G MAT H
S T R A N D - B Y- S T R A N D
GEOMETRY E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B IS N INO ATN H E MPLE CSSON NNEC A D O I S E C TE D T S U I I D TH PERM REPRO C OM M ON C OR E STA N D AR 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
G
S T R A N D - B Y- S T R A N D
GEOMETRY E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B N INO ATN H E MPLE CSSOIONN N ISECT A D S E C E D T S U I I D TH PERM REPRO C OM MON CO R E STA N D A R D S
1 © 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 .
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
Make a Chart or List, Graph, Sort Data Work Backwards Use Manipulatives or Act Out Write a Number Sentence, Use Ratio or Proportion Use a Formula or Rule Guess and Check
STER. A M E IN In the Independent Practice section, students respond to four math for each ACKLproblems L B A T E O student expectation on their own. T IS N BOOK TO B I . D E T THIS YRIGH from R In each book, there are student expectations the particular grade level as well as, P O O F C N S E I . V Y I K A G O when appropriate, student T the previous ANY W grade that are important LE BOexpectations S NOfrom I P N I M N A D O I S E building blocks IStoS review.PRODUC THIS for students PERM RE 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 978-1-4204-6276-0 R 6276-0 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 – Geometry Shapes . . . . . . . . . . . . . . . . . . . . 4 Grade 7 Student Expectation
Guided Practice
Independent Practice
7.G.1 . . . . . . . . . . . . . 5 . . . . . . . . . 6 7.G.2 . . . . . . . . . . . . . 9. . . . . . . . . 10 7.G.3. . . . . . . . . . . . . 16 . . . . . . . . 17 7.G.4. . . . . . . . . . . . . 19 . . . . . . . . 20
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Geometric Relationships . . . . . 24 Grade 7 Student Expectation
Guided Practice
7.G.5. . . . . . . . . . . . . 25 7.G.6. . . . . . . . . . . . . 29 7.G.7. . . . . . . . . . . . . 34 7.G.8. . . . . . . . . . . . . 37 7.G.9. . . . . . . . . . . . . 42
Independent Practice
. . . . . . . . 26 . . . . . . . . 30 . . . . . . . . 35 . . . . . . . . 38 . . . . . . . . 44
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . D Coordinate Geometry . . . . . . . 48 YRIGHTE HIS BO T R P O O IVEN F Y WAY. K IS C G Grade 7 O T O O B PLE MGuided N IS N UCED IN AN Student Independent A O I S S S S I I D ExpectationTH Practice PERM Practice REPRO 7.G.10. . . . . . . . . . . . 49 . . . . . . . . 50
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 .
Shapes E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Student Expectation
7.G.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Calculate the radius or diameter, given the circumference or area of a circle 7.G.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 ER. Calculate the volume of prisms and cylinders, using a given E MAST KLIN formula and a calculator A BLAC
S NOT OK TO BE I T I . 7.G.3. . . . . . . . . . . . . . . . . .IG . .H.T.E.D. . . . . . . H . I.S. .B.O. . . . . . . 16 T R Y R P O O F make up Identify the two-dimensional shapes Y. the faces IVENthat K IS C A G O W T O Y O B and bases AN cylinders, IN(prisms, MPLEof three-dimensional N IS N Ushapes A D O I S E S C S S I I D M TH cones, and PERpyramids) REPRO
7.G.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
4 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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 7.G.1
1
Shapes Calculate the radius or diameter, given the circumference or area of a circle
Brian puts a border of bricks 24π feet long around the edge of a circular patio.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 24π
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B =IN 2πrAN IS N MPLE SSIONcircumference A D S E C S U I I D TH PERM REPRO What is the length of the radius from the inside edge of the bricks to the center of the circular patio?
HINT Work Backwards. Substitute 24π for the circumference in the formula given. Then work backwards to find the value of r.
A 6 feet B 8 feet C 12 feet D 24 feet
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
The area of the smaller circle on a high school wrestling mat is 25π square feet.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 area = 25π
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I TH ROD = πr2 PERM REParea What is the length of the diameter of the smaller circle on the wrestling mat? A 5 feet B 10 feet C 15 feet D 20 feet
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 .
3
A circle has a circumference that measures 40π inches. What is the length of the radius of the circle? circumference = 2πr A 10 inches B 20 inches C 30 inches D 40 inches
4
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
A circle has an area that measures 36π square centimeters. What is the length of the radius of the circle? area = πr2
STER. A M E 12 centimeters ACKLIN L B A S NOT OK TO BE 18 centimeters I T I . GHTED OR THIS BO I R 24 centimeters Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
A 6 centimeters B C D
7 © 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 Ferris wheel at the carnival has a string of lights 28π meters long around the edge of the wheel. 28π
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the length of the radius from the outside edge of the wheel to TER. MAS the center of the wheel? CKLINE A B C D
A BLA BE T O N 56 meters . IT IS IS BOOK TO D E T H G H 28 meters OPYRI IVEN FOR T Y. C S I 21 meters E BOOK OT G IN ANY WA N L S I P M S SA ISSION PRODUCED 14 THImeters PERM RE
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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 7.G.2
1
Shapes Calculate the volume of prisms and cylinders, using a given formula and a calculator
Kyle draws a picture of his cylinder shown below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 9 cm
18 cm
STER. A M E ACKLIN L B A T Calculate the volume of Kyle’s cylinder. Round your to the tenth. E O Bnearest S NOanswer I T T K I O . GHTED OR THIS BO I R Y P HINT IS CO IVEN F Y WAY. K G O T O O B Use a Formula Rule.ISYou the N IN Aformula MPLE 2 or N N canUCuse A D O I S E S S S I I h Volume = πr TH OD PERM REPRcylinder. to find the volume of Kyle’s Show your work.
Answer
cubic centimeters
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 .
Independent Practice Directions: Solve the problems on your own.
2
Whitney draws a picture of her cylinder shown below. 3 in.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 10 in.
Calculate the volume of Whitney’s cylinder. Round your answer to the nearest tenth.
STER. A M E Show your work. ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
Answer
cubic inches
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 .
3
Manuel draws a picture of his cylinder shown below. 9 cm
5 cm
Calculate the volume of Manuel’s cylinder. Round your answer to the nearest tenth. Show your work.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN Answer cubic centimeters L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
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
Jenna is filling the swimming pool shown below with water. She wants to know how much water it will hold. 6 ft
3 ft
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Calculate the volume, in cubic feet, of the swimming pool. Round your answer to the nearest tenth. Show your work.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSIOcubic N IS Nfeet UCED IN AN A S S I Answer I D TH PERM REPRO
12 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 .
Part B The hose that Jenna uses fills the pool at a rate of 2 cubic feet per minute. About how many minutes will it take to fill the pool? Round your answer to the nearest minute. Show your work.
Answer
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 minutes
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
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 .
5
Victor wants to fill a cylindrical planter with potting soil. He needs to know the volume of the planter shown below. 12 in.
19 in.
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Calculate the volume, in cubic inches, of the planter. Round your answer to the nearest tenth.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
Show your work.
Answer
cubic inches
14 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 .
Part B One bag of potting soil contains 1,728 cubic inches of soil. How many bags of potting soil must Victor purchase to fill the planter? Show your work.
Answer
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 bags of potting soil
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 7.G.3
1
Shapes Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)
The triangular prism shown below has how many faces?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A S NOT OK TO BE I HINT T I . D BO HTEMake IS the GList. Hof I T R Organize—Make a Chart or aRlist types of polygons that Y P O O F C N S E I . V Y K and the are faces of the of each. GI Y WAThen find the total number OT number BOOfigure N N E A L S I P N I M of faces. A D ON THIS S PERMISSI EPRODUCE R A 1 B 3 C 5 D 6
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 .
Independent Practice Directions: Solve the problems on your own.
2
What is the shape of each base of a cylinder? A square B rectangle C triangle D circle
3
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
All of the figures below have at least one rectangular face except for which figure?
A
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO C
B
D
17 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 .
4
The triangular pyramid shown below has how many faces?
A 3 B 4 C 5 D 6
5
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
All of the figures below have at least one triangular face except for which figure?
A
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVCEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
B
D
18 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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 7.G.4
1
Shapes Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
Phillip needs to buy adhesive paper to cover a box. He must calculate the surface area of the box to determine how much paper to buy. A diagram of the box is shown below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 3 ft
STER. A M E ACKLIN L B A BE Obox? S NOtoT coverOKthe I How much adhesive paper does Phillip need to buy T T I . GHTED OR THIS BO I R Y P O HINT IVEN F Y WAY. K IS C G O T O O B N N can use the PLE orSRule. IN Aformula UseSAaMFormula N ISYou D O I E C S S U I I D THTotal Surface PERMArea = 2wl REP⫹RO2lh ⫹ 2wh 5 ft
2 ft
to find the volume of Kyle’s cylinder. Show your work.
Answer
square feet
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
Lydia wants to cover a box with fabric. She must calculate the surface area of the box to determine how much fabric to buy. A diagram of the box is shown below.
6 in.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 10 in.
6 in.
How much fabric does Lydia need to buy to cover the box? Show your work.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
Answer
square inches
20 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 .
3
Monique is going to paint her brother’s toy box. She must calculate the surface area of the toy box to determine how much paint to buy. A diagram of the toy box is shown below.
2 ft
4 ft
1 ft
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the surface area of the toy box? Show your work.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P CO IVEN F Y WAY. K ISsquare G O T O Answer feet O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
21 © 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
Hector must paint the cylindrical tank shown below. h = 10 ft r = 3 ft
Part A What is the surface area of the entire tank to the nearest square foot?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Show your work
STER. A M E ACKLIN L B A Answer square feet S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G Part B O T O O B MPLE SSION IS N UCED IN AN A S S I I H of paintPEwill OneTcan 50 square RMcover PROD feet. How many cans of paint must Hector E R purchase to paint the entire surface area of the tank? Show your work
Answer
cans of paint
22 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
The Conrad Tank Company is building the cylindrical tank shown below out of sheet metal. h = 15 ft r = 4 ft
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the surface area of the entire tank to the nearest square foot? Show your work
STER. A M E ACKLIN L B A S NOT OK TO BE Answer square feet I T I . GHTED OR THIS BO I R Y P IS CO IVEN F Y WAY. K G O T O O B Part B MPLE SSION IS N UCED IN AN A S S I H ERMIit will be PROD One can of paint will cover AfterT the tank isPbuilt, REpainted. 85 square feet. How many cans of paint will the painter need to get from the storeroom to paint the entire surface area of the tank? Show your work
Answer
cans of paint
23 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 .
Geometric Relationships E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Student Expectation
7.G.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Identify the right angle, hypotenuse, and legs of a right triangle 7.G.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Explore the relationship between the lengths of the three TER. sides of a right triangle to develop the Pythagorean Theorem E MAS
ACKLIN L B A E 7.G.7. . . . . . . . . . . . . . . . . . . . . . . . . . .I.S. N .O . .T. . . . . . .T.O. .B34 T K I O . D of aHquadrilateral Find a missing angle when given IS BO GHTEangles I T R Y R P O O IVEN F . Y. .W. .A.Y.. . . . . . . . 37 K IS C 7.G.8. . L. E. .B.O. O . . . . . . . S. .N.O. T. .G. . . . . . . A. N I MPPythagorean D IN IONTheorem S toCEdetermine the unknown S SAthe S U I D M THIUse O R R E P P E R length of a side of a right triangle 7.G.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator
24 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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 7.G.5 1
Geometric Relationships Identify the right angle, hypotenuse, and legs of a right triangle
Rectangle QRST is formed by triangle QRS and triangle QST, as shown below. Q
R
T
S
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A HINT S NOT OK TO BE I T I . BO and its vertex labels HTEDjust triangle Draw a Picture or Diagram. GTrace HISQRS I T R Y R P O O F onto a piece ofOpaper. . the side opposite the VENhypotenuse, Ithe K IS CThen Ofind AYor G W T O Y B N N E A L rightAangle. MP D IN ON IS THIS S PERMISSI EPRODUCE R
Which side of triangle QRS is the hypotenuse?
— — A ST — — B QT — — C QR — — D QS
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 .
Independent Practice Directions: Solve the problems on your own.
2
Rectangle ABCD is formed by triangle ABC and triangle ACD, as shown below. A
B
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 D
C
Which angle of triangle ABC is the right angle? A ⬔ACB B ⬔BAC
STER. A M E ACKLIN L B A ⬔ACD S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
C ⬔ABC D
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 .
3
Rectangle WXYZ is formed by triangle WXY and triangle WYZ, as shown below. W
X
Z
Y
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Which sides of triangle WXY are the legs? —— —— A WX and WY —— — — B WX and XY — — — — C XY and WY —— —— D WZ and WY
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
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 .
4
Rectangle MNPQ is formed by triangle MNP and triangle MPQ, as shown below. M
N
Q
P
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Which side of triangle MNP is the hypotenuse? — — A MP —— B MN — — C NP —— D MQ
5
STER. A M E ACKLIN L B A O BE below. S NOTJML, OasK shown I T T Rectangle JKLM is formed by triangle JKL and triangle I . GHTED OR THIS BO I R Y P O IVEN F YK WAY. K JIS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
M
L
Which sides of triangle JKL are the legs? — — — A LM and LJ — — — B KL and LM — — C KL and JL — — D KL and JK
28 © 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: 7.G.6
1
Geometric Relationships Explore the relationship between the lengths of the three sides of a right triangle to develop the Pythagorean Theorem
Right triangle ABC is formed by the placement of three squares. The diagram below shows the areas of two of the squares.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 A
25 in.2
16 in.2
STER. A M E ACKLIN L B A C B S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I D What MI shaded Esquare? THis the areaPofERthe R PRO HINT Use a Formula or Rule. Remember that the Pythagorean Theorem states that in any right triangle the sum of the squares of the two legs is equal to the square of the hypotenuse. Use the Pythagorean Theorem to help you find the area of the shaded square. A 5 square inches B 9 square inches C 41 square inches D 400 square inches
29 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
Right triangle RST is formed by the placement of three squares. The diagram below shows the areas of two of the squares.
R
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 225 cm2
T
S
81 cm2
STER. A M E ACKLIN What is the area of the shaded square? L B A BE NOT O S I T T K I O . A 12 square centimeters GHTED OR THIS BO I R Y P B 24 square centimetersIS CO IVEN F Y WAY. K G O T O O B LE C 144 square MPcentimeters N IS N UCED IN AN A O I S S S S I I D TH PERM D 306 square centimeters REPRO
30 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 .
3
Right triangle DEF is formed by the placement of three squares. The diagram below shows the areas of two of the squares.
D
144 in.2
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 E
F
25 in.2
What is the length of each side of the shaded square?
STER. A M E 13 inches ACKLIN L B A 119 inches S NOT OK TO BE I T I . 169 inches GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
A 12 inches B C D
31 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 .
4
Right triangle XYZ is formed by the placement of three squares. The diagram below shows the areas of two of the squares.
X 289 cm2
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Y
Z
64 cm2
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . What is the length of each side of theHshaded G TED square? HIS BO I T R Y R P O CO A 15 centimeters OOK IS IVEN F Y WAY. G T O B MPLE SSION IS N UCED IN AN A B 17 Icentimeters S S D TH RMI E P REPRO C 225 centimeters D 353 centimeters
32 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
Right triangle KLM is formed by the placement of three squares. The diagram below shows the areas of two of the squares.
K 2
400 in.
256 in.2
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 M
L
What is the area of the shaded square? A 12 square inches B 25 square inches
STER. A M E ACKLIN L B A 656 square inches S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
C 144 square inches D
33 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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 7.G.7 1
Geometric Relationships Find a missing angle when given angles of a quadrilateral
Carlos measured the angles of a quadrilateral. Two of the angles measured 60° each and another angle measured 120°. What was the measure of the fourth angle of Carlos’ quadrilateral?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
HINT
Compute—Write a Number Sentence. Write a number sentence to find the sum of the three given angle measures. Then write a number sentence to find the difference between 360° and your sum.
A B C D
STER. A M E 110° ACKLIN L B A 120° S NOT OK TO BE I T I . 130° GHTED OR THIS BO I R Y P O IVEN F Y WAY. 140° K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
34 © 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
Rebecca measured the angles of a quadrilateral. One of the angles measured 75°, another angle measured 120°, and another angle measured 65°. What was the measure of the fourth angle of Rebecca’s quadrilateral? A 100° B 110° C 120° D 130°
3
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Brian drew the quadrilateral below but did not write the degree measure for ⬔C.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C 130° G O T O O B MPLE SSION IS N UCEDCIN AN A S S I I D TH PERM REPRO 50°
50°
What is the measure of ⬔C? A 50° B 80° C 130° D 150°
35 © 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
Gabriella drew the quadrilateral below but did not write the degree measure for ⬔R. R
100°
What is the measure of ⬔R? A 40° B 80° C 90° D 100°
5
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Daquan measured the angles of a quadrilateral. One of the angles measured 55°, . TERthe Swas another angle measured 115°, and another angle measured 125°. What A M E IN measure of the fourth angle of Daquan’s quadrilateral? BLACKL A B C D
OT A N O BE S I T T K I O . 35° GHTED OR THIS BO I R Y P O 45° IVEN F Y WAY. K IS C G O T O O B 55° MPLE SSION IS N UCED IN AN A S S I I D TH 65° PERM REPRO
36 © 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: 7.G.8
1
Geometric Relationships Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle
Triangle XYZ is a right triangle.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Y
26
10
STER. A M E ACKLIN L B A OT 2 2T IS 2N O BE T Pythagorean theorem: c = a + b K I O . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K ISx?C G O T O O B What is the length of side MPLE SSION IS N UCED IN AN A S S I D TH RMI E P REPRO HINT X
x
Z
Use a Formula or Rule. Use the Pythagorean theorem, c2 ⫽ a2 ⫹ b2, to find the length of side x. Remember that a and b in the theorem represent the legs of the right triangle and c represents the hypotenuse. Show your work.
Answer
37 © 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
What is the length, in centimeters, of side x in the right triangle below?
x
6 cm
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 8 cm
Pythagorean theorem: c2 = a2 + b2
A B C D
STER. A M E ACKLIN 8 L B A S NOT OK TO BE I T 9 I . GHTED OR THIS BO I R Y P 10 O IVEN F Y WAY. K IS C G O T O O B 14 MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
38 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 .
3
What is the length, in inches, of side x in the right triangle below?
x
5 in.
12 in. A 18 B 17 C 14 D 13
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
39 © 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
Triangle ABC is a right triangle. B 25
A
24
x
C
What is the length of side x?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Show your work.
STER. A M E ACKLIN L B A Answer S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
40 © 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
Triangle PQR is a right triangle. Q
x
P
12
16
R
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the length of side x? Show your work.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B Answer MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
41 © 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: 7.G.9
1
Geometric Relationships Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator
Zachary drew the triangle below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 14 in.
9 in.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O VEN F Y WAY. Iin. K IS C G O T O O B 10 MPLE SSION IS N UCED IN AN A S S I I D TH PERMa right triangle? Is Zachary’s triangle REPRO Use the Pythagorean theorem to prove whether his triangle is a right triangle.
HINT Compute—Write a Number Sentence. Use the Pythagorean theorem, c2 ⫽ a2 ⫹ b2, and the measure of the lengths of the triangle’s sides to write a number sentence. Then determine whether the number sentence is true.
42 © 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 .
Show your work.
On the lines below, explain why your answer is correct.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
43 © 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
Jasmine drew the triangle below.
29 cm
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 20 cm
21 cm
.
Is Jasmine’s triangle a right triangle? Use the Pythagorean theorem toMprove STER A E N whether her triangle is a right triangle. LACKLI
OT A B TO BE N S I T Show your work. BOOK TED. I S H I G H I T R COPY GIVEN FOR S I K AY. O W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R On the lines below, explain why your answer is correct.
44 © 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
Armando drew the triangle below.
7 cm
25 cm
22 cm Is Armando’s triangle a right triangle? Use the Pythagorean theorem to prove whether his triangle is a right triangle.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Show your work.
STER. A M E LIN On the lines below, explain why your answer is correct.A BLACK S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
45 © 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
Jon drew the triangle below.
18 in.
8 in.
15 in. Is Jon’s triangle a right triangle? Use the Pythagorean theorem to prove whether his triangle is a right triangle.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Show your work.
STER. A M E ACKLIN L B A On the lines below, explain why your answerITis Icorrect. S NOT OK TO BE . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
46 © 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
Chloe drew the triangle below.
26 cm
10 cm
24 cm
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Is Chloe’s triangle a right triangle? Use the Pythagorean theorem to prove whether her triangle is a right triangle. Show your work.
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . TED is correct. GHanswer HIS BO I On the lines below, explain whyPYyour T R R O O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
47 © 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 .
Coordinate Geometry E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Student Expectation
7.G.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Graph the solution set of an inequality (positive coefficients only) on a number line
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
48 © 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: Coordinate Geometry 7.G.10 Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)
1
Which inequality is shown on the graph below?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
28 27 26 25 24 23 22 21
0
1
2
3
4
5
6
7
8
HINT
Guess and Check. Solve the inequality in each answer choice. Then check each solution against the graph.
A B C
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO x⫹3>6 I R Y P O IVEN F Y WAY. K IS C G x⫹3<6 O T O O B MPLE SSION IS N UCED IN AN xTH ⫺IS3 S<A6 I D PERM REPRO
D x⫹6>3
49 © 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 graph shows the solution set of the inequality below? m⫺7≤4 A 22 21
B
D
1
2
3
4
5
6
7
8
9
10 11 12 13 14
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
22 21
C
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
STER. A M E 22 21 0 1 2 3 4 5 6 7 8 9 10KL11 AC IN 12 13 14 L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B 22SA21 MPL0E 1 SS2ION 3IS N4 U5CED6 IN 7AN 8 9 10 11 12 13 14 S I I D TH PERM REPRO
50 © 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 inequality is shown on the graph below?
28 27 26 25 24 23 22 21
0
1
2
3
4
5
6
7
8
A 2y ≥ ⫺4 B 2y ≤ ⫺4 C 2y > ⫺4 D 2y < 4
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
51 © 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
Which graph shows the solution set of the inequality below? a⫺5>2 A 22 21
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
22 21
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
B
C
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
22 21
D
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14
TER. S A M E 22 21 0 1 2 3 4 5 6 7 8 9 10KL11 12 13 14 AC IN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
52 © 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
Which inequality is shown on the graph below?
28 27 26 25 24 23 22 21
0
1
2
3
4
5
6
7
8
A b–4≤3 B b⫹3≤4 C b⫹4≤3 D b⫹4≥3
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
53 © 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
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
54 © 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
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
55 © 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
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
56 © 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
STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO
G
Strand Strand BY
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
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 ProbabilityIGHTED.
STER. A M E ACKLIN L B A E OT IT IS N BOOK TO B THIS YR R P O O F C GIVEN NY WAY. OK IS T O O B N E L IN A MP N IS A D O I S E S C S S U I I D TH PERM REPRO