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Descriptive Statements:
- Demonstrate knowledge of place value, computational fluency, and reasonable estimation.
- Demonstrate knowledge of the order of operations.
- Apply addition, subtraction, multiplication, and division to solve multidigit computations with positive and negative integers, fractions, decimals, and percentages.
- Recognize and identify equivalent ways of representing integers, fractions, decimals, and percentages, including the use of exponents and scientific notation.
- Solve word problems involving integers, fractions, decimals, percentages, ratios, and proportions.
Sample Item:
Perform the operation below.
59 × 327 + 2759 times 327 plus 27
- 10,422
- 19,320
- 20,886
- 28,122
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
B. Multiply and add the numbers in the order they appear. 59 times 327 equals 19,293 plus 27 equals 19,320.
Descriptive Statements:
- Evaluate algebraic expressions by substituting numbers for variables.
- Identify and extend arithmetic and geometric patterns and sequences.
- Solve linear algebraic equations and inequalities involving one variable.
- Identify equivalent algebraic expressions.
- Graph ordered pairs and number relationships presented in tabular or symbolic form.
- Identify linear equations that accurately represent data presented in tabular or graphic form.
Sample Item:
If the pattern continues, which figure comes next in the sequence?
- a parallelogram with 12 dots
- a parallelogram with 15 dots
- a parallelogram with 18 dots
- a parallelogram with 20 dots
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
A. The pattern is in multiples of 3 (3, 6, 9). If the pattern continues, then the next figure will be a parallelogram with 12 dots.
Descriptive Statements:
- Identify the proper measurement tool or unit to solve a given problem.
- Solve problems involving the conversion of units within and between standard and metric measurement systems and calculate derived measurements.
- Solve problems involving scale, lines, line segments, and angles.
- Analyze and identify fundamental types and properties of two- and three-dimensional figures.
- Solve real-world problems involving basic measurement (e.g., length, perimeter, area) and geometric concepts, including the Pythagorean theorem.
Sample Item:
Which of the following shapes is a quadrilateral?
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
D. A quadrilateral is a four-sided polygon that has four corners and four edges. The trapezoid in response D is the only shape with four sides, four edges, and four corners.
Descriptive Statements:
- Calculate and evaluate the probability of a specific event and/or outcome.
- Analyze data presented in various formats (e.g., tables, line graphs, scatter plots, pictographs, bar graphs, histograms, pie charts, box-and-whisker plots).
- Demonstrate knowledge of the appropriate ways to collect, organize, and represent data.
- Calculate and interpret the mean, median, and mode of a set of data.
- Demonstrate knowledge of the concepts of range, standard deviation, and spread.
- Recognize appropriate and inappropriate uses of basic statistics, such as making predictions and/or influencing decisions.
Sample Item:
In order to calculate standard deviation, a scientist would first need to know which of the following data values?
- median
- range
- mean
- mode
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
C. To calculate standard deviation, one must first determine the mean of the numbers. The mean must then be subtracted from each number and the difference squared. The squared numbers must then be used to calculate the variance. The square root of the variance will then determine the standard deviation.
Descriptive Statements:
- Evaluate whether a solution to a given computation or problem is reasonable.
- Use algorithms (i.e., a set of instructions) to perform a given calculation or solve a problem.
- Apply inductive reasoning to identify missing terms in numerical and graphical patterns.
- Apply deductive reasoning to draw conclusions, evaluate arguments, and make predictions.
- Apply, and translate between, the various forms of mathematical communication (e.g., mathematical terminology, equations, diagrams, graphs).
Sample Item:
A commuter drove for 4 hours from Butte, Montana, to Roundup, Montana, at an average speed of 60 miles per hour. The return trip from Roundup to Butte took an extra 2 hours due to heavy traffic. Which of the following expressions most reasonably represents the average speed for the return drive in miles per hour?
- (60)(4)/660 times 4 over 6
- (60)(6)/460 times 6 over 4
- (60)(4)/260 times 4 over 2
- (60)(2)/460 times 2 over 4
Correct Response and Explanation (Show Correct ResponseHide Correct Response)
A. The commuter drove 60 miles per hour for 4 hours to get from Butte, Montana, to Roundup, Montana. If the return trip from Roundup to Butte took an extra 2 hours, then 60 times 4 must be divided by 6 hours total (4 hours plus 2 extra hours for traffic). Therefore, 60 times 4 divided by 6 will most reasonably represent the return drive in miles per hour.
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