# Grade K-Algebra 2. Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2

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1 Grade K-Algebra 2 Diagnostic and Placement Tests for Grades K through 8, Algebra 1, Geometry, and Algebra 2 Scoring Guide Sco ide Diagnostic Chart Intervention/Remediation simplify placement decisions suggestions for intervention and remediation suggested materials

2 Scoring Guide Placement Test 4 Student Name For each part, mark the box under the number of correctly answered questions. Number and Operations in Base Ten Number and Operations-Fractions Operations and Algebraic Thinking Measurement and Data Geometry Mark the total number correct below Total Key: Consider this student for Math Triumphs Grade 4 Strategic Intervention See page 4 for materials list. My Math, Grade 4 41 Diagnostic and Placement Tests

3 Placement Test Learning Objectives 4 Student Name In the column on the left, mark the questions that the student answered incorrectly. Domain Number and Operations in Base Ten Number and Operations Fractions Question Number Objective Compare two multi-digit numbers based on meanings of the digits in each place, using.,, and, symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. Multiply a whole number of up to four digits by a one-digit whole number using strategies based on place value and the properties of operations. Compare two multi-digit numbers based on meanings of the digits in each place, using.,, and, symbols to record the results of comparisons. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Compare two fractions with different numerators and different denominators. Explain why a fraction a is equivalent to a fraction (n 3 a) b (n 3 b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Explain why a fraction a is equivalent to a fraction (n 3 a) b (n 3 b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Compare two decimals to hundredths by reasoning about their 9 size. Use decimal notation for fractions with denominators 10 or Solve word problems involving addition and subtraction of 11 fractions referring to the same whole and having like denominators. 12 Understand a fraction a b as a multiple of 1 b. Diagnostic and Placement Tests 42

4 Domain Operations and Algebraic Thinking Measurement and Data Geometry Question Number Objective 13 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations. 14 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations. Multiply or divide to solve word problems involving 1 multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 16 Represent verbal statements of multiplicative comparisons as multiplication equations. 17 Generate a number or shape pattern that follows a given rule. 18 Generate a number or shape pattern that follows a given rule. 19 Find all factor pairs for a whole number in the range Generate a number or shape pattern that follows a given rule. 21 Generate a number or shape pattern that follows a given rule. 22 Use the four operations to solve word problems involving money. 23 Know relative sizes of measurement units within one system of units including km, m, cm. 24 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 2 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 26 Use the four operations to solve word problems involving intervals of time Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify angles (right, acute, obtuse) in two-dimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. 43 Diagnostic and Placement Tests

5 4 Student Performance Level Intensive Intervention Strategic Intervention Number of Suggestions for Intervention and Remediation Questions Correct 0 17 Use Math Triumphs to accelerate the achievement of students who are two or more years below grade level. Students should follow a personalized remediation plan. A variety of materials and instructional methods are recommended. For example, instruction and practice should be provided in print, technology, and hands-on lessons Use the additional Intervention and Remediation materials listed on the next page. This list of materials can provide helpful resources for students who struggle in the traditional mathematics program. Strategic intervention allows students to continue to remain in the My Math program, while receiving the differentiated instruction they need. Teaching Tips and other resources are also listed in the Teacher Edition. Grade 4 24 or more Use My Math. This student does not require overall intervention. However, based on the student s performance on the different sections, intervention may be required. For example, a student who missed 2 or more questions in the Measurement and Data section may require extra assistance as you cover these skills throughout the year. A Special Note About Intervention When using diagnostic tests, teachers should always question the reason behind the students scores. Students can struggle with mathematics concepts for a variety of reasons. Personalized instruction is recommended for English language learners, students with specific learning disabilities, students with certain medical conditions, or for those who struggle with traditional instructional practice. Teachers should always consider the needs of the individual student when determining the best approach for instruction and program placement. Diagnostic and Placement Tests 44

6 Grade 4 Get ConnectED Find these materials at Reteach Masters Self-Check Quizzes Chapter Readiness Quizzes Personal Tutor Math Songs Strategic Intervention Guide Additional Technology ExamView Assessment Suite A brief explanation, along with examples and exercises, for every lesson in the Student Edition (Two pages for Problem-Solving Lessons and one page per lesson for all other lessons) and included in the Chapter Resource Masters Students can check their understanding for each lesson and their results to the teacher Online assessment to use at the beginning of each chapter in the Student Edition Online instructions for step-by-step solutions for the examples of each lesson in the student textbook Collections of songs, raps, and chants Additional assessment with follow-up suggestions and activities for remediation Networkable software includes a Worksheet Builder to make worksheets and tests, a Student Module to take tests on-screen, and a Management System to keep student records 4 Diagnostic and Placement Tests

7 Mathematics Chart Centimeters LENGTH Metric 1 meter = 100 centimeters 1 centimeter = 10 millimeters Customary 1 yard = 3 feet 1 foot = 12 inches Perimeter square P = 4s rectangle P = 2l + 2w or P = 2(l + w ) TIME 1 year = 36 days 1 year = 12 months 1 year = 2 weeks 1 week = 7 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds Area rectangle A = lw or A = bh 0 Inches Diagnostic and Placement Tests 46

8 Diagnostic and Placement Grade 4 Name Date This test contains 30 multiple-choice questions. Work each problem in the space on this page. Select the best answer. Write the letter of the answer on the blank at the right. 1 Which set of numbers is in order from least 1 to greatest? A 4324, 4432, 4243, 4234 C 4243, 4234, 4324, 4432 B 4432, 4324, 4243, 4234 D 4234, 4243, 4324, To enter a dog show, Tehya must weigh her 2 Great Dane and record his weight rounded to the nearest ten pounds. Tehya s Great Dane weighs 123 pounds. Which weight should Tehya record for the dog show? F 100 pounds G 120 pounds H 12 pounds J 130 pounds 3 Find the unknown x A 46 C 3,204 B 2,86 D 3, Diagnostic and Placement Tests

9 4 Which symbol makes the number sentence 4 27,43 27,343 true? F. G, H J 1 Find the unknown y A 4 R4 C 6 B 4 R2 D 6 R4 6 Marley makes an apple pie and a blueberry pie 6 to serve at Thanksgiving dinner. After dessert, she notices that 3 8 of the apple pie remains and 1 4 of the blueberry pie remains. Which statement is TRUE concerning Marley s observation? F More apple pie remained than blueberry pie because G More blueberry pie remained than apple pie because H More apple pie was eaten than blueberry pie because 3 8, 1 4. J Both pies had the same amount remaining because Diagnostic and Placement Tests 48

10 7 What fraction is not equivalent to the fraction of 7 cows in the group of animals? A 2 6 C 1 4 B 10 D 4 8 Identify a fraction equivalent to the fraction 8 shown on the number line. 0 1/2 1 F 1 3 H 3 4 G 4 6 J Which of the following numbers is the greatest? 9 A 11.6 C 4.63 B 2.09 D Which point could represent 1.6? 10 1 P Q R S 1. 2 F Point P G Point Q H Point R J Point S 49 Diagnostic and Placement Tests

11 11 On Field Day, Camille hopped on one foot around 2 11 of the track. Payton hopped on one foot around 1 of the track. Together, how far did they hop around the track on one foot? A 1 B 2 C 3 D 4 12 Which of the following number sentences is true 12 about 8? F H G J Jordan buys twenty-four gumballs at the candy 13 store. On the way home, he chews six gumballs and gives three to his sister. How many gumballs does Jordan have left when he gets home? A 13 B 14 C 1 D Which signs go in the boxes to make the number 14 sentence true? F 4; 1 G 2; 1 H 4; 3 J 2; 3 Diagnostic and Placement Tests 0

12 1 Drew owns 4 sheets of stickers. Each sheet has 1 12 stickers. Which number sentence does not show how to find the total number of stickers Drew owns? A C B D Heather and Matt both collect rocks. Heather 16 says that she has thirty-two rocks in her collection. Matt says that he has three times as many rocks as Heather does. Which number sentence could Heather use to find the number of rocks in Matt s collection? F H G J The table below shows the number of crayons 17 in each box. If every box has the same number of crayons, how many crayons will be in 8 boxes? Number of Boxes Number of Crayons A 8 B 32 C 64 D 72 1 Diagnostic and Placement Tests

13 18 A line of ants is moving across Denise s picnic 18 blanket. She counts 6 legs on the first ant, 12 legs on the first two ants, and 18 legs on the first three ants. If Denise continues to count, how many legs will she count on the first 12 ants? F 24 legs G 6 legs H 60 legs J 72 legs 19 Which factor pair does not belong to 36? 19 A 1, 36 C 6, 6 B 2, 12 D 4, 9 20 Hector saves \$.00 of his allowance every week. 20 After 12 weeks he has \$60.00 saved. Which table could he use to show the amount of money he will save after 20 weeks? F Week Money Saved 1 \$ \$ \$ \$ \$ \$90.00 G Week Money Saved 1 \$ \$ \$ \$ \$ \$9.00 H Week Money Saved 1 \$ \$ \$ \$ \$ \$ J Week Money Saved 1 \$ \$ \$ \$ \$ \$10.00 Diagnostic and Placement Tests 2

14 21 Bianca is building a tower with wooden blocks. 21 She counts the number of blocks on each level and records it in the chart below. Level Blocks Which statement describes the number of blocks on each level of her tower? A Bianca adds 4 blocks with every level of the tower. B Bianca adds 6 blocks with every level of the tower. C Bianca subtracts 6 blocks with every level of the tower. D Bianca subtracts 4 blocks with every level of the tower. 22 Kiyoshi has three quarters, five dimes, and one 22 nickel in her piggy bank. Identify Kiyoshi s total amount of money and the operation used to calculate it. F \$1.10, addition G \$1.10, subtraction H \$1.30, addition J \$1.30, subtraction 3 Diagnostic and Placement Tests

15 23 Measure the length of the ribbon in centimeters. 23 About how long is the ribbon? A 8 centimeters B 9 centimeters C 10 centimeters D 11 centimeters 24 A classroom is shaped like a rectangle with 24 a length of 30 feet and a width of 24 feet. 30 ft 24 ft What is the perimeter in feet of the classroom? F 4 feet G 84 feet H 108 feet J 720 feet 2 What is the area of this figure? 2 A 4 square units C 7 square units B 6 square units D 8 square units Diagnostic and Placement Tests 4

16 26 Sam s baseball practice starts at 3:1. 26 His practice is hours long. What time does his practice end? F H G J 27 How many lines of symmetry are there in 27 the figure below? A 0 C B 1 D 10 Diagnostic and Placement Tests

17 28 Look at the four angles marked on the picture 28 of a bicycle. Which angle appears to be a right angle? F angle 1 H angle 3 G angle 2 J angle 4 29 The polygon below has two right angles. 29 Which side of the polygon is parallel to side AB? A BC C DE B CD D EA 30 Bella drew an angle that measured What type of angle did she draw? F right H obtuse G acute J straight Diagnostic and Placement Tests 6

18 Answers (Grade 4) Diagnostic and Placement Grade 4 Name Date This test contains 30 multiple-choice questions. Work each problem in the space on this page. Select the best answer. Write the letter of the answer on the blank at the right. 1 Which set of numbers is in order from least 1 D to greatest? A 4324, 4432, 4243, 4234 C 4243, 4234, 4324, 4432 B 4432, 4324, 4243, 4234 D 4234, 4243, 4324, To enter a dog show, Tehya must weigh her 2 G Great Dane and record his weight rounded to the nearest ten pounds. Tehya s Great Dane weighs 123 pounds. Which weight should Tehya record for the dog show? F 100 pounds H 12 pounds G 120 pounds J 130 pounds 3 Find the unknown. 3 D x A 46 C 3,204 B 2,86 D 3, Diagnostic and Placement Tests 4 Which symbol makes the number sentence 4 F 27,43 27,343 true? F. G, H J 1 Find the unknown. A y A 4 R4 C 6 B 4 R2 D 6 R4 6 Marley makes an apple pie and a blueberry pie 8 of the apple pie remains and F to serve at Thanksgiving dinner. After dessert, she notices that 3 of the blueberry pie remains. Which statement is TRUE concerning Marley s observation? F More apple pie remained than blueberry pie because G More blueberry pie remained than apple pie because H More apple pie was eaten than blueberry pie because 3 8, 1 4. J Both pies had the same amount remaining because Diagnostic and Placement Tests 48 Diagnostic and Placement Tests 172

19 Answers (Grade 4) 7 What fraction is not equivalent to the fraction of 7 D cows in the group of animals? A 2 C 6 1 B 4 10 D 4 8 Identify a fraction equivalent to the fraction 8 H shown on the number line. 0 1/2 1 F G H 3 J Which of the following numbers is the greatest? 9 A A 11.6 C 4.63 B 2.09 D Which point could represent 1.6? 10 H P Q R S F Point P G Point Q H Point R J Point S 49 Diagnostic and Placement Tests 11 On Field Day, Camille hopped on one foot around 2 11 C 11 of the track. Payton hopped on one foot around 1 of the track. Together, how far did they hop around the track on one foot? A 1 B 2 C 3 D 4 B 2 C D 4 12 Which of the following number sentences is true 12 J about 8? F H G J Jordan buys twenty-four gumballs at the candy 13 C store. On the way home, he chews six gumballs and gives three to his sister. How many gumballs does Jordan have left when he gets home? A 13 B 14 C 1 D Which signs go in the boxes to make the number 14 F sentence true? F 4; 1 G 2; 1 H 4; 3 J 2; 3 Diagnostic and Placement Tests Diagnostic and Placement Tests

20 Answers (Grade 4) 1 Drew owns 4 sheets of stickers. Each sheet has 1 A 12 stickers. Which number sentence does not show how to find the total number of stickers Drew owns? A C B D Heather and Matt both collect rocks. Heather 16 H says that she has thirty-two rocks in her collection. Matt says that he has three times as many rocks as Heather does. Which number sentence could Heather use to find the number of rocks in Matt s collection? F H G J The table below shows the number of crayons 17 C in each box. If every box has the same number of crayons, how many crayons will be in 8 boxes? Number of Boxes Number of Crayons A 8 B 32 C 64 D 72 1 Diagnostic and Placement Tests 18 A line of ants is moving across Denise s picnic 18 J blanket. She counts 6 legs on the first ant, 12 legs on the first two ants, and 18 legs on the first three ants. If Denise continues to count, how many legs will she count on the first 12 ants? F 24 legs G 6 legs H 60 legs J 72 legs 19 Which factor pair does not belong to 36? 19 B A 1, 36 C 6, 6 B 2, 12 D 4, 9 20 Hector saves \$.00 of his allowance every week. 20 H After 12 weeks he has \$60.00 saved. Which table could he use to show the amount of money he will save after 20 weeks? F Week Money Saved 1 \$ \$ \$ \$ \$ \$90.00 H Week Money Saved 1 \$ \$ \$ \$ \$ \$ G Week Money Saved 1 \$ \$ \$ \$ \$ \$9.00 J Week Money Saved 1 \$ \$ \$ \$ \$ \$10.00 Diagnostic and Placement Tests 2 Diagnostic and Placement Tests 174

21 Answers (Grade 4) 21 Bianca is building a tower with wooden blocks. 21 D She counts the number of blocks on each level and records it in the chart below. Level Blocks Which statement describes the number of blocks on each level of her tower? A Bianca adds 4 blocks with every level of the tower. B Bianca adds 6 blocks with every level of the tower. C Bianca subtracts 6 blocks with every level of the tower. D Bianca subtracts 4 blocks with every level of the tower. 22 Kiyoshi has three quarters, five dimes, and one 22 H nickel in her piggy bank. Identify Kiyoshi s total amount of money and the operation used to calculate it. F \$1.10, addition G \$1.10, subtraction H \$1.30, addition J \$1.30, subtraction 3 Diagnostic and Placement Tests 23 Measure the length of the ribbon in centimeters. 23 A About how long is the ribbon? A 8 centimeters C 10 centimeters B 9 centimeters D 11 centimeters 24 A classroom is shaped like a rectangle with 24 H a length of 30 feet and a width of 24 feet. 30 ft 24 ft What is the perimeter in feet of the classroom? F 4 feet G 84 feet H 108 feet J 720 feet 2 What is the area of this figure? 2 C A 4 square units C 7 square units B 6 square units D 8 square units Diagnostic and Placement Tests 4 17 Diagnostic and Placement Tests

22 Answers (Grade 4) 26 Sam s baseball practice starts at 3:1. 26 J His practice is 1 1 hours long. What time 2 does his practice end? F H G J 27 How many lines of symmetry are there in 27 C the figure below? A 0 C B 1 D 10 Diagnostic and Placement Tests 28 Look at the four angles marked on the picture 28 F of a bicycle. Which angle appears to be a right angle? F angle 1 H angle 3 G angle 2 J angle 4 29 The polygon below has two right angles. 29 C Which side of the polygon is parallel to side AB? A B BC C DE CD D EA 30 Bella drew an angle that measured H What type of angle did she draw? F right H obtuse G acute J straight Diagnostic and Placement Tests 6 Diagnostic and Placement Tests 176

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