| Elementary Whole Number and Integer Concepts and Computation Item Specification Chart | |||||||
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Mathematics Content | S | T | A | 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. |
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b. large numbers | 1 | 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 |
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| 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 | 0 | 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 | ||||