day 1, session 2 - the progression of multiplication and division
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Progression of Multiplication and Division
@MathletePearcewww.tapintoteenminds.com
tapintoteenminds.com/sudbury
From: foreverence.com/legends/
From: foreverence.com/legends/
VisualConcrete
@MathletePearcewww.tapintoteenminds.com
2 Iconic
Visual
1 3Enactive
Concrete
Symbolic
Abstract
“BE MORE PRINCE”
What Do You…
Notice? Wonder?
How many doughnuts are there?
Make a Prediction
How many doughnuts are there?
Update Your Prediction32 doughnuts
25
dou
ghnu
ts
How many doughnuts are there?
Update Your Prediction32 doughnuts
25
dou
ghnu
ts
800
How many doughnuts are there?
Update Your Prediction32 doughnuts
25
dou
ghnu
ts
800
How many doughnuts are there?
How many doughnuts are there?
DOUBLE DOZEN
How many doughnuts are there?
DOUBLE DOZEN
2,4002 x 100 x 12
How many doughnuts are there?
DOUBLE DOZEN
2 x 100 x 12= 2,400
How many doughnuts are there?
2 x 100 x 12
= 2,400
How many doughnuts are there?
Side View
2,400
How many doughnuts are there?
Side View800
800
800
2,400800-
1,600800-
800800-
0
2,400
If your school bought this box of doughnuts to split between 8 classes, how many would each class get?
2,400
8
2,400
@MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split between 8 classes, how many would each class get?
2,4002,3922,384
888
8-2,384
2,3928-
2,4001 group of 8
1 group of 8
@MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split between 8 classes, how many would each class get?
2,4002,32080
80
2,240
80-2,320
2,40010 groups of 8
80-2,240
10 groups of 8
@MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split between 8 classes, how many would each class get?
2,400800-
800
100 groups of 8
1,600800- 100 groups of 8800800800
800800- 100 groups of 8
0 300 groups of 8300
8
8
8
8
@MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split between 8 classes, how many would each class get?
2,400800-
800
100 groups of 8
1,600800- 100 groups of 8800800800
800
800- 100 groups of 8
0 300 groups of 8
30088888
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
19515
?
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
19515
?
15
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
19515
?
15
195- 15
180
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
19515
?
15
195- 15
180
180
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
19515
?
15
195- 15
180
18015
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
19515
?
15
195- 15
180
18015
- 15
165
165
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
195
15 15
195- 15
180
18015
- 15
165
16515 - 15
150150
?
15 15 15 15 15 15 15 15 15 15
1 1 1 1 1 1 1 1 1 1 1 1 1
- 15...
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = 13÷195 15
195
15 15
195- 15
180
18015
- 15
165
16515 - 15
150150
15 15 15 15 15 15 15 15 15 15
- 15...
13
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
195
15 15
195- 15
180
18015
- 15
165
16515 - 15
150150
?
@MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive Property = ?÷195 15
195
15 15
195- 15
180
18015
- 15
165
16515 - 15
150150
?
- 15(10)
150- 150
0
@MathletePearcewww.tapintoteenminds.com
?APPLY:
Distributive Property = 13÷195 15
195
15
1
15
195- 15
180
18015
- 15
165
16515 - 15
150150
1 1 10
- 15(10)
150- 150
0
OPEN
ARRAY
@MathletePearcewww.tapintoteenminds.com
?
APPLY:
Distributive Property
= 13÷195 15
195
15
1
15
195- 15
180
18015
- 15
165
16515 - 15
150150
1 1 10
- 15(10)
150- 150
0
OPEN
ARRAY
45
3
@MathletePearcewww.tapintoteenminds.com
?
APPLY:
Distributive Property
= 13÷195 15
15
1
15
195- 15
180
15
- 15
16515 - 15
150
150
1 1 10
- 15(10)
150- 150
0
OPEN
ARRAY
45
3
@MathletePearcewww.tapintoteenminds.com
@MathletePearcewww.tapintoteenminds.com
@MathletePearcewww.tapintoteenminds.com
RECALL
YOUR TURN
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 700 m2
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 700 m2
10 m
140 m2
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 560 m2
10 m
140 m2
700- 140
560
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 420 m2
10 m
140 m2
700- 140
56010 m
140 m2
- 140
420
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 280 m2
10 m
140 m2
700- 140
56010 m
140 m2
- 140
420
10 m
140 m2- 140
280
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 140 m2
10 m
140 m2
700- 140
56010 m
140 m2
- 140
420
10 m
140 m2- 140
280
10 m
140 m2
- 140
140
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 140 m2
10 m
140 m2
700- 140
56010 m
140 m2
- 140
420
10 m
140 m2
- 140
280
10 m
140 m2 - 140
140
10 m
140 m2
- 140
0
@MathletePearcewww.tapintoteenminds.com
YOUR TURNA pool has a width of 14 m and an
area of 700 m2. What is the length?
RECALL
14 m 140 m2
10 m
140 m2
700- 140
560
10 m
140 m2
- 140
42010 m
140 m2
- 140
280
10 m
140 m2 - 140
140
10 m
140 m2
- 140
0
50 m
700 m2
@MathletePearcewww.tapintoteenminds.com
@MathletePearcewww.tapintoteenminds.com
@MathletePearcewww.tapintoteenminds.com
A pool has a width of 3 m and an area of 12 times a number. What is the length?
@MathletePearcewww.tapintoteenminds.com
111
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x
@MathletePearcewww.tapintoteenminds.com
111
12x
x
A pool has a width of 3 m and an area of 12 times a number. What is the length?
@MathletePearcewww.tapintoteenminds.com
111
12x
x
xxx
A pool has a width of 3 m and an area of 12 times a number. What is the length?
@MathletePearcewww.tapintoteenminds.com
111
9x
x
xxx
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x- 3x
9x
@MathletePearcewww.tapintoteenminds.com
111
9x
x x
xxx
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x- 3x
9x
@MathletePearcewww.tapintoteenminds.com
111
6x
x x
x xx xx x
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x- 3x
9x- 3x
6x
@MathletePearcewww.tapintoteenminds.com
111
6x
x x x
x xx xx x
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x- 3x
9x- 3x
6x
@MathletePearcewww.tapintoteenminds.com
111
3x
x x x
x x xx x xx x x
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x- 3x
9x- 3x
6x- 3x
3x
@MathletePearcewww.tapintoteenminds.com
111
3x
x x x x
x x x xx x x xx x x x
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x- 3x
9x- 3x
6x- 3x
3x- 3x
0x
@MathletePearcewww.tapintoteenminds.com
111
3x
x x x x
x x x xx x x xx x x x
A pool has a width of 3 m and an area of 12 times a number. What is the length?
12x- 3x
9x- 3x
6x- 3x
3x- 3x
0x
4x
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x2 x2 x2
x x xx x xx x x
xx
11 1 11 1
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x2 x2 x2
x x xx x xx x xx x 11 1 11 1
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x2 x2 x2
x x xx x xx x xx x
1
1
1
1
1
1
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x2 x2 x2
x x xx x xx x x
x x
1
1
1
1
1
1
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
x
1
1
1
1
1
1
x2 x2 x2
x x xx x xx x x
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
1
1
1
1
1
1
x2 x2 x2
x x xx x xx x x
x
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
xx2 x2 x2
x x xx x xx x x
x
1
11
1
11
@MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
xx
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
xx x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
xx x x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
x1x x x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
x1 1x x x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
x1 1
1
x x x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
x1 1
1
x
1
x x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
x1 1
1
1
x
1
x x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
x1 1
1
1
x
1
x x
A pool has an area of 3x2 + 11x + 6. What are the dimensions?
x
11
1
x2 x2 x2
x x xx x xx x x
x
1
11
(x + 3)(3x + 2)
Concreteness Fading
1 2 3Enactive
Concrete
Iconic
Visual
Symbolic
Abstract
x
1 1
1
1
x
1
xx
11
1
x2
xx
x
xx
x
x
1
11
x2 x
3 6x 6
2x2
2x 2
2x
= (2x + 2)(x + 3)
2x2 + 8x + 6Factor:
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