XI. Mathematics, Grade 5
Grade 5 Mathematics Test The spring 2011 grade 5 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework identifies five major content strands, listed below. Specific learning standards for grade 5 are found in the Supplement to the Massachusetts Mathematics Curriculum Framework (2004). Page numbers for the grades 5–6 Framework learning standards and for the grade 5 Supplement standards appear in parentheses. ■ Number Sense and Operations (Framework, pages 25–26; Supplement, pages 7–8) ■ Patterns, Relations, and Algebra (Framework, page 34; Supplement, page 8) ■ Geometry (Framework, page 42; Supplement, page 9) ■ Measurement (Framework, page 50; Supplement, pages 9–10) ■ Data Analysis, Statistics, and Probability (Framework, page 58; Supplement, page 10) The Mathematics Curriculum Framework and Supplement are available on the Department website 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 Mathematics Curriculum Framework content strands listed above.
Test Sessions The MCAS grade 5 Mathematics test included two separate test sessions. Each session included multiple-choice, short-answer, and open-response questions. Approximately half of the common test items are shown on the following pages as they appeared in test booklets.
Reference Materials and Tools Each student taking the grade 5 Mathematics test was provided with a plastic ruler and a grade 5 Mathematics Reference Sheet. A copy of the reference sheet 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 tables at the conclusion of this chapter indicate each released and unreleased common item’s reporting category and the framework learning standard it assesses. The correct answers for released multiple-choice and short-answer questions are also displayed in the released item table.
174
Mathematics Session 1 You may use your reference sheet and MCAS ruler during this session. You may not use a calculator during this session. DIRECTIONS This session contains six multiple-choice questions, one short-answer question, and one openresponse question. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. ID:280473 C Common
1 ●
Which expression is equivalent to 106 ? A. 10 6 B. 10 6 C. 10 10 10 10 10 10 D. 10 10 10 10 10 10 10
175
Mathematics
Session 1
Question 2 is a short-answer question. Write your answer to question 2 in the box provided in your Student Answer Booklet. ID:280503 Common
2 ●
and less than 15 . Write a mixed number that is greater than 12 4 4
176
Mathematics
Session 1
Mark your answers to multiple-choice questions 3 through 7 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:261584 AL562212_tables.eps [opt_ C Common
ID:294280 B Common
3 ●
In Edward’s class, 18 of the students 24 like swimming better than they like running. What is A.
2 3
B.
3 4
C.
6 8
D.
9 12
18 24
5 ●
A cafeteria sold drinks in small, medium, and large cups one day. • The number of small cups sold was 2 times the number of medium cups sold.
in simplest form?
• The number of medium cups sold was 3 times the number of large cups sold.
Which of the following tables could represent the number of small, medium, and large cups sold on this day at the cafeteria? A.
Small 40
ID:272772 D Common
4 ●
It was reported that 6,437,193 people were living in Massachusetts in 2006.
What is the value of 4 in 6,437,193?
Number of Cups Sold
B.
A. four million
Large 10
Number of Cups Sold Small 60
B. forty thousand
Medium 20
Medium 20
Large 10
C. four hundred million D. four hundred thousand
C.
Number of Cups Sold Small 60
D.
Large 10
Number of Cups Sold Small 90
177
Medium 30
Medium 30
Large 10
Mathematics
Session 1
ID:261579 B Common
6 ●
The equation below is true. 13
20
Which of the following equations must also be true? A.
13
33
B.
26
33
C.
26
40
D.
33
33
178
Mathematics
Session 1
ID:272898 Rectangle_ER62.eps [stem C Common
Use your MCAS ruler to answer question 7. 7 ●
Tracey cut out the shape shown below.
Which of the following shapes is congruent to Tracey’s shape? A.
C.
B.
D.
179
Mathematics
Session 1
Question 8 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 8 in the space provided in your Student Answer Booklet. ID:272899 ER76_picture.eps, ER76_fl Common
8 ●
Kiesha is decorating her bedroom. She wants to put ribbon around the picture shown below.
8 inches
The picture is in the shape of an equilateral triangle. a. What is the perimeter, in inches, of the picture? Show or explain how you got your answer.
Kiesha plans to cover one wall of her bedroom with wallpaper. The wall is in the shape of a rectangle. The dimensions of the wall are 13 feet by 9 feet. b. What is the area, in square feet, of the wall? Show or explain how you got your answer. Kiesha plans to carpet the floor of her bedroom. A diagram of the floor is shown below. 6 feet 3 feet
8 feet
13 feet c. What is the area, in square feet, of the floor? Show or explain how you got your answer.
180
Mathematics Session 2 You may use your reference sheet and MCAS ruler during this session. You may not use a calculator during this session. DIRECTIONS This session contains ten multiple-choice questions, two short-answer questions, and one openresponse question. Mark your answers to these questions in the spaces provided in your Student Answer Booklet. ID:204737 D Common
● 9
ID:280695 AL852218_submarine.eps B Common
11 ●
Ari wrote the pattern below.
The graph below represents the depth, in meters, that a submarine dove over time.
2, 14, 98, 686, . . . Which of the following could be the rule for Ari’s pattern?
175
A. add 14
125
150
Depth (in meters)
Submarine Depth over Time
B. add 12 C. multiply by 14 D. multiply by 7
100 75 50 25 0
ID:272777 B Common
3 24
10 ●
Yuan needs recipe.
Which of the following is another way to write 2 3 ?
9 4
B.
11 4
C.
18 4
D.
23 4
10 15 20 25 30 35
Time (in minutes)
cups of milk for a
4
A.
5
The submarine started diving at 6:00 a.m. Based on the graph, what time did the submarine reach a depth of 100 meters? A. 6:00 a.m. B. 6:20 a.m. C. 6:50 a.m. D. 8:00 a.m.
181
Mathematics
Session 2
ID:248905 AL54116-number_line_point B Common
12 ●
ID:221154 A Common
What point on the number line below best represents the location of 6.4 ? A
B
C
D
6
7
A. point A
14 ●
Matthew wants to put 75 photos in a photo album. A full page can hold 6 photos.
What is the total number of photos that Matthew will have left over after he fills all of the pages that he can with 6 photos on each page?
B. point B
A. 3
C. point C
B. 5
D. point D
C. 6 D. 12
ID:248737 D Common
13 ●
Which of the following is equivalent to the expression below? (3
10)
(1
0.1)
(5
0.001)
A. 31.5 B. 31.05 C. 30.15 D. 30.105
182
Mathematics
Session 2
Questions 15 and 16 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:261596 Common
15 ●
What is the value of the expression below when 4
(18
5 6?
)
ID:217411 Common
16 ●
Walter made a pyramid with a base that was a square. What was the total number of edges in Walter’s pyramid?
183
Mathematics
Session 2
Mark your answers to multiple-choice questions 17 through 20 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:280510 C Common
ID:280730 AL852307_lines.eps C Common
17 ●
19 ●
Lines w, x, y, and z are shown below. w
x
Which of the following numbers is a common multiple of 6 and 8? A. 12 B. 16 C. 24
y
D. 30
z ID:207077 B Common
20 ●
What is the total number of lines that are perpendicular to line w ? A. 0
The cost of an adult ticket to a concert is $3 more than the cost of a student ticket to the same concert. If the cost dollars, which of an adult ticket is expression represents the cost of a student ticket, in dollars?
B. 1
A.
3
C. 2
B.
3
D. 3
C. 3 D. 3 ×
ID:261589 B Common
18 ●
Rafael can make 30 jars of applesauce from 2 bushels of apples. What is the total number of jars of applesauce that Rafael can make from 5 bushels of apples? A. 60 B. 75 C. 150 D. 300
184
Mathematics
Session 2
Question 21 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 21 in the space provided in your Student Answer Booklet. ID:273032 Common
21 ●
The chart below shows the attendance at a ballpark for the last 5 games.
Ballpark Attendance Game Attendance
Game 1
Game 2
Game 3
Game 4
Game 5
908
875
943
850
794
a. What is the range of attendance for the 5 games? Show or explain how you got your answer. b. What is the median attendance for the 5 games? Show or explain how you got your answer. c. The attendance for Game 6 was 861. What is the median attendance for all 6 games? Show or explain how you got your answer.
185
Massachusetts Comprehensive Assessment System Grade 5 Mathematics Reference Sheet
Massachusetts Department of
ELEMENTAR TTA AR RY Y & SECONDAR RY R Y ELEMENTARY SECONDARY
PERIMETER (P) FORMULAS
VOLUME (V) FORMULAS
perimeter 5 distance around
l w h rectangular prism . . . . . V (l 5 length; w 5 width; h 5 height)
square . . . . . . . . . . . P 4 s (s 5 length of a side)
s s s cube . . . . . . . . . . . . . . . V (s 5 length of an edge)
(2 l) (2 w) rectangle. . . . . . . . . P (l 5 length; w 5 width) triangle . . . . . . . . . . P a b c (a, b, and c are the lengths of the sides)
AREA (A) FORMULAS s s square . . . . . . . . . . . A (s 5 length of a side) rectangle. . . . . . . . . A l w (l 5 length; w 5 width) triangle . . . . . . . . . . A
1 2
b
h
(b 5 length of the base; h 5 height)
186
Grade 5 Mathematics Spring 2011 Released Items: Reporting Categories, Standards, and Correct Answers*
Standard
Correct Answer (MC/SA)*
Number Sense and Operations
5.N.1
C
176
Number Sense and Operations
5.N.7
Any mixed number greater than 3 and less than 3 43
3
177
Number Sense and Operations
5.N.13
B
4
177
Number Sense and Operations
5.N.2
D
5
177
Patterns, Relations, and Algebra
5.P.4
C
6
178
Patterns, Relations, and Algebra
5.P.3
B
7
179
Geometry
5.G.7
C
8
180
Measurement
5.M.1
9
181
Patterns, Relations, and Algebra
5.P.1
D
10
181
Number Sense and Operations
5.N.5
B
11
181
Patterns, Relations, and Algebra
5.P.6
B
12
182
Number Sense and Operations
5.N.6
B
13
182
Number Sense and Operations
5.N.3
D
14
182
Number Sense and Operations
5.N.9
A
15
183
Patterns, Relations, and Algebra
5.P.2
12
16
183
Geometry
5.G.2
8
17
184
Geometry
5.G.3
C
18
184
Patterns, Relations, and Algebra
5.P.5
B
19
184
Number Sense and Operations
5.N.8
C
20
184
Patterns, Relations, and Algebra
5.P.4
B
21
185
Data Analysis, Statistics, and Probability
5.D.1
Item No.
Page No.
1
175
2
Reporting Category
* 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 website later this year.
187
Grade 5 Mathematics Spring 2011 Unreleased Common Items: Reporting Categories and Standards
Item No.
Reporting Category
Standard
22
Number Sense and Operations
5.N.4
23
Measurement
5.M.4
24
Patterns, Relations, and Algebra
5.P.5
25
Patterns, Relations, and Algebra
5.P.4
26
Patterns, Relations, and Algebra
5.P.3
27
Data Analysis, Statistics, and Probability
5.D.2
28
Number Sense and Operations
5.N.12
29
Data Analysis, Statistics, and Probability
5.D.1
30
Measurement
5.M.5
31
Patterns, Relations, and Algebra
5.P.6
32
Geometry
5.G.5
33
Number Sense and Operations
5.N.10
34
Data Analysis, Statistics, and Probability
5.D.2
35
Data Analysis, Statistics, and Probability
5.D.3
36
Number Sense and Operations
5.N.7
37
Measurement
5.M.2
38
Number Sense and Operations
5.N.11
39
Geometry
5.G.4
40
Number Sense and Operations
5.N.14
41
Geometry
5.G.6
42
Geometry
5.G.2
188