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Mathematics, Grade 6

Massachusetts Comprehensive Assessment System: 1 Release of Spring 2000, 2001 & 2002 Test Items Rev. 6/03 srm

The Massachusetts

Comprehensive Assessment System

(MCAS)

Release of

2001

Test Items

Mathematics Grade 6



Use the picture below to answer question 9.

Marion wants to rent a canoe to go out on a lake. The cost is $2.00 plus $1.50 for each hour.

a. Make a table showing how much it would cost to rent a canoe for 1, 2, 3,

and 4 hours. b. Using numbers, symbols, and the variable n, write an expression for how

much it would cost to rent the canoe for n hours.

c. Marion has $14.00. What is the greatest number of hours she can rent the canoe? Show your work or explain how you found your answer.

Reporting Category for item 9: Patterns, Relations, and Algebra

Session 1, Open Response Question 9

9



Score Description

4

Student demonstrates comprehensive understanding of a pattern in a real life situation by consistently identifying correct extensions of the pattern, generalizing the pattern using an algebraic expression, and finding and explaining a solution to a problem related to the pattern.

3

Student demonstrates general understanding of a pattern by identifying the correct extension(s), generalizing the problem, and finding and explaining a solution to a problem related to the pattern with minor errors.

2 Student shows basic understanding of the concept of the pattern by identifying correct extension(s) and/or generalizing the pattern.

1 Student shows minimal understanding of the pattern.

0 Response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.

Blank No response

a)a)a)a)

b)b)b)b) n $1.50 + $2.00 = cost to rent the canoe for n hours c)c)c)c) $14.00 - $2.00 = $12.00 8 hours

8 1.5¢ 12.00 1.5 12.0 8

0 21.0

hours 1 2 3 4 cost $ 3.50 5.00 6.50 8.00

Question 9, Scoring Guide

Score Point 4



start with $2.00 for the cost

a.a.a.a. plus $2.00 $1.50 $1.50 $1.50 x 2 x 3 x 4 $3.00 $4.50 $6.00

b.b.b.b. cost to rent canoe for n hours as an –expression = $2.00 x n x $1.50

c.c.c.c. $14.00 -2.00 cost for canoe $12.00 8 $1.50 12.00 8 hours Marion has $2.00 left, so you divide $1.50 (cost per hour) into $12.00 to see how many hours she can rent it for.

Hrs. 1 2 3 4 Cost $1.50 $3.00 $4.50 $6.00Total $3.50 $5.00 $6.50 $8.00

Score Point 3



$2.00 $2.00 +1.50 1.50 $3.50 for 1 hour 1.50 $5.00 for 2 hours $2.00 2 1.50 2.00 1.50 1.50 +1.50 1.50 $6.50 for 3 hours 1.50 1.50 8.00 N + hours = 6.50 8.00 1 $3.50 +1.50 2 $5.00 9.50 3 $6.50 1.50 4 $8.00 $11.00 1.50 $12.50 7 hours 1.50 14.00

Score Point 2



1 hour 2 hour 3 hour 4 hour canoe $3.50 $7.00 $10.50 $14.00 for rent 1 hour cost $3.50 I got my answer 2 hour cost $7.00 by adding $3.50 3 hour cost $10.50 to 2 hours, 3 hours, 4 hour cost $14.00 and 4 hours.

Score Point 1

Score Point 0



Use the spinner shown below to answer question 12.

Melinda and Henry are playing a game with this three-color spinner.

a. Henry thinks that the probability of landing on gold is .

Is Henry correct?

• If he is correct, explain how you know. • If he is not correct, give the correct probability and

explain how you know it is correct.

b. If Melinda and Henry will spin the spinner 60 times in the game, about how many times can they expect it to land on each of the three colors? Explain or show how you found your answer.

c. Melinda and Henry started playing the game, and after 30 spins the

spinner had landed on black 10 times. Henry told Melinda that this shows that the probability of landing on black must be. Is Henry correct?

• If he is correct, explain how you know. • If he is not correct, tell what is the probability of landing on black.

Explain how it is possible that the spinner could have landed on black 10 times out of a total of 30 spins.

Reporting Category for item 12: Data Analysis, Statistics, and Probability


12



Score Description

4

Student demonstrates a thorough understanding of probability and expected value by correctly finding the probabilities involved, applying the probabilities to compute the expected values, and explaining that actual results may vary from expected results.

3

Student demonstrates a general understanding of probability and expected value by modeling and finding the probabilities involved, applying the probabilities to compute the expected values, and explaining that actual results may vary from expected results, with only minor errors.

2 Student demonstrates some understanding of probability and expected value.

1 Student demonstrates a minimal understanding of probability and expected value.


Blank No response

Henry is incorrect. The correct probability would be ¼ because if the board was divided into 4 sections gold would take up ¼. . They would land on gold about 15 times because 15/60 is an equivalent fraction to ¼. They would land on green about 15 times because 15/60 is an equivalent fraction of ¼. They would land on black about 30 times because 30/60 is equivalent to 2/4.


Score Point 4

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Question 12, Score Point 4 continuedQuestion 12, Score Point 4 continuedQuestion 12, Score Point 4 continuedQuestion 12, Score Point 4 continued Henry is incorrect. The probability of landing on black is ½ It is possible because a probability is definatley going to happen. I believe that Henry is correct because there is more of a chance that it will land on black because it’s ½ the circle. Green probably has the same chance because green and gold are both ¼ so they have less of a chance. If they spin the spinner 60 times then black would most likely come up 30 times because black is ½ of 60. Since green and gold are ¼ of the circle, then they would most likely come up 15 times because 15 is ½ of 30 and 30 is ½ of 60. I believe that Henry is incorrect. The probability would more likely to be 15 . 30

cccc

Score Point 3

AAAA

BBBB

CCCC



A. A. A. A. not correct, correct possibility 1111 4444 black green gold spinner really has four parts 30 B.B.B.B. black 30 2 x 0.0 = 4 120 green 15 -121 gold 15 15 0 4 60 60 C. C. C. C. correct

10101010 1111 10 out of 30 = reduced to

30303030 3333

Score Point 2



A.A.A.A. No because his chance is ¼. B.B.B.B. ?

C.C.C.C. Yes

a)a)a)a) yes he is correct because it shows on the chart. b)b)b)b) I guess it would just be lucky.

c)c)c)c) Yes he is correct because what are the odds?

Score Point 1

Score Point 0



Daniel has invented a new game with its own money system. The money system has the following three coins:

To challenge his friends to find the relationship among the values of the coins, he gave them the following three coins:

Clue 1: is the same as

Clue 2: is the same as

a. Use Clue 1 to find how many rectangles are worth the same as 1 triangle. Use words or pictures to explain your reasoning.

b. Use Clues 1 and 2 to find how many triangles are worth the same as 1

circle. Use words or pictures to explain your reasoning.

c. If 1 rectangle is worth 15 cents in U.S. money, what is the value in U.S. money of the other two coins? Explain how you found your answer.

Reporting Category for item 23: Patterns, Relations, and Algebra.


23



Score Description

4

Student demonstrates thorough understanding of models of simple linear situations by correctly solving equations represented by models, accurately explaining the process, and evaluating the expressions for given values.

3 Student demonstrates general understanding of simple linear situations by solving equations, explaining the process, and evaluating the expressions for given values, with only one minor error.

2 Student shows basic understanding of the concept of simple linear situations by solving equation(s), and/or the expression(s) for given values.

1 Student shows minimal understanding of the simple linear situations.


Blank No response

==== -2 rectangles = 1 triangle = = = = =3 triangles = 1 circle


Score Point 4

AAAA

BBBB



Question 23, Score Point 4 continuedQuestion 23, Score Point 4 continuedQuestion 23, Score Point 4 continuedQuestion 23, Score Point 4 continued = 15¢ = 30¢ = 90¢ or or = 15 15 = 30¢ 30 30 30 15 15 15 15 15 15

= ==== ==== 90¢ AAAA. . . . 2 rectangles ==== 1 triangle I know this because I thought that = 1 and so must equal 4. But when I saw the picture beside it I knew that the had taken the place of the And I also figured it was the only way because it had to add up to the amount of which was 4, so I knew =

CCCC

Score Point 3



Question 23, Score Point 3 continuedQuestion 23, Score Point 3 continuedQuestion 23, Score Point 3 continuedQuestion 23, Score Point 3 continued = B. B. B. B. 3 triangles equals 1 circle I know this because in clue 2 the sum of the triangles which I figured equaled 2 a piece added up to 8. Then I saw the equivalent next to it with which I

knew = 2. so that meant the circle had to equal 6 to fit the sum of the triangles. C.C.C.C. = 7 ½ cents = 15 cents = 90 I came up with this answer because I found out the value of which is 2 and the which is 1. And

is half of . So I did 15 ÷ 2 = 7 ½ which is the . Then for the I did is x6 = 90 which is 0. = = = = = = = = = = = =

Score Point 2



a)a)a)a) 2 rectangles are worth 1 triangle. b)b)b)b) 5 triangles are worth 1 circle.

c)c)c)c) I found my answer from finding out there are 2

rectangles in 1 triangle and 5 triangles in 1 circle and I multiplied them.

60¢60¢60¢60¢

$2.40$2.40$2.40$2.40

Score Point 1

Score Point 0



Use the ruler and protractor included in your reference sheet and the table below to answer the question.

A right triangle has one right angle. An isosceles triangle has at least 2 congruent sides. An acute triangle contains three acute angles. An obtuse triangle contains one obtuse angle.

a. Is it possible to draw a right triangle that is isosceles?

• If it is possible, draw such a triangle. Label the parts of the triangle that make it right and isosceles.

• If it is not possible, explain why it is not possible.

b. Is it possible to draw an acute triangle that is isosceles?

• If it is possible, draw such a triangle. Label the parts of the triangle that make it acute and isosceles.


c. Is it possible to draw a right triangle that is obtuse?

• If it is possible, draw such a triangle. Label the parts of the triangle

that make it right and obtuse.


Reporting Category for item 38: Geometry.


38



Score Description

4

Student shows a thorough understanding of the meaning of isosceles, acute, obtuse, and right triangles by accurately drawing the isosceles right and acute isosceles triangles and correctly explaining why it is impossible to draw an obtuse right angle.

3 Student shows a general understanding of the meaning of isosceles, acute, obtuse, and right triangles and performs the required procedures with only a minor error.

2 Student demonstrates some understanding of the meanings and applies that understanding to correctly complete a significant portion of the problem.

1 Student demonstrates minimal understanding of the types of triangles or of drawing isosceles, acute, obtuse or right triangles.


Blank No response

a.a.a.a. 1 of the two congruent sides right 1 of the 2 angle congruent sides


Score Point 4



Question 38, Score Point 4 continuedQuestion 38, Score Point 4 continuedQuestion 38, Score Point 4 continuedQuestion 38, Score Point 4 continued b.b.b.b. 2 congruent sides 1 acute angle 1 acute angle c.c.c.c. It is not possible to make a right triangle that is obtuse. to make an obtuse angle you need to make it go beyond a right angle. You cannot connect the right and obtuse angle unless you make another line which would make it a quadrilateral and it would not be considered a triangle anymore. example A.A.A.A. B.B.B.B.

Score Point 3



Question 38, Score Question 38, Score Question 38, Score Question 38, Score Point 3 continuedPoint 3 continuedPoint 3 continuedPoint 3 continued C.C.C.C. No, because it’s already a RIGHT triangle and so it has a RIGHT angle, the other angles can’t be obtuse because they have to reach between the two lines that make up the right angle. A.A.A.A. No, because then the right triangle would have 2 right angles. BBBB.... B. No, because you have to have 3 acute angle if you want an acute triangle, the side would not be congruent then. C.C.C.C. C. No, because then it would have 1 right angle and 2 acute angles instead of an right angle and one obtuse angle.

Score Point 2



No, a right triangle cannot be congruent. acute Yes: is congruent acute acute No, a right triangle cannot be obtuse.

a.a.a.a. Not possible because the are 2 different shapes that can’t go together.

b.b.b.b. Not possible because you can’t they are 2 different

shapes that can’t go together.

c.c.c.c. Yes obtuse angle right triangle

Score Point 1

Score Point 0



Jade was invited to participate in a quiz show that has two parts. There are 20 questions in each part.

• In the first part of the quiz show the contestant wins $50 for each correct

answer.

• In the second part of the quiz show the contestant wins $100 for each correct answer.

a. Jade got of the 20 questions correct in the first part. How much money did she win? Show or explain how you found your answer.

b. Jade got 40% of the 20 questions correct in the second part. How much

money did she win? Show or explain how you found your answer.

c. What part of the total possible money did Jade win? Show your answer in two of these three ways: as a fraction, as a decimal, or as a percent.

Reporting Category for item 39: Number Sense and Operations.


39



Score Description

4

The student shows a thorough understanding of fractions, decimals, and percents as applied to a real life situation by finding specified parts of the whole, effectively explaining procedures, and writing fractions, decimals, or percents to represent a part of the whole

3

The student shows a general understanding of fractions, decimals, and percents as applied to a real life situation by finding specified parts of the whole, adequately explaining procedures, and writing fractions, decimals, or percents to represent a part of the whole

2

The student shows a partial understanding of fractions, decimals, and percents as applied to a real life situation by finding specified parts of the whole, adequately explaining procedures, and/or writing fractions, decimals, or percents to represent a part of the whole

1 The student shows a minimal understanding of fractions, decimals, or percents.


Blank No response

2

a.a.a.a. she gets 700 dollars because 14 I did this because 14 is double x50

of the seven tenths and then I 706 multiplied it times the 50 dollars.

b.b.b.b. she got 800 dollars because 40% of 20 is 8 and you multiply that to 100

dollars and get 800 dollars.


Score Point 4



Question 39, Score Point 4 Question 39, Score Point 4 Question 39, Score Point 4 Question 39, Score Point 4 continuedcontinuedcontinuedcontinued

c.c.c.c. Jade got 1,500 dollars. Jade got ½ of the money and 50% of the money.

50 20 x20 x100 1000 2000 1000 2000 3000 7 x 2 = 14 aaaa. Jade won $700.00 10 2 20 2 14 x50 00 700 700 59 5 100 bbbb. Jade won $800.00 20 100.00 x8 x 8 100 40 800 1000 50 100 cccc. Jade could have won x20 x20 1,500 00 000 3,000 1,500 1000 2000 +2000 3,000 700 +800 1500

Score Point 3



aaaa. If Jade got 7 of 20 ques. correct 10 in the first part she would win $700. $50 x 14 = $700 because 7 rounded up is 14. 10 20 bbbb. Jade got 40% right she won $850. cccc. fraction – 1,550 decimal – 0.01550 3100 850 +700 1550 7 7 aaaa. 7 = 14 10 180 10 20 50 50 x14 200 50 $250 = $250 bbbb. .5 40 40 20.0 = x5 20.0 00 $500 cccc. 750 or .750 1000

Score Point 2

Score Point 1



20 40 x7 x20 140 00 - 7 +800 132 800 -10 -100 122 -100 -50 100 $72.00

Score Point 0

1111 2222



The Massachusetts Comprehensive Assessment System

(MCAS)

Release of

2002

Test Items

Mathematics Grade 6



Use the number line below to answer question 10.

a. Draw a number line like the one above in your Student Answer Booklet. Correctly position the following set of integers beneath the marks on your number line.

+10, –3, +6, +1, –9, –6

b. Explain why you decided where to place –3 on your number line.

c. Which number is greater: –10 or + 3? Explain your answer.

d. Which number is greater: –3 or –6? Explain your answer.

Reporting Category for item 10: Number Sense and Operations


10



Score Description

4 The response demonstrates an exemplary understanding of the mathematical concepts involving integers that underlie the task.

3 The response demonstrates good understanding of the mathematical concepts involving integers that underlie the task. Although there is significant evidence that the student was able to work with the concepts involved, some aspect of the response is flawed.

2 The response contains fair evidence of understanding some of the mathematical concepts involving integers that underlie the task. While some aspects of the task are completed correctly, others are not.

1 The response contains only minimal evidence of understanding the mathematical concepts involving integers that underlie the task.

0 The response contains insufficient evidence of understanding the mathematical concepts involving integers that underlie the task to merit any points.

Blank No Response.

-9 -6 -3 +1 +6 +10 I drew the numberline and made 13 little lines on the numberline. And I put –3 on the third line to the left from zero. +3 is greater than –10. -10 is below zero and +3 is above zero. Therefore +3 is greater. -3 is greater than –6. -3 is higher in the numberline. In other words it is closer to zero, on the negative side, than –6. Therefore –3 is greater than –6.


Score Point 4

AAAA

BBBB

CCCC

DDDD



a. a. a. a. -9 -6 -3 0 +1 +6 +10 b. b. b. b. I counted back 3 from zero. c.c.c.c. +3 because just be looking at the + symbol you can tell its. Greater. d.d.d.d. –3 because –6 is farthest away from 0. 10 +6 1 0 -3 -6 -9 -10 b. b. b. b. I knew where to put the 3 because everything on the right side of the 0 is – what ever number and it just goes like you would count from 0 – when it stops say to -20° c. c. c. c. +3 is greater cause it is higher than -10 cause 10 is below zero and +3 is above zero. d.d.d.d. –3, -3 is because it is on – and if you look at the line above then the –3 is higher then the –10 or 8 just look at the line to answer the question.

Score Point 3

Score Point 2



I choose to put it next to the ZERO because it’s the smallest negative number. A positive 3 is bigger because a negative –10 means you don’t have 10 there both the same. 9 3 0 6 1 6 +10 – 3, + 6 + 1 – 9 - 6 The Answer is 6 because it is bigger than 3.

Score Point 1

Score Point 0



Todd, Chi, and Janet are making posters for art class. They decide that each poster will have the same area, but different dimensions.

Todd makes his poster on a square with a side that measures 12 inches.

Chi wants to make his poster on a rectangle with a width of 8 inches.

Janet will use a right triangle with a base of 24 inches.

a. What is the area of Todd's square? Show or explain your work.

b. What would the length of Chi's rectangle need to be in order for the rectangle to have the same area as Todd's square? Show or explain your work.

c. What would the height of Janet's triangle need to be in order for the

triangle to have the same area as Todd's square? Show or explain your work.

Reporting Category for item 13: Measurement


13



Score Description

4 The response shows complete understanding of how to find the areas of triangles and parallelograms and also shows that figures with different appearances can have the same area

3 The response shows good understanding of how to find the areas of triangles and parallelograms, and also shows that figures with different appearances can have the same area.

2 The response shows basic understanding of how to find the areas of triangles and parallelograms, and also shows that figures with different appearances can have the same area.

1 The response shows a minimal understanding of how to find the areas of triangles and parallelograms, and a minimal understanding of the knowledge that figures with different appearances can have the same area.

0 The response shows neither a real understanding of how to find the areas of triangles and parallelograms, or an understanding that figures with different appearances can have the same area.

Blank No Response.

Well Todd wants a square poster and a poster has 4 equal sides so if 1 of his sides is 12 inches the rest are too. To find his area youd mytiply the length x the width, 12 x 12 = 144 sq. inches.

Chr’s Poster is a rectangle with a width of 8 inches, I’d divide 144 by 8 to find out what the length has to be. 144 ÷ 8 = 18. the length is 18 inches

Janet has a right angle triangle with a base of 24 inches, to find out an area of a triangle you mytply ½ base x height. So you’d need to find what 24 ÷ by 2 = 144. The answer is 12 Janet’s posters height is 12. 24 x 12 = 288 ÷ 2 = 144.


Score Point 4

AAAA

BBBB

CCCC



A. The area of Todd’s square is side x side. since we all know the sides of the square is equal we can just do 12 x 12. When I did that problem I got 144 in2 as my answer.

B. that would make the area of this figure 144 in2. If I do 18 x 8, I get 144 in2, so that must be the length.

C. This question is basically asking 24 x what = 144 in2. If I try 6 x 24 I get 144 in2, so 6 must be the height.

the area of todds square is 144 inches. the length would have to be 18 inches The height of THE Triangle needs to be 6.

a. The area of Todd’s poster would be 24. b. For Chris poster to be the same area as Todd’s his

length would have to be 12 inches.

c. Janets height for her Triangle would have to be 12 inches high.

Score Point 3

Score Point 2

aaaa

bbbb

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Score Point 1



Tods poster is 48” 12 12 12 12 Chris poster is 48” 16 8 8 16 Janet’s Poster 27 12 12

Score Point 0



A group of students measured their heights for a class project. The results are shown in the table below.

Students' Heights

Student Height in Centimeters

Victor 132

Tim 142

Jackie 147

Jani 141

Bill 153

Ellen 147

Maureen 135

a. What is the mode of the students' heights? b. Copy the stem-and-leaf plot below into your Student Answer Booklet.

Correctly complete the stem-and-leaf plot by entering the remaining heights. Victor's height is already shown.

c. What is the median height of the students? Show or explain your work.

d. Later, two more students joined the group; their heights were added to the

table. This did not change the median height of all nine students. What must have been correct about the heights of these two students? Show or explain your work.

Reporting Category for item 17: Data Analysis, Statistics, and Probability


17



Score Description

4 The response shows a comprehensive understanding of stem-and-leaf plots and how to interpret and draw conclusions from them.

3 The response shows a general understanding of stem-and-leaf plots and how to interpret and draw conclusions from them.

2 The response shows a basic understanding of stem-and-leaf plots.

1 The response shows a minimal understanding of stem-and-leaf plots.

0 The response is incorrect or contains some correct work that is irrelevant to the skill or concept skill or concept being measured.

Blank No Response.

The mode of the kids is the height of 147 centimeters. heights in centimeters 15 3 14 1277 13 25 132 135 141 142 147 153 //// 142 was the median of all these heights. If the median didn’t change then either they were 142 or one was above 142 and the other was below.


Score Point 4

A

B

C

D



147 mode Height C in centimeters 15 3 14 2 13 2 median number 132, 135, 141, 142, 147, 153, 154 Well that would mean the height must have been lower than 132 but higher than 154 for it to stay the same. a. a. a. a. 147 – Jackie & Ellen b.b.b.b. 15 3 14 2771 13 25 median c. c. c. c. 132, 135, 141, 142 147, 147, 153 d. d. d. d. the mode of the heights.

A

Score Point 3

B

C

D

Score Point 2



A)A)A)A) 147 is the mode in students height. B)B)B)B) Heights (in centimeters)

15 3 14 2 15 2

C)C)C)C) 13 14 15 42 14 3)42 42 8

D)D)D)D) There all in the 100’s 147 There weight may have been in the 100’s Student Height in centimeters Victor 135 Tim 142 Jackie 147 Jani 141 Bill 153 Ellen 147 Maureen 135

Score Point 1

Score Point 0

A

C D

B



Jody is making the circle graph below to show the results of the election for the sixth-grade class president. There are 520 students in the sixth grade. All 520 students voted. Each student voted for only one of four candidates.

a. What percent of the votes did Maria receive? Show or explain your work. b. How many students voted for James? Show or explain your work.

c. How many more students voted for Chan than for Sara? Show or explain

your work.

d. If the class size increases to 640, how many votes would Maria need to receive 40 percent of the votes? Show or explain your work.

Reporting Category for item 27: Number Sense Operations


27



Score Description

4 The response shows a comprehensive understanding of meaning of percents and relationships among them by analyzing and computing real-life problems.

3 The response shows a general understanding of meaning of percents and relationships among them by analyzing and computing real-life problems.

2 The response shows a basic understanding of meaning of percents.

1 The response shows a minimal understanding of meaning of percents.

0 The response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured

Blank No Response.

a.a.a.a.Maria received 35% of the votes. I know because I added the percents that the other students got, and it came out to 65%. I knew that all of the percents had to have a sum of 100%, so I subtracted 65% from 100% and got 35%. b.b.b.b. 15% of 520 78 people voted for James. 15 x 100 X 530

100 x = 7800 100 100

x = 78 c.c.c.c.Chan: Sara: 156 52 more students 30 x 20 x =104 voted for Chan than 100 X 520 100 x 520 52 for Sara.

100 = 15600 100 = 10400 100 100 100 100

x = 156 x = 104


Score Point 4



Question 27, Score Point 4 continuedQuestion 27, Score Point 4 continuedQuestion 27, Score Point 4 continuedQuestion 27, Score Point 4 continued d. d. d. d. If the class increased to 640 Maria would need 256 votes

40 x 100 X 640

100 x= 25600 100 100

x = 256 Maria received 35% of the votes. I know this because Chan received 30%, Sara got 20%, and James got 15%, when added up these percentages equal 65%. Since all 520 students voted, or 100% of the students voted there is 35% left over. Therefor Maria most have gotten 35% of the votes. 78 students voted for James. Work: 15% of 100 = 15. 15% of 500 = 75. The 75% represents 500 students ther is still 20% left. 15% of 20 = 3. So when added up, James received 78 votes. Chan received 54 more votes than Sara. 20% of 540 is 104, which is the amount of votes Sara received. Chan received 10% of 540 I added 104 and 54. So in the end this was my final conclusion: Sara received 104 votes and Chan received 54 more votes than Sara. If thr class size was 640 Maria would need 248 votes to receive 40% of the votes. I came upon this by cross multiplying and dividing to find 40% of 640. 40% of 640 is 248.

a)a)a)a) Maria received 34% of the votes. I know because I multiplied 520 by 65 and got 33.800. I then rounded it to 34 so it was 34%. I did 520 because that’s how many people voted and .65 because that’s how many votes I already know.

Score Point 3

Score Point 2



Question 27, Score Point 2 continuedQuestion 27, Score Point 2 continuedQuestion 27, Score Point 2 continuedQuestion 27, Score Point 2 continued b)b)b)b) 108 people voted for James. I know because I

multiplied the number of people who voted (520) by the number of percent that voted for James (15%). Thats how I got my answer.

c)c)c)c) 52 more people voted for Chan than Sara. I know because I multiplied each of their percents by 520 (the number of kids who voted) and Chan’s came out to be 52 more.

d)d)d)d) Maria would need 256 votes to receive 40% of the 640 kids. I once again, multiplied 640 (number of voters) by 40 (percent) and that’s how I got my answer.

A. Maria received 35% of the votes. This is because all the others kid’s percents, added together equal ed 65% 100 minus 65 = 35 so Maria got 35% of the votes: B. 80 students voted for James. This is because 15 x 5 = 80 15 is 15% of 100% so there are five hundreds in 500 so that’s 75 students and than another 5 out of the 20 left over and that’s 80. C. 10 more students voted for Chan. This is because Chan = 30% and Sarah = 20 percent and 30 – 20 = 10. D. She already has 35% so she needs five % more to get 40%. The difference between 520 and 640 is 120 and 5% of 120 is 6 so she will need 6 more votes.

Score Point 1



A. Mario got 88% of the votes. b) 15 students voted for James I go this by looking at the circle again and seeing how the percentage was. c) 10 more students voted for Chan than for Sara, I got this by subtracting Chans percentage (20) and I got 10. d) If the 6th grade had 640 students Maria would get 40 more votes so you add 88 plus 40 votes to get a total of 128 votes. % 188 % 50 % 20 % 15

Score Point 0



A booth at the State Fair is offering pony rides for children. The table below shows the relationship between the number of rides a child takes and the cost of the rides.

Pony Rides

Number Cost

1 $2.00

2 $2.50

3 $3.00

4 $3.50

5 ?

10 ?

a. If the pattern continues in the same way, what is the cost for 5 rides and

the cost for 10 rides? b. Francie had $5.50 to spend. What is the greatest number of rides she

could take? Explain how you found your answer.

c. Write an expression using n to show the cost of n rides.

Reporting Category for item 31: Patterns, Relations, and Algebra


31



Score Description

4 The response shows a comprehensive understanding of linear equations and how to solve them and represent them with rules and words.

3 The response shows a general understanding of linear equations and how to solve them and represent them with rules and words.

2 The response shows a basic understanding of linear equations.

1 The response shows a minimal understanding of linear equations.

0 The response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.

Blank No response.

5 $4.00 6 4.50 10 $6.50 8 5.50 10 6.50 8 rides I made a table until I got $5.50. $1.50 + 50¢ x n


Score Point 4

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a. The cost for 5 rides is $4.00. I know this because every ride is increased by 50¢. For ten rides it would be $6.50. I know this because for 5 rides the cost is $4.00, 50 for 10 rides it would be $6.50, if you count up.

b. If Francie had a maximum of $5.50 he could Take 8 rides. I know this because each ride is increased by 50¢. So I just counted up until I reached $5.50. You could also, write all the #’s between 5 10 then add 50¢ to all the prices, as the #’s increase.

c. key expression: “n” rides = how much # n=15 # of rides $cost 1 $2.00 2 $2.50 3 $3.00 4 $3.50 5 $4.00 10 $6.50 n $9.00

A. The cost of 5 rides $4.00 and the ten rides is $9.00. B. 8 rides because you add 50¢ until you get $5.50. C. The n rides will cost 23.00.

Score Point 3

Score Point 2



the cost of 5 rides is $4.00 and the cost of 10 rides is $8.00. She could only ride 7 times. b. She could take about three rides out of all the other rides she could do that because Adding 2.50 + 2.50 will give you 3.00. Subtract 3.00 from 5.50 and 2.50. so you’ll have an extra ride.

Score Point 1

Score Point 0

(mcas) - wrsd.netwrsd.net/instructionalsupport/mcasmathquestionsgrade6.pdf · test items...

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