National Evaluation Series™ Profile: Foundations of Classroom Support and Instruction (519)

Content Domain III: Numeracy

Competencies:

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0007 Understand number properties and number operations.

Descriptive Statements:

Solve problems and make reasonable estimates for addition, subtraction, multiplication, and division with whole numbers, fractions, and decimals.
Demonstrate knowledge of ways to compose and decompose (i.e., build and break down) whole numbers.
Demonstrate knowledge of common errors in writing and solving equations and word problems.
Identify and order different forms of numbers (e.g., integers, fractions, decimals) and locate them on a number line.
Demonstrate knowledge of place value for whole numbers and decimal numbers.
Solve problems and make reasonable estimates using whole numbers, fractions, decimals, percentages, and ratios.

Sample Item:

A teacher is organizing a field trip for 60 students. The bus rental company charges a base fee of 300 dollars and then 10 dollars per student. What is the estimated total cost for the bus rental?

360 dollars
600 dollars
900 dollars
1,200 dollars

Correct Response and Explanation (Show Correct ResponseHide Correct Response)

Correct Response: C. To determine the total cost of the bus rental for a field trip with 60 students, start with the bus rental company's pricing. The base fee is 300 dollars and an additional charge of 10 dollars for each student. Calculate the total cost for the students by multiplying the number of students, which is 60, by the cost per student, which is 10 dollars. That equals 600 dollars. Finally, add the base fee of 300 dollars to 600 dollars, which is 900 dollars.

0008 Understand algebraic principles and data analysis.

Descriptive Statements:

Solve single-step and two-step equations involving one variable.
Solve real-world mathematical problems using numerical or algebraic expressions and equations.
Recognize and extend basic numerical and visual patterns.
Represent data in a variety of graphical formats (e.g., tables, pie charts, line graphs, paragraphs, pictographs).
Analyze data presented in tables, line graphs, pictographs, bar graphs, and pie charts.

Sample Item:

After eating at a restaurant, a group of friends received a bill for 75 dollars. They decided to split the bill evenly by having each person contribute an equal amount. If there were n people in the group of friends, which of the following expressions represents how much each person contributed to the bill?

$75 divided by n
$75 times n
$75 minus n
$75 + n

Correct Response and Explanation (Show Correct ResponseHide Correct Response)

Correct Response: A. The total bill of $75 is being split equally among the number of people represented by "n." To find out how much each person needs to contribute, divide the total bill by the number of people "n." The expression $75 divided by n equals the amount that each person needs to contribute to split the bill equally.

0009 Understand concepts in measurement and geometry.

Descriptive Statements:

Convert between units of time, money, length, mass, volume, and weight in the standard measurement system.
Use metric units to convert units within the metric system.
Identify and describe geometric figures based on their properties (e.g., square, circle, triangle, rectangle).
Solve real-world word problems involving the area, perimeter, and volume of two-dimensional and three-dimensional geometric figures.
Locate points and recognize geometric figures on a coordinate plane.
Solve real-world problems using measurement (e.g., standard, metric).

Sample Item:

A rectangular box has a length of 6 meters, a width of 4 meters, and a height of 3 meters. Which of the following equations can be used to find the volume of the box?

volume = length + width + height
volume = length times width times height
volume = (length + width) times height
volume = length times width minus height

Correct Response and Explanation (Show Correct ResponseHide Correct Response)

Correct Response: B. The formula for the volume of a rectangular box is given by the product of its length, width, and height. The length is 6 meters, the width is 4 meters, and the height is 3 meters. By substituting these values into the formula, volume = length times width times height.

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