D M AT 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 L Y L L RA A R . 9 9 888.
HTED. G I GIVEN R T Y O P N O N IS K IS C O I O S O S I B WAY. ERM PLE Y P M N A A . S R N THIS MASTE RODUCED I E N I L BLACK TO BE REP A T O K IT IS N THIS BOO FOR C O NNE C TED T O T HE 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
GEOMETRY 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
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
Draw a Picture or Diagram Make a Chart or List, Graph, Sort Data Use Manipulatives or Act Out Use a Formula or Rule Guess and Check Make it Simpler Write a Number Sentence, Use Ratio or Proportion In the Independent Practice section, students respond to four math problems for each student expectation on their own. D.
GHTE I GIVEN R T Y O P N O C In each book, there are student expectations particular level as K ISfrom the ION IS Agrade O S . O S Y I B M E W R PL well as, when appropriate, student grade that ANY R. PEfromCEDtheINprevious E S SAM expectations I T H S T A are important building blocks forIN to review. EM RODU L students P K E C A R L B TO BEto the Common Core State Standards: OT A are K N O The RALLY! Math Strands connected S O I IT HIS B FOR T • Operations & Algebraic Thinking • Number & Operations in Base Ten • Number & Operations—Fractions • Measurement & Data • Geometry
ISBN 978-1-4204-6273-9 R 6273-9 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 BAND: Shapes . . . . . . . . . . . . 4 Grade 4 Student Expectation
Guided Practice
Independent Practice
4.G.1. . . . . . . . . . . . 5 . . . . . . . . 7 4.G.2 . . . . . . . . . . . 10 . . . . . . . 11 4.G.3 . . . . . . . . . . . 14 . . . . . . . 16 4.G.4 . . . . . . . . . . . 20 . . . . . . . 22 4.G.5 . . . . . . . . . . . 26 . . . . . . . 27
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
BAND: Geometric Relationships . . . . . . . . . . . . 31 Grade 4 Student Expectation
Guided Practice
Independent Practice
4.G.6 . . . . . . . . . . . 32 . . . . . . . 33 4.G.7 . . . . . . . . . . . 35 . . . . . . . 36 4.G.8 . . . . . . . . . . . 38 . . . . . . . 39
. 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
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
4.G.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Identify and name polygons, recognizing that their names are related to the number of sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon) 4.G.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . Identify points and line segments when Y drawing GHTEDa OT GIVEN I R P CO SN plane figure SION I . OOK IS
MIS WAY LE B R E P Y P M N A A . S R N 4.G.3. . . . . . T.H.I.S. . . . . E. .M.A.S.T.E. . . . . .D.U.C.E.D. I. . . . . . . 14 O N I CK L REPR sides Find perimeter of by LApolygons E adding B B A O T T O T IS N THIS BOOK I 4.G.4. . .F.O.R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Find the area of a rectangle by counting the number of squares needed to cover the rectangle 4.G.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Define and identify vertices, faces, and edges of three-dimensional shapes
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: 4.G.1
1
Shapes Identify and name polygons, recognizing that their names are related to the number of sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon)
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Jason used three different shapes to draw Figure A below. FIGURE A 1
3
2
. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O Part A O MI WAY LE B R E P Y P M N A A . S three shapes? HISthe ASTER ODUCED IN What are the namesTof M E N I LACKL TO BE REPR B A T O K HINT IT IS N THIS BOO Make It Simpler. FOR Trace Figure A. Then break the figure into simpler figures by cutting out each of the three shapes. Now identify each of the shapes. – OR – Draw a Picture or Diagram. Trace each of the three shapes separately. Use your tracings to help you identify each shape.
Shape 1 Shape 2 Shape 3
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Part B Based on the number of sides, what type of polygon is Figure A? Answer
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
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 .
Independent Practice Directions: Solve the problems on your own.
2
The shape of a floor tile is shown below. What is the name of the shape?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
A rectangle
B pentagon C hexagon D octagon
3
What is the name of the shape below?
A
. 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 triangle
B trapezoid C pentagon D hexagon
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 .
4
Sonia used three different shapes to draw Figure B below. FIGURE B 1 2
Part A
3
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What are the names of the three shapes? Shape 1 Shape 2
. 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 Part B R KLI C A L E REP B B A O T T O Based on theISnumber of sides,K what type of polygon is Figure B? IT N THIS BOO FOR Shape 3
Answer
8 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
Emilio used three different shapes to draw Figure C below. FIGURE C 1 3
2
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What are the names of the three shapes? Shape 1 Shape 2
. 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 Part B R KLI C A L E REP B B A O T T O Based on theISnumber of sides,K what type of polygon is Figure C? IT N THIS BOO FOR Shape 3
Answer
9 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: 4.G.2 1
Shapes Identify points and line segments when drawing a plane figure
Tasha draws a polygon on grid paper. The figure below shows the first 5 sides of Tasha’s polygon.
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 I segments AY the Mline Won Complete Tasha’s polygon by drawing LE B 3. more R E P Y P M N A A THIS S NE MASTER ODUCED IN grid above. R KLI C A L E REP B B A O T T O K HINT IT IS N THIS BOO Draw a Picture FOR or Diagram. Remember that a polygon is a closed
Part A
figure. When you draw your 3 lines, be sure each line connects to another line at each end.
Part B What is the name of the completed polygon? Answer
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
Isabella wants to draw a pentagon. She draws the 2 line segments shown below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
How many more line segments must Isabella draw to complete the pentagon? A 2 B 3 C 4
. 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 . S ER the U3CEline D INsegments shown below. ASTdraws Kevin wants to drawTHaIS hexagon. He M D E O N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR D 6
3
How many more line segments must Kevin draw to complete the hexagon? A 1 B 2 C 3 D 5
11 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
Aseem draws a polygon on grid paper. The figure below shows the first 3 sides of Aseem’s polygon.
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Complete Aseem’s polygon by drawing 2 more line segments on the grid above.
Part B
What is the name of the completed polygon? 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
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 .
5
Kim wants to draw a trapezoid on the diagram below. She has drawn 2 line segments so far.
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Draw the rest of Kim’s trapezoid on the diagram.
Part B
How many sides does a trapezoid have? 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 sides
13 © 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.G.3 1
Shapes Find perimeter of polygons by adding sides
Parker City is building a new dog park. The diagram of the new dog park is shown on the grid below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 PARKER CITY DOG PARK
KEY
= 1 unit
. GHTED OT GIVEN I R Y P Part A IS CO SSION IS N . K O O B WAY RMI E Y P MPLEof theTEdog N A A . What is the perimeter,IS inSunits, park? TH AS R ODUCED IN M E N I R A CK L E REP B HINT NOT A BL O T IS BOOKRemember that the perimeter of a figure is S I UseITa Formula or Rule. H T FOR
the distance around it. Count the number of units around the outside of the diagram.
Show your work.
Answer
units
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 The dog park will have a place for small dogs in the shaded part of the dog park, as shown below. PARKER CITY DOG PARK
KEY = 1 unit
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the area, in square units, of the shaded part of the dog park? Answer
square units
. 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
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 .
Independent Practice Directions: Solve the problems on your own.
2
A drawing of a tennis court is shown below. 78 ft
36 ft
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
36 ft
78 ft
[not drawn to scale]
ED. GIVEN T O N O C K IS ION IS AY. O S O S I B 114 M E YW P ER MPL N A A . S R N I E S I TH 228 MAST UCED D E O N I R L P K E A BLAC K TO BE R 456 T O N T IS IS BOO H T 2,808 I R FO
HT What is the perimeter, in feet, of the tennis court? PYRIG A B C D
16 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
Christopher drew a picture of a giraffe on a sheet of paper, as shown below. 25 cm
25 cm
25 cm
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 25 cm
Christopher needs to find the perimeter of the sheet of paper in order to make a frame kit for it. What is the perimeter of the sheet of paper? A 50 centimeters
B 75 centimeters
. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI 200 centimeters 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
C 100 centimeters 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
Mr. Philips wants to build a fence around his garden, as shown below. 8m 6m
6m
6m
6m 8m
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
How many meters long must the fence be in order to go all the way around Mr. Philip’s garden? Show your work.
Answer
Part B
. 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 Smeters ASTER ODUCED IN M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR
On the lines below, explain how you found how many meters long Mr. Philip’s garden fence will be.
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 .
5
On the grid below, draw a rectangle that has a length of 8 units and a width of 6 units.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the perimeter of the rectangle you drew? Show your work.
. 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
Answer
units
19 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: 4.G.4
1
Shapes Find the area of a rectangle by counting the number of squares needed to cover the rectangle
A diagram of Ms. Lee’s kitchen floor is shown below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 KEY
= 1 square foot
. 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 Part A O T T O K IT IS N THIS BOO What is the area, FOinR square feet, of the kitchen floor? HINT Use a Formula or Rule. Remember that area is the measure of the interior surface of a figure. Think about the best way to find the total number of square feet in the kitchen floor. – OR – Use manipulatives. Build an array using square tiles to match the diagram of Ms. Lee’s kitchen. Count the total number of tiles used to find the area in square feet.
Answer
square feet 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 .
Part B What is the perimeter, in feet, of the kitchen floor? Show your work.
Answer
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 feet
. 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 © 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
Look at the rectangular patio shown below.
KEY
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
= 1 square unit
What is the area, in square units, of the patio? A 15 B 18 C 30 D 54
. 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
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 .
3
Look at the rectangular classroom floor shown below.
KEY = 1 square unit
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the area, in square units, of the classroom floor? A 20 B 40 C 96 D 108
. 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
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 .
4
A diagram of Mr. Kirby’s deck is shown below.
KEY = 1 square meter
Part A
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What is the area, in square meters, of the deck? Answer
Part B
square meters
What is the perimeter, in meters, of the deck?
. 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
Show your work.
Answer
meters
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 .
5
A diagram of Sarah’s flower bed is shown below.
KEY = 1 square foot
Part A What is the area, in square feet, of the flower bed? Answer
Part B
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 square feet
What is the perimeter, in feet, of the flower bed? Show your work.
. 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
Answer
feet
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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 4.G.5
1
Shapes Define and identify vertices, faces, and edges of threedimensional shapes
Which three-dimensional shape has exactly 5 faces?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
HINT Organize—Make a List or Chart. Make a chart that uses the headings Name of Figure and Number of Faces. Count the number of faces in each figure in the answer choices and record it in your chart. Which figure has 5 faces?
A
. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O WAY LE B C . PERMI P Y 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
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 .
Independent Practice Directions: Solve the problems on your own.
2
Which three-dimensional shape has exactly 6 faces?
A
B
C
D
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
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 .
3
Which three-dimensional shape has exactly 6 edges?
A
B
C
D
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
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 .
4
Which three-dimensional shape has exactly 12 edges?
A
B
C
D
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 .
5
Which three-dimensional shape has exactly 5 vertices?
A
B
C
D
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 .
Geometric Relationships 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.G.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Draw and identify intersecting, perpendicular, and parallel lines .
GHTED OT GIVEN I R Y P 4.G.7. . . . . . . . . . . . . . . . . . . .K. I.S. C. O . . . . . . .O.N. .IS. .N. . 35 O O ISSI B drawing M E WAY. L R Identify points and Arays when angles E P Y P M N A . THIS S NE MASTER ODUCED IN 4.G.8. . . . . . . B . L. A. C.K.L.I . . . . . .E. R . .EP .R . . . . . . . . . . . . . . . 38 B A O T T O Classify BOOK obtuse, right, and straight IT IS NanglesTHasISacute, FOR
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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 4.G.6 1
Geometric Relationships Draw and identify intersecting, perpendicular, and parallel lines
Which shape has only one pair of parallel sides?
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
HINT Guess and Check. Look at each answer choice. Remember that parallel lines do not intersect and are always the same distance apart. Choose the figure that has only one pair of parallel lines.
A
B
. 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
C
D
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 .
Independent Practice Directions: Solve the problems on your own.
2
Which pair of lines are not intersecting lines?
A
B
3
C
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 D
. 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 Which pair of lines areBLperpendicular C A REPR E lines? B A O T T O K IT IS N THIS BOO FOR A
C
B
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 .
4
Which shape has two pairs of parallel sides?
A
B
5
C
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 D
. GHTED OT GIVEN I R Y P Which shape has only one pair of perpendicular IS N IS CO Ssides? N K O I O S O I M 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 A C FOR
B
D
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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 4.G.7 1
Geometric Relationships Identify points and rays when drawing angles
The diagram below shows angle ABC.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 A
B
C
Which ray is part of the angle?
. GHTED OT GIVEN I R Y P HINT IS CO SSION IS N . K O O I Guess and Check. LookPLat Remember Mchoice. E Beach answer WAY that when R E Y P M N A A . N is the first point you name a ray STERvertexDofUCthe ED Iangle THIofS San angle, Athe M E O N I R that you name.BLACKL E REP B A O T T O K IT IS N THIS BOO FOR
A ᎏ AB B ᎏ CB C ᎏ BC ᎏ D DC
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 .
Independent Practice Directions: Solve the problems on your own.
2
The diagram below shows angle NMP. M
Q
R
N
S
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 T
P
Which is a point on ray MP? A N B R C Q
. 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 . The diagram below Tshows RST. HIS S angle ASTER ODUCED IN M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO R FOR D S
3
S
T Which ray is part of the angle? A ᎏ SR B ᎏ RS ᎏ C TS ᎏ D RT 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 .
4
The diagram below shows angle DEF.
E
Y Z F
X W D
Which is a point on ray EF? A D B Y C W D X
5
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
The diagram below shows angle MNO.
. 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 . HIS S E MASTER TM CED IN U D O N I LACKL TO BE REPR B A T O K IT IS N THIS BOON FOR O Which ray is part of the angle? ᎏ A MN ᎏ B NO ᎏ C OM ᎏ D ON
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 .
Guided Practice Directions: Use the hint to help you solve the problem.
Band: 4.G.8 1
Geometric Relationships Classify angles as acute, obtuse, right, and straight
Alissa drew the angle shown below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What type of angle did Alissa draw?
. GHTED OT GIVEN I R Y P HINT IS CO SSION IS N . K O O B The corner Use Manipulatives or Act MI of a rectangular WAY piece of LE Out. R E P Y P M N A A . IN above to the corner ER IS S YouMcan paper is a right the THangle. ASTcompare CEDangle U D E O N I of a piece of paper. LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR
A straight B right C obtuse D acute
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 .
Independent Practice Directions: Solve the problems on your own.
2
Alberto drew the angle shown below.
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
What type of angle did Alberto draw? A acute B obtuse C right
. 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 . IN ER SS EDangle THIshown ASTWhat Cof M U D Nicole drew the angle below. type did Nicole draw? E O N I KL EP R C A R L E B B OT A K TO IT IS N THIS BOO FOR D straight
3
A obtuse B straight C right D acute
39 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
Audrey drew the angle shown below.
What kind of angle did Audrey draw? A right B straight C obtuse D acute
5
E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8
Payton drew the angle shown below.
. 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 What type of angle did Payton R KLI draw? C A L E REP B B A O T T A acute IT IS NO BOOK S I H T FOR B obtuse C right D straight
40 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
D
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 Probability BOOK IS
. GHTED OT GIVEN I R Y P CO N IS N Y. O I S S I MPLE TER. PERM IN ANY WA A S S I TH MAS UCED 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