The document discusses progression of multiplication and division concepts through examples of doughnuts and splitting them between classes. It uses visual representations and step-by-step working to solve word problems involving multiplying and dividing large numbers. Interactive examples are provided to reinforce concepts like area, distributive property, and setting up multi-step word problems algebraically.
109. If your school bought this box of doughnuts to split
between 8 classes, how many would each class get?
2,400
8
2,400
110. @MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split
between 8 classes, how many would each class get?
2,400
2,392
2,384
8
88
8-
2,384
2,392
8-
2,400
1 group of 8
1 group of 8
111. @MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split
between 8 classes, how many would each class get?
2,400
2,32080
80
2,240
80-
2,320
2,400
10 groups of 8
80-
2,240
10 groups of 8
112. @MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split
between 8 classes, how many would each class get?
2,400
800-
800
100 groups of 8
1,600
800- 100 groups of 8
800
800800
800
800- 100 groups of 8
0 300 groups of 8300
8
8
8
8
113. @MathletePearcewww.tapintoteenminds.com
If your school bought this box of doughnuts to split
between 8 classes, how many would each class get?
2,400
800-
800
100 groups of 8
1,600
800- 100 groups of 8800
800800
800
800- 100 groups of 8
0 300 groups of 8
300
88888
137. @MathletePearcewww.tapintoteenminds.com
YO
UR
TURN
A pool has a width of 14 m and an
area of 700 m2. What is the length?
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
138. @MathletePearcewww.tapintoteenminds.com
YO
UR
TURN
A pool has a width of 14 m and an
area of 700 m2. What is the length?
14 m 140 m2
10 m
140 m2
700
- 140
560
10 m
140 m2
- 140
420
10 m
140 m2
- 140
280
10 m
140 m2
- 140
140
10 m
140 m2
- 140
0
50 m
700 m2
161. A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
162. x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
163. x x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
164. x x x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
165. x 1x x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
166. x 1 1x x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
167. x 1 1
1
x x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
168. x 1 1
1
x
1
x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
169. x 1 1
1
1
x
1
x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
170. x 1 1
1
1
x
1
x x
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
1
1
1
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
(x + 3)(3x + 2)
171. Concreteness Fading
1 2 3Enactive
Concrete
Iconic
Visual
Symbolic
Abstract
x
1 1
1
1
x
1
x
x
1
1
1
x2
x
x
x
x
x
x
x
1
1
1
x2 x
3 6x 6
2x2
2x 2
2x
= (2x + 2)(x + 3)
2x2 + 8x + 6
Factor: