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Sample Booklet
Grade 3
Mathematics — Book III
Measurement & Data–Geometric Measurement
Geometry
Published by:
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Sample pages from Teacher Guide...................................................................................... 2–11
Sample pages from Student Work Text ............................................................................12–26
Selected pages from
Student Work Text
Mathematics
Grade 3, Book III
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Measurement & Data–Geometric Measurement
Geometry
Teacher Guide
Lori Mammen
Editorial Director
ISBN: 978-1-60539-887-7
Copyright infringement is a violation of Federal Law.
©2013 by ECS Learning Systems, Inc., Bulverde, Texas. All rights reserved. No part of this publication may be reproduced,
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recording, or otherwise) without prior written permission from ECS Learning Systems, Inc.
Reproduction of any part of this publication for an entire school or for a school system, by for-profit institutions and tutoring
centers, or for commercial sale is strictly prohibited.
Printed in the United States of America.
Disclaimer Statement
ECS Learning Systems, Inc. recommends that the purchaser/user of this publication preview and use his/her own judgment
when selecting lessons and activities. Please assess the appropriateness of the content and activities according to grade level
and maturity of your students. The responsibility to adhere to safety standards and best professional practices is the duty of
the teachers, students, and/or others who use the content of this publication. ECS Learning Systems is not responsible for
any damage, to property or person, that results from the performance of the activities in this publication.
TestSMART is a registered trademark of ECS Learning Systems, Inc.
2
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Table of Contents
What’s Inside the Student Work Text?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
How to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Understanding Rigor and Cognitive Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Descriptions of TestSMART® Complexity Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Fostering Mathematical Understanding and Inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Definition of the Common Core State Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
The Precise Language of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Mathematics Manipulatives and Tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Text-Marking in Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Integrating the Literacy Strands in the Mathematics Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Master Skills List. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
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Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
ECS Learning Systems, Inc. • P. O. Box 440 • Bulverde, TX 78163-0440
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TestSMART® Common Core Student Work Text, Teacher Guide
© ECS Learning Systems, Inc.
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
3
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
What’s Inside the Student Work Text?
Overview
The TestSMART® Common Core Student Work Text addresses the Common Core State
Standards (CCSS) for Mathematics (National Governors Association Center for Best
Practices/Council of Chief State School Officers [NGA/CCSSO], 2010b) in separate books.
However, students benefit from an integrated view of mathematics (cross-domain
experiences). For instance, instead of isolating concepts, this approach groups ideas
and draws parallels. Students move beyond memorization and routine procedures to
construct mathematics using their own strategies and representations. As they grow in
understanding, they begin to generalize and transfer patterns of responding to other
mathematical and non-mathematical problems and situations.
The exercises included in the work text focus on the critical areas (major work) of the
grade as defined in the CCSS (NGA/CCSSO, 2013). The work text provides practice in
a variety of mathematical and real-world contexts. Tasks require appropriate use of
manipulatives, tools, and technology.
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The TestSMART Common Core Student Work Text should supplement and support
research, planning, instruction, and both informal and formal assessment. It is
recommended that teachers introduce new math concepts through everyday problems
and situations.
How to Use This Book
Time Requirement
The time requirement depends on the activity type and topic. Activity types include
guided (whole-class and small-group), independent, and extension/homework. Most
activities will take about 15 minutes, and some—such as finding the area of rectilinear
figures—will take up to 3 days.
Getting Started
Teachers should implement the activities from the TestSMART Common Core Student
Work Text in sequential order. The activities logically progress, building upon prior
knowledge and personal experience. The activities also appropriately relate thinking
across domains and grades. The activities should move students toward self-directed
mathematics learning and problem solving.
Within each activity are opportunities for students to question, think about, and talk
about their learning. In addition to the specific mathematic expectations involved,
these moments during activities help students develop the following types of skills—
•
•
•
•
•
analytical thinking
evaluative thinking
reflective thinking
metacognitive thinking
communication
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text, Teacher Guide
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
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© ECS Learning Systems, Inc.
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TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
For instance, students may need to connect information with prior knowledge or
personal experience, make predictions, infer, determine importance, visualize,
synthesize, or monitor comprehension. The Teacher Guide provides specific guidance
for supporting students throughout the learning process.
Lesson Features
Think About It: Students are asked to think about math-related questions and
situations and to think about their thinking. Students can think independently, or
teachers can guide “think-aloud” sessions in small or large groups (see Box 4
“Scaffolding through ‘Think Aloud,’” page 16).
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Talk About It: Students are asked to talk about math concepts and situations and
to talk about their thinking. This includes examining problem situations, making
observations, explaining their problem-solving processes, and discussing math
terminology and concepts (see “Math-Talk,” pages 13–14).
Try It: Students are asked to try a guided example. Teachers can present the guided
example in a whole-class or small-group setting. Teachers should engage students in
“math-talk” during these examples (see “Math-Talk,” pages 13–14).
Working Together: Students are asked to work together, or collaborate, in various
guided settings (pairs, small-group, whole-class). Teachers can support students with
open-ended questions (see Box 5 “Scaffolding through Open-Ended Questions,” pages
16–18).
On Your Own: Students are asked to independently explore a concept or skill, as well as
their own ways of problem solving. Teachers can support students with open-ended
questions (see Box 5 “Scaffolding through Open-Ended Questions,” pages 16–18).
Write About It: Students are asked to write about math concepts and situations and
to write about their thinking. This includes examining problem situations, making
observations, explaining their problem-solving processes, and reflecting on their
learning. Teachers should allow time for students to share their writing.
Did You Know…?: Students are given tidbits and trivia about their world and how it
works. These relate to the math domains, math vocabulary, the history of mathematics,
or real-life applications. The following are suggestions for using these tidbits and trivia:
• Challenge students to find other interesting facts related to the topic. This
provides an opportunity for students to learn effective research techniques.
• Create a “Did You Know…?” display where students can post the facts they learn.
• Use the tidbits and trivia as prompts for a class discussion. Talk about what
students already know and what they would like to learn more about. Have
students generate questions for further research or discussion.
• Have students respond to the tidbits and trivia in their math journals. Provide
time for students to share their journal entries with classmates. (Students may
benefit from a guiding question related to the tidbit or trivia.)
• Have students represent the idea(s) from the tidbits and trivia in a new way.
Provide time for students to share their representations with classmates.
4
TestSMART® Common Core Student Work Text, Teacher Guide
© ECS Learning Systems, Inc.
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
5
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Descriptions of TestSMART® Complexity Levels
The following descriptions provide an overview of the three complexity levels used to
align the TestSMART® Common Core Student Work Text items to the Common Core State
Standards (CCSS) for Mathematics (NGA/CCSSO, 2010b). Each explanation details the
kinds of activities that occur within each level. However, they do not represent all of the
possible thought processes for each level.
Low Complexity
Low Complexity (L)
Section I—Measurement & Data–Geometric Measurement
Mathematics, Grade 3—Book III
Low-complexity items align with
Line Segments
the CCSS at Level 1 of the Webb
A line segment is part of a line that extends from one endpoint to another. Every line
segment has two endpoints. One endpoint shows where the line segment begins. The other
(2002a) model. Activities and
endpoint shows where the line segment ends. Each endpoint is labeled with a letter of the
alphabet. The example below shows a line segment.
problems at this level require
routine, single-step methods.
A
B
An item may ask students to
In math, you name a line segment by using its endpoints.
recognize or restate a fact,
AB
definition, or term. For example,
You read the text above as “line segment A B.”
AB h
dpoints, A and B.
students may need to identify
the attributes of a geometric figure.
Items of this complexity may require students to follow a basic procedure with clearly
defined steps. At this cognitive level, students may need to apply a formula or perform
a simple algorithm. Some major concepts represented at this level include arithmetic
facts, perimeter, and converting units of measure. A low-complexity item may ask
students to identify, recognize, use, or measure information and concepts.
ced.
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Standard 3.MD.5 (L)
Moderate Complexity
Moderate Complexity (M)
Section I—Measurement & Data–Geometric Measurement
Mathematics, Grade 3—Book III
Moderate-complexity items
Enlarging Area
align with the CCSS at Level 2
You already know how to find the area of a rectangle by counting square units, using arrays,
and multiplying length times width. How would you find the area of a rectangle after it is
of the Webb model. Items of
enlarged (made bigger)? Look at the examples below.
Current Porch
Example #1
moderate complexity involve
The diagram to the right shows a porch on a house.
both comprehension and the
Talk About It–1
subsequent processing of
• What are the dimensions of the porch?
• What is the area of the whole porch?
information. Activities at this
The owner of the house wants to enlarge (make bigger)
1 ft
the porch. The diagram below shows the owner’s porch
level demand more than one
now and the owner’s planned addition to the porch.
1 ft
step in the reasoning process.
di ion
Students are asked to determine
how to best solve the problem. An item may ask students to generate a table of paired
numbers based on a real-life situation. Items may involve using a model to solve a
problem. At this cognitive level, students will need to visualize for tasks such as
extending patterns and determining nonexamples. Items may involve interpreting
information from a simple graph, table, or diagram. Some major concepts represented
at this level include classifying geometric figures and using strategies to estimate. Items
of this complexity may ask students to classify, organize, observe, collect and display
data, or compare data. Some items also require students to apply low-complexity skills
and concepts.
ced.
Standard 3.MD.7 (M)
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text, Teacher Guide
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
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© ECS Learning Systems, Inc.
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TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
High Complexity
High Complexity (H)
Mathematics, Grade 3—Book III
Section II—Geometry
High-complexity items align
Problem Solving XII
with the CCSS at Level 3 and/or
Directions: Read each sentence below. Then, write a sentence that explains why the
statement is true or false. Draw figures to support your answers.
*
4 of the Webb model. Items of
1. Every quadrilateral is a rectangle.
high complexity require students
to use strategic, multi-step thinking;
develop a deeper understanding
_________________________________________________________________________
of the information; and extend
_________________________________________________________________________
thinking. The problems at this level
2
le is a rhombus.
are non-routine and more abstract.
Students are asked to demonstrate
more flexible thinking, apply prior knowledge, make and test conjectures, and support
their responses. High-complexity items may require students to make generalizations
from patterns. Items may involve interpreting information from a complex graph, table,
or diagram. At this cognitive level, students must justify the reasonableness of a
solution process when more than one solution exists. Students will use concepts to
solve and explain problems, such as how changes in dimensions affect the volume of
a figure. A high-complexity item may ask students to plan, reason, explain, compare,
differentiate, draw conclusions, cite evidence, analyze, synthesize, apply, or prove.
Some items also require students to apply low- and/or moderate-complexity skills
and concepts.
Standard 3.G.1 (M–H)
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This p
* Note: Although the CCSS or state standards may include expectations that require extended thinking,
many large-scale assessment activities are not classified as Level 4. Performance and open-ended
assessment may require activities at Level 4.
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TestSMART® Common Core Student Work Text, Teacher Guide
© ECS Learning Systems, Inc.
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
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TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Fostering Mathematical Understanding and Inquiry
Common Core State Standards*
The Common Core State Standards (CCSS) (NGA/CCSSO, 2012) is a standards-based
U.S. education reform initiative sponsored by the National Governors Association
(NGA) and the Council of Chief State School Officers (CCSSO). The initiative seeks to
provide a set of national curriculum standards to create more rigorous, consistent
instruction and learning across the country. These standards were developed based
on models from various states and countries, as well as recommendations from K–12
educators and students. The expectations, aimed at college and career readiness,
focus on core concepts and processes at deep and complex levels. The curriculum
standards for ELA/literacy and mathematics were released in 2010. Science and
history standards are in development.
•
•
•
•
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Forty-five states and the District of Columbia have adopted the standards, but Alaska,
Minnesota, Nebraska, Texas, and Virginia have yet to adopt them. During the
2014–2015 academic year, adopting states should begin formal CCSS assessments.
Assessments will include the following types of items:
selected-response items (multiple-choice items)
constructed-response items
technology-enhanced items/tasks
performance tasks
For more information about the CCSS initiative, please visit
http://www.corestandards.org.
*
This information was current at time of publication.
Box 2: Definition of the Common Core State Standards
Mathematics Instruction and Learning
Mathematics is a study of patterns, relationships, measurement, and properties in
numbers, quantity, magnitude, shape, space, and symbols. Effective mathematics
instruction requires students to mindfully attend to elements of structure and
content—including patterns and language choice. This disciplined study involves trying
and retrying during problem solving to better understand how structure and content
work together in systems of meaning (Paul & Elder, 2008). The ability to recognize,
analyze, and use patterns and relationships is essential to problem solving.
Mathematical thinking skills are closely tied to skills that are essential for success in
school, career/work, and life, such as—
•
•
•
•
•
•
•
•
•
critical/evaluative thinking
creative/innovative thinking
elaborative thinking
problem solving
decision making
researching
collaboration
communication
organizing and connecting ideas
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text, Teacher Guide
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
8
© ECS Learning Systems, Inc.
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TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
“
Research...supports
a focus on teaching
for meaning and
understanding.”
These skills are essential to achieving learning goals in the areas of information and
communication technology (ICT) literacy and science. As students develop in
mathematics, they should also see connections in reading, language arts, social studies,
history, art, music, physical education and sports, and other areas of the curriculum.
Research (e.g., Fennema & Romberg, 1999; Hiebert et al., 1997; Simon, 2006; Skemp,
1976) supports a focus on teaching for meaning and understanding. Fluency with
computational procedures and basic facts allows students to expend less cognitive
energy when problem solving. However, drilling on isolated skills can become
meaningless (e.g., Grouws, 2004; Schoenfeld, 1988). In addition, these rote activities
sometimes involve the use of mnemonic devices. These types of “tricks” are not
suggested strategies for achieving long-term understanding and flexible use of skills.
Students understand more when they actively construct meaning during rich, complex
tasks (e.g., Fosnot, 1996; Fosnot, 2005; Noddings, 1990).
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Appropriate Tasks
The CCSS emphasize the need for understanding and its impact on carrying out
effective mathematical practices and true mastery of mathematical content
(NGA/CCSSO, 2010b). (Refer to Box 1 “Balance in Rigorous Mathematics Instruction” on
page 6 for a list of the Standards for Mathematical Practice.) Rich mathematics tasks
often involve persistent problem solving and, therefore, can require time. Rich tasks
allow all students—even struggling learners—the opportunity to adequately explore
and discuss complex problems, situations, and ideas. Rich mathematics experiences
provide students with opportunities to see structure, patterns, and relationships in
many different contexts.
Rich, complex mathematics tasks—
•
•
•
•
•
“
Rich mathematics
experiences provide
students with
opportunities to see
structure, patterns,
and relationships in
many different
contexts.”
10
•
•
•
•
•
•
•
•
begin with a clear, explicit, reasonable, actionable learning goal
incorporate the use of sound number sense and basic computational skills
rely on the integrated development of mathematical skills and understandings
build on prior knowledge and personal experience
utilize a variety of settings in which to explore and share mathematical ideas with
others (i.e., paired, small-group, whole-class)
encourage risk-taking to further the learning process
encourage students to work and think mathematically
invite all students to participate in constructive math inquiries and discussions
promote complex thinking and transfer of understanding by focusing on the “big
ideas” and “essential questions”
apply mathematical ideas to a broad range of real-life and imagined situations
help students learn to use the precise language of mathematics for specific
purposes
require students to make conjectures, hypothesize, test and retest ideas, justify
thinking, represent findings in meaningful ways, and reflect
require students to look for and utilize the underlying order and logic of
mathematics when problem solving
TestSMART® Common Core Student Work Text, Teacher Guide
© ECS Learning Systems, Inc.
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
9
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
• allow for diversity in thinking and offer many valid entry points to mathematical
challenges for all students (e.g., multiple solution paths, multiple representations)
• explore and reinforce concepts through hands-on activities involving the use of
technology, manipulatives, tools, and play
• allow students to generalize and transfer patterns of responding to other
mathematical and non-mathematical problems and situations
• require extended engagement (e.g., Hiebert et al., 1997; National Council of
Teachers of Mathematics [NCTM], 2000)
A
T
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TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
Mathematics, Grade 3—Book III
Answer Key
ed.
Section I—Measurement & Data–
Geometric Measurement
p. 4
On Your Own: 1. DE 2. GH 3. RS 4. XY 5. ST
p. 5
Talk About It: AB, BC, CD, and DA; RS, ST, and TR; WX,
XY, YZ, and ZW. Think About It: Students should
conclude that polygons require three or more line
segments. Two line segments meeting at the
endpoints would be on top of each other and thus
would not create a closed figure. On Your Own:
Students should circle 2, 4, 5, and 6.
p. 7
Talk About It: It is important to understand twodimensional plane figures because people encounter
two-dimensional figures daily—on paper, on TV, on a
white board, etc.
p
add the area of the unshaded part to the area of the
shaded part to find 19 square units. On Your Own:
Answers will vary but should reflect students’
understanding that the number of unit squares that fit
inside a figure equals the figure’s area and that half a
unit square within a figure counts as half a unit toward
the total area of the figure.
pp. 15–16
1. 12 square meters 2. 5 square centimeters 3. 14
square inches 4. 16 square feet 5. 8 square centimeters
6. 18 square inches
p. 17
Drawings will vary but should contain the correct
number of square units.
pp. 18–19
1. 10 square meters 2. 15 square inches 3. 12 square
centimeters 4. 23 square feet 5. 4 square inches 6. 17
squar
ntimeters
p
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
10
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
References
* All Web sites listed were active at time of publication.
Adams, T. (2003). Reading mathematics: More than words can say. Reading Teacher, 56, 786–795.
Aiken, L. R. (1972). Language factors in learning mathematics. Review of Education Research, 42(3),
359–385.
Allington, R. L., & Johnston, P. H. (2002). Reading to learn: Lessons from exemplary fourth-grade
classrooms. New York: Guilford.
Barnes, D. (1976/1992). From communication to curriculum. London: Penguin. (2nd ed., 1992,
Portsmouth, NH: Boynton/Cook-Heinemann.)
Block, C. C., & Parris, S. R. (Eds.). (2008). Comprehension instruction: Research-based best practices
(2nd ed.). New York: Guilford Press.
Brummett, B. (2010). Techniques of close reading. Thousand Oaks, California: SAGE Publications.
This page may not be reproduced.
This page may not be reproduced.
Butler, D. L., & Winnie, P. H. (1995). Feedback and self-regulated learning: A theoretical synthesis.
Review of Educational Research, 65(3), 245–281.
Chapin, S. H., O’Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help
students learn (2nd ed.). Sausalito, CA: Math Solutions.
Fennema, E., & Romberg, T. (Eds.). (1999). Mathematics classrooms that promote understanding.
Mahwah, NJ: Lawrence Erlbaum Associates.
Fosnot, C. T. (Ed.). (1996). Constructivism: Theory, perspectives, and practice. New York: Teachers College
Press.
Fosnot, C. T. (2005). Constructivism revisited: Implications and reflections. The Constructivist, 16(1).
Fraivilig, J., Murphy, L. A., & Fuson, K. (1999). Advancing children’s mathematical thinking in everyday
mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148–170.
Grouws, D. A. (2004). Chapter 7: Mathematics. In G. Cawelti (Ed.), Handbook of research on improving
student achievement (3rd ed.). Arlington, VA: Educational Research Service.
Harmon, J., Hedrick, W., & Wood, K. (2005). Research on vocabulary instruction in the content areas:
Implications for struggling readers. Reading & Writing Quarterly, 21, 261–280.
Harvey, S., & Daniels, H. (2009). Comprehension and collaboration: Inquiry circles in action. Portsmouth,
NH: Heinemann.
Hattie, J., & Timperley, H. (2007, March). The power of feedback. Review of Educational Research, 77(1),
81–112.
Herbel-Eisenmann, B., & Cirillo, M. (Eds.). (2009). Promoting purposeful discourse. Reston, VA: NCTM.
Hess, K. K. (2006). Applying Webb’s depth-of-knowledge and NAEP levels of complexity in mathematics.
Retrieved from National Center for the Improvement of Educational Assessment (NCIEA) Web site:
http://www.nciea.org/publications/DOKmath_KH08.pdf
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TestSMART® Common Core Student Work Text, Teacher Guide
© ECS Learning Systems, Inc.
TestSMART® Common Core Teacher Guide—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
11
Selected pages from
Student Work Text
Mathematics
Grade 3, Book III
This page may not be reproduced.
Measurement & Data–Geometric Measurement
Geometry
Lori Mammen
Editorial Director
ISBN: 978-1-60539-886-0
Copyright infringement is a violation of Federal Law.
©2013 by ECS Learning Systems, Inc., Bulverde, Texas. All rights reserved. No part of this publication may be reproduced,
translated, stored in a retrieval system, or transmitted in any way or by any means (electronic, mechanical, photocopying,
recording, or otherwise) without prior written permission from ECS Learning Systems, Inc.
Reproduction of any part of this publication for an entire school or for a school system, by for-profit institutions and tutoring
centers, or for commercial sale is strictly prohibited.
Printed in the United States of America.
Disclaimer Statement
ECS Learning Systems, Inc. recommends that the purchaser/user of this publication preview and use his/her own judgment
when selecting lessons and activities. Please assess the appropriateness of the content and activities according to grade level
and maturity of your students. The responsibility to adhere to safety standards and best professional practices is the duty of
the teachers, students, and/or others who use the content of this publication. ECS Learning Systems is not responsible for
any damage, to property or person, that results from the performance of the activities in this publication.
TestSMART is a registered trademark of ECS Learning Systems, Inc.
12
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Section I
Measurement & Data–Geometric Measurement..............................................................3
Section II
Geometry ......................................................................................................................................83
Mathematics Vocabulary...................................................................................................104
Reference Materials .............................................................................................................105
Scratch Paper ..........................................................................................................................109
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ECS Learning Systems, Inc.
P. O. Box 440
Bulverde, TX 78163-0440
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TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
13
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Section I—Measurement & Data–Geometric Measurement
Section I—Measurement & Data–Geometric Measurement
3.MD—Understand concepts of area, and relate area to multiplication and to
addition
5. Recognize area as an attribute of plane figures, and understand concepts of
area measurement.
a. A square with side length 1 unit, called a “unit square,” is said to have “one
square unit” of area, and can be used to measure area.
b. A plane figure which can be covered without gaps or overlaps by n unit
squares is said to have an area of n square units.
This page may not be reproduced.
6. Measure areas by counting unit squares (square cm, square m, square in.,
square ft, and improvised units).
This page may not be reproduced.
7. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it,
and show that the area is the same as would be found by multiplying the
side lengths.
b. Multiply side lengths to find areas of rectangles with whole-number side
lengths in the context of solving real world and mathematical problems,
and represent whole-number products as rectangular areas in
mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with
whole-number side lengths a and b + c is the sum of a x b and a x c. Use
area models to represent the distributive property in mathematical
reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by
decomposing them into non-overlapping rectangles and adding the areas
of the non-overlapping parts, applying this technique to solve real world
problems.
3.MD—Recognize perimeter as an attribute of plane figures, and distinguish
between linear and area measures
8. Solve real world and mathematical problems involving perimeters of
polygons, including finding the perimeter given the side lengths, finding an
unknown side length, and exhibiting rectangles with the same perimeter and
different areas or with the same area and different perimeters.
Note: The Common Core State Standards (CCSS) identify understanding the structure of
rectangular arrays and of area as a critical area of instruction for Grade 3.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
14
© ECS Learning Systems, Inc.
3
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Section I—Measurement & Data–Geometric Measurement
Standard 3.MD.5 (L–M)
Polygons
A polygon is a figure (shape) made from three or more line segments. Every polygon is a
closed figure. Closed means that the line segments meet at their endpoints. In other words,
there are no “doors” into the figure. The examples below show polygons.
A
B
R
D
C
T
square
S
W
X
Z
Y
rectangle
triangle
Talk About It
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• What line segments form the square?
This page may not be reproduced.
• What line segments form the triangle?
• What line segments form the rectangle?
Think About It: Could you make a polygon with only two line segments? Why or why not?
On Your Own: Look at the drawings below. Circle each polygon.
1.
4.
2.
5.
3.
6.
Challenge: Label the endpoints on each polygon above.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
5
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
15
TestSMART® Common Core Sample Booklet
Section I—Measurement & Data–Geometric Measurement
Mathematics, Grade 3—Book III
On Your Own–2: Look at each rectangle below. Then, complete the equation for each one.
Double check your answers by counting square units in each rectangle. The first one is
completed for you.
3.
1
7
13
19
25
2 3 4 5 6
8 9 10 11 12
14 15 16 17 18
20 21 22 23 24
26 27 28 29 30
5
6
30
Number of rows
Number of
square units
in each row
Total number
of square units
(Area)
_______________ x _______________ = _______________
1 unit
This page may not be reproduced.
This page may not be reproduced.
1 unit
4.
1 unit
_______________ x _______________ = _______________
Number of rows
1 unit
Number of
square units
in each row
Total number
of square units
(Area)
5.
_______________ x _______________ = _______________
Number of rows
Number of
square units
in each row
Total number
of square units
(Area)
1 unit
1 unit
continue to next page
34
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
16
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Section I—Measurement & Data–Geometric Measurement
Mathematics, Grade 3—Book III
Standard 3.MD.7 (M)
Enlarging Area
You already know how to find the area of a rectangle by counting square units, using arrays,
and multiplying length times width. How would you find the area of a rectangle after it is
enlarged (made bigger)? Look at the examples below.
Current Porch
Example #1
The diagram to the right shows a porch on a house.
Talk About It–1
• What are the dimensions of the porch?
• What is the area of the whole porch?
1 ft
1 ft
Current Porch
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This page may not be reproduced.
The owner of the house wants to enlarge (make bigger)
the porch. The diagram below shows the owner’s porch
now and the owner’s planned addition to the porch.
Addition
Talk About It–2
• What are the dimensions of the addition
to the porch?
• What is the area of the addition to the porch?
• How could you find the area of the whole
porch after it is enlarged?
• What are the dimensions of the whole porch
after it is enlarged?
1 ft
1 ft
Current Porch
Addition
The diagram to the right shows one way to find the
area of the enlarged porch.
6 x 5 = 30
6 x 3 = 18
30 + 18 = 48
OR
6 x (5 + 3) =
6 x 8 = 48
Area of enlarged porch = 48 square feet
46
TestSMART® Common Core Student Work Text
1 ft
1 ft
continue to next page
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
17
TestSMART® Common Core Sample Booklet
Section I—Measurement & Data–Geometric Measurement
Mathematics, Grade 3—Book III
Standard 3.MD.7 (M–H)
Problem Solving VII
Directions: Read the following information about making a garden. Use the information to
draw correct diagrams and to answer each question.
1. A park has two flower gardens. One garden
is on the west side of the park. The other
garden is on the east side of the park. Each
garden is 5 feet long and 4 feet wide. Draw
a diagram that shows each flower garden
on the grid to the right. Label one garden
as Garden A. Label the other garden
as Garden B. Lightly shade the area of
each garden.
N
W
E
1 ft
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This page may not be reproduced.
S
1 ft
2. What number sentence would you use to find the area of each flower garden?
______________________________________
3. The area of each garden is ___________________.
4. The park gardener decided that Garden A was too small. The gardener increased the size
of Garden A so that it was 7 feet long and 5 feet wide. Show the enlarged Garden A by
adding to the diagram on the grid above.
5. What number sentence would you use to find the new area of Garden A?
______________________________________
6. The area of Garden A is now ___________________.
7. What is the difference between the area of Garden A and the area of Garden B? ____________
8. The park gardener decides that Garden B is also too small. The gardener increases the
size of Garden B to 6 feet long and 5 feet wide. Show the enlarged Garden B by adding
to the diagram on the grid above.
9. The area of Garden B is now ___________________.
10. What is the combined area of Garden A and Garden B after each one was enlarged?
___________________
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TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
18
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Section I—Measurement & Data–Geometric Measurement
Mathematics, Grade 3—Book III
Standard 3.MD.7 (M–H)
An Area Challenge
A math teacher showed students the diagram below. The diagram shows the floor plan for a
playroom. The teacher wants students to find the area of the playroom.
2m
3m
2m
3m
6m
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This page may not be reproduced.
6m
4m
10 m
Think About It
• Why is finding the area of the playroom a challenge?
• Why would “rectangles” be important for finding the playroom’s area?
• How would you find the area of the playroom?
Working Together: Working with a partner, find the area of the playroom. Look for
rectangles. You may draw lines on the diagram to help you find the playroom’s area. Show
your work in the box below.
58
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
19
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Section I—Measurement & Data–Geometric Measurement
Standard 3.MD.8 (M–H)
A Look at Area & Perimeter
Look at the two rectangles on the grid below. Then, answer the questions that follow.
1 cm
A
1 cm
B
1 cm
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This page may not be reproduced.
1 cm
1. What is the perimeter of rectangle A? ________________
2. What is the perimeter of rectangle B? ________________
3. What is the area of rectangle A? ________________
4. What is the area of rectangle B? ________________
Talk About It: Based on your answers for 1–4, how would you complete the following
sentence?
5. Rectangles A and B have different ____________________ , but they have the same
____________________.
On Your Own: On the grid above, draw two other rectangles that have the same area as
rectangles A and B. Label one rectangle “C” and the other rectangle “D.”
6. What are the dimensions of rectangle C? ________________________________
7. What is the perimeter of rectangle C? ________________
8. What are the dimensions of rectangle D? ________________________________
9. What is the perimeter of rectangle D? ________________
Be ready to explain what you learned about perimeter and area by completing this page.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
20
© ECS Learning Systems, Inc.
71
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Section II—Geometry
Section II—Geometry
3.G—Reason with shapes and their attributes
1. Understand that shapes in different categories (e.g., rhombuses, rectangles,
and others) may share attributes (e.g., having four sides), and that the shared
attributes can define a larger category (e.g., quadrilaterals). Recognize
rhombuses, rectangles, and squares as examples of quadrilaterals, and draw
examples of quadrilaterals that do not belong to any of these subcategories.
2. Partition shapes into parts with equal areas. Express the area of each part as a
unit fraction of the whole.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
This page may not be reproduced.
This page may not be reproduced.
Note: The Common Core State Standards (CCSS) identify describing and analyzing
two-dimensional shapes as a critical area of instruction for Grade 3.
83
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
21
TestSMART® Common Core Sample Booklet
Section II—Geometry
Mathematics, Grade 3—Book III
Standard 3.G.1 (L–M)
Another Look at Polygons
Let’s see how much you remember about polygons.
Directions: Complete the paragraph below by writing the correct word in each blank.
What is a polygon?
A polygon is a ___________________ made from three or more line ___________________.
Every polygon is a ___________________ figure. This means that the line segments meet at
their ___________________. In other words, there are no “doors” into the figure.
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This page may not be reproduced.
Try It: Draw three different polygons in the box below.
Talk About It
• What is the name of each polygon that you drew?
• How are the polygons similar to each other?
• How are the polygons different from each other?
84
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
22
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Section II—Geometry
Mathematics, Grade 3—Book III
Standard 3.G.1 (L–M)
All About Quadrilaterals
Quadrilaterals are a category of polygons. A category is a group of things that have the
same attributes, or properties. You already know that all quadrilaterals—
• have four sides
• are closed figures
• have two dimensions
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This page may not be reproduced.
Look at the figures below. They are all quadrilaterals.
There are also many subcategories of quadrilaterals. A subcategory is a smaller group of
things that is also part of a larger group (category). The smaller group has all the attributes
of the larger group. Things in the smaller group also have an attribute that sets them apart.
You already know about a category of figures called quadrilaterals. Now you will learn about
some subcategories of quadrilaterals.
Parallelogram
Parallelograms are one subcategory of quadrilaterals. All parallelograms have two pairs of
parallel sides. Parallel means that the opposite sides are always the same distance apart.
Parallel sides will never intersect (cross one another).
Look at the figures below. They are all parallelograms.
continue to next page
86
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
23
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Section II—Geometry
Standard 3.G.1 (M)
Name That Figure
Directions: Circle all the names that fit each figure shown below. The first one is completed
for you.
1.
3.
4.
6.
parallelogram
rectangle
rectangle
square
square
rhombus
rhombus
quadrilateral
7.
© ECS Learning Systems, Inc.
quadrilateral
parallelogram
parallelogram
rectangle
rectangle
square
square
rhombus
rhombus
quadrilateral
8.
quadrilateral
parallelogram
parallelogram
rectangle
rectangle
square
square
rhombus
rhombus
quadrilateral
parallelogram
9.
quadrilateral
parallelogram
rectangle
rectangle
square
square
rhombus
rhombus
quadrilateral
quadrilateral
5.
quadrilateral
parallelogram
parallelogram
10.
parallelogram
rectangle
rectangle
square
square
rhombus
rhombus
TestSMART® Common Core Student Work Text
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
24
© ECS Learning Systems, Inc.
This page may not be reproduced.
This page may not be reproduced.
2.
quadrilateral
89
TestSMART® Common Core Sample Booklet
Section II—Geometry
Mathematics, Grade 3—Book III
Standard 3.G.1 (M)
How are the figures alike?
Directions: Look at each pair of figures below. Then, list at least two ways the figures are
alike. The first one is completed for you.
1.
Both figures are quadrilaterals. Both figures are rectangles.
________________________________________________________________________
Both figures have “square corners.”
________________________________________________________________________
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This page may not be reproduced.
2.
________________________________________________________________________
________________________________________________________________________
3.
________________________________________________________________________
________________________________________________________________________
4.
________________________________________________________________________
________________________________________________________________________
continue to next page
92
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
© ECS Learning Systems, Inc.
25
TestSMART® Common Core Sample Booklet
Mathematics, Grade 3—Book III
Section II—Geometry
Standard 3.G.2 (L)
Reviewing Fractions
Let’s review what you know about fractions.
A fraction is a number that shows a part, or parts, of a whole. The bottom number in a
fraction is the denominator. The bottom number in a fraction tells how many equal parts are
in one whole. The top number in a fraction is the numerator. The top number in a fraction
tells how many of the equal parts you have. Look at the example below.
Example
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This page may not be reproduced.
Here is one whole circle.
One whole circle is divided into 4 equal parts.
1 of the whole circle.
The shaded part shows —
4
1
—
4
numerator
denominator
In the example, one circle is partitioned (divided) into 4 equal parts. One of the equal parts
1 of the whole circle is shaded.
is shaded. So, —
4
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
TestSMART® Common Core Student Work Text—Mathematics, Grade 3—Book IIII
26
© ECS Learning Systems, Inc.
99
It’s On The Test
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Close Reading • Mathematics
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