fractions
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UNIT FRACTION
Bar Figure Number Line
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FRACTION EQUIVALENCY
13
515
Bar Figure Number Line
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April 02, 2016
COMPARE/ORDER FRACTIONS
Bar Figure Number Line
34
78< 1
478
58
12
38
least to greatest:34
56<
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April 02, 2016
ADDING/SUBTRACTING FRACTIONS(can use any figure or a number line)
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April 02, 2016
FRACTION MULTIPLICATION(can use any type of figure)
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April 02, 2016
FRACTION MULTIPLICATION: Area Model
"of "
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April 02, 2016
FRACTION MULTIPLICATION: Number Line
What, Why, and How of Number Bonds and Bar Models
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April 02, 2016
FRACTIONS AND DIVISION
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April 02, 2016
FRACTIONS AND DIVISION
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April 02, 2016
FRACTIONS AND DIVISION: Common Denominator Area Model
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April 02, 2016
DIVIDING FRACTIONS: NUMBER LINE
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April 02, 2016
FRACTIONS OF A SET
What is of 49?27 7 7 7 7 7 7 7
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12 12121248
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April 02, 2016
12 12121248
12 12 12
12 x 7$84
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April 02, 2016
"The Toolkit"
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April 02, 2016
What is 64 + 18?
Number Bond Bar Model
64 18
64 18
How will we find the sum?
PartPartWholeMat
64 18
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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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April 02, 2016
What is 64 + 18?Using a number line:
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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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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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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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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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April 02, 2016
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.