Using%20Math%20Manipulatives%20To%20Teach%20For%20Understanding

1
Using Math Manipulatives ToTeach For
Understanding

• Problem Solving With Manipulatives
• Or
• Is That A Pattern I See?

Mel Twitchell, Provo School District
2
Use the tooth picks you havebeen given to
construct thefigure shown below.
This represents one toothpick.
We have constructed a box using four toothpicks.
3
Use the tooth picks you havebeen given to
construct thefigure shown below.
The perimeter of this box is made by four
toothpicks. We will call the perimeter 4. We
will measure the perimeter by counting the
toothpicks in the perimeter.
4
Use the tooth picks you havebeen given to
construct thefigure shown below.
The box we have made with four toothpicks will be
called figure one (1).
We will call the area of this figure, one unit
meaning, one square unit.
The perimeter is four toothpicks and the area is
1 square unit.
5
Use the tooth picks you havebeen given to
construct thefigure shown below.
This will represent figure two.
6
What is the perimeter?
7
5
8
8
1
4
2
3
6
Use the tooth picks you havebeen given to
construct thefigure shown below.
This will represent figure two.
What is the perimeter?
1
8
What is the area?
2
3
3
7
Use the tooth picks you havebeen given to
construct thefigure shown below.
This will represent figure two.
10
What is the perimeter?
8
9
8
7
6
What is the area?
1
5
4
3
How many total toothpicks?
2
3
10
8
Use the tooth picks you havebeen given to
construct thefigure shown below.
8
Figure 3. Find
7
9
Perimeter
10
12
11
6
12
1
5
2
4
3
9
Use the tooth picks you havebeen given to
construct thefigure shown below.
Figure 3. Find
1
Perimeter
12
2
3
Area
6
4
5
6
10
Use the tooth picks you havebeen given to
construct thefigure shown below.
18
Figure 3. Find
16
17
Perimeter
15
14
12
13
12
11
8
9
Area
10
6
7
4
6
5
Number of toothpicks
18
2
3
1
11
Figure 4
Area ?
10
Perimeter ?
16
Number of Toothpicks ?
28
12
Is There A Pattern?
Figure Number
Number of Toothpicks
Perimeter
Area
4
1 2 3 4 5 6 7
1
4

13
Is There A Pattern?
Figure Number
Number of Toothpicks
Perimeter
Area
4
14
1 2 3 4 5 6 7
1
4
8
3
10
25
6
18
36
12
10
28
47
16
20
15
40
58
24
21
54
69
28
28
70
710
n(n1) 2
n
4n
n(n3)