MATH STRAND V:
ALGEBRA
13. Use the distributive property in arithmetic computations.
Test items may assess the students ability to use the distributive property in arithmetic computations or may involve a problem situation in which students apply the distributive property to the solution of the problem.
At this grade level, the distributive property will apply to whole numbers, decimals, fractions (and mixed numbers), but not to positive or negative numbers.
Students will not be expected to know or apply the distributive property of division over subtraction at this grade level, e.g., 252 ÷ 7 = (280 - 28) ÷ 7 = (280 ÷ 7) - (28 ÷ 7).
14. Explain and reflect differences between calculators with arithmetic logic and calculators with algebraic logic when symbolizing a keying sequence and in the display as each key is pressed.
Assessing the students' understanding of the differences between calculators with arithmetic logic and calculators with algebraic logic is the focus of items developed for this outcome. Each item will include an illustration of a keying sequence and what is displayed on the calculator as a result of the keying sequence.
Each digit or operation in the keying sequence is represented as a separate entry or step. The following are examples of how a keying sequence and resulting display may be illustrated in a test item:
Note: Calculator A illustrates arithmetic logic as each operation was performed when the operation key was pressed; i.e., added 8 to 4 and multiplied sum by 2. Calculator B illustrates algebraic logic as operations were performed following the order of operations when the “=“ key was pressed; i.e., multiplied 8 by 2 and then added 4 to that product.
Students may be asked to use this information to identify the type of logic represented or used in each keying sequence and/or to apply the information to a problem situation. Students may be asked to determine the resulting display for a keying sequence for a calculator with arithmetic and/or a calculator with algebraic logic or to identify the order in which the operations will be performed in a given keying sequence when a calculator with a specified type of logic is used. An understanding of order of operations is essential.
Students may use certain calculators on the Sixth-grade Proficiency Test in Mathematics. See page 37 for examples of acceptable and unacceptable calculators.
15. Use variables to describe arithmetic processes, to generalize arithmetic statements, and to generalize a problem situation.
This outcome emphasizes recognizing and/or using variables in problem-solving situations and mathematical phrases and equations as statements. Students may be given a mathematical sentence such as ‘Six less than some number is equal to ten,” and may be asked to identify the phrase or equation represented by this sentence.
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