MATHEMATICS NAVIGATOR

Transcription

1 MATHEMATICS NAVIGATOR Screener Test VII Decimals and Powers of Ten Rational Numbers Operations and Word Problems Expressions and Equations Percents Data and Probability

2 This Screener Test has been designed to correlate with the NCTM Curriculum Focal Points. Each Screener Test focuses on three to eight Mathematics Navigator modules, which in turn focus on addressing misconceptions students may have about mathematics concepts. Screener Test VII is designed to be given at the beginning of the school year. It covers the standards that students need in order to be successful at their grade level. The results of this Screener Test will help instructors identify gaps in students knowledge and determine which Mathematics Navigator modules will help fill those gaps. Participation in these modules will help students succeed in mathematics and on their state assessments tests. America s Choice is a subsidiary of the National Center on Education and the Economy (NCEE), a Washington, DC-based non-profit organization and a leader in standards-based reform. In the late 1990s, NCEE launched the America s Choice School Design, a comprehensive, standards-based, school-improvement program that serves students through partnerships with states, school districts, and schools nationwide. In addition to the school design, America s Choice provides instructional systems in literacy, mathematics, and school leadership. Consulting services are available to help school leaders build strategies for raising student performance on a large scale by America s Choice All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system without permission from the America s Choice permissions department. America s Choice and the America s Choice logo are registered trademarks of America s Choice. The National Center on Education and the Economy is a registered trademark of The National Center on Education and the Economy. First Printing ISBN products@americaschoice.org

3 1. Find the difference. A B C D When Jan was 10 years old he was 1.35 meters tall. One year later, he was 0.1 meter taller. How tall was Jan when he was 11 years old? A meters tall B meters tall C meters tall D meters tall 2. Ryan finished a race in seconds. Tom finished 0.1 second later. What was Tom s time? A seconds B seconds C seconds D seconds 5. Find the sum. A B C D = 3. Find the difference. A B C D = 6. What number do you get if you subtract one-tenth from 11? A B. 10 C. 1 D Mathematics Navigator

4 =? 9. What fraction of this square is white? A. B. C. D Which symbol would you use to compare this fraction and decimal? A. B. C. D A. = B. < C. > D. 2 13? = A B C D Screener Test VII

5 11. John and Valerie were late returning a book from the library and had to pay overdue fines. John had 1 5 of the money they owed. Valerie had 2 3 of the money they owed. Together, what fraction of the money owed did they have? A. B. C. D = A. 5 B. C A box containing 30 blank DVDs has a price tag of $ How much is each DVD? A. $0.68 B. $1.11 C. $1.47 D. $ Which word problem goes with this calculation? = A. Joe paid $6.75 for gas. The gas costs $4.84 per gallon. How many gallons did he buy? B. Joe has a garden that has an area of 6.75 square meters. It is 4.84 meters long. How wide is it? C. Joe bought 6.75 meters of fabric at $4.84 per meter. How much does the fabric cost? D. Joe bought a bag of carrots that was priced at $6.75 and reduced to $4.84 in a sale. How much did Joe save? D Mathematics Navigator

6 15. Suppose 3 dozen cans of tomato paste cost $5.76. What is the cost of 2 cans? A. $0.16 B. $0.32 C. $0.96 D. $ If a truck can move 8,775 pounds of dirt in one trip, how much dirt can it move in 225 trips? A. 9,000 pounds B. 39 pounds C. 393,875 pounds D. 1,974,375 pounds 16. How many 1 -cup portions can you 4 get from a can that contains 4 5 of a cup? A. 1 5 B Which expression shows the cost of renting a bicycle at $1.50 per hour for x hours? A. x dollars B. x 1. 5 dollars C. 15x dollars C D. 1.5x dollars D Jin drove for one and one-half hours at 65 miles per hour. How far did she drive? 20. Write an algebraic expression for the following instructions. The letter x stands for any number. Multiply x by 4, then square your answer. A miles B miles C. 65 miles D miles A. 16x 2 B. x 4 2 C. 8x 2 D. 16x Screener Test VII

7 21. Find the expression that goes with this table. x Answers Pablo s summer job paid him $7.80 an hour and 50% more for overtime. In June, his overtime pay was $ If x represents the number of hours he worked overtime, which equation could be used for calculating x? A. 6x 2 B. 6(x 2) C. 6(x + 2) D. 2(x + 6) A x = B x = C x = D. ( )x = Solve. 2 x 5 = Is this equation always true, never true, sometimes true, or you can t tell? 3(x + 5) = 3x + 15 A. x = B. x = C. x = 3 20 A. Always true B. Never true C. Sometimes true D. Can t tell D. x = Mathematics Navigator

8 25. Write 7 as a percent. 10 A. 70% B. 7% C. 0.7% D. 0.07% 27. Jong ordered chicken to be delivered. The bill was $7.77. He paid $9.00. What percent tip did he give? Round to the nearest percent. A. 1% B. 16% C. 30% D. 14% 26. For this problem, refer to the following sale sign from a clothing store: Swimsuits T-shirts Ties Shorts Coats Summer Sale! were $35, now reduced by 25% were $20, now reduced by 15% were $24, now reduced by 40% were $31, now reduced by 10% were $72, now reduced by 30% 28. Jin bought some roses for her friend. She had 15 red roses and 5 white roses. What percent were white roses? A. 25% B. 33% C. 20% D. 400% How much would you pay if you bought a swimsuit and a coat? A. $76.65 B. $30.35 C. $77.57 D. $ Screener Test VII

9 29. Mario saw a jacket that was priced at $80. Then, the price was reduced by 25%. What decimal multiplier should you use to find the new price? A B C D Daniel and Greta are playing a word game. They have played 30 games. Daniel has won 6 times and Greta has won 24 times. Based on these results, what is the probability that Daniel will win the next game? A. 0.2 B. 5 C D Mary correctly answered 27 out of 40 problems on an English test, 13 out of 20 on a history test, and 42 out of 60 on an algebra test. Which subject did she do best in? A. English B. Algebra C. History D. Cannot compare 32. A spinner has 5 sections. Below are the results from spinning the spinner 200 times. Section Frequency Based on these results, if a spinner is spun 100 times, about how many times will it land on section 1? A. 10 B. 20 C. 5 D. You cannot predict; the sample is too small. Mathematics Navigator

10 33. A survey was taken showing the number of brothers and sisters 30 students have. This table shows the data with the frequency of responses. What is the mode of this data set? Siblings Frequency A. 1 B. 2 C. 2.5 D This graph shows the annual salaries of graduates from a small college. Annual Salaries (dollars) What is the approximate median salary? 25,000 35,000 45,000 55,000 65,000 A. 39,500 B. 40,000 C. 45,000 D. 35,000 Screener Test VII

11 35. The table below shows the number of students who are involved with musical instruments at Middleview High School. 10th Grade 11th Grade 12th Grade Jazz School Marching Orchestra Which graph best represents this data set? A. Jazz B. 100 School Marching Orchestra Students Enrolled Jazz School Marching Orchestra C. Students Enrolled D. School Marching Jazz Orchestra 0 Jazz School Marching Orchestra Mathematics Navigator

12 36. Jerry worked at odd jobs during the summer and kept a log of his daily earnings. He earned the following amounts: What is the mean of his daily earnings? A. 16 B. 15 C D STOP! 10 Screener Test VII

13 Answer Key Question Number Answer Key 1 B 2 B 3 B 4 B 5 C 6 D 7 B 8 C 9 B 10 A 11 C 12 D Content Description Applies an understanding of decimal models, place value, and number properties to subtract two decimals Applies an understanding of decimal models, place value, and number properties to add two decimals in the context of a word problem Applies an understanding of decimal models, place value, and number properties to subtract a decimal from a whole number Applies an understanding of decimal models, place value, and number properties to add decimals in the context of a word problem involving measurement Applies an understanding of decimal models, place value, and number properties to add two decimals Applies an understanding of decimal models, place value, and number properties in order to subtract a fraction given in words from a whole number Uses a knowledge of the meanings of fractions and properties of operations to find equivalent fractions Applies knowledge of converting fractions to decimals to compare and order a fraction and a decimal using an inequality symbol Applies an understanding of fractions, area models, and part versus whole to determine what fraction of a figure is not shaded Applies an understanding of fractions and fraction models to add and subtract fractions with unlike denominators Applies an understanding of fractions and fraction models to add and subtract fractions with unlike denominators in the context of a word problem Uses a knowledge of the rules for multiplying and dividing fractions to solve a two-step problem Unit Decimals and Powers of Ten Rational Numbers Mathematics Navigator 11

14 Answer Key Question Number Answer Key 13 C 14 C 15 B 16 B 17 D 18 D 19 D 20 A 21 A 22 D 23 C 24 A Content Description Uses simple reasoning about multiplication and division to solve one-step word problems involving ratio and rate Uses simple reasoning about multiplication and division to select a word problem that illustrates a multiplication problem involving decimals Uses simple reasoning about multiplication and division to solve multistep word problems involving ratio and rate Builds on a knowledge of fractions to solve a word problem that involves finding the fractional part of a fractional whole Uses simple reasoning about multiplication and division to solve one-step word problems involving ratio and rate Uses simple reasoning about multiplication and division to solve one-step word problems involving ratio and rate, as well as multiplication of three- and four-digit numbers Uses simple reasoning about multiplication to write an expression that could be used to solve a word problem involving rate Identifies an algebraic expression based on a verbal description Describes simple relationships by selecting an expression that matches a given table Understands that variables represent numbers whose exact values are not yet specified and uses knowledge of the arithmetic of rational numbers to solve linear equations in one variable Understands that variables represent numbers whose exact values are not yet specified and uses knowledge of the arithmetic of rational numbers to write an equation that represents a word problem Uses the commutative, associative, and distributive properties to determine whether an equation is always true, never true, or sometimes true Unit Operations and Word Problems Expressions and Equations 12 Screener Test VII

15 Answer Key Question Number Answer Key 25 A 26 A 27 B 28 A 29 C 30 B 31 A 32 C 33 A 34 A 35 B 36 A Content Description Uses division and an understanding of fractions and decimals to express a fraction as a percent Develops an understanding of percents in everyday situations by solving a multistep word problem involving percent discounts Develops an understanding of percents in everyday situations by solving a multistep word problem involving tips Develops an understanding of percents in everyday situations by solving a multistep word problem involving tips Uses division and an understanding of fractions and decimals to determine the percent in a word problem Develops an understanding of percents in everyday situations by solving a word problem involving percent discounts Uses division and an understanding of fractions and decimals to determine percents in a word problem and use the information to solve the problem Applies an understanding of the concept that when all outcomes of an experiment are equally likely, the theoretical probability of an event is the fraction of outcomes in which the event occurs to find a probability Applies an understanding of proportions to make predictions based on data in a table Uses descriptive statistics, including mean, median, mode, and range, to describe data represented in a table Uses descriptive statistics, including mean, median, and range, to describe data represented in a box and whisker plot Analyzes different bar graphs and pie charts in order to determine which graph best represents the data in a table Uses descriptive statistics, including mean, median, and range, to describe data represented in a stem-and-leaf plot Unit Percents Data and Probability Mathematics Navigator 13

16