S

T

A

Type I

Type II

Type III

Type IV

1. Whole Numbers

a. ratio and proportions

7

6

13

12. Solve problem involving ratios and proportions.

17. Identify proportional reasoning (additive vs. multiplicative thinking).

b. solve proportions

6

6

12

c. estimation strategies

7

5

12

20. Explain student thinking in estimating the product of two numbers

d. select/use variety of computation methods

6

6

12

11. Find date of one million minutes or seconds.

16. Explain student error on multiplication algorithm.

e. standard/non-standard algorithms

6

5

11

f. large & small numbers/ scientific notation

6

2

8

g. squaring/square roots/abs. value

4

1

5

h. positive/negative exponents

4

1

5

i. order of operations

1

2

3

2. Rational Numbers

a. rational number representations

7

6

13

6. Identify rational number on a number line.

b. use a variety of models

7

4

11

c. fractions & decimals operations

7

6

13

18. Explain why division or multiplication of fractions works.

d. rational numbers comparisons

7

5

12

7. Name 2 rational numbers between 2 numbers.

Identify rational numbers larger or smaller than other rational numbers.

e. select/use variety of computation methods

6

6

12

2. Solve simple percentage problems—three types.

13. Solve applications involving increases and decreases over time.

f. solve percentage problems

7

6

12

g. rational vs. irrational

3

3

6

3. Integers

a. integer representations

7

6

13

19. Explain how to use models to correct student misconceptions about adding and subtracting integers.

b. integers comparisons

7

5

12

3. Identify integers greater or less than integers.

Determine largest and smallest integers in a list.

8. Given number line representing x or ÷, identify number sentence.

c. integer operations

6

6

12

9. Determine rules for integer addition, subtraction, multiplication, and division.

14. Solve problem involving adding integers and justify solution.

4. Number Theory & Number Systems

a. primes and composites

6

4

10

15. Find smallest prime greater than a number.

b. factors and multiples

5

4

9

4. Find LCD of two fractions.

10. Find three smallest numbers given GCF and LCM.

c. identity and use properties

4

5

9

5. Identify law (associative, commutative, or distributive) that justifies equation.

d. containment relationships

2

5

7

1. Identify false statement regarding containment relationships among numbers (real, rational, irrational, integers, whole numbers).

e. subsystem properties

2

5

7

f. permutations and combinations

1

3

4

g. complex numbers

0

2

2

h. bases other than 10

0

1

1

i. history of numbers

1

0

1

j. union/intersection of sets

0

1

1