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Applying the Readiness and Supporting TEKS for the STAAR

E L P SAM ATION C U D E ! SRATA AAR Y L L Y L L R . MAT H 9 9 . 888

TER. S 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

GEOMETRY — AND —

SPATIAL REASONING

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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 for STAAR Math

………….. Mastering STAAR Math with RALLY! Words Applying the Readiness & Supporting TEKS Grade Levels 3–8 • • • •

Guided Instruction Independent Practice Math Journal/Answer Book Academic Vocabulary FREE   SHIPPING  

Price $389 10 Copies of 5 Strand Books per grade level-Total of 50 books RALLY! Words Math Essential Vocabulary (Online Access for 15 Students) Level C D E F G H

Grade 3 4 5 6 7 8

Item # 6314-9 6321-7 6328-6 6335-4 6342-2 6349-1

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888-99-RALLY www.RALLYEDUCATION.com


LEVEL

G

Applying the Readiness and Supporting TEKS for the STAAR

E L P S TA R SAM A N O I T A C U MAT H D E ! Y L L Y L A L R A R . 9 9 . 888

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

GEOMETRY — AND —

SPATIAL REASONING

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4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet To the Teacher Mastering STAAR Math prepares students to succeed on the STAAR Math Test. The STAAR Math Test assesses the TEKS in the STAAR Reporting Categories. The program is organized into five books: • • • • •

Numbers, Operations, and Quantitive Reasoning Patterns, Relationships, and Algebraic Reasoning Geometry and Spatial Reasoning Measurement Probability and Statistics

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Each TEKS 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: Draw a Picture or Diagram STER. Make a Chart or List, Graph, Sort Data A M E ACKLIN Use Manipulatives or Act Out L B A S NOT OK TO BE Write a Number Sentence, Use Ratio or Proportion I T I . GHTED OR THIS BO I Use a Formula or Rule R Y P CO IVEN F Y WAY. Guess and CheckBOOK IS G T O N IN AN AMPLE SSION IS Make Iit S SSimpler UCED

TH

I PERM

D REPRO

In the Independent Practice section, students respond to four math problems for each TEKS on their own. After each TEKS, students can write in a two-page math journal. This journal is where students can show their work and answer questions about the TEKS they have just learned. ISBN 978-1-4204-6338-5 R 6338-5 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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Contents TEKS (7.6) . . . . . . . . . . . . . . . 4

TEKS (7.8) . . . . . . . . . . . . . . 44

TEKS Skill

TEKS Skill

Guided Practice

Independent Practice

(D) Readiness . . . . . 5 . . . . . . . . 6 (A) Supporting. . . . 10 . . . . . . . 11 (B) Supporting. . . . 17 . . . . . . . 18 (C) Supporting. . . . 22 . . . . . . . 23

Guided Practice

Independent Practice

(A) Supporting. . . . 45 . . . . . . . 46 (B) Supporting. . . . 52 . . . . . . . 53 (C) Supporting. . . . 59 . . . . . . . 60

TEKS (7.7) . . . . . . . . . . . . . . 27 TEKS Skill

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Guided Practice

Independent Practice

(B) Readiness. . . . . 28 . . . . . . . 30 (A) Supporting. . . . 36 . . . . . . . 38

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

3 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet

TEKS (7.6) The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

(D) Readiness . . . . . . . . . . . . . . . . . . . . . . 5 (A) Supporting . . . . . . . . . . . . . . . . . . . . 10 (B) Supporting . . . . . . . . . . . . . . . . . . . . 17 E (C) Supporting . . . . . . . . . . . . . . . . . . .B.L22 ACKLIN

R. MASTE

OT A N O BE S I T T K I O . 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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.6) The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. (D) Readiness. The student is expected to use critical attributes to define similarity.

1 Look at the 2 rectangles below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Q

A 2.5 units D

R

B

5 units

7.5 units

C

T

15 units

S

ER.

ST Which method could be used to prove that the rectangles are similar? NE MA

ACKLI L B A S NOT OK TO BE I HINT T I . BO TED of the GHlengths HIScorresponding I T Use a Formula or Rule. The sides of R Y R P O O F C N S E I . V Y I K the same A get the same quotient similar figures So, you Y Wwill OT Gratio. BOOhave N N E A L S I P N I M ON lengths. UCED IS SA youEdivide ISSItheir D THwhen O R P P RM RE

A Divide 2.5 by 15 and 5 by 7.5 to see whether the quotients are the same B Divide 5 by 2.5 and 15 by 7.5 to see whether the quotients are the same C Divide 7.5 by 5 and 15 by 2.5 to see whether the quotients are the same D Divide 15 by 2.5 and 5 by 7.5 to see whether the quotients are the same

5 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 Look at the 2 rectangles below.

I E 4 units H

J

F 8 units 9.5 units

G L

K

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 19 units

Which method could be used to prove that the rectangles are similar? F Divide 4 by 19 and 8 by 9.5 to see whether the quotients are the same G Divide 8 by 4 and 19 by 9.5 to see whether the quotients are the same H Divide 9.5 by 8 and 19 by 4 to see whether the quotients are the same J Divide 19 by 4 and 8 by 9.5 to see whether the quotients are the Asame STER.

LINE M K C A L OT A B TO BE N S I 3 Look at the 2 parallelograms below. TED. IT BOOK S H I G H I T R COPY GIVEN FOR I AY. S I K O W T E PLE BO SION ISF NO CED IN ANY 130° M A S THIS130° PERMIS 50° EPRODU R 10 units 8 units 50° H

130° G 12 units

50° L

15 units

J 50°

130° K

Which method could be used to prove that the parallelograms are similar? A Divide 15 by 10 and 8 by 12 to see whether the quotients are the same B Divide 10 by 8 and 15 by 12 to see whether the quotients are the same C Divide 8 by 10 and 15 by 12 to see whether the quotients are the same D Divide 8 by 15 and 12 by 10 to see whether the quotients are the same

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 TIAL ry and REASONING Spatial Reasoning Geomet 4 Look at the 2 triangles below.

P

12 units

20 units

X 4.8 units

R

Q

16 units

8 units

Z 6.4 units Y

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Which method could be used to prove that the triangles are similar? F Divide 12 by 4.8 and 20 by 8 to see whether the quotients are the same G Divide 8 by 20 and 12 by 4.8 to see whether the quotients are the same H Divide 6.4 by 16 and 8 by 12 to see whether the quotients are the same J Divide 4.8 by 12 and 6.4 by 20 to see whether the quotients are the same

STER. A M E ACKLIN L B A 5 Look at the 2 triangles below. S NOT OK TO BE I T I . GHTED OR THIS BO I R Y D P O IVEN F Y WAY. K IS C G O T O O B MPLE S13 N IS N UCED IN AN A O I S V S S units I I D TH 5 units O R P PERM 6.5 units RE 2.5 units

E

F

12 units

W

6 units

X

Which method could be used to prove that the triangles are similar? A Divide 6 by 12 and 5 by 2.5 to see whether the quotients are the same B Divide 12 by 5 and 6.5 by 2.5 to see whether the quotients are the same C Divide 12 by 6.5 and 13 by 6 to see whether the quotients are the same D Divide 13 by 6.5 and 12 by 6 to see whether the quotients are the same

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.6) The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. (A) Supporting. The student is expected to use angle measurements to classify pairs of angles as complementary or supplementary.

1 The drawing below shows the side view of a picture frame on a desk.

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 . GHTED1 OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B LE is theIOmeasure IN AN MPwhat N IS N ofUCitsEDcomplementary A If m⬔1ISisS85°, angle? S S I D TH O R P PERM RE HINT Write a Number Sentence. The sum of the measures of two complementary angles is 90°. So, the measure of the complementary angle is equal to 90° – 85°.

A 5° B 15° C 95° D 105°

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 The drawing below shows the side view of a picture frame on a desk.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 1

STER. A M E 25° ACKLIN L B A S NOT OK TO BE I 35° T I . GHTED OR THIS BO I R Y P 115° O IVEN F Y WAY. K IS C G O T O O B 125° MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

If m⬔1 is 65°, what is the measure of its supplementary angle? F G H J

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 3 The drawing below shows the side view of a book on a shelf.

1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

If m⬔1 is 70°, what is the measure of its supplementary angle? A 20° B 30° C 100°

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

D 110°

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet 4 The drawing below shows the side view of a book on a shelf.

1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

If m⬔1 is 80°, what is the measure of its complementary angle? F 10° G 20° H 100°

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

J 120°

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 5 The drawing below shows the side view of a book on a shelf.

1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

If m⬔1 is 45°, what is the measure of its complementary angle? A 45° B 55° C 120°

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

D 135°

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 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

15 © 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.6) The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. (B) Supporting. The student is expected to use properties to classify triangles and quadrilaterals.

1 A triangle with two congruent sides and an angle of 50° is —

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

HINT Draw a Picture or Diagram. Draw the triangle described above. Cross out the answers choices that don’t make sense, then choose the correct description of your triangle from the remaining choices.

A B C D

STER. A M E isosceles and right ACKLIN L B A S NOT OK TO BE I isosceles and obtuse T I . GHTED OR THIS BO I R Y isosceles and acute P IS CO IVEN F Y WAY. K G O T O O B scalene and E MPLobtuse N IS N UCED IN AN A O I S S S S I I D TH PERM REPRO

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 A triangle with no congruent sides and an angle of 90° is — F isosceles and acute G isosceles and right H scalene and obtuse J scalene and right

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

3 A triangle with no congruent sides and an angle of 100° is — A isosceles and acute

B isosceles and obtuse C scalene and acute

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

D scalene and obtuse

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet 4 A triangle with two congruent sides and an angle of 120° is — F isosceles and obtuse G isosceles and right H scalene and acute J scalene and right

5 A triangle with three congruent sides and an angle of 60° is — A equilateral and acute B equilateral and obtuse

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

C isosceles and acute

D isosceles and obtuse

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

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

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 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.6) The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties. (C) Supporting. The student is expected to use properties to classify three-dimensional figures, including pyramids, cones, prisms, and cylinders.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

1 Which of the following has 1 base that is not a polygon, and no other bases?

HINT Make a Chart or List. Write the names of the four solid figures given below. For each figure, write the number of bases and the shape of each base. Find the figure that matches the description above.

A B C D

STER. A M E ACKLIN L B A Cone S NOT OK TO BE I T I . GHTED OR THIS BO I Prism R Y P O IVEN F Y WAY. K IS C G O T O Pyramid O B MPLE SSION IS N UCED IN AN A S S I I D Cylinder TH PERM REPRO

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 Which of the following has two congruent bases that are polygons? F Cone G Cylinder H Prism J Pyramid

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

3 Which of the following can have exactly 4 faces? A Cone

B Cylinder C Prism

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

D Pyramid

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 4 Which of the following can have all triangular faces? F Cone G Cylinder H Prism J Pyramid

5 Which of the following has 2 parallel bases that are polygons? A Cone B Prism

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

C Pyramid

D Cylinder

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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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

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 TIAL ry and REASONING Spatial Reasoning Geomet

TEKS (7.7) The student uses coordinate geometry to describe location on a plane.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

(B) Readiness . . . . . . . . . . . . . . . . . . . . . 28 (A) Supporting . . . . . . . . . . . . . . . . . . . . 36

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.7) The student uses coordinate geometry to describe location on a plane. (B) Readiness. The student is expected to graph reflections across the horizontal or vertical axis and graph translations on a coordinate plane.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

1 Lucas translated trapezoid RSTU to trapezoid R⬘S⬘T⬘U⬘. Vertex S was at (3, 2). y

9 8 7

STER. A M E 4 ACKLIN L B A 3 BE NOT O S I T T K I O . 2 GHTED OR THIS BO I R 1 Y P x IS CO Y. IVEN F O –9 –8 –7 B –6 –5K–4 –3 –2 –1O0T G1 2 3 4 5Y 6WA 7 8 9 O N N E A L S AMP D IN ON I –1 THIS S PERMISSI EPRO–2DUCE R 6 5

–3 –4 –5 –6 –7 –8 –9

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 TIAL ry and REASONING Spatial Reasoning Geomet If vertex S⬘ is at (–2, 6), which best describes this translation?

HINT Use Manipulatives or Act it Out. Graph both vertices on the coordinate grid. Count how many units left or right and up or down you need to move to get from vertex S to vertex S⬘.

A Move 1 unit left and 4 units down B Move 4 units left and 5 units up

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

C Move 5 units left and 4 units up

D Move 5 units left and 8 units up

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

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 Chloe translated trapezoid WXYZ to trapezoid W⬘X⬘Y⬘Z⬘. Vertex W was at (6, –3). y 9 8

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 7 6 5 4 3 2 1

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

STER. A M E –3 ACKLIN L B A –4 BE NOT O S I T T K I O . –5 GHTED OR THIS BO I R Y –6 P O EN F K IS C –7T GIV O WAY. O Y O B N N E A L S AMP D IN ON I –8 THIS S PERMISSI EPRO–9DUCE R –2

If vertex W⬘ is at (7, 2), which best describes this translation? F Move 1 unit left and 1 unit down G Move 1 unit right and 5 units up H Move 5 units right and 1 unit up J Move 5 units left and 13 units down

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet 3 Rigo translated trapezoid KLMN to trapezoid K⬘L⬘M⬘N⬘. Vertex K was at (–3, 2). y 9 8 7 6 5 4 3 2 1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

–2 –3 –4 –5 –6 –7 –8

STER. A M E ACKLIN L B A T O BE S NOtranslation? If vertex K⬘ is at (2, –2), which best describes this I T T K I O . GHTED OR THIS BO I R Y P A Move 4 units left and S5 Cunits O up IVEN F KI AY. G O W T O Y O B N N E A L S B Move 4Aunits P right and 5 Iunits down IN IS S M ERMISSION RODUCED H T C Move 5 units P left and 4 units REP up –9

D Move 5 units right and 4 units down

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 4 Annie translated trapezoid TUVW to trapezoid T⬘U⬘V⬘W⬘. Vertex T was at (2, 6). y 9 8 7 6 5 4 3 2 1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

–2 –3 –4 –5 –6 –7 –8

STER. A M E ACKLIN L B A NOTtranslation? O BE Sthis If vertex T⬘ is at (–2, –3), which best describes I T T K I O . GHTED OR THIS BO I R Y P F Move 4 units down and 9Ounits left EN F K IS C AY. GIV O W T O Y O B N N E A L S G Move 4Aunits I right P up and 9 units IN IS S M ERMISSION RODUCED H T H Move 9 units P up and 4 units REP down –9

J Move 9 units down and 4 units left

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet 5 Jude translated trapezoid FGHI to trapezoid F⬘G⬘H⬘I⬘. Vertex F was at (–3, 2). y 9 8 7 6 5 4 3 2 1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

–2 –3 –4 –5 –6 –7 –8

STER. A M E ACKLIN L B A OT O BE S Ntranslation? If vertex F⬘ is at (0, 7), which best describesITthis I T K O . GHTED OR THIS BO I R Y P A Move 3 units up and 5S units O right IVEN F KI C AY. G O W T O Y O B N N E A L S B Move 3Aunits P down and 5Iunits left IN IS S M ERMISSION RODUCED H T C Move 5 units P up and 3 units REP right –9

D Move 5 units down and 3 units left

33 © 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.7) The student uses coordinate geometry to describe location on a plane. (A) Supporting. The student is expected to locate and name points on a coordinate plane using ordered pairs of integers.

1 Edna drew a triangle on the coordinate plane shown below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 y

9 8 7 6

F

5

STER. A M E 3 ACKLIN L B A 2 E S NOT OK TO BE I T I 1 . GHTEDG 4R5TH6IS7 BO8 9 x I –9 –8 –7 –6 –5 –4 –3 –2PY –1R 0 1 2 3 O O –1 IVEN F K IS C G O WAY. T O Y O B N N E A L S AMP D IN ON I –2 THIS S PERMISSI EPR–3ODUCE R 4

–4 –5 –6 –7 –8 –9

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 TIAL ry and REASONING Spatial Reasoning Geomet Which of the following best represents the coordinates of the vertices of 䉭EFG?

HINT Make it Simpler. Identify the coordinates of vertex E. Cross out the answer choices that do not have those coordinates listed. Do the same for vertices F and G. If you identified all the coordinates correctly, you should be left with only one answer choice.

A (2, –6), (4, –2), (1, 2) B (2, 6), (4, 2), (1, 2)

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

C (6, 2), (2, 4), (2, 1)

D (–6, 2), (–2, 4), (2, 1)

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

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 Horatio drew a triangle on the coordinate plane shown below. y 9 8 7

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 6 5 4 3 2 1

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

STER. A M E –4 ACKLIN X L B A –5 BE NOT O S I T T K I O . –6 GHTED OR THIS BO I R Y –7 P O Y EN F K IS C –8T GIV O WAY. O Y O B N N E A L S AMP D IN ON I –9 THIS S PERMISSI EPRODUCE R –2

Z

–3

Which of the following best represents the coordinates of the vertices of 䉭XYZ? F (–5, 3), (–7, 1), (–4, –2) G (3, –5), (1, –7), (–2, –4) H (3, 5), (1, 7), (2, 4) J (5, 3), (7, 1), (2, 4)

38 © 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 TIAL ry and REASONING Spatial Reasoning Geomet 3 Lena drew a triangle on the coordinate plane shown below. y 9 8 7 6 5 4 3

D

2 1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

–2 –3

C

–4 –5 –6

E

–7 –8

STER. A M E ACKLIN L B A BE of 䉭CDE? Overtices S NOT ofOthe Which of the following best represents the Icoordinates I T T K . HTED R THIS BO G I R Y P A (–5, –4), (–3, 1), (2, –6)S CO N FO E I V I K G O WAY. T O Y O B N N E A L B (–4, –5), M (1, –3), (–6, 2) S P ION I ODUCED IN S S IS SA I H M T R –2) REPR C (4, 5), (–1, 3), PE(6, –9

D (5, 4), (3, –1), (–2, 6)

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 4 Parker drew a triangle on the coordinate plane shown below. y 9 8 7 6 5 4 3

W

2

U

1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

–2

V

–3 –4 –5 –6 –7 –8

STER. A M E ACKLIN L B A BE of 䉭UVW? Overtices S NOT ofOthe Which of the following best represents the Icoordinates I T T K . HTED R THIS BO G I R Y P F (–4, –1), (1, 3), (5, –2) S CO N FO E I V I K G O WAY. T O Y O B N N E A L G (–1, –4), M (3, 1), (–2, 5) S P ION I ODUCED IN S S IS SA I H M T H (1, 4), (–3, –1), PER(2, –5) REPR –9

J (4, 1), (–1, –3), (–5, 2)

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet 5 Mary Jane drew a triangle on the coordinate plane shown below. y 9 8 7 6 5 4 3 2

I

1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

–9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1

1

2

3

4

5

6

7

8

9

x

–2 –3

H

–4 –5 –6 –7

G

–8

STER. A M E ACKLIN L B A BE of 䉭GHI? Overtices S NOT ofOthe Which of the following best represents the Icoordinates I T T K . HTED R THIS BO G I R Y P A (–7, 3), (–4, 6), (0, –7) S CO N FO E I V I K G O WAY. T O Y O B N N E A L B (–3, 7), (–6, 4), (7, 0) S I P IN IS SAM ERMISSION RODUCED H T C (3, –7), (6, –4), P (–7, 0) REP –9

D (7, –3), (4, –6), (0, &)

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet

TEKS (7.8) The student uses geometry to model and describe the physical world.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

(A) Supporting . . . . . . . . . . . . . . . . . . . . 45 (B) Supporting . . . . . . . . . . . . . . . . . . . . 52 (C) Supporting . . . . . . . . . . . . . . . . . . . . 59

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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.8) The student uses geometry to model and describe the physical world. (A) Supporting. The student is expected to sketch three-dimensional figures when given the top, side, and front views. 1 The top, front, and side views of a solid figure made of cubes are shown below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Top

Front

Side

STER. A M E ACKLIN L B HINT A BE NOT Ofigure SBuild I T T K I Guess and Check. Choose anTanswer. the solid out of O . ED BO S H I G H I T R cubes, then check each the pictures given. FOifR they match COPYview Gand Nsee S E I . V Y I K A O W T PLE BO SION IS NO CED IN ANY M A S IS DU THIS PERM REPRO

Which solid figure is best represented by these views?

C

A

Front

Front

B

D

Front

Front 45

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 The top, front, and side views of a solid figure made of cubes are shown below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Top

Front

Side

Which solid figure is best represented by these views?

F

G

STER. A M E ACKLIN L B A Front O BE S NOT Front I T T K I O . 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 H

J

Front

Front

46 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 TIAL ry and REASONING Spatial Reasoning Geomet 3 The top, front, and side views of a solid figure made of cubes are shown below.

Top

Front

Side

Which solid figure is best represented by these views?

A

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 C

Front

B

Front

STER. A M E CKLIN A L B A D S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O Front IVEN F Y WAY.Front 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 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 4 The top, front, and side views of a solid figure made of cubes are shown below.

Top

Front

Side

Which solid figure is best represented by these views?

F

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 H

Front

Front

G

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . J GHTED OR THIS BO I R Y P O IVEN F Y WFront K IS C AY. G O T O O B N N E A L S AMP ION I ODUCED IN S S I M THIS S Front P ER REPR

48 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 TIAL ry and REASONING Spatial Reasoning Geomet 5 The top, front, and side views of a solid figure made of cubes are shown below.

Top

Front

Side

Which solid figure is best represented by these views?

A

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 C

Front

B

Front

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTEDD 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 Front Front PERM REPRO

49 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.8) The student uses geometry to model and describe the physical world. (B) Supporting. The student is expected to make a net (two-dimensional model) of the surface area of a three-dimensional figure.

1 The final project in Jennifer’s art class is to create a 3-dimensional square pyramid out of paper. Which net below could Jennifer use to create a square pyramid?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

HINT Use Manipulatives or Act it Out. Trace each of the nets below. Cut out each net along the solid lines, and fold along the dashed lines. Which net folds into a square pyramid?

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 UCECD IN AN A S S I I D TH PERM REPRO

B

D

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 The final project in Bob’s art class is to create a 3-dimensional cylinder out of paper. Which net below could Bob use to create a cylinder?

F

G

H

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 OT O BE J. IT IS N T K O 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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 3 The final project in Rayann’s art class is to create a 3-dimensional square prism out of paper. Which net below could Rayann use to create a square prism?

A

B

C

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 D

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet 4 The final project in Tommy’s art class is to create a 3-dimensional pentagonal prism out of paper. Which net below could Tommy use to create a pentagonal prism?

F

G

H

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 J

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 .


4 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 5 The final project in Ehla’s art class is to create a 3-dimensional triangular pyramid out of paper. Which net below could Ehla use to create a triangular pyramid?

A

B

C

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 D

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 .


4 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

57 © 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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

58 © 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 TIAL ry and REASONING Spatial Reasoning Geomet Guided Practice Directions: Use the hint to help you solve the problem.

TEKS (7.8) The student uses geometry to model and describe the physical world. (C) Supporting. The student is expected to use geometric concepts and properties to solve problems in fields such as art and architecture.

1 Look at the picture of the building below.

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 THkind of triangles RODon this building? What PERM can you REPfind HINT Draw a Picture or Diagram. Trace the triangles on the picture of the building to help identify the types of triangles.

A equilateral triangles B scalene triangles C obtuse triangles D right triangles

59 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Independent Practice Directions: Solve the problems on your own. 2 Look at the picture of the Texas State Capitol building below.

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 flag? IN AN LE MPtriangle What kind of isSIbelow N IS the A O S S S UCED I I D TH O R P PERM RE F acute triangle

G equilateral triangle H obtuse triangle J right triangle

60 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 TIAL ry and REASONING Spatial Reasoning Geomet 3 Look at the picture of the jewelry box below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

You can see different solid figures that were used in the design of the jewelry box. What is one of the solid figures you can see in the picture? A cone

B pyramid

STER. A M E ACKLIN L B D trapezoid A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F thatYused K IS Cfor hisOTpaintings Piet Mondrian was famous G O WAY.black lines and bright O B N N E A L S I in the Mondrian P colors. What do you AMshapes D IN picture below? ONsee THIS S PERMISSI EPRODUCE R C sphere

4

F only squares G rectangles and triangles H squares and rectangles J trapezoids and squares

61 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet 5 What shapes do you see in the Amish quilt square pattern shown below?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

A scalene triangles and rectangles

STER. A M E obtuse triangles and trapezoids ACKLIN L B A NOT O BE T equilateral triangles and squares D. IT IS K O GHTE 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

B right triangles and squares C D

62 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 TIAL ry and REASONING Spatial Reasoning Geomet Choose One: • Write directions for how to solve one of the practice problems. • What questions would you like to ask your teacher to help you better understand the math you have just learned?

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

63 © 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 SPAT GEOMETRY Geometry and Spatial Reasoning Geomet Choose One: • Write two math problems that are similar to the ones you have just solved. • What is something you would like to do or learn about in math class?

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

64 © 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


E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

TER. S 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

S TA A R MATH

Mastering STAAR Math: Applying the Readiness and Supporting TEKS for the STAAR prepares students for the STAAR Math test. Each book focuses on a different TEKS Reporting Category assessed on the test. There is one guided practice problem and four independent practice problems for each TEKS that will be assessed on the STAAR. The series provides instructional practice in math problem solving. Students are taught several different problem-solving strategies. Each of the 5 TEKS Reporting Categories are in a separate book: • • • • •

Numbers, Operations, and Quantitive Reasoning Patterns, Relationships, and Algebraic Reasoning Geometry and Spatial Reasoning Measurement Probability and Statistics


Staar math g geometry sample