Math sbs d algebra sample

D M AT H

S T R A N D - B Y- S T R A N D

ALGEBRA

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

HTED. G I GIVEN R T Y O P N O K IS C ION IS AY. O S O S I B M E AMPL STER. PER D IN ANY W S S I H T MA UCE D E O N I R L P BLACK TO BE RE A T O K IT IS N THIS BOO FOR C O NNE C TE D T O T H E C O M M O N C O R E S TA N D A R D S

RALLY! EDUCATION 22 Railroad Avenue Glen Head, NY 11545 888-99-RALLY Fax: 1-516-671-7900 www.RALLYEDUCATION.com LESLIE@RALLYEDUCATION.com …………………………………………………………………………………………………………………………

Math Problem-Solving Skills & Strategies by Strand

…………..

Math Strand-by-Strand Aligned to the Common Core State Standards Grade Levels 3–8

• Focuses on 5 specific math strands Number Sense & Operations, Measurement, Geometry, Statistics & Probability, Algebra

• Guided & independent practice with hints Each book provides math problem-solving practice.

Hints offer strategies to help students solve the problem

Class Set: 10 Copies of each Strand Book – Total of 50 books Level C D E F G H

Grade 3 4 5 6 7 8

______ 6002-5 6003-2 6004-9 6005-6 6006-3 6007-0

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888-99-RALLY www.RALLYEDUCATION.com

LEVEL M AT H

D

S T R A N D - B Y- S T R A N D

ALGEBRA E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN KLI ECT EBEDRETPOR T H E C A L C O NN B OT A K TO IT IS N THIS BOO OR CFOM MON CO R E STA N D A R D S

To the Teacher Math Strand-by-Strand prepares students to succeed on the student expectations that appear on math tests. The program is organized into five books: • Number Sense and Operations • Algebra • Geometry • Measurement • Statistics and Probability Each student expectation has Guided Practice and Independent Practice math problems. The Guided Practice math problems have a hint for every problem.

The hints offer strategies to help students solve the problem. Students are introduced to several different problem-solving strategies:

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Draw a Picture or Diagram Use Manipulatives or Act Out Write a Number Sentence, Use Ratio or Proportion Use a Formula or Rule Guess and Check Look for a Pattern

TED.

EN

GIVproblems In the Independent Practice section, students respond math T YRIGHto four O P N O C IS for each student expectation on their B own.

OOK IS ISSION AY.

MPLE TER. PERM IN ANY W A S S I TH CEDparticular grade level as MAS from Uthe In each book, there are student expectations D E O N I R L P K LAC expectations BE RE from the previous grade that well as, when appropriate, A Bstudent O T T O K N BOOstudents to review.

IT IS blocks are important building IS for H T R FO The RALLY! Math Strands are connected to the Common Core State Standards: • Operations & Algebraic Thinking • Number & Operations in Base Ten • Number & Operations—Fractions • Measurement & Data • Geometry ISBN 978-1-4204-6267-8 R 6267-8 Copyright ©2012 RALLY! EDUCATION. All rights reserved. No part of the material protected by this copyright may be reproduced in any form by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner. Printed in the U.S.A. 0811.MAQ RALLY! EDUCATION • 22 Railroad Avenue, Glen Head, NY 11545 • (888) 99-RALLY

2 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Contents – Algebra BAND: Variables and Expressions . . . . . . . . . . . . . . 4 Grade 4 Student Expectation

Guided Practice

Independent Practice

4.A.1 . . . . . . . . . . . . 5 . . . . . . . . 6 BAND: Equations and Inequalities . . . . . . . . . . . . . . 9 Grade 4 Student Expectation

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 Guided Practice

Independent Practice

4.A.2 . . . . . . . . . . . 10 . . . . . . . 11 4.A.3 . . . . . . . . . . . 13 . . . . . . . 14

BAND: Patterns, Relations and Functions . . . . . . . . . . . 17

.

GHTED OT GIVEN I R Y P O IS N Student Guided Independent OK IS C N O I S O S I M Expectation Practice Practice WAY. LE B R E P Y P M N A A .

ER SS CED IN 4.A.4 . . . . . . . . . . . 18 . . T. H. I. . . 20NE MAST U D O I R L 4.A.5 . . . . . . . . . . . 23 . . A. .B.LA . C. K25 E REP B O T T O K IT IS N THIS BOO FOR

Grade 4

3 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Variables and Expressions E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Student Expectation

4.A.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Evaluate and express relationships using open sentences with one operation

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

4 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 4.A.1

1

Variables and Expressions Evaluate and express relationships using open sentences with one operation

Mr. Evert is going to buy tennis balls for a tennis tournament. He needs to buy 96 tennis balls. The tennis balls are sold in packages of 3 tennis balls each. Mr. Evert uses the number sentence below to find the number of packages he should buy.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 96 ⫼ 3 =

Part A

䊐

What number belongs in the box to make the number sentence correct?

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K Answer O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L Part B E REP B B A O T T NO OOK Bpackages T ISalso S I H Mr. Evert Iwill buy 12 of towels. Each package has 4 towels.

T FOR

Write a number sentence that finds the total number of towels Mr. Evert will buy. Use the numbers 4 and 12 in your number sentence.

HINT Compute—Write a Number Sentence. You need to know the total number of towels Mr. Evert will buy. Think about whether you should write an addition, subtraction, multiplication, or division number sentence.

Number sentence

5 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

There are 8 bicycle stands at the park. Each stand can hold 6 bicycles.

Which number sentence can be used to find the total number of bicycles the bicycle stands in the park can hold?

A 8⫻6=

䊐

䊐=6 6⫹䊐=8 8⫼6=䊐

B 8⫺ C D

3

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

A newspaper page has 6 columns. Each column has the same number of classified ads. There are 90 classified ads in all. Which number sentence can be used to find the number of classified ads in each column?

A 6 ⫻ 90 = B C D

䊐

HTED. G I GIVEN R T Y O P 90 ⫺ 䊐 = 6 N O C K IS ION IS AY. O S O S I B M E 6 ⫹ 90 = 䊐 YW P ER MPL N A A .

S R N I E S I TH MAST UCED 90 ⫼ 6 = 䊐 D E O N I R L P K E A BLAC K TO BE R T O N IT IS IS BOO H T R FO

6 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Rosie and Alex collect baseball cards. Rosie has 143 baseball cards, which is 48 more baseball cards than Alex has.

On the line below, write a number sentence that could be used to determine how many baseball cards Alex has.

Number sentence How many baseball cards does Alex have?

Show your work.

Answer

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 baseball cards

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

7 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Mike is going to buy 15 packages of pencils that are on sale. Each package holds 8 pencils. Mike uses the number sentence below to find the total number of pencils he will buy.

15 ⫻ 8 =

䊐

Part A What number belongs in the box to make the number sentence correct?

Answer

Part B

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Mike is also wants to buy 75 erasers. The erasers are sold in packages of 5 erasers each. Write a number sentence that finds the number of packages he should buy. Use the numbers 75 and 5 in your number sentence.

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Number sentence

8 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Equations and Inequalities E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Student Expectation

4.A.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Use the symbols <, >, =, and ≠ (with and without the use of a number line) to compare whole numbers and unit fractions and decimals (up to hundredths) 4.A.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 .

Find the value or values that will make an open GHTEDsentence I GIVEN R T Y O P N O C S true, if it contains < or > SION I .

OOK IS

MIS WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

9 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 4.A.2

1

Use the symbols <, >, =, and ≠ (with and without the use of a number line) to compare whole numbers and unit fractions and decimals (up to hundredths)

Equations and Inequalities

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Jason wrote the number sentence shown below.

䊐 > 25 ⫹ 17

Which number belongs in the box to make the number sentence true?

HINT Guess and Check. Choose an answer. Check to see if it is greater than the sum of 25 and 17.

A 25 B 32 C 42 D 48

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

10 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Carly wrote the number sentence shown below.

䊐 = 12 ⫹ 15 Which number belongs in the box to make the number sentence true?

A 25 B 27 C 35 D 37

3

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Sue wrote the number sentence shown below.

䊐 < 90 ⫺ 54

Which number belongs in the box to make the number N HTED. sentenceVEtrue?

A 35 B 36 C 45 D 46

I G OPYRI N IS NOT G C S I ISSIO BOOK M E WAY. L R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

11 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Michael wrote the number sentence shown below.

䊐 > 4 ⫻ 13 Which number belongs in the box to make the number sentence true?

A 17 B 27 C 52 D 55

5

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Linda wrote the number sentence shown below.

䊐 < 132 ⫼ 6

Which number belongs in the box to make the number sentence true?

A 12 B 22 C 32 D 42

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

12 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 4.A.3

1

Equations and Inequalities Find the value or values that will make an open sentence true, if it contains < or >

Lisette and Alain work at a sandwich shop.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Part A

On Monday, Lisette made 48 sandwiches and Alain made 39 sandwiches.

On the line below, write a number sentence to show the relationship between the number of sandwiches Lisette made and the number of sandwiches Alain made. Use either < or > in your number sentence.

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

Part B THIS S NE MASTER ODUCED IN KLI thanB2, EPRfewer than 8, sandwiches. The C A L In one hour, Alain made more E Rbut B A O T T O two statements describe BOOK the number of sandwiches Alain made.

IT IS Nbelow S I H T FOR Number sentence

number of sandwiches < 5 number of sandwiches â&#x2030; 3

How many sandwiches did Alain make?

HINT Draw a Picture or Diagram. Draw a number line from 0 to 8. Circle the numbers that are greater than 2 and less than 8. Think about which of the circled numbers are less than 5 and not equal to 3.

Answer

sandwiches 13

Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Which number belongs on the line below to make the number sentence correct?

5+4>

+4

A 4 B 5 C 6 D 7

3

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Which number belongs on the line below to make the number sentence correct?

9⫺3<

A 7 B 9 C 10 D 13

⫺5

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

14 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Carmen and Jack work at a delivery company.

Part A Last week, Carmen delivered 150 packages and Zack delivered 175 packages.

On the line below, write a number sentence to show the relationship between the number of packages Carmen delivered and the number of packages Zack delivered. Use either < or > in your number sentence.

Number sentence

Part B

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

On Tuesday Carmen delivered more than 25, but fewer than 30, packages. The two statements below describe the number of packages Carmen delivered. number of packages < 28 number of packages >26

.

GHTED OT GIVEN I R Y P How many packages did Carmen deliver?

IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS Spackages ASTER ODUCED IN M Answer E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR

15 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Mrs. Mesa and Mr. Davenport work for a real estate company.

Part A Last year, Mrs. Mesa sold 40 houses and Mr. Davenport sold 25 houses.

On the line below, write a number sentence to show the relationship between the number of houses Mrs. Mesa sold and the number of houses Mr. Davenport sold. Use either < or > in your number sentence.

Number sentence

Part B

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Last month, Mrs. Mesa sold more than 2 but fewer than 6, houses. The two statements below describe the number of houses Mrs. Mesa sold.

Number of houses > 3 Number of houses ≠ 5

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y houses P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

How many houses did Mrs. Mesa sell?

Answer

16 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Patterns, Relations and Functions E

L P M SA N O I T Student Expectation UCA D E !

Y L L Y L A L R A R .

9 9 .

888

4.A.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Describe, extend, and make generalizations about numeric (⫹, ⫺, ⫻, ⫼) and geometric patterns .

GHTED OT GIVEN I R Y P 4.A.5 . . . . . . . . . . . . . . . . . . . .K. I.S. C. O . . . . . . .O.N. .IS. .N. . 23 O O ISSI andYstate M WAY. LE B R Analyze a pattern orAM a Pwhole-number function E P N A .

S TER ED IN THaIStable Cbox the rule, given orE M anASinput/output U D O N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR

17 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 4.A.4

1

Patterns, Relations and Functions Describe, extend, and make generalizations about numeric (⫹, ⫺, ⫻, ⫼) and geometric patterns

Ed writes the number pattern below.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 23, 30, 37, 44, ?

Part A

What is the next number in the pattern?

HINT Look for a Pattern. Look at the numbers in the pattern. Are they increasing or decreasing? Compare the first two numbers. What relationship do you see? Compare the second ED. third numbers.

VEN GHTand I GIfind R T Y O P N O the relationship Do you see the same relationship?ISUse to the C IS N K O I O S .

O S Y I B next number.

PERM MPLE NY WA

Answer

A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

On the lines below, write the rule for Ed’s pattern.

18 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Part B On the lines below, complete the number pattern using the same rule as Ed’s pattern.

Pattern

, 20,

,

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

19 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Roberto wrote the rule below to describe a number pattern add 4, subtract 3, add 4, subtract 3 Which pattern was made using Roberto’s rule starting with the number 31?

A 31, 34, 29, 32, 28

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 ?

8 8

B 31, 35, 38, 42, 45

C 31, 27, 30, 26, 29

D 31, 35, 32, 36, 33

3

If the pattern below continues, how many squares

A 9

will be in figure 5?

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN I 1 2ACKL 3 BE REPR4 5 L B A O T T O K N IT IS IS BOO H T R FO

B 10 C 12 D 14

20 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Darby is making a pattern with circles. The drawing below shows the first 4 rows of his pattern.

Row 1 Row 2 Row 3 Row 4 If Darby continues the pattern, how many circles will be in Row 6?

Answer

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 circles

On the lines below, explain how you found your answer.

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

21 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Natalie writes the number pattern below.

73, 67, 61, 55, 49, ?

Part A What is the next number in the pattern?

Answer

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

On the lines below, describe Natalie’s pattern.

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C Part B A L E REP B B A O T T NO OK BaOdifferent IT ISbelow, S On the lines write set of numbers that uses the same rule I H T FOR Do not use any of the numbers Natalie wrote. as Natalie’s pattern.

Pattern

,

,

,

22 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 4.A.5

1

Patterns, Relations and Functions Analyze a pattern or a whole-number function and state the rule, given a table or an input/output box

The number machine below follows a rule for all numbers that go into it.

E L P 5SAM 8 ION T A C U D E !

Y L L Y L A L R A R .

9 9 .

888 Number Machine

Complete the number machine table below by writing the two missing numbers.

.

GHTED OT GIVEN I R Y P O NUMBER MACHINE IS N IS CTABLE N K O I O S O S I M WAY. LE B R E P Y P M N A A .

THIS SIN NE MASTER OUT CED IN U D O I LACK5L TO BE REPR8 B A T O K IT IS N THIS B7OO 10 FOR 9

12

11 16

HINT Use a Formula or Rule. Look at each IN number and it’s OUT number in the table. What relationship do you see? Write a rule for the relationship. Use the rule to find the two missing numbers.

23 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

On the lines below, write the rule used to change IN numbers to OUT numbers in this number machine.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

24 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Mario made the Input-Output table below.

MARIO’S INPUT-OUPUT TABLE Input

Output

2

10

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 5

25

3

15

8

40

What rule can be used to find each Output number?

A Multiply by 5.

.

GHTED OT GIVEN I R Y P Multiply by 10.

IS CO SSION IS N .

K O O MI WAY LE B R E P Y Divide by 10.

P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

B Divide by 5.

C D

25 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Which In-Out table follows the rule below?

In ⫹ 8 = Out A

B

In

Out

5

C

In

Out

12

10

17

6

13

11

18

7

14

12

19

8

15

13

20

In 10 11 12 13

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 D

Out

In

Out

18

10

2

19

11

3

20

12

4

21

13

ED. 5 GIVEN T H G I COPYR ON IS NOT S I K ISSI BOO M E WAY. L R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

26 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Nico made the Input-Output table below.

NICO’S INPUT-OUPUT TABLE Input

Output

24

8

48

16

15

5

36

12

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

What rule can be used to find each Output number?

A Multiply by 2.

B Divide by 2.

C Multiply by 3.

D Divide by 3.

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

27 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

The number machine below follows a rule for all numbers that go into it.

10

60

Number Machine

Complete the number machine table below by writing the two missing numbers.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 NUMBER MACHINE TABLE IN

OUT

10

60

3

18

5

30

20

ED. GIVEN T O P N O C K IS ION IS AY. O S O S I B M E L ER INNnumbers Y W to Pchange MPrule N A A .

S On the lines below, write the used to R I E S I TH MAST UCED D E O N I OUT numbers in this coding machine.

R L P K E A BLAC K TO BE R T O N IT IS IS BOO H T R FO 300 YRIGHT

28 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

29 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

30 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

31 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

32 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

.

GHTED OT GIVEN I R Y P IS CO SSION IS N .

K O O MI WAY LE B R E P Y P M N A A .

THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

D

Strand Strand BY

Math Strand-by-Strand provides instructional practice in math problem-solving. Students are taught several different problem-solving strategies.

Each of the 5 math strands are in a separate book: • • • • •

Number Sense and Operations Algebra Geometry Measurement Statistics and Probability

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

TED. H G I GIVEN R T Y O P N O C S ION I OK IS S O S I B M E WAY. L R E P Y P M N A A .

S THIS ASTER ODUCED IN M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR