| Middle School Number/Computation Item Specification Chart | |||||||
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S | T | A | Type I | Type II | Type III | Type IV | |
1. Whole Numbers | |||||||
a. ratio and proportions | 7 | 6 | 13 |
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| 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 |
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| 20. Explain student thinking in estimating the product of two numbers |
d. select/use variety of computation methods | 6 | 6 | 12 |
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| 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 |
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h. positive/negative exponents | 4 | 1 | 5 |
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i. order of operations | 1 | 2 | 3 |
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2. Rational Numbers | |||||||
a. rational number representations | 7 | 6 | 13 |
| 6. Identify rational number on a number line. |
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b. use a variety of models | 7 | 4 | 11 | ||||
c. fractions & decimals operations | 7 | 6 | 13 |
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| 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. |
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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. |
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f. solve percentage problems | 7 | 6 | 12 | ||||
g. rational vs. irrational | 3 | 3 | 6 |
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3. Integers |
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a. integer representations | 7 | 6 | 13 |
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| 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. |
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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. |
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4. Number Theory & Number Systems | |||||||
a. primes and composites | 6 | 4 | 10 |
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| 15. Find smallest prime greater than a number. |
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b. factors and multiples | 5 | 4 | 9 | 4. Find LCD of two fractions. | 10. Find three smallest numbers given GCF and LCM. |
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c. identity and use properties | 4 | 5 | 9 | 5. Identify law (associative, commutative, or distributive) that justifies equation. |
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d. containment relationships | 2 | 5 | 7 | 1. Identify false statement regarding containment relationships among numbers (real, rational, irrational, integers, whole numbers). |
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e. subsystem properties | 2 | 5 | 7 |
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f. permutations and combinations | 1 | 3 | 4 |
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g. complex numbers | 0 | 2 | 2 |
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h. bases other than 10 | 0 | 1 | 1 |
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i. history of numbers | 1 | 0 | 1 |
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j. union/intersection of sets | 0 | 1 | 1 |
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