Mathematics Content

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Type 1 Items

Type II Items

Type III Items

Type IV Items

1. Whole Number Concepts & Representations

a. place value

7

5

12

1.Determine expanded notation of a number.

6. Determine the symbolic representation of numbers named in words.

b. large numbers

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3

4

c. relationships/comparisons

5

3

8

2. Determine number rounded to the nearest thousand, etc.

7. Approximate the location of numbers on a number line.

16. Identify and correct misconception about counting.

d. counting strategies

6

1

7

e. estimate/approximate/round

5

2

7

2. Operations/Computation

a. compute with whole numbers

7

6

13

11. Solve a problem using computation of whole numbers.

12. Place number in a four-square that add to given numbers.

17. Explain how to help students make estimates in computation.

b. estimation/reasonableness of results

5

6

11

c. effects of adding, subtracting, multiplying, dividing

4

3

7

d. meaning of whole number operations

7

5

12

3. Determine examples of commutative, associative, and distributive properties.

8. Determine a picture that represents multiplication or division.

13. Explain how an alternative algorithm works.

18. Identify and correct consistent error that student makes in computation.

e. understand standard & non-standard algorithms

5

5

10

f. identify, understand, and use properties (associative, commutative, distributive)

5

2

7

g. inverse operations

5

4

9

h. meaning of integer operations; computing with integers

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3

3

4. Solve number equation with integers.

14. Find three integers with a given sum and product.

19. Provide real-world explanations of operations with integers.

i. integer concepts

2

4

6

3. Number Theory & Number Systems

a. factors, multiples, divisors

5

4

9

5. Determine true or false statements about multiples of numbers.

9. Determine the number of factors of a whole number.

10. Find the sum of the prime factors of a number.

15. Determine generalizations about special kinds of numbers (square, triangular, etc.).

20. Determine if student generalizations about numbers are correct.

b. primes and composites

4

4

8

c. classes of numbers (evens, multiples of 3, etc.)

4

4

8