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Standardized GRADE Test Tutor MATH Michael Priestley Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Scholastic Inc grants teachers permission to photocopy the designated reproducible pages from this book for classroom use No other part of this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission of the publisher For information regarding permission, write to Scholastic Inc., 557 Broadway, New York, NY 10012 Editor: Mela Ottaiano Cover design: Brian LaRossa Interior design: Creative Pages, Inc Interior illustrations: Creative Pages, Inc ISBN-13: 978-0-545-09606-5 ISBN-10: 0-545-09606-5 Copyright © 2009 by Michael Priestley All rights reserved Published by Scholastic Inc Printed in the U.S.A 10 40 15 14 13 12 11 10 09 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Contents Welcome to Test Tutor Test Test 27 Test 45 Answer Sheet 65 Answer Keys Test 67 Test 76 Test 85 Scoring Charts Student Scoring Chart 94 Classroom Scoring Chart 95 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Welcome to Test Tutor! Students in schools today take a lot of tests, especially in reading and math Some students naturally perform well on tests, and some not But just about everyone can get better at taking tests by learning more about what’s on the test and how to answer the questions How many students you know who could benefit from working with a tutor? How many would love to have someone sit beside them and help them work their way through the tests they have to take? That’s where Test Tutor comes in The main purpose of Test Tutor is to help students learn what they need to know in order to better on tests Along the way, Test Tutor will help students feel more confident as they come to understand the content and learn some of the secrets of success for multiple-choice tests The Test Tutor series includes books for reading and math in a range of grade levels Each Test Tutor book in mathematics has three full-length practice tests designed specifically to resemble the state tests that students take each year The math skills measured on these practice tests have been selected from an analysis of the skills tested in ten major states, and the questions have been written to match the multiple-choice format used in most states The most important feature of this book is the friendly Test Tutor He will help students work through the tests and achieve the kind of success they are looking for This program is designed so students may work through the tests independently by reading the Test Tutor’s helpful hints Or you may work with the student as a tutor yourself, helping him or her understand each problem and test-taking strategy along the way You can this most effectively by following Test Tutor’s guidelines included in the pages of this book Three Different Tests There are three practice tests in this book: Test 1, Test 2, and Test Each test has 45 multiple-choice items with four answer choices (A, B, C, D) All three tests measure the same skills in almost the same order, but they provide different levels of tutoring help Test provides step-by-step guidance to help students work through each problem, as in the sample on the next page The tips in Test are detailed and thorough, and they are written specifically for each math item to help students figure out how to solve the problem Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Sample S age is feet inches tall Her brother Dylan is feet inches tall How much taller is Sage than Dylan? A B C D inches inches inches To find how much taller Sage is, you’ve got to find the difference in their heights Subtract Dylan’s height from Sage’s height to find how much taller she is foot inches Test provides a test-taking tip for each item, as in the sample below, but the tips are less detailed than in Test They help guide the student toward the solution to each problem without giving away too much Students must take a little more initiative Sample I n 2006 the population of Aztec, New Mexico, was 7,056 In 1990 the population was 5,480 How much did the population of Aztec grow from 1990 to 2006? A B C D 16 1,576 Look for key words to help you understand the question In this question, the key words are How much and grow 1,676 12,536 Test does not provide test-taking tips It assesses the progress students have made After working through Tests and with the help of the Test Tutor, students should be more than ready to score well on Test without too much assistance Success on this test will help students feel confident and ready for taking real tests Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Other Helpful Features In addition to the tests, this book provides some other helpful features First, on page 65, you will find an answer sheet When students take the tests, they may mark their answers by filling in bubbles on the test pages Or, they may mark their answers on a copy of the answer sheet instead, as they will be required to in most standardized tests You may want to have students mark their answers on the test pages for Test and then use an answer sheet for Tests and to help the student get used to filling in bubbles Second, beginning on page 67, you will find a detailed answer key for each test The answer key lists the correct response and explains how to solve the problem It also identifies the skill tested by each question, as in the sample below Answer Key for Sample Correct response: B (Add, subtract, multiply, and divide whole numbers) To find the difference in population, subtract the population in 1990 (5,480) from the population in 2006 (7,056): 7,056 5,480 1,576 Incorrect choices: A is the result of subtracting the years (2006 1990) instead of the populations C is the result of a computation error in subtracting 7,056 5,480 as the student “borrows” a hundred to subtract in the tens column but forgets to reflect this in the hundreds column D is the result of adding 7,056 5,480 instead of subtracting As the sample answer indicates, this question measures the student’s ability to add, subtract, multiply, and divide whole numbers This information can help you determine which skills the student has mastered and which ones still cause difficulty Finally, the answer key explains why each incorrect answer choice, or “distractor,” is incorrect This explanation can help reveal what error students might have made For example, one distractor in an addition problem might be the result of subtracting two numbers instead of adding them together Knowing this could help the student understand that he or she used the wrong operation Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources At the back of this book, you will find two scoring charts The Student Scoring Chart can help you keep track of each student’s scores on all three tests and in different subtests, such as “Number and Number Sense” or “Measurement and Geometry.” The Classroom Scoring Chart can be used to record the scores for all students on all three tests, illustrating the progress they have made from Test to Test Ideally, students should score higher on each test as they go through them However, keep in mind that students get a lot of tutoring help on Test 1, some help on Test 2, and no help on Test So, if a student’s scores on all three tests are all fairly similar, that could still be a very positive sign that the student is better able to solve problems independently and will achieve even greater success on future tests Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Test Name Date Directions: Read each question Look at the Test Tutor’s tip for answering the question Then find the answer You may your work on this page or on scrap paper Mark your answer by filling in the bubble Test Tutor says: In 2006 the population of New York City was about eight million two hundred fifty thousand What is this number in standard form? A B C D 8,250 825,000 8,000,250 8,250,000 To write a number in standard form, write the number in the largest place first Then fill in the rest of the numbers one part at a time For example, begin with “eight million” as 8,000,000 2 Four friends share a pizza The table below shows what fraction of the pizza each person ate Amount of Pizza Eaten Jerome _ 1 12 Sheena 1 Charlotte 1 Bruce 1 Since all of these fractions have in the numerator (top of fraction), compare the amounts in the denominators (bottom of fraction) Remember: The denominator shows how many equal pieces a whole is divided into So the smaller the denominator, the bigger the piece Who ate the most pizza? A B C D Jerome Sheena Charlotte Bruce Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Test Test Tutor says: Name Where is point M located on the number line? M A B C D between 0.2 and 0.4 between 0.3 and 0.5 between 0.1 and 0.2 between and Ms Ritchie buys 25 pounds of rice What is another way to write this number? 12 pounds A 17 B 5 pounds 30 pounds C 32 pounds D 5 In March, 628,451 letters were mailed from a post office Which digit in this number is in the ten thousands place? A B C D There are 81 students in the fourth grade at Franklin School The principal wants to divide them into equal groups with no students left over Into how many groups should the students be divided? A B C D First, figure out how to read the number line correctly Count the number of hash marks between and Then you’ll know what each mark represents To change a mixed number to an improper fraction, remember to multiply the denominator by the whole number and then add that product to the numerator To find the place value of one digit in a number, write out the number in expanded form This will tell you the place value of each digit For example, 641 would be 600 + 40 + 1; the in this number is in the tens place The number of groups must be a factor of 81 That means that you can divide 81 by that number, without a remainder Try dividing 81 by each answer choice 11 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Test Test Tutor says: Name On Monday, a grocery store had 8,120 cans of soup On Saturday, 6,529 of the cans were left How many cans of soup were sold during the week? A B C D 1,591 1,691 2,501 14,649 Sandy bought 34 pounds of green apples and 12 pounds of red apples How many pounds of apples did she buy all together? A B C D To find the number of cans that were sold, subtract the number of cans left over on Saturday from the total number of cans on Monday 14 pounds 23 pounds First, find a common denominator for the fractions _ 34 and _ 12 Then add the two mixed numbers to find the total number of pounds of apples pounds 14 pounds Brody has a set of blocks Each block is 6.4 centimeters tall If he stacks blocks on top of one another, how tall will the stack of blocks be? A B C D 10 48.2 centimeters 482 centimeters To find the height of the stack, take the height of each block and multiply it by the number of blocks 51.2 centimeters 512 centimeters Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 33 Correct response: C 35 Correct response: D (Match 3-dimensional objects and their 2-dimensional representations) The figure in answer choice C can be folded to form a triangular pyramid like the one shown This may be demonstrated by cutting this figure from a piece of paper and folding it (Interpret data presented in line, bar, and circle graphs, pictographs, tables, charts) Betsy’s handstand time was seconds in both June and September Incorrect choices: Incorrect choices: A Betsy’s times did not increase steadily; her time even fell from August to September In A , this figure cannot be folded to form a triangular pyramid (it would have only three faces) B The greatest increase in Betsy’s times was between September and October In B , this figure cannot be folded to form a triangular pyramid (the triangular “base” is not drawn in the correct location) In D , this figure cannot be folded to form a triangular pyramid (it would have five faces) 34 Correct response: B (Interpret data presented in line, bar, and circle graphs, pictographs, tables, charts) The cost for a child visiting the main aquarium, sea otter exhibit, and dolphin show is $8 $3 $4 $15; this is the same price as an adult ticket to the main aquarium Incorrect choices: A It costs only $5 for a senior ticket to the dolphin show, which is less than the $8 child’s ticket to the main aquarium C It costs $10 for a senior to visit the main aquarium, which is less than the total of $12 it would cost for an adult to visit the sea otter exhibit and the dolphin show D It would cost $9 for a senior to visit the sea otter exhibit and the dolphin show, which is not the same as the $8 ticket for a child to visit the main aquarium C Betsy’s time was greatest in October, not August 36 Correct response: D (List all possible outcomes or construct sample spaces using lists, charts, frequency tables, and tree diagrams) Each time the arrow is spun, it could land on any of the sections If the arrow is spun twice, there are possible outcomes, as listed in answer choice D Incorrect choices: A lists all possible combinations of the letters B lists all the possible outcomes if repetition were not possible C lists all the possible outcomes for three spins if repetition were not possible 37 Correct response: A (Find probabilities) There are a total of 10 candies in the bag, and of the 10 candies are blue The probability of 3 picking a blue candy is out of 10, or 10 Incorrect choices: B represents the number of blue candies over the number of red and yellow candies C represents the probability of choosing a red 5 , or candy ( 12 ) 10 D represents the probability of choosing a candy that is not blue 82 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 38 Correct response: B 41 Correct response: D (Determine and describe the mean, median, mode, and range of data) To find the mean, add all of the numbers of pages (125 96 157 278) and divide the sum (656) by the number of books (4); 656 164 (Identify, describe, and extend numerical and geometric patterns) In the number pattern, each number is greater than the number before To find the next number in the pattern, add to the last number listed The correct expression is 12 Incorrect choices: Incorrect choices: A represents the median of the data A is the result of multiplying the first number in the pattern (3) by the total number of numbers in the pattern (4) C represents the range of the data D represents the total number of pages 39 Correct response: C (Determine and describe the mean, median, mode, and range of data) The mode is the number that occurs the greatest number of times in a data set The number appears times in this data set, more than any other number Incorrect choices: A The number appears times in the data set B 8.5 is the median of the data D 11 is the range of the data 40 Correct response: B (Collect, organize, display, and interpret data to solve problems) The bar graph shows that students chose a hamster and students chose a fish The difference between them is Incorrect choices: A is the number of students who chose a fish C is the difference between the number of students who chose a lizard and the number of students who chose a fish (9 6) D is the number of students who chose a hamster B is the result of multiplying times the last number instead of adding C represents a misunderstanding of the number pattern or how to describe it 42 Correct response: A (Apply basic properties and order of operations with algebraic expressions) By the distributive property, $0.50(b d) $10.00 is equivalent to $0.50b $0.50d $10.00 Incorrect choices: In B, the number sentence is not equivalent because (b d) is not the same as (bd) In C and D, the number sentences are not equivalent; they represent misunderstandings of the basic properties of operations 43 Correct response: D (Use algebraic expressions, patterns, and simple equations and inequalities to represent problem situations) The number of stickers each student will receive is the total number of stickers divided by the number of students, or 360 s Incorrect choices: A reflects adding the number of stickers and number of students instead of dividing B reflects subtracting the number of students from the number of stickers instead of dividing C reflects multiplying the number of stickers by number of students instead of dividing Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 83 44 Correct response: B (Represent and describe mathematical relationships with lists, tables, charts, graphs, and diagrams) Answer choice B shows the relationship between the number of hours and number of miles walked Every y-value on the line is times its corresponding x-value For example, if he walks hours, he goes miles; in hours, he walks miles Incorrect choices: A shows that the number of miles he walks is miles, regardless of the number of hours C shows that the number of hours walked is hours, regardless of the number of miles D shows the opposite relationship (for every hours he walks, he goes mile) 45 Correct response: C (Evaluate the reasonableness of a solution) The area of the swimming pool is its length times its width If the length is greater than the width, then the area must be at least 60 ft 60 ft 3,600 sq ft But the length cannot be greater than 100 ft, so the area can not be greater than 6,000 sq ft (60 ft 100 ft) The best estimate of the area is 4,800 sq ft, which is between 3,600 and 6,000 sq ft Incorrect choices: A is the result of adding the width and the greatest possible length (60 100) B is the perimeter (based on 60 ft 100 ft) instead of the area D is an overestimate because the dimensions cannot exceed 60 ft 100 ft 84 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Test Answer Key C 10 B 19 B 28 C 37 B C 11 C 20 A 29 D 38 A A 12 B 21 D 30 B 39 C D 13 B 22 C 31 A 40 D C 14 D 23 A 32 C 41 B B 15 D 24 C 33 C 42 D D 16 A 25 D 34 A 43 A A 17 A 26 B 35 B 44 C D 18 B 27 A 36 C 45 B Answer Key Explanations Correct response: C (Read and write whole numbers (to the millions) and decimals) The standard form of five hundred sixty thousand three hundred twenty will have a in the hundred thousands place (500,000), a in the ten thousands place (60,000), a in the thousands place, a in the hundreds place (300), a in the tens place (20), and a in the ones place: 560,320 Incorrect choices: A is five thousand six hundred thirty-two B is fifty-six thousand three hundred twenty D is five hundred sixty-three thousand twenty Correct response: C (Compare and order whole numbers, fractions, and decimals) On this number line, each hash mark represents 0.5 Point H is between 2.0 and 2.5 on the number line, but closer to 2.5 The number 2.4 is between 2.0 and 2.5, closer to 2.5 (continued) Incorrect responses: A 1.8 would be located to the left of 2.0 B 2.2 would be located closer to 2.0 than 2.5 D 2.8 would be located to the right of 2.5 and closer to 3.0 Correct response: A (Compare and order whole numbers, fractions, and decimals) All of these fractions can be compared by putting them over the common denominator 3 27 ; 4 72 ; 2 60 ; and 59 50 Sasha of 90: 10 90 90 90 90 3 , is the smallest read the least because 27 , or 10 90 fraction Incorrect choices: B José read 45 of the book, which is greater 3 than 10 C Fran read 23 of the book, which is greater 3 than 10 D Neal read 59 of the book, which is greater 3 than 10 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 85 Correct response: D Correct response: D (Represent, convert, and find equivalent fractions and mixed numbers) Equivalent fractions can be reduced to the 8 can be reduced to 23 (dividing same fraction 12 (Add, subtract, multiply, and divide whole numbers) To find the number of seats on the train, multiply the number of cars (7) by the number of seats on each car (128): 128 896 can be reduced to 23 (dividing the numerator and denominator by 12) Incorrect responses: the numerator and denominator by 4), and 24 36 Incorrect choices: A i s the result of adding 128 instead of multiplying A is incorrect because 34 cannot be reduced 8 to 23 and is not equivalent to 12 B reflects an error in multiplication (not carrying the from 56 or the from 14) 8 are not B is incorrect because 12 and 12 8 equivalent 12 can be simplified to 12 ; 12 can be reduced to 23 C is incorrect because 49 cannot be reduced 8 and is not equivalent to 12 Correct response: C (Identify and use place value) The tenths place is one digit to the right of the decimal In $1,653.89, the number that is one digit to the right of the decimal is That 8 represents 0.8, or tenths, or 10 Incorrect choices: A The is in the ones place B The is in the tens place D The is in the hundredths place Correct response: B (Identify prime numbers, factors, and multiples) The number of students in Grade (23) is a prime number because it is divisible only by and itself Incorrect choices: A The number of students in Grade (27) is divisible by and C The number of students in Grade (34) is divisible by and 17 D The number of students in Grade (33) is divisible by and 11 86 C r eflects an error in multiplication (not carrying from 14) Correct response: A (Add and subtract fractions and mixed numbers) To subtract the fractions, first give them common denominators The least common 5 5 4 and 12 12 12 multiple of 12 and is 12: 13 5 4 1 Then subtract the numerators: 12 12 12 Incorrect choices: 3 B is the result of converting 13 incorrectly to 12 5 2 , or and subtracting 12 3 12 16 12 1 C is the result of converting 13 incorrectly to 12 5 1 4 , or and subtracting 12 12 12 13 D is the result of subtracting the numerators (5 1) and denominators (12 3) Correct response: D (Add, subtract, multiply, and divide decimals) To find the total cost, add all of the prices together, being careful to line up the decimals: $25.95 $7.39 $12.60 $45.94 Incorrect choices: A is the result of adding only two prices: $25.95 $7.39 B is the result of adding $25.95 $7.39 $1.26 C is the result of an error in addition (tens are not carried over) Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 10 Correct response: B (Solve problems involving integers) The number of spaces Nicole should move can be determined by finding the sum of the two cards: (1) Incorrect choices: A is the absolute value of the first card (1) C is the number on the second card (4) D is the result of subtracting (1), or 11 Correct response: C (Estimate using whole numbers and decimals) To estimate the total weight, round each weight to the nearest ten and then add the weights together Ned’s weight of 98 pounds can be rounded to 100 lb; his brother’s weight of 111 pounds can be rounded to 110 lb, and his father’s weight of 169 pounds can be rounded to 170 lb 100 110 170 380 Incorrect choices: A is the result of rounding each weight to 100 B is the result of rounding the numbers down and adding: 90 110 160 D is the result of rounding the numbers to the nearest 100 and adding: 100 100 200 12 Correct response: B (Apply the properties of operations) Because addition and subtraction have an inverse relationship, 24 m 45 is equivalent to 45 m 24 Incorrect choices: A Subtracting m from 24 is not the same as adding m 24 C Adding m to 45 is not the same as adding m 24 D reflects a misunderstanding of the inverse relationship between subtraction and addition 13 Correct response: B (Solve multi-step problems involving whole numbers, fractions, decimals) First, find the total number of balloons Ozzie bought by multiplying the number of packages (6) times the number of balloons in each package (12): 12 72 Since Ozzie gives the same number to each guest with none left over, the number of balloons each guest receives is the total number of balloons (72) divided by the number of guests (9): 72 Incorrect choices: A is the result of adding 12 (instead of multiplying) and then dividing by C is the result of adding 12 and then subtracting (instead of dividing) D is the result of adding 12 and then adding (instead of dividing) 14 Correct response: D (Solve multi-step problems involving whole numbers, fractions, decimals) The total distance Cherry travels to school is 1.8 km 5.6 km 7.4 km Since she makes the same trip on the way home, the total distance she travels going to school and back is 7.4 km 14.8 km Incorrect choices: A reflects a mistake in adding 1.8 km and 5.6 km, and not multiplying by B represents the distance one way; it was not multiplied by C represents a mistake in adding 1.8 km and 5.6 km (not carrying the and getting 6.4) and then multiplying by 15 Correct response: D (Solve number sentences with one variable) To solve the number sentence, add to both sides of the equation: n ( 6) 18 ( 6) n 24 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 87 15 (continued) Incorrect choices: A is the result of dividing 18 B is a number in the equation C is the result of subtracting 18 16 Correct response: A (Tell time and find elapsed time) Since there are 60 minutes in hour, the time between 4:45 and 6:02 is hour 17 minutes (There is hour between 4:45 is 5:45; an additional 15 minutes brings the time to 6:00 (45 15 60), and an additional minutes brings the time to 6:02 15 minutes minutes 17 minutes.) Incorrect choices: B would be correct if there were 100 minutes in an hour C is the result of adding an extra hour D is the result of adding an extra hour and assuming 100 minutes in an hour 17 Correct response: A (Convert or estimate conversions of measures) One quart is equal to cups To find how many quarts are equal to 10 cups, divide 10 cups by cups/quart: 10 cups cups/quart 2.5 quarts, or 12 quarts 19 Correct response: B (Use rulers and other instruments to measure accurately) The carrot is lined up with the 1-inch hash mark on one end and the 5.5-inch hash mark on the other end Its length is 5.5 inches inch 4.5 inches Incorrect choices: A disregards the last half-inch of the carrot C disregards the last half-inch of the carrot and the fact that it begins at the 1-inch hash mark D is incorrect; 12 represents the hash mark at the end of the carrot 20 Correct response: A B is the number of pints Gary would need (1 pint cups) (Estimate and find length, perimeter, and area) The perimeter of the triangle is the sum of the lengths of its sides If Haley uses a total of 96 feet of fencing for the perimeter, the length of the third side of the triangle is 96 feet minus the lengths of the other two sides 96 feet 24 feet 32 feet 40 feet C is the result of subtracting 10 cups cups Incorrect choices: Incorrect choices: D is the result of multiplying 10 cups cups 18 Correct response: B (Select appropriate unit for measuring weight/ mass, capacity, length, perimeter, and area) A shoe is generally somewhere between 15 and 30 centimeters, so centimeters is a good unit of measurement to use 88 18 (continued) Incorrect choices: A A meter is a little longer than one yard—too large to measure a shoe C A centimeter equals 10 millimeters, so millimeters are too small to measure a shoe 6 of a mile—too large D A kilometer is about 10 to measure a shoe B reflects a mistake in subtraction C is the sum of the two sides given: 32 24 D is the result of subtracting only one side (32 ft) from the total: 96 32 21 Correct response: D (Estimate and find length, perimeter, and area) The area of the field is the length times the width: 100 m 20 m 2,000 m2 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 21 (continued) Incorrect choices: A is the result of adding 100 m 20 m instead of multiplying B reflects a mistake in multiplication (by a power of 10) C is the perimeter of the field instead of the area 22 Correct response: C (Identify and classify acute, obtuse, and right angles and triangles) An acute triangle has three angles less than 90º Incorrect choices: A is a right triangle B and D are both obtuse triangles 23 Correct response: A (Identify, classify, and describe plane figures and their attributes) A rectangle must have two pairs of parallel sides Incorrect choices: B The two pairs of sides in a rectangle need not be equal in length C a nd D are incorrect because rectangles have four right angles 24 Correct response: C (Determine congruence and similarity) The sides of similar figures have the same ratio Jee’s drawing is twice as tall (2 m) as it is wide (1 m) The figure in answer choice C is similar because it is twice as tall (6 m) as it is wide (3 m) 25 Correct response: D (Identify, classify, and describe solid figures and their attributes) A square pyramid has five faces: the square base and four triangular sides Incorrect responses: A A cube has six faces B A sphere has no faces C A rectangular prism has six faces 26 Correct response: B (Locate and name points on a coordinate plane using ordered pairs) In an ordered pair, the first number (x) indicates the number of units across and the second number (y) indicates the number of units up or down On the grid, point F is located at (4, 6) Incorrect responses: A is the result of reading the y coordinate first (up 6) and then the x coordinate (4 across) C is the result of reading only the y coordinate (6) D is the result of reading only the x coordinate (4) 27 Correct response: A (Locate and name points on a coordinate plane using ordered pairs) In an ordered pair, the first number (x) indicates the number of units across and the second number (y) indicates the number of units up or down On the grid, vertex P is located at (2, 7) Incorrect responses: B Vertex Q is located at (7, 7) Incorrect choices: C Vertex R is located at (7, 2) In A, the figure has a ratio of to and is not similar to Jee’s drawing D Vertex S is located at (2, 2) In B, the figure also has a ratio of to and is not similar to Jee’s drawing In D, the figure has a ratio of to and is not similar to Jee’s drawing Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 89 28 Correct response: C 31 Correct response: A (Identify parallel, intersecting, and perpendicular lines) Parallel lines are lines that never intersect The lines in answer choice C will never intersect and thus are parallel Incorrect choices: (Solve problems involving length, perimeter, area, time, temperature, volume, and weight/mass) The weight of the stick is the total weight of the stick and rock together (3.3 lb) minus the weight of the rock (2.4 lb): 3.3 lb 2.4 lb 0.9 lb In A , the figure contains lines that are perpendicular, not parallel Incorrect choices: In B , the figure contains lines that intersect to form a pair of acute angles and a pair of obtuse angles C is the weight of the rock and stick together In D , the figure contains lines that will eventually intersect 29 Correct response: D (Identify lines of symmetry) The drawing of a candy has one vertical line of symmetry and one horizontal line of symmetry, giving it two lines of symmetry Incorrect responses: In A , the figure has radial symmetry, and thus has more than two lines of symmetry In B , the figure has one vertical line of symmetry In C , the figure has one horizontal line of symmetry 30 Correct response: B (Transform figures in the coordinate plane, e.g., translation, rotation, reflection) The figure in answer choice B has been rotated 90º about the point located at (5, 3) Incorrect choices: In A , the picture shows the figure translated units to the right B reflects a mistake in subtraction D is the result of adding 2.4 lb 3.3 lb instead of subtracting 32 Correct response: C (Solve problems involving length, perimeter, area, time, temperature, volume, and weight/mass) The perimeter of the field is two times the length plus two times the width: 2(50 m) 2(30 m) 160 m Incorrect choices: A is the result of adding the length and the width: 50 m 30 m B is the result of doubling the length and adding the width: 2(50 m) 30 m D is the area of the parking lot (50 m 30 m) instead of the perimeter 33 Correct response: C (Match 3-dimensional objects and their 2-dimensional representations e.g., nets) The figure in answer choice C can be folded to form a cube like the one shown This may be demonstrated by cutting this figure from a piece of paper and folding it Incorrect choices: In C , the picture shows a reflection of the figure In A, this figure cannot be folded to form a cube (it would have only four faces) In D , the picture shows the figure translated down units In B, this figure cannot be folded to form a cube (it would have only four faces) In D, this figure cannot be folded to form a cube because the faces have not been drawn in the correct locations 90 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 34 Correct response: A (Interpret data presented in line, bar, and circle graphs, pictographs, tables, charts) Nine classmates take the bus to school (9), while six walk and two bike (6 8), and is greater than Incorrect choices: B The same number of classmates walk (6) as drive and bike combined (4 6) C More classmates take the bus (9) than walk (6) D Fewer students bike (2) than drive (3) 35 Correct response: B (Interpret data presented in line, bar, and circle graphs, pictographs, tables, charts) Fernando made $15 in week 3, which is more than he earned in any other week Incorrect choices: A The amount of money Fernando earned increased and decreased across six weeks C The greatest decrease in the amount of money Fernando earned was between weeks and D Fernando earned the least amount of money in week 6, not week 36 Correct response: C (List all possible outcomes or construct sample spaces using lists, charts, frequency tables, and tree diagrams) The customer chooses one of the two types of pancake and one of the four toppings There are eight possible outcomes (2 4), because each of the two types of pancakes can be paired with any of the four toppings 36 (continued) Incorrect choices: A lists three possible pairs out of the six choices B lists two groupings, the pancake choices and the topping choices D lists all of the possible pairs of letters without regard to whether they are pancakes or toppings 37 Correct response: B (Find probabilities) The spinner is divided into equal spaces, and of the spaces are blue The probability that 14 the arrow will land on a blue space is 28 , or Incorrect choices: A represents the probability that the arrow will land on yellow C represents the probability that the arrow will land on red D is “1” over the number of blue spaces 38 Correct response: A (Determine and describe the mean, median, mode, and range of data) The median of the data is the number in the middle of the data set when the data are listed from least to greatest When the weights of Julio’s dogs are listed from least to greatest (23, 38, 48, 54, 82), 48 is in the middle Incorrect choices: B is incorrect; 49 is the mean of the data (245 5) C is incorrect; 59 is the range of the data (82 23) D is incorrect; 245 is the sum of the five weights 39 Correct response: C (Determine and describe the mean, median, mode, and range of data) The range is the difference between the highest temperature (32F) and the lowest temperature (14F): 32F 14F 18F Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 91 39 (continued) Incorrect choices: A is the difference between the last temperature listed (27F) and the first temperature listed (16F) B is the difference between the highest temperature and the second lowest: 32F 16F D is the sum of all the temperatures listed 40 Correct response: D (Collect, organize, display, and interpret data to solve problems) The circle graph shows that 12 of the students chose pencils; 12 of the total number of students (24) is 12 Incorrect choices: A is the denominator of the fraction of students who chose pencils B is the number of students who chose markers ( 16 of 24) C is the number of students who chose pens ( 13 of 24) 41 Correct response: B (Identify, describe, and extend numerical and geometric patterns) In the number pattern, each number is times as large as the number before it The next number in the pattern will be 16 Incorrect choices: A is the result of subtracting the first two numbers in the pattern (4 2) to determine that the rule is “ 2.” C is the result of subtracting the last two numbers in the pattern (16 8) to determine that the rule is “ 8.” D reflects a misunderstanding of the number pattern or how to describe it 42 Correct response: D (Apply basic properties and order of operations with algebraic expressions) By the associative property, ($25 $5) m $50 is equivalent to $25 ($5 m) $50 92 42 (continued) Incorrect choices: A, B, and C are incorrect; they are not equivalent to ($25 $5) m $50, and they all represent misunderstandings of the basic properties of operations 43 Correct response: A (Use algebraic expressions, patterns, and simple equations and inequalities to represent problem situations) Terry started with c crackers and then gave to Diana This situation is represented by the expression c After he gave crackers to Diana, he had 14 left That means that c 14 Incorrect choices: B The equation represents a situation in which Terry started with 14 crackers, gave away 9, and c is the number of crackers he had left C The equation represents a situation in which Terry started with c crackers, got more, and ended up with 14 D The equation represents a situation in which Terry started with 14 crackers, gave away some number (c), and ended up with 44 Correct response: C (Represent and describe mathematical relationships with lists, tables, charts, graphs, and diagrams) Answer choice C shows the relationship between the number of minutes and the cost of the call For each number of minutes, the cost is one-half, or 0.5, that number For example, the cost of a call that lasts minutes is 0.5 4, or $2.00 Incorrect choices: A shows that the number of minutes and the cost of the call are the same (the cost would be $1.00 per minute) B shows that the cost for each minute is $1.50 D shows that the total cost of a call is $0.50 per minute plus $0.50 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 45 Correct response: B (Evaluate the reasonableness of a solution) The total cost of the tickets will be the number of tickets (62) times the cost of one ticket ($8.95) By rounding these numbers to the nearest ten (60) and the nearest whole number ($9), you can determine that a reasonable estimate of the cost is 60 $9, or $540 Incorrect choices: In A, the estimate is too high by almost a power of 10 In C, the estimate is too low and may be based on 60 $5 In D, the estimate is too low and may be based on adding 60 $10 instead of multiplying Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources 93 Standardized Test Tutor: Math Grade Student Scoring Chart Student Name Teacher Name Item Numbers No Correct/ Total Number and Number Sense 1–6 /6 Operations 7–15 /9 Measurement and Geometry 16–33 /18 Statistics and Probability 34–40 /7 Patterns, Relations, and Algebra 41–45 /5 Total 1–45 /45 Item Numbers No Correct/ Total Number and Number Sense 1–6 /6 Operations 7–15 /9 Measurement and Geometry 16–33 /18 Statistics and Probability 34–40 /7 Patterns, Relations, and Algebra 41–45 /5 Total 1–45 /45 Item Numbers No Correct/ Total Number and Number Sense 1–6 /6 Operations 7–15 /9 Measurement and Geometry 16–33 /18 Statistics and Probability 34–40 /7 Patterns, Relations, and Algebra 41–45 /5 Total 1–45 /45 Test Test Test Comments/Notes: 94 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Percent (%) Percent (%) Percent (%) Standardized Test Tutor: Math Grade Classroom Scoring Chart Teacher Name Student Name Test Test Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Test 95 Notes: 96 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources ... 978-0 -54 5-09606 -5 ISBN-10: 0 -54 5-09606 -5 Copyright © 2009 by Michael Priestley All rights reserved Published by Scholastic Inc Printed in the U.S.A 10 40 15 14 13 12 11 10 09 Standardized Test Tutor: ... subtract the value of the coupon $18. 85 $ 75. 40 $93. 25 $99.20 Standardized Test Tutor: Math, Grade © Michael Priestley, Scholastic Teaching Resources Test Test Tutor says: Name 14 Little Horse Elementary... by following Test Tutor? ??s guidelines included in the pages of this book Three Different Tests There are three practice tests in this book: Test 1, Test 2, and Test Each test has 45 multiple-choice
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