Number & Operations for Teachers

Exercises

1. Model the following operations using the indicated approach:

a. Sets: 4 + 7

b. Sets: 11 – 7

c. Number Line: 4 + 7

d. Number Line: 11 - 4

2. The statements 4 + 7 = 11, 11 – 7 = 4, and 11 – 4 = 7 are related. Discuss the nature of that relationship.

3. Complete the following tables for operations on whole numbers. To compute M – N, select M from the leftmost column and N from the topmost row. If no answer exists for a given cell (e.g., 4 – 7 = -3 is not a whole number), enter an X.

· Base Ten --- Addition of Whole Numbers

+	0	1	2	3	4	5	6	7	8	9
0
1
2
3
4
5
6
7
8
9

Subtraction of Whole Numbers

-	0	1	2	3	4	5	6	7	8	9
0
1
2
3
4
5
6
7
8
9

· Base Five --- Addition of Whole Numbers

+	0	1	2	3	4	10	11	12	13	14
0
1
2
3
4
10
11
12
13
14

Subtraction of Whole Numbers

-	0	1	2	3	4	10	11	12	13	14
0
1
2
3
4
10
11
12
13
14

· Base Two --- Addition of Whole Numbers

+	0	1	10	11	100	101	110	111	1000	1001
0
1
10
11
100
101
110
111
1000
1001

Subtraction of Whole Numbers

-	0	1	10	11	100	101	110	111	1000	1001
0
1
10
11
100
101
110
111
1000
1001

4. Compare the tables in exercise #3.

a. Which tables are symmetric?

b. Which tables are commutative?

c. If an operation is commutative in one base, is it commutative in the others as well? Why or why not?

5. When adding or subtracting two single-digit base ten numbers, what is the

a. Largest sum possible

b. Smallest sum possible

c. Largest difference possible

d. Smallest difference possible