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X. Mathematics, Grade 4 Grade 4 Mathematics Test The spring 2008 grade 4 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework identifies five major content strands, listed below. Page numbers for the grades 3–4 learning standards appear in parentheses. ■ Number Sense and Operations (Framework, pages 22–23) ■ Patterns, Relations, and Algebra (Framework, page 32) ■ Geometry (Framework, page 40) ■ Measurement (Framework, page 48) ■ Data Analysis, Statistics, and Probability (Framework, page 56) The Mathematics Curriculum Framework is available on the Department Web site at www.doe.mass.edu/frameworks/current.html. In Test Item Analysis Reports and on the Subject Area Subscore pages of the MCAS School Reports and District Reports, Mathematics test results are reported under five MCAS reporting categories, which are identical to the five Framework content strands listed above. Test Sessions The MCAS grade 4 Mathematics test included two separate test sessions. Each session included multiple- choice, short-answer, and open-response questions. Reference Materials and Tools Each student taking the grade 4 Mathematics test was provided with a plastic ruler and a grade 4 Mathematics Tool Kit. A copy of the tool kit follows the final question in this chapter. An image of the ruler is not reproduced in this publication. The use of bilingual word-to-word dictionaries was allowed for current and former limited English proficient students only, during both Mathematics test sessions. No calculators, other reference tools, or materials were allowed. Cross-Reference Information The table at the conclusion of this chapter indicates each item’s reporting category and the Framework learning standard it assesses. The correct answers for multiple-choice and short-answer questions are also displayed in the table. 260 Mathematics SeSSion 1 You may use your tool kit and MCAS ruler during this session. You may not use a calculator during this session. DIRECTIONS This session contains twelve multiple-choice questions, two short-answer questions, and three open-response questions. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. ID:228590 3221504_AR1.eps, 3221504_ B Common ID:227459 EBH239_map.eps A Common ● 1 Angelo used the rule “add 4, subtract 2” to make a number pattern, as shown below. 2 ● The map below shows Kim’s neighborhood. Kim’s Neighborhood 11 15 13 17 15 19 4 –2 4 –2 4 Elm Drive Pine Road e Which of the following number patterns u ven uses the same rule? kA Oa A. Main Street 10 14 18 14 12 16 B. M 10 14 12 16 14 18 ap le La ne C. 10 14 10 18 22 20 Which street is parallel to Main Street? D. A. Elm Drive 10 14 16 18 24 26 B. Maple Lane C. Oak Avenue D. Pine Road 261 Mathematics Session 1 ID:227363 227363_clues.eps C Common ID:227464 EBH243_lines_of_symmetry. B Common ● 3 Jamal’s clues about his mystery number are shown in the box below. ● 5 Which of the following shapes has more than one line of symmetry? A. My number has 5 tens 8 thousands 2 ones 6 ten thousands B. 0 hundreds What is Jamal’s mystery number? C. A. 5,826 B. 6,285 C. 68,052 D. 86,520 D. ID:227388 C Common ● 4 Mr. Dolan bought 9 boxes of erasers. There were 12 erasers in each box. How many erasers did Mr. Dolan buy? A. 96 B. 98 C. 108 D. 120 262 Mathematics Session 1 ID:227510 EBH264_school.eps [stem_0 D Common ● 6 The tally chart below shows the different ways the 24 students in Ms. Mitchell’s class get to school. How We Get to School Way Number of Students car bus bike walk Which circle graph best represents the information in the tally chart? A. How We Get to School C. How We Get to School car car bus bus walk bike walk bike B. How We Get to School D. How We Get to School car car bus bus walk bike walk bike 263 Mathematics Session 1 ID:227592 AL4213_Scale.eps A Common ID:218935 TK0407_map.eps D Common ● 7 The grid below shows the locations of some places in Jim’s neighborhood. ● 9 The scale shown below is balanced. Each has the same weight, and each 1 block has the same weight. 8 Jim’s 1 block 7 house 6 Library 5 4 3 School 2 Park 1 How many are needed to balance 0 1 2 3 4 5 6 7 8 five ? Moving along the grid lines, what is the A. 10 least number of blocks from Jim’s house to the school? B. 11 C. 15 A. 3 D. 18 B. 4 C. 6 D. 7 ID:229061 C Common ● 8 What is the solution to the following problem? 162 3 ? A. 50 R2 B. 51 R1 C. 54 D. 57 264 Mathematics Session 1 Question 10 is an open-response question. • BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. • Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. • If you do the work in your head, explain in writing how you did the work. Write your answer to question 10 in the space provided in your Student Answer Booklet. ID:250869 TK0464_Park.eps, Perimete Common ● 10 The grid below represents Ginger’s garden. Ginger’s Garden 1 foot 1 foot a. What is the perimeter, in feet, of Ginger’s garden? Show or explain how you got your answer. Perimeter is the distance around a shape. b. What is the area, in square feet, of Ginger’s garden? Show or explain how you got your answer. Ginger wants to increase the area of her garden so that it is 96 square feet. Her garden will still be a rectangle. c. What could be the length and width of Ginger’s garden after she increases the area? Show or explain how you got your answer. 265 Mathematics Session 1 Questions 11 and 12 are short-answer questions. Write your answers to these questions in the boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. ID:227603 Common ● 11 What is the value of that makes the number sentence below true? 2 160 ID:247633 Common ● 12 Write a decimal that is equivalent to the fraction below. 1 4 266 Mathematics Session 1 Question 13 is an open-response question. • BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. • Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. • If you do the work in your head, explain in writing how you did the work. Write your answer to question 13 in the space provided in your Student Answer Booklet. ID:250554 Common ● 13 The chart below shows the numbers of students at four different schools. Number of School Students Pine Street 517 Apple Lane 675 Sanders 419 East Side 566 a. Use estimation to decide which school has about 100 fewer students than Apple Lane School. Show or explain your estimation strategy. All the students at the schools are going to form two teams for a reading contest. • There will be two schools on each team. • The teams will each have about the same number of students. b. Use estimation to decide which two schools should be on each team. Show or explain your estimation strategy. 267 Mathematics Session 1 Mark your answers to multiple-choice questions 14 through 16 in the spaces provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. ID:218881 A Common ID:219003 TK0433_spinners.eps [opt_ A Common ● 14 Which number is equivalent to three hundredths? ● 16 On which of the following spinners is the arrow most likely to land on a section labeled B? A. 0.03 B. 0.30 A. C. 3.00 Y B D. 300 B G ID:218884 B Common ● 15 Ms. Caruso wants to arrange 16 desks in rows to form a square. B. Which of the following number sentences shows how all of the desks G Y can be arranged in rows to form a square? B B A. 2 8 16 Y G B. 4 4 16 C. 4 12 16 D. 8 8 16 C. B Y G B Y Y B G D. Y G B 268 Mathematics Session 1 Question 17 is an open-response question. • BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. • Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. • If you do the work in your head, explain in writing how you did the work. Write your answer to question 17 in the space provided in your Student Answer Booklet. ID:250841 Common Use the two triangles labeled 1 from your tool kit to answer question 17. ● 17 For all parts of this question, the triangles should be lying flat on your desk. • The triangles must be label side up. • The triangles may touch but not overlap. a. Put the triangles together so that a side labeled a is next to a side labeled c. What shape did you make when you put the two triangles together in this way? Explain how you know. b. Put the triangles together so that the sides labeled b are next to each other. What shape did you make when you put the two triangles together in this way? Explain how you know. c. Make a shape with the two triangles that is different from the shapes you made in parts (a) and (b). Only congruent sides may touch, and they must match exactly. In your Student Answer Booklet, trace your shape and label the sides of both triangles with the correct letters. d. What shape did you make in part (c)? Explain how you know. 269 Mathematics SeSSion 2 You may use your tool kit and MCAS ruler during this session. You may not use a calculator during this session. DIRECTIONS This session contains seventeen multiple-choice questions, three short-answer questions, and two open-response questions. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. ID:250435 B Common ID:247703 EBH526_A_B.eps A Common ● 18 There are 22 students in a class. There are students absent today. 20 ● Figure G, figure H, and a line are shown below. Which of the following represents the number of students who are in class today? A. 22 B. 22 C. 22 D. 22 G H ID:228799 C Common ● 19 The population of Keith’s hometown is 57,619. What is 57,619 rounded to the nearest thousand? Ping believes that figure G and figure H A. 55,000 are congruent. B. 57,000 Which of the following best describes C. 58,000 how Ping could move figure G so that it D. 60,000 exactly covers figure H? A. Reflect (flip) figure G over the line. B. Translate (slide) figure G over the line. C. Rotate (turn) figure G 90° clockwise, and translate (slide) it over the line. D. Rotate (turn) figure G 90° clockwise, and then reflect (flip) it over the line. 270 Mathematics Session 2 ID:247536 EBH488_groups.eps [opt_a0 A Common ● 21 Juan used a model to solve the problem below. Bob had 28 strawberries to share equally among 4 friends. How many strawberries did each friend get? Which of the following could be Juan’s model? A. C. B. D. XXXX 271 Mathematics Session 2 ID:273868 EBH479_candy_bars.eps D Common ID:247759 EBH544_line.eps C Common ● 22 Ken is using the two rectangles shown below to compare fractions. Use your MCAS ruler to answer question 23. ● 23 Julie drew the line segment shown below. Keegan drew a line segment that was 2 inches longer than Julie’s line segment. Which of the following is closest to the length of Keegan’s line segment? 1 A. inch 4 B. 2 1 inches 4 C. 4 1 inches 4 Which of the following is true? 1 1 D. 6 1 inches A. 3 2 4 1 3 B. 3 6 1 3 C. 3 6 ID:247586 D Common 1 2 ● 24 All the students in Mr. Conner’s class are working in groups. There are 6 groups of D. 3 6 4 students and 1 group of 3 students. What is the total number of students in Mr. Conner’s class? A. 18 B. 24 C. 26 D. 27 272 Mathematics Session 2 ID:222172 3247438_AR1.eps, 3247438_ C Common ID:250317 A Common ● 25 Two number sentences are shown below. ● 26 Erin recorded the height of a tomato plant each week for four weeks. Which of the following would be best for Erin 4 4 9 9 to use to display the change in the height of the tomato plant? 11 11 A. a line graph B. a pictograph What values for and make C. a circle graph both number sentences true? D. a Venn diagram A. 7 4 B. 6 5 C. 5 6 D. 2 9 273 Mathematics Session 2 Question 27 is an open-response question. • BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. • Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. • If you do the work in your head, explain in writing how you did the work. Write your answer to question 27 in the space provided in your Student Answer Booklet. ID:250388 Common ● 27 Lee wrote the number sentence shown below to represent the rule for his input-output table. input output ↓ ↓ n3 p a. Copy Lee’s table below into your Student Answer Booklet. Use Lee’s number sentence to complete the table. Lee’s Table Input n 1 2 5 10 12 Output p b. Lee’s friend Maya wrote the input-output table below. Maya’s Table Input n 5 6 8 12 21 Output p 3 4 6 10 19 Write a number sentence to represent the rule for Maya’s table. Use n for the input and p for the output. c. A new input-output table is shown below. Input n 1 2 5 7 Output p 4 20 28 36 What are the missing numbers that complete the input-output table? Show or explain how you got each of your answers. 274 Mathematics Session 2 Questions 28, 29, and 30 are short-answer questions. Write your answers to these questions in the boxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. ID:219076 TK0465-bags-of-marbles.ep Common ● 28 Cassie has three black marbles and four white marbles, as shown below. Each marble is the same shape and size. Cassie will put all her marbles into a bag. She will pick a marble out of the bag without looking. What is the probability that Cassie will pick a black marble? Write your answer as a fraction. 275 Mathematics Session 2 Write your answers to questions 29 and 30 in the boxes provided in your Student Answer Booklet. ID:219075 TK0461-alan.eps Common ● 29 Alan painted his name on a grid, as shown below. = 1 square unit What is the total area, in square units, that Alan painted? ID:219065 TK0442-number-line.eps Common ● 30 Mr. Miller drew the number line shown below. P 0 1 1 2 What fraction best represents the location of point P ? 276 Mathematics Session 2 Question 31 is an open-response question. • BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. • Show all your work (diagrams, tables, or computations) in your Student Answer Booklet. • If you do the work in your head, explain in writing how you did the work. Write your answer to question 31 in the space provided in your Student Answer Booklet. ID:219127 TK0496_data.eps, TK0469_l Common ● 31 On Monday, Ms. Smith asked her students to write the number of hours they spent reading over the weekend. Their answers are shown below. 2 4 6 2 0 3 2 3 4 6 4 4 3 2 8 5 a. In your Student Answer Booklet, copy the number line below. 0 1 2 3 4 5 6 7 8 Based on the answers the students wrote, make a line plot using the number line you copied. Be sure to label your line plot. b. How many of Ms. Smith’s students read 4 or more hours over the weekend? Use your line plot to explain how you know. 277 Mathematics Session 2 Mark your answers to multiple-choice questions 32 through 39 in the spaces provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test booklet. ID:218917 TK0395_cds.eps C Common ID:247595 C Common ● 32 The CDs in the box shown below all cost the same amount. ● 34 Mr. Janson bought 47 packs of pencils. There are 22 pencils in each pack. Which of the following has a value that is closest to the number of pencils Mr. Janson bought? A. 40 20 B. 40 30 CDs: 4 for $20.00 C. 50 20 D. 50 30 How much does one CD cost? A. $4.00 B. $4.50 C. $5.00 D. $5.50 ID:273874 B Common ● 33 The Blakes spent $8,762 to paint their house. They also spent $987 to repair the roof. What was the total amount the Blakes spent to paint their house and repair the roof? A. $7,775 B. $9,749 C. $9,750 D. $18,632 278 Mathematics Session 2 ID:250360 SEB_leaf_graph.eps A Common ID:218912 B Common ● 35 The graph below shows how much money Chris earned each day last week ● 36 Ms. Martin played a number game with her class. Every time a student said raking leaves. a number, Ms. Martin used a rule to change it to a new number. The table Money Chris Earned below shows the students’ numbers and Raking Leaves Ms. Martin’s new numbers. 27 Number Game 24 Money Earned (dollars) 21 Students’ New 18 Numbers Numbers 15 8 4 12 16 8 9 20 10 6 32 16 3 0 Ms. Martin used the same rule each time. Mon. Tue. Wed. Thu. Fri. Sat. Sun. Which of the following could be Day Ms. Martin’s rule? Chris earns $6 per hour for raking A. subtract 4 leaves. How many hours did he rake B. divide by 2 leaves on Saturday? C. subtract 10 A. 4 hours D. divide by 4 B. 8 hours C. 12 hours D. 24 hours 279 Mathematics Session 2 ID:247561 B Common ID:273875 TK0434_hat.eps D Common ● 37 Which number sentence is not true? ● 38 Marcus will pick a number card from the hat shown below without looking. Each A. 7 8 5 15 5 number card is the same size and shape. B. 7 8 5 15 7 C. 7 8 5 5 8 7 D. 7 8 5 8 7 5 3 4 2 3 1 2 3 1 3 2 What is the probability that Marcus will pick a card with the number 3 on it? 4 A. 6 6 B. 10 3 C. 6 4 D. 10 280 Mathematics Session 2 ID:247623 EBH505_game.eps A Common ● 39 Pat and Meg wrote their names in some of the squares on a grid, as shown below. Pat Meg Pat Pat Meg Meg Meg Pat Meg Meg Which number sentence shows the fraction of squares on the grid that have Pat’s name or Meg’s name in them? 4 6 10 A. 12 12 12 4 6 10 B. 12 12 24 4 6 10 C. 8 6 14 4 6 10 D. 2 2 2 281 Massachusetts Comprehensive Assessment System Grade 4 Mathematics Tool Kit a b a b 1 1 c c 282 Grade 4 Mathematics Spring 2008 Released Items: Reporting Categories, Standards, and Correct Answers* Correct Answer Item No. Page No. Reporting Category Standard (MC/SA)* 1 261 Patterns, Relations, and Algebra 4.P.1 B 2 261 Geometry 4.G.5 A 3 262 Number Sense and Operations 4.N.1 C 4 262 Number Sense and Operations 4.N.11 C 5 262 Geometry 4.G.8 B 6 263 Data Analysis, Statistics, and Probability 4.D.2 D 7 264 Geometry 4.G.6 D 8 264 Number Sense and Operations 4.N.13 C 9 264 Patterns, Relations, and Algebra 4.P.4 A 10 265 Measurement 4.M.4 11 266 Patterns, Relations, and Algebra 4.P.3 80 12 266 Number Sense and Operations 4.N.5 0.25 13 267 Number Sense and Operations 4.N.17 14 268 Number Sense and Operations 4.N.6 A 15 268 Number Sense and Operations 4.N.7 B 16 268 Data Analysis, Statistics, and Probability 4.D.6 A 17 269 Geometry 4.G.9 18 270 Patterns, Relations, and Algebra 4.P.2 B 19 270 Number Sense and Operations 4.N.16 C 20 270 Geometry 4.G.7 A 21 271 Number Sense and Operations 4.N.8 A 22 272 Number Sense and Operations 4.N.4 D 23 272 Measurement 4.M.5 C 24 272 Number Sense and Operations 4.N.10 D 25 273 Patterns, Relations, and Algebra 4.P.3 C 26 273 Data Analysis, Statistics, and Probability 4.D.1 A 27 274 Patterns, Relations, and Algebra 4.P.6 3 28 275 Data Analysis, Statistics, and Probability 4.D.4 7 29 276 Measurement 4.M.4 32 3 30 276 Number Sense and Operations 4.N.3 8 31 277 Data Analysis, Statistics, and Probability 4.D.3 32 278 Patterns, Relations, and Algebra 4.P.5 C 33 278 Number Sense and Operations 4.N.12 B 34 278 Number Sense and Operations 4.N.17 C 35 279 Data Analysis, Statistics, and Probability 4.D.3 A 36 279 Patterns, Relations, and Algebra 4.P.6 B 37 280 Number Sense and Operations 4.N.9 B 38 280 Data Analysis, Statistics, and Probability 4.D.4 D 39 281 Number Sense and Operations 4.N.18 A * Answers are provided here for multiple-choice items and short-answer items only. Sample responses and scoring guidelines for open-response items, which are indicated by shaded cells, will be posted to the Department’s Web site later this year. 283