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.

1. Progression of
Multiplication and Division
@MathletePearcewww.tapintoteenminds.com
tapintoteenminds.com/sudbury

86. From: foreverence.com/legends/

87. From: foreverence.com/legends/
VisualConcrete

89. @MathletePearcewww.tapintoteenminds.com
2 Iconic
Visual
1 3Enactive
Concrete
Symbolic
Abstract
“BE MORE PRINCE”

96. What Do You…
Notice? Wonder?

97. How many doughnuts are there?
Make a Prediction

98. Update Your Prediction
32 doughnuts
25doughnuts

99. Update Your Prediction
32 doughnuts
25doughnuts
800

100. Update Your Prediction
32 doughnuts
25doughnuts
800

102. DOUBLE DOZEN

103. DOUBLE DOZEN
2 x 100 x 12

104. DOUBLE DOZEN
2 x 100 x 12
= 2,400

105. 2 x 100 x 12
= 2,400

106. Side View
2,400

107. 800
800
800
2,400
800-
1,600
800-
800
800-
0

108. 2,400

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

114. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
19515
?

115. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
19515
?
15

116. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
19515
?
15
195
- 15
180

117. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
195
15
?
15
195
- 15
180
180

118. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
195
15
?
15
195
- 15
180
18015

119. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
195
15
?
15
195
- 15
180
18015
- 15
165
165

120. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
195
15 15
195
- 15
180
180
15
- 15
165
165
15 - 15
150
150
?
15 15 15 15 15 15 15 15 15 15
1 1 1 1 1 1 1 1 1 1 1 1 1
- 15
.
.
.

121. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= 13÷195 15
195
15 15
195
- 15
180
180
15
- 15
165
165
15 - 15
150
150
15 15 15 15 15 15 15 15 15 15
- 15
.
.
.
13

122. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
195
15 15
195
- 15
180
180
15
- 15
165
165
15 - 15
150
150
?

123. @MathletePearcewww.tapintoteenminds.com
APPLY:
Distributive
Property
= ?÷195 15
195
15 15
195
- 15
180
180
15
- 15
165
165
15 - 15
150
150
?
- 15(10)
150
- 150
0

124. @MathletePearcewww.tapintoteenminds.com
?
APPLY:
Distributive
Property
= 13÷195 15
195
15
1
15
195
- 15
180
180
15
- 15
165
165
15 - 15
150
150
1 1 10
- 15(10)
150
- 150
0

125. @MathletePearcewww.tapintoteenminds.com
?
= 13÷195 15
195
15
1
15
195
- 15
180
180
15
- 15
165
165
15 - 15
150
150
1 1 10
- 15(10)
150
- 150
0
O
PEN
ARRAY
45
3

126. @MathletePearcewww.tapintoteenminds.com
?
= 13÷195 15
15
1
15
195
- 15
180
15
- 15
165
15 - 15
150
150
1 1 10
- 15(10)
150
- 150
0
O
PEN
ARRAY
45
3

127. @MathletePearcewww.tapintoteenminds.com

128. @MathletePearcewww.tapintoteenminds.com

129. @MathletePearcewww.tapintoteenminds.com
RECALL

130. @MathletePearcewww.tapintoteenminds.com
YO
UR
TURN
A pool has a width of 14 m and an
area of 700 m2. What is the length?

131. @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 700 m2

132. @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 700 m2
10 m
140 m2

133. @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 560 m2
10 m
140 m2
700
- 140
560

134. @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 420 m2
10 m
140 m2
700
- 140
560
10 m
140 m2
- 140
420

135. @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 280 m2
10 m
140 m2
700
- 140
560
10 m
140 m2
- 140
420
10 m
140 m2
- 140
280

136. @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

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

139. @MathletePearcewww.tapintoteenminds.com

140. @MathletePearcewww.tapintoteenminds.com

141. @MathletePearcewww.tapintoteenminds.com
A pool has a width of 3 m and an area of
12 times a number. What is the length?

142. @MathletePearcewww.tapintoteenminds.com
1
1
1
A pool has a width of 3 m and an area of
12 times a number. What is the length?
12x

143. @MathletePearcewww.tapintoteenminds.com
1
1
1
12x
x
A pool has a width of 3 m and an area of
12 times a number. What is the length?

144. @MathletePearcewww.tapintoteenminds.com
1
1
1
12x
x
x
x
x
A pool has a width of 3 m and an area of
12 times a number. What is the length?

145. @MathletePearcewww.tapintoteenminds.com
1
1
1
9x
x
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

146. @MathletePearcewww.tapintoteenminds.com
1
1
1
9x
x x
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

147. @MathletePearcewww.tapintoteenminds.com
1
1
1
6x
x x
x x
x 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

148. @MathletePearcewww.tapintoteenminds.com
1
1
1
6x
x x x
x x
x 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

149. @MathletePearcewww.tapintoteenminds.com
1
1
1
3x
x x x
x x x
x x x
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

150. @MathletePearcewww.tapintoteenminds.com
1
1
1
3x
x x x x
x x x x
x x x x
x 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

151. @MathletePearcewww.tapintoteenminds.com
1
1
1
3x
x x x x
x x x x
x x x x
x 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

152. @MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?

153. @MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x2 x2 x2
x x x
x x x
x x x
x
x
11 1 11 1

154. @MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x2 x2 x2
x x x
x x x
x x x
x x 11 1 11 1

155. @MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x2 x2 x2
x x x
x x x
x x x
x x
1
1
1
1
1
1

156. @MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x2 x2 x2
x x x
x x x
x x x
x x
1
1
1
1
1
1

157. @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 x
x x x
x x x

158. @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 x
x x x
x x x
x

159. @MathletePearcewww.tapintoteenminds.com
A pool has an area of 3x2 + 11x + 6.
What are the dimensions?
x
x2 x2 x2
x x x
x x x
x x x
x
1
1
1
1
1
1

160. @MathletePearcewww.tapintoteenminds.com
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

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: