Math On Your Own

IndependentMath

Problem-SolvingActivities

Level C

On Your OwnMATHEMATICS

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Mathematics On Your Own

……………

Independent Math Problem-Solving Activities Grade Levels 3-8 Students work independently to reinforce math skills during summer vacation. Parts 1 & 2 Mathematical Problems with Multiple-Choice Questions

• Multiple-Step problems • Higher-Level problems • Stamina Builder

Part 3 Open-Ended Problems • Higher-Level Short and Extended-Response Math Problems

Answer Key includes answers and scoring rubrics with possible answers for open-ended questions.

Level Grade (prefix: 978-1-4204)

Level 25-Pack 100-Pack C 3 7046-8 7047-5 D 4 7049-9 7050-5 E 5 7052-9 7053-6 F 6 7055-0 7056-7 G 7 7058-1 7059-8 H 8 7061-1 7062-8

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Mathematics On Your Own • Level C

2 © RALLY! EDUCATION. NO PART OF THIS DOCUMENT MAY BE REPRODUCED WITHOUT WRITTEN PERMISSION OF THE PUBLISHER.

ISBN 978-1-4204-7045-1R 7045-1

Copyright ©2013 RALLY! EDUCATION. All rights reserved. No part of the material protected bythis copyright may be reproduced in any form by any means, electronic or mechanical, includingphotocopying, recording, or by any information storage and retrieval system, without permissionin writing from the copyright owner. Printed in the U.S.A.

0512.MAQ

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Contents

Mathematics On Your Own

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Part 1: Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Part 2: Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Part 3: Open-Ended Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Ruler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Answer Key

RALLY!’s Math Strands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Part 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Total Your Score. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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Introduction

Mathematics On Your Own:Independent Math Problem-Solving Activities

Mathematics On Your Own gives you problem-solving activities to reinforce your math skills.

Parts 1 & 2: Mathematical Problems with Multiple-Choice Questions

• Multi-Step problems• Higher-Level problems• Stamina Builder

Each multiple-choice problem is worth 1 point.

Part 3: Open-Ended Math Problems

• Higher-Level Short and Extended-Response Math Problems

Some open-ended problems are worth 2-points. Problems that require greater stamina are worth 3-points.

The answer key in the back of the book includes answers to the problems and scoring rubrics for open-ended questions. You can remove the answer key if you choose to.

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Mathematics On Your Own • Level C Part 1


Part 1Multiple-Choice Questions

Directions

Part 1 asks only multiple-choice questions. Each question has only one correct answer.

Read the questions and answer choices very carefully. Be sure to markthe answer you have selected.

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Part 1 Mathematics On Your Own • Level C


Sample questionsRead each sample question and mark your answer for each one.

S1 Look at the equation below.

46 � 24 � 70

Which operation belongs in the box?

A �

B �

C �

C �

S2 Maggie’s piano lesson begins at 3:30 P.M. and ends at 4:00 P.M.How long is her lesson?

A 20 minutes

B 30 minutes

C 45 minutes

D 60 minutes

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Directions

For Part 1, read each question and mark your answer for each one.

1 Which of the following is the value of the digit 7 in 879?

A 7

B 70

C 77

D 700

2 Which number shows 637 rounded to the nearest ten?

A 600

B 630

C 640

D 700

3 Which fraction has the numerator 3?

A �13

�

B �23

�

C �34

�

D �45

�

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4 Look at the grid below.

Which decimal represents the SHADED portion of this model?

A 0.40

B 0.42

C 0.43

D 0.58

5 The weather report says that there is a 90% chance of snow. Which word describes this event?

A certain

B likely

C unlikely

D impossible

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6 Sandy made 5 bracelets each week for 3 weeks. Which model shows how many bracelets she made IN ALL?

A

B

C

D

7 Look at the equation below.

5 � � � 40

Which number belongs in the box?

A 7

B 8

C 35

D 45

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8 Alex wants to buy a bike that costs $150. He has saved $82. Whichequation shows how much more Alex needs to save for his bike?

A 150 � 82 � b

B 150 � 82 � b

C 82 � b � 150

D 150 � b � 82


24 � 3 � 8


A �

B �

C �

D �

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10 Which of the following shows a right angle?

A

B

C

D

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11 Which solid figure has a curved surface and no faces?

A cube

B cylinder

C sphere

D pyramid

12 Which pair of shapes is congruent?

A

B

C

D

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13 Which letter has one line of symmetry?

A B

B F

C P

D L

14 Juan measures the sides of a triangle.

4 feet 2 inches

2 feet 8 inches

� 3 feet 7 inches

What is the sum of its measurements?

A 9 feet 7 inches

B 9 feet 16 inches

C 10 feet 3 inches

D 10 feet 5 inches

15 Josh filled a box with cubes. The box had 2 rows of 5 cubes along the bottom and was 3 layers high. How many cubes fit into the box?

A 10 cubes

B 13 cubes

C 20 cubes

D 30 cubes

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16 It is 1:00 P.M. Rose has been weeding the garden for 40 minutes. At what time did Rose START weeding?

A 12:20 P.M.

B 12:40 P.M.

C 1:30 P.M.

D 1:40 P.M.

17 Tess has 3 pennies, 4 nickels, 6 dimes, 5 quarters, and 1 dollar bill. How much money does Tess have?

A $2.88

B $2.98

C $3.03

D $3.08

18 Anthony bought 3 notebooks for $21.00 and 5 markers for $3.95. Hestopped for lunch and had a tuna sandwich. Then he bought a juice for$1.25.

What other information is needed to find how much Anthony spent IN ALL?

A how much each notebook cost

B how much the tuna sandwich cost

C how long he stopped for lunch

D what sort of juice he bought

12

6

48

210

39

11 1

57

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19 Mr. Bell bought 5 dozen pencils for his class. Each of his 20 studentsreceived an equal number of pencils. Joe wants to work out how manypencils each student received. What is the BEST way to make thisproblem simpler?

A multiply 5 times 20

B find out how many pencils are in 5 dozen

C divide 20 by 4

D estimate how many pencils Mr. Bell bought

20 60 � 4 �

A 24

B 64

C 240

D 640

21 �59

� � �29

� �

A �39

�

B �13

�

C �79

�

D �89

�

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22 Which of the following is the same as 7 � 3?

A 7 � 3

B 7 � 7 � 7

C 3 � 3 � 3

D 7 � 3 � 3 � 3

23 �15

� � �45

� �

A �35

�

B �45

�

C �140�

D 1

24 What is the next number in the following pattern?

7, 14, 21, 28, 35, ___

A 39

B 40

C 42

D 49

25 2 � 8 �

A 6

B 10

C 16

C 18

26 Which of the following shapes is a cylinder?

A B C D

27 Santos purchased a book for $15.95 and a magazine that cost $4.25. Which of the following is the BEST estimate of the total amount he spent?

A $18.00

B $19.00

C $20.00

D $21.00

28 Kim wants to check if 6 � 3 � 2 is correct. Which number sentenceshould he use?

A 6 � 3 � 18

B 6 � 3 � 3

C 3 � 2 � 6

D 3 � 2 � 5


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29 �58

� � �28

� �

A �28

�

B �38

�

C �48

�

D �58

�


6, 12, 18, 24, 30, ___

A 34

B 35

C 36

D 38

31 5 � 6 �

A 25

B 30

C 35

D 40


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STOP

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Part 2Multiple-Choice Questions

Directions

Part 2 asks only multiple-choice questions. Each question has only one correct answer.

Read the questions and answer choices very carefully. Be sure to markthe answer you have selected.

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1 Which of these is nine hundred ninety-three?

A 93

B 903

C 933

D 993

2 Which of these is the same as four hundred seventy-three?

A 40 � 7 � 3

B 400 � 70 � 3

C 400 � 700 � 3

D 4 � 7 � 3

3 Which model shows a fraction equivalent to �23

�?

A

B

C

D

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4 The circle graph shows the favorite kind of juice in Mr. Moore’s class.Which fraction shows the number of students who chose grape juice astheir favorite?

A �18

�

B �14

�

C �13

�

D �12

�

5 647 � 233 �

A 414

B 800

C 870

D 880

Cran- berry

Apple

Grape

Orange

Favorite Juice

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6 Mario has 35 markers to share equally between 5 friends. Which modelshows how many markers one friend will receive?

A

B

C

D

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7 96 � 42 �

A 56

B 44

C 54

D 72

8 John estimated that 68 � 16 is about 40. What is a better ESTIMATE?

A 50

B 70

C 80

D 90

9 Ira bought 24 apples. He gave 6 to his brother. Then his sister gave him 4 of her apples. Which equation shows how many apples Ira has now?

A 24 � 6 � 4 � a

B 24 � 6 � 4 � a

C 24 � 6 � 4 � a

D 24 � 6 � 4 � a

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7 � 7 � 49


A �

B �

C �

D ÷


5, 20, 35, 50, 65, ___

A 70

B 75

C 80

D 85

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12 Which number line shows the position of 4?

A

B

C

D

0 10

P

0 10

N

0 10

M

0 10

R

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13 Which clock appears to have a right angle?

A

B

C

D

12

6

48

210

39

11 1

57

12

6

48

210

39

11 1

57

12

6

48

210

39

11 1

57

12

6

48

210

39

11 1

57

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14 Which of the following BEST describes AB?

A end point

B line segment

C curve

D face

15 Which of the following does NOT show a line of symmetry?

A

B

C

D

A B

C

E

D

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16 Toby ran 3,000 meters on Tuesday. How many KILOMETERS did herun?

A 50 kilometers

B 30 kilometers

C 3 kilometers

D 5 kilometers

17 Brad plans to tile his kitchen floor. How many square tiles will he needto cover the kitchen floor?

A 13 square tiles

B 26 square tiles

C 32 square tiles

D 40 square tiles

18 Taylor started cleaning her bedroom at 12:15 P.M. and finished 1 hour 30 minutes later. What time did she FINISH cleaning her bedroom?

A 1:15 P.M.

B 1:30 P.M.

C 1:45 P.M.

D 2:00 P.M.

= 1 square tile

Kitchen Floor

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19 Jacob wants to buy a notebook for $1.95 and a marker for $3.25. Jacobhas $5.00. How much MORE money does Jacob need?

A $0.10

B $0.20

C $1.00

D $5.20

20 Maggie bought 3 packets of pens. Each packet had 6 pens in it. Howmany pens did Maggie buy IN ALL?

A 2

B 9

C 18

D 24


24 � y � 3

What is the value of y?

A 6

B 10

C 21

D 23

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22 10 � 10 �

A 20

B 100

C 110

D 1,000


15 � x � 5

What is the value of x?

A 3

B 15

C 20

D 25

24 Which of the following shapes is a quadrilateral?

A

B

C

D

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25 Megan purchased a sweater for $25.99 and a shirt for $9.99. Which ofthe following is the BEST estimate of the total amount she spent?

A $27.00

B $35.00

C $36.00

D $40.00

26 Ray leaves his house for school at 8:30 A.M. each morning. He waits 5 minutes for his friend Mike to arrive so they can walk to schooltogether. It takes Ray and Mike about 5 minutes to walk one block. He arrives at school at 9:00 A.M. From the time Ray leaves his house,how long does it take for him to get to school?

A 20 minutes

B 25 minutes

C 30 minutes

D 40 minutes

27 2 � 12 �

A 6

B 14

C 22

D 24

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56 � 34 � 90


A �

B �

C �

D �

29 Sam reads 3 books each month. How many books does Sam read in 6 months?

A 2

B 18

C 9

D 3

30 �27

� � �17

� �

A �07

�

B �17

�

C �27

�

D �37

�

STOP

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Part 3Open-Ended Questions

Directions

Part 3 asks only open-ended questions.

Since you may receive partial credit for many of the problems, it isimportant to show ALL work in the spaces provided in this book.When you see the words Show All Work, be sure to

• show all the steps needed to solve the problem• make your handwriting clear and easy to read• write the answer on the answer line

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1 Ling has 24 stickers to share equally among 4 friends. Complete thenumber sentence below to tell how many stickers each friend received.

Number Sentence � �

On the lines below, write a MULTIPLICATION number sentence that belongs to the same fact family as the sentence above.

Number Sentence � �

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2 Mr. Summers bought 3 half gallons of grape juice, 2 quarts of cranberryjuice, and 1 gallon of apple juice for his class. How many GALLONS ofjuice did he buy IN ALL?

Show All Work

Answer gallons

How many QUARTS of juice did he buy in all?

Answer quarts

On the lines below, explain how you found how many quarts of juiceMr. Summers bought.

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3 How is five hundred eighty-nine written in standard form?

Answer

How is the number written in expanded form?

Answer � �

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4 Ray has the coins shown below.

Ray wants to buy a marker that costs 95¢. After Ray buys the marker,how much money does he have left?

Answer

Ray’s friend gives him two dimes. How much money does Ray have now?

Answer

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5 In the box below are the numbered ticket stubs from the movie theater.

List the ODD numbered stubs.

Answer

List the EVEN numbered stubs.

Answer

On the lines below, explain how you know which of the numbers are even.

31

979

351

788

99222223

54

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6 Students at the Burr School sold raffle tickets for new school computers.The chart below shows the number of raffle tickets each class sold.

On the lines below, write the number of tickets sold in order fromGREATEST to LEAST.

, , ,

On the line below, write a number sentence that shows the SUM ofraffle tickets sold at the Burr School.

Number Sentence

How many raffle tickets did the school sell?

Answer raffle tickets

Grade Tickets 1 63 2 95 3 78 4 89

Tickets Sold

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7 The circle graph below shows the favorite parka colors of girls in Ms. Carr’s class.

What is the favorite parka color?

Answer

On the lines below, explain how to use the graph to find the number ofgirls who like pink, if you know there are 6 girls who like baby blue.

White

Red

Pink

BabyBlue

Favorite Parka Colors

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8 Look at the shape below. On the grid provided, draw the mirror-imagereflection of the shape across the line.

STOP

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Cen

tim

eter

s

Inch

es1

1817

1615

1413

1211

109

87

65

43

21

23

45

67

Ruler

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line.

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Mathematics On Your Own • Level C Answer Key


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Answer KeyCut along the dotted line to remove this section.

RALLY!’s Math Strands

1: Numbers & Operations

2: Patterns & Fuctions

3: Algebra

4: Geometry

5: Measurement

6: Data Analysis

7: Probability & Uncertainty

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Answer Key Mathematics On Your Own • Level C


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Answer Key – Part 1

Question Correct RALLY!s Math StrandAnswer

Sample 1 A 2 Patterns & Functions, 3 Algebra

Sample 2 B 5 Measurement

1 B 1 Numbers & Operations

2 C 1 Numbers & Operations



5 B 7 Probability

6 D 1 Numbers & Operations


8 B 2 Patterns & Functions, 3 Algebra

9 D 2 Patterns & Functions, 3 Algebra

10 D 4 Geometry

11 C 4 Geometry

12 C 4 Geometry

13 A 4 Geometry

14 D 5 Measurement

15 D 5 Measurement

16 A 5 Measurement

17 D 5 Measurement

18 B 1–7 All

19 B 1–7 All

20 C 1–7 All




24 C 2 Patterns & Functions, 3 Algebra


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26 A 4 Geometry

27 C 1–7 All





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Answer Key – Part 2





4 B 6 Data Analysis




8 A 1 Numbers & Operations





13 D 4 Geometry

14 B 4 Geometry

15 D 4 Geometry

16 C 5 Measurement

17 D 5 Measurement

18 C 5 Measurement

19 B 5 Measurement





24 D 4 Geometry

25 C 1–7 All

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26 C 1–7 All


28 A 2 Patterns & Functions, 3 Algebra



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Answer Key – Part 3All of the questions in Part 3 are open-ended. Students can earn up to 2 or 3 points for fullcredit, depending upon the number of components within the question and its complexity.Use the rubrics below to determine students’ scores for each question.

Question 1Full Credit: 2 points

Answer: 24 � 4 � 6; 4 � 6 � 24 or 6 � 4 � 24

RALLY! Skill: 1 Numbers & Operations


Answer: 3 gallons; 12 quarts; Because 1 gallon � 4 quarts, multiply 4 quarts times 3 gallons tofind the number of quarts. 4 � 3 � 12; So, 3 gallons � 12 quarts.

RALLY! Skill: 5 Measurement


Answer: 589; 500 � 80 � 9



Answer: 17¢; 37¢

RALLY! Skill: 5 Measurement

2-POINT QUESTIONS

2 points Exemplary response

1 point One correct component

0 points Other

3-POINT QUESTIONS


2 points Two correct components


0 points Other


2 points Two correct components


0 points Other

3-POINT QUESTIONS



0 points Other

2-POINT QUESTIONS

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Answer: The odd numbers are 979, 351, 31, 99, 223. The even numbers are 222, 788, 54.

An even number is divisible by 2. Example: 788 � 2 � 394.

An odd number is not divisible by 2. Example: 31 � 2 � 15�12

�



Answer: 95, 89, 78, 63; 63 � 95 � 78 � 89 � 325; 325 tickets

RALLY! Skills: 1–7 All


Answer: The favorite color is baby blue. To find the number of girls who like pink, divide 6 by 2. 3 girls like pink.

RALLY! Skill: 6 Data Analysis


Answer:

RALLY! Skill: 4 Geometry

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Total Your Score - Part 1

Question Correct Your PointsAnswer Score Possible

1 B 1

2 C 1

3 C 1

4 B 1

5 B 1

6 D 1

7 B 1

8 B 1

9 D 1

10 D 1

11 C 1

12 C 1

13 A 1

14 D 1

15 D 1

16 A 1

17 D 1

18 B 1

19 B 1

20 C 1


21 C 1

22 B 1

23 D 1

24 C 1

25 C 1

26 A 1

27 C 1

28 C 1

29 B 1

30 C 1

31 B 1

Your Total Score 31

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1 D 1

2 B 1

3 D 1

4 B 1

5 D 1

6 B 1

7 C 1

8 A 1

9 C 1

10 C 1

11 C 1

12 B 1

13 D 1

14 B 1

15 D 1

16 C 1

17 D 1

18 C 1

19 B 1

20 C 1


21 C 1

22 B 1

23 C 1

24 D 1

25 C 1

26 C 1

27 D 1

28 A 1

29 B 1

30 B 1

Your Total Score 30

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Question Your PointsScore Possible

1 2

2 3

3 2

4 2

5 3

6 3

7 3

8 2

Your Total Score 20

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MATHEMATICSOn Your OwnSAMPLE

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Mathematics On Your Own gives you problem-solving activities toreinforce your math skills.

Parts 1 & 2: Mathematical Problems with Multiple-Choice Questions

• Multi-Step problems• Higher-Level problems• Stamina Builder

Each multiple-choice problem is worth 1 point.

Part 3: Open-Ended Math Problems

• Higher-Level Short-Response andExtended-Response Math Problems

Documents

Math On Your Own