CBEST Math Content Specification

CALIFORNIA BASIC EDUCATIONAL SKILLS TEST™ (CBEST ®)

TEST SPECIFICATIONS MATHEMATICS – Three Skill Factors

Skill Factor 1: Estimation, Measurement, & Statistical Principles

Skill Factor 2: Computation & Problem Solving

Skill Factor 3: Numerical & Graphic Relationships


-1-  ESTIMATION, MEASUREMENT, & STATISTICAL PRINCIPLES

A. Estimation and Measurement:

Understand and use standard units of length, temperature, weight, and
capacity in the U.S. measurement system.

Measure length and perimeter.

Understand and use estimates of time to plan and achieve work-related
objectives.

Estimate the results of problems involving addition, subtraction,
multiplication, and division prior to computation.

B. Statistical Principles:

Perform arithmetic operations with basic statistical data related to test scores
(e.g., averages, ratios, proportions, and percentile scores).

Understand basic principles of probability and predict likely outcomes based
on data provided (e.g., estimate the likelihood that an event will occur).

Interpret the meaning of standardized test scores (e.g., stanine scores,
percentiles) to determine how individuals performed relative to other
students.


-2-  COMPUTATION & PROBLEM SOLVING

Add, subtract, multiply, and divide with whole numbers.

Add and subtract with positive and negative numbers.

Add, subtract, multiply, and divide with fractions, decimals, and percentages.

Determine and perform necessary arithmetic operations to solve a practical
mathematics problem (e.g., determine the total invoice cost for ordered
supplies by multiplying quantity by unit price, summing all items).

Solve simple algebraic problems (e.g., equations with one unknown).

Determine whether enough information is given to solve a problem; identify
the facts given in a problem.

Recognize alternative mathematical methods of solving a problem.


-3-  NUMERICAL & GRAPHIC RELATIONSHIPS

Recognize relationships in numerical data (e.g., compute a percentage
change from one year to the next).

Recognize the position of numbers in relation to each other (e.g., 1/3 is
between 1/4 and 1/2; -7<-4).

Use the relations less than, greater than, or equal to, and their associated
symbols to express a numerical relationship.

Identify numbers, formulas, and mathematical expressions that are
mathematically equivalent (e.g., 2/4 = 1/2, 1/4 = 25%).

Understand and use rounding rules when solving problems.

Understand and apply the meaning of logical connectives (e.g., and, or,
if-then) and quantifiers (e.g., some, all, noUse numerical information contained in tables, spreadsheets, and various kinds of graphs (e.g., bar, line, circle) to solve mathematics problems.


PLEASE NOTE:  Copyright © 2007 by the Commission on Teacher Credentialing

California Basic Educational Skills Test, CBEST, and the CBEST logo are trademarks, in the U.S. and/or other countries, of the Commission on Teacher Credentialing and Pearson Education, Inc. or its affiliate(s). NES and its logo are trademarks in the U.S. and/or other countries of Pearson Education, Inc. or its affiliate(s).
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Lessons in Estimation, Measurement, and Statistical Principles

Basics Review

The Number Line

Places and Digitsa

Integer  Arithmetic

Arithmetic Operations

Factors and Multiples

Fraction  Arithmetic

Decimal Arithmetic

Percentage

Three Types of Questions

Questions of Process

Word Problems

Conceptual Understanding

Measurement: Standard units & conversions

Length

Temperature

Weight

Capacity

Time

Unit fractions and Conversions

Basic Geometry: Measure angles, length, perimeter and area

Triangles – Angles, Perimeter, Pythagorean Theorem and Area

Rectangles – Angles, Perimeter an Area

Circles – Degrees,  Diameters, Circumference, lines, segments and Area

Angle Measurement

Parallel Lines

Estimation: Find arithmetic results without complex computation

Rounding

Addition – Subtractio

Multiplication – Division

Statistical principles: Averages, ratios, and proportions

Levels of Data

Averages – Normal and Weighted

Ratios

Proportions

Probability

Defined

Expressed as a Fraction

Standardized test scores

Measures of Relative Standing

Percentile Scores

Stanine Scores

Relating Stanine with Percental

CBEST Mathematics Test

On the CBEST Math Section

The CBEST Mathematics Section contains 50 multiple-choice questions.

There is no specific time limit, as you have four hours to complete the entire exam. Spending about eighty minutes is recommended.

You need to answer approximately 60 percent of the questions correctly in order to pass the Mathematics Section of the CBEST.

Math Skill Areas & Topics

The test covers three three major skill areas:

— Math Topics covered in Estimation, Measurement, and Statistical Principles

• Standard units of length, temperature, weight and capacity
• Measure length and perimeter
• Estimation of answers using arithmetic
• Statistical principles such as averages, ratios, and proportions
• Basic probability
• Interpret meaning of standardized test scores

— Math Topics Covered in Computation and Problem Solving

• Basic operations of addition, subtraction, multiplication, and division
• Solving algebraic word problems
• Determining whether enough information is given to solve math problems.
• Recognizing multiple methods of solving a word problem

— Math Topics covered in Numerical and Graphic Relationships

• Solving questions involving changes in data from one year to the next
• Using rounding rules correctly

• Understanding logical connectives
• Using information presented in bar, line, and pie charts to solve math problems.

Test Preparation

Find out what you know, how well you know it and what you don’t know.  Become familiar with the topic, the question, the solution approach and the steps to get the result,  Then review at least three times spread out  in time and using different question orders.

First, take the test below  without revealing any answers. 

Study your response to each question and compare with the given solution approach and the”show-the-work” steps for the correct answer.

Repeat reviewing the topics and questions to familiarize yourself with the questions, the solution approach and finally the “show-the-work answers. Before revealing any answers formulate an answer in your own words.

Test Questions  1-15; Estimation, Measurement, and Statistical Principles

 

—-  1.    During a semester, a student received scores of 76, 80, 83, 71, 80, and 78 on six tests. What is the student’s average score for these six tests?.

Find an average score  – given six scores.  An average of N numbers is the sum of the N numbers divided by their number N.    The sum 76+80+83+71+80+78 =  468. The average is  468/6 = 78.  The average score for the six tests is 78.

 

—- 2.   On the three sections of a math test, a student correctly answered the number of questions shown below. What percent of the questions on the entire test did the student answer correctly? Section/Total Number of Questions/Number of Questions Correctly AnsweredAlgebra / 20 / 17;  Trigonometry / 15  / 11 ;  Geometry   25  / 20

Find per cent, P, of test questions answered correctly, C, given the number of total questions, T,and those answered correctly for each of 3 tests.  Percent, P = 100 (C/T).  T = sum of  the 3 questions on each test  – or T = 20+15+25 = 60.  C is the sum of the correctly answered questions on each of)) the three tests – or C = 17+11+20 = 48. And so, P = 100(48/60) = 4800/60 = 80%.  Students correctly answered 80%  of the questions on the entire test.

 

3.   If the actual length of the bridge is 4200 feet, then what is the scale of the diagram of the bridge?  See the figures below.

3 t0 10

4. Which of the following is the most appropriate unit for expressing the weight of a pencil?


yes

5. Ms. Gutierrez needs to order rope for her gym class of 32 students. Each student will receive a piece of rope that is 5 feet 8 inches long. What is the total length of rope Ms. Gutierrez needs to order for her class?

yes

6. Use the diagram below to answer the question that follows. What is the total length of Clear Lake’s shoreline?

yes

7.  Use the diagram below to answer the question that follows. A glass tabletop is supported by a rectangular pedestal. If the tabletop is 8 inches wider than the pedestal on each side, what is the perimeter of the glass tabletop?

ys

8. Rob uses 1 box of cat food every 5 days to feed his cats. Approximately how many boxes of cat food does he use per month?

yes

9.  Tara can develop 2 rolls of film in about 18 minutes. At this rate, how long will it take her to develop 8 rollsof film?

yes

10.  Liliana has a bag of marbles. The bag contains 18 black, 15 red, 11 blue, and 8 white marbles. Liliana randomly takes a red marble from the bag and leaves the marble on a table. What is the probability that she will next take a red or a white marble from the bag?

yes

11.   At a college, approximately 2 out of 5 seniors go on to attend graduate school. If there are 750 seniors at the college, how many would be expected to attend graduate school?

yes

12. The Mills Library has 1,007,199 books. The Springvale Library has 907,082 books. Which of the following is the best estimate of how many more books the Mills Library has than
the Springvale Library?

yes

13. Which of the following is the best estimate for 4,286 × 390?
A. 12,000,000   B. 1,600,000  C. 1,200,000  D. 16,000  E. 12,000

yes

14. The lowest point on Earth is the bottom of the Mariana Trench at a depth of 35,840 feet below sea level. The highest point on Earth is the summit of Mt. Everest at a height of 29,028 feet above sea level. Which of the following is the best estimate of the distance between the lowest and highest points on Earth?

yes

15. Kim is in the tenth grade and takes a standardized science
test. Use his test scores below to answer the question that
follows.
Raw Score Percentile Stanine Grade Equivalent
72               88              8             12.1
Kim’s test scores indicate that:
A. he scored as well as or better than 72 of the test takers.
B. 28% of the test takers scored better than he did.
C. he would perform adequately in a twelfth grade science class.
D. he scored as well as or better than 88% of the test takers.
E. he answered 72% of the questions correctly.

yes

Test Questions 16-32: Computation and Problem Solving

 

yes

 

 

 

 

 

 

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