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Sample Booklet
Grade 5
Mathematics — Book III
Measurement and Data
Geometry
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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 5, Book III
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Measurement and Data
Geometry
Teacher Guide
Lori Mammen
Editorial Director
ISBN: 978-1-60539-903-4
Copyright infringement is a violation of Federal Law.
©2014 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
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Printed in the United States of America.
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ECS Learning Systems, Inc. recommends that the purchaser/user of this publication preview and use his/her own judgment
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© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Table of Contents
What’s Inside the Student Work Text?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
How to Use the Student Work Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Text-Marking in Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Integrating the Literacy Strands in the Mathematics Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Master Skills List. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
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Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
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 5—Book III
© ECS Learning Systems, Inc.
3
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—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 the Student Work Text
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 15–30 minutes.
Getting Started
Teachers should implement the activities from the TestSMART Common Core Student
Work Text in sequential order. The activities logically progress within each domain,
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 5—Book III
4
© ECS Learning Systems, Inc.
3
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Understanding Rigor and Cognitive Complexity
Increased Rigor
The Common Core State Standards (CCSS) (NGA/CCSSO, 2012) hope to create more
rigorous instruction and learning across the country. But what does academic rigor
mean? Academic rigor is a measure of cognitive demand. In a rigorous system,
standards, curriculum, instruction, and assessment tightly align with congruent
measures of cognitive complexity. Students must demonstrate a deep mastery of
processes, skills, and understandings through rich, complex tasks. The TestSMART ®
Common Core Student Work Text provides items written at varying levels of complexity
to accommodate the demands of the expectations in the CCSS for Mathematics
(NGA/CCSSO, 2010b). (Refer to the “Depth of Knowledge” section on this page and
the “Descriptions of TestSMART® Complexity Levels” section on pages 7–8 for more
information about the complexity levels of practice items.)
In addition, the work text provides a range of opportunities to develop mathematical
practices. The content was designed to support student progress to algebra by—
This page may not be reproduced.
focusing on the critical areas of the grade (as defined in the CCSS)
linking major topics within each grade
thinking across grades
providing balanced attention to all aspects of rigor (NGA/CCSSO, 2013)
This page may not be reproduced.
•
•
•
•
Depth of Knowledge
Norman Webb’s (2002a) “depth-of-knowledge” model is currently one of the most
influential alignment models in the field of education. “Depth of knowledge” describes
the degree of complexity of knowledge required for a curricular item. Webb identifies
four levels of depth of knowledge: recall (Level 1), skill or concept (Level 2), strategic
thinking (Level 3), and extended thinking (Level 4). Distinct cognitive demands occur
during each activity, or thinking process, level.
The items in the TestSMARTCommon Core Student Work Text were aligned to the CCSS
for Mathematics using a modified version of the “depth-of-knowledge” model (see
“Descriptions of TestSMART® Complexity Levels,” pages 7–8). During the alignment
process, the complexity level of each item (designated “Low,” “Moderate,” or “High”)
was determined. The level can be found in the skill tag of each practice item.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text, Teacher Guide
5
TestSMART® Common Core Teacher Guide—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
5
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book II
Understanding Rigor and Cognitive Complexity
Increased Rigor
The Common Core State Standards (CCSS) (NGA/CCSSO, 2012) hope to create more
rigorous instruction and learning across the country. But what does academic rigor
mean? Academic rigor is a measure of cognitive demand. In a rigorous system,
standards, curriculum, instruction, and assessment tightly align with congruent
measures of cognitive complexity. Students must demonstrate a deep mastery of
processes, skills, and understandings through rich, complex tasks. The TestSMART ®
Common Core Student Work Text provides items written at varying levels of complexity
to accommodate the demands of the expectations in the CCSS for Mathematics
(NGA/CCSSO, 2010b). (Refer to the “Depth of Knowledge” section on this page and
the “Descriptions of TestSMART® Complexity Levels” section on pages 7–8 for more
information about the complexity levels of practice items.)
In addition, the work text provides a range of opportunities to develop mathematical
practices. The content was designed to support student progress to algebra by—
This page may not be reproduced.
focusing on the critical areas of the grade (as defined in the CCSS)
linking major topics within each grade
thinking across grades
providing balanced attention to all aspects of rigor (NGA/CCSSO, 2013)
This page may not be reproduced.
•
•
•
•
Depth of Knowledge
Norman Webb’s (2002a) “depth-of-knowledge” model is currently one of the most
influential alignment models in the field of education. “Depth of knowledge” describes
the degree of complexity of knowledge required for a curricular item. Webb identifies
four levels of depth of knowledge: recall (Level 1), skill or concept (Level 2), strategic
thinking (Level 3), and extended thinking (Level 4). Distinct cognitive demands occur
during each activity, or thinking process, level.
The items in the TestSMARTCommon Core Student Work Text were aligned to the CCSS
for Mathematics using a modified version of the “depth-of-knowledge” model (see
“Descriptions of TestSMART® Complexity Levels,” pages 7–8). During the alignment
process, the complexity level of each item (designated “Low,” “Moderate,” or “High”)
was determined. The level can be found in the skill tag of each practice item.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text, Teacher Guide
TestSMART® Common Core Teacher Guide—Mathematics, Grade 5—Book III
6
© ECS Learning Systems, Inc.
5
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Overall, rigorous mathematics instruction focuses on the critical areas of the grade (as
defined in the CCSS) while providing balanced attention to the following processes
and proficiencies, which are considered mutually reinforcing (e.g., Grouws, 2004;
Kilpatrick, Swafford, & Findell, 2001; NAGB, 2012; NMAP, 2008; NCTM, 2000;
NGA/CCSSO, 2010b).
NCTM Process Standards
•
•
•
•
•
problem solving
reasoning and proof
communication
representation
connections
NRC’s Proficiency Strands
•
•
•
•
•
adaptive reasoning
strategic competence
conceptual understanding
procedural fluency
productive disposition
(Kilpatrick et al., 2001, Adding It Up)
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The “processes and proficiencies” are the foundation for the Standards for
Mathematical Practice (NGA/CCSSO, 2010b).
1. Make sense of problems, and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments, and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
An effective mathematics curriculum integrates the mathematics domains of the
grade (Grouws, 2004).
“
It is the
relationship between
the knowledge types
that gives one’s
knowledge the power
of application in a
wide variety of
settings”
(p. 183, Silver, 1987).
6
•
•
•
•
•
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations—Fractions
Measurement and Data
Geometry
Box 1: Balance in Rigorous Mathematics Instruction
TestSMART® Common Core Student Work Text, Teacher Guide
© ECS Learning Systems, Inc.
TestSMART® Common Core Teacher Guide—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
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TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book II
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 5—Book III
8
© ECS Learning Systems, Inc.
9
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—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 5—Book III
© ECS Learning Systems, Inc.
9
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book II
• 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
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TestSMART® Common Core Teacher Guide—Mathematics, Grade 5—Book III
Mathematics, Grade 5—Book III
Answer Key
Section I—Measurement and Data
ed.
pp. 4–5
Think About It: We add the three measurements in
inches first so that we only have to convert to feet once
instead of three times; The remainder is in inches
because the dividend wasn’t converted to feet. There
are 12 inches in a foot, but 12 cannot go into 3, so the
3 inches weren’t converted to feet; You can write the
answer as a fraction or decimal: 6 3/12 ft OR 6 1/4 ft, 6.25
ft Talk About It: 1 yd = 3 ft and 1 ft = 12 in., so 1 yd = 3 ft
x 12 OR 1 yd = 36 in.
p. 6
1. 8 2. 108 3. 5 ft 4 in. 4. 144 5. 31,680 6. 12 7. 5,280 8. 1 mi
4,720 ft 9. 6 yd 2 ft 10. 30 11. 3 12. 190,080
pp. 7–8
Working Together: 28,800 sec; Students need to know
that 1 hr = 60 min and 1 min = 60 sec. Students first
convert hours to minutes: 8 hr x 60 = 480 min. Then,
s
d
the next place value. So, each time you convert, you
change the place value of the number, whether you are
moving the decimal or adding zeros to hold the place.
p. 21
1. 3,320 2. 8,700 3. 69,000 4. 50 5. 8,230 6. 892.39 7. 2
8. 389 9. 60.35 10. 135,000 11. 430 12. 2,945 13. 39,000
14. 30,200 15. 63 16. 5,200
pp. 22–23
Try It: a. 0.12 b. 0.12; 0.012 c. 0.012; 0.0012 Talk About It:
The place value system is in base ten. Each time you form
a group of 10, you regroup to the next place value. So,
each time you convert, you change the place value of the
number, whether you are moving the decimal or adding
zeros to hold the place.
p. 24
1. 0.764 2. 4.53 3. 0.02371 4. 3.4 5. 9 6. 0.0028 7. 0.4005
8. 0.124 9. 0.07575 10. 450 11. 0.0018 12. 82.67 13. 1.2
14. 0.073 15. 0.3 16. 0.01999
p. 25
1
8d
0
TestSMART® Common Core Teacher Guide—Mathematics, Grade 5—Book III
©
10
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—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). Exploring cognitive demand in instruction and assessment. Retrieved
from National Center for the Improvement of Educational Assessment (NCIEA) Web site:
http://www.nciea.org/publications/DOK_ApplyingWebb_KH08.pdf
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Olivier, A., & Human, P.
(1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH:
Heinemann.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text, Teacher Guide
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TestSMART® Common Core Teacher Guide—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
11
Selected pages from
Student Work Text
Mathematics
Grade 5, Book III
This page may not be reproduced.
Measurement and Data
Geometry
Lori Mammen
Editorial Director
ISBN: 978-1-60539-902-7
Copyright infringement is a violation of Federal Law.
©2014 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 5—Book III
Section I
Measurement and Data..............................................................................................................3
Section II
Geometry ......................................................................................................................................99
Mathematics Vocabulary...................................................................................................143
Scratch Paper ..........................................................................................................................144
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ECS Learning Systems, Inc.
P. O. Box 440
Bulverde, TX 78163-0440
ecslearningsystems.com
1.800.688.3224 (t)
1.877.688.3226 (f )
[email protected]
2
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
13
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Section I—Measurement and Data
Section I—Measurement and Data
5.MD—Convert like measurement units within a given measurement system
1. Convert among different-sized standard measurement units within a given
measurement system, and use these conversions in solving multi-step, real-world
problems.
5.MD—Represent and interpret data
2. Make a line plot to display a data set of measurements in fractions of a unit
5.MD—Geometric measurement: Understand concepts of volume, and relate
volume to multiplication and to addition
3. Recognize volume as an attribute of solid figures, and understand concepts of
volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic
unit” of volume and can be used to measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit
cubes is said to have a volume of n cubic units.
4. Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft, and
improvised units.
5. Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume.
a. Find the volume of a right rectangular prism with whole-number side lengths
by packing it with unit cubes, and show that the volume is the same as would
be found by multiplying the edge lengths, equivalently by multiplying the
height by the area of the base. Represent threefold whole-number products
as volumes, e.g., to represent the associative property of multiplication.
b. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find
volumes of right rectangular prisms with whole-number edge lengths in the
context of solving real-world and mathematical problems.
c. Recognize volume as additive. Find volumes of solid figures composed of two
non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real-world problems.
Note: The Common Core State Standards (CCSS) identify developing understanding of
volume as one of three critical areas of instruction for Grade 5.
T
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
14
© ECS Learning Systems, Inc.
T
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1,—
1,—
1 ). Use operations on fractions for this grade to solve problems involving
(—
2 4 8
information presented in line plots.
TestSMART® Common Core Sample Booklet
Section I—Measurement and Data
Mathematics, Grade 5—Book III
Standard 5.MD.1 (L)
Customary Measurement: Converting Length
The customary measurement units for length, from shortest to longest, are inches (in.),
feet (ft), yards (yd), and miles (mi).
12 inches = 1 foot
3 feet = 1 yard
36 inches = 1 yard
5,280 feet = 1 mile
1,760 yards = 1 mile
Read the problem below.
Nelson measured three sections of a wall. The lengths of the sections were
16 inches, 31 inches, and 25 inches. How many feet of lumber will Nelson
need to run the entire length of all three sections?
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In this problem, Nelson measures in one unit (inches) but the question asks for an answer in
a different unit (feet).
Before you convert the measurements, you must add the lengths of the three sections.
16 in. + 31 in. + 25 in. = 72 in.
Next, you must know how many inches are in a foot.
12 inches = 1 foot
When converting a smaller unit to a larger unit, you divide.
72 inches ÷ 12 = 6 feet
What if Nelson’s measurements added up to 75 inches?
75 inches ÷ 12 = 6 r 3
= 6 feet 3 inches
Think About It
• Why did we add the three measurements before converting to feet?
• Why is the remainder in the previous example in inches instead of feet?
• How can you write the answer using only feet?
continue to next page
4
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
15
TestSMART® Common Core Sample Booklet
Section I—Measurement and Data
Mathematics, Grade 5—Book III
Standard 5.MD.1 (L–M)
Metric Measurement: Converting from Smaller to Larger
Look at the chart below.
kilo-
hecto-
deca-
base
deci-
centi-
milli-
1,000
100
10
1
1
—
10
1
—
100
1
—
1,000
The chart shows the prefixes used in the metric system. The prefixes are used to compare
1
the size of
the size of each unit to the size of the base unit. For example, 1 meter is —
1,000
1 the size of the
1 kilometer, and 1 liter is 1,000 times greater than 1 milliliter. Each unit is —
10
When converting a smaller unit to a larger unit, you move to the left. Each time you move
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unit to the left. For example, 10 decigrams is equal to 1 gram.
1 of a decigram. One
to the left, you divide the number by 10. For example, 1 centigram is —
10
1 of a decagram. One hectogram is —
1 of a kilogram.
gram is —
10
10
1 cg = 0.1 dg
1 g = 0.1 Dg
1 hg = 0.1 kg
Let’s practice converting smaller units to larger units.
Convert 26,000 millimeters to meters.
÷ 10
÷ 10
÷ 10
26 meters = 260 decimeters = 2,600 centimeters = 26,000 millimeters
26,000 millimeters = 26 meters
Convert 38,000 liters to hectoliters.
÷ 10
÷ 10
380 hectoliters = 3,800 decaliters = 38,000 liters
38,000 liters = 380 hectoliters
continue to next page
22
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
16
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Section I—Measurement and Data
Mathematics, Grade 5—Book III
Standard 5.MD.2 (L–M)
Line Plots
A line plot is a graph that shows frequency of data along a number line. Remember that
frequency means the number of times that something happens or appears in a set of data.
Look at the example below.
Lengths of Items in a Desk
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1
—
8
1
—
4
3
—
8
X
X
X
X
X
1
—
2
5
—
8
3
—
4
7
—
8
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0
X
X
X
X
X
X
X
X
X
X
X
X
1
Inches
1,—
1 , or —
1 inch. The data is presented
The objects in a desk were measured to the nearest —
8 4
2
on the line plot above.
You can use a line plot to answer simple questions.
1 inch? The graph shows 6 Xs above —
1 , so 6 items measured
How many items measured —
2
2
1 inch.
—
2
3 inch? The graph shows no Xs above —
3 , so no items measured
How many items measured —
8
8
that length.
What was the total number of items measured? The graph has 17 Xs, so 17 items were
measured.
Think About It: Using data from the line plot, you can use basic addition and subtraction to
calculate different amounts.
1 inch or —
7 inch? How do you know?
• How many items measured either —
8
8
1 inch than —
3 inch? How do you know?
• How many more items measured —
4
4
continue to next page
30
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
17
TestSMART® Common Core Sample Booklet
Section I—Measurement and Data
Mathematics, Grade 5—Book III
Standard 5.MD.2 (M–H)
Problem Solving V
Directions: Read each item below. Answer the questions after creating a line plot using the
data in each problem.
1,—
1 , or —
1 inch. Record the data
1. Use a ruler to measure the pencils below to the nearest —
2 4
8
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This page may not be reproduced.
on the lines.
A.
__________
B.
__________
C.
__________
D.
__________
E.
__________
F.
__________
G.
__________
H.
__________
I.
__________
J.
__________
a. Create a line plot to display the lengths of the pencils.
1 inches long than 5 —
1 inches? _______________
b. How many more pencils are 4 —
2
2
1 inches long? _______________
c. How many pencils are more than 4 —
2
d. What size pencil is needed for the group to have a total length of 4 feet?
_______________
continue to next page
36
TestSMART® Common Core Student Work Text
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
18
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Section I—Measurement and Data
Mathematics, Grade 5—Book III
Standard 5.MD.5 (L–M)
Which one is different?
Directions: Find the volume of each rectangular prism below. Circle the volume that is
different from the other two. The first one is completed for you.
1.
a.
b.
1 cm
1 cm
1 cm
45 cm
30 cm
3
3
Volume: _____________ Volume: _____________
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30 cm
3
Volume: _____________
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c.
2.
a.
b.
1 in.
c.
1 in.
1 in.
Volume: _____________
Volume: _____________ Volume: _____________
3.
a.
1 ft
Volume: _____________
b.
1 ft
c.
1 ft
Volume: _____________ Volume: _____________
continue to next page
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TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
19
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Section II—Geometry
Section II—Geometry
5.G—Graph points on the coordinate plane to solve real-world and
mathematical problems
1. Use a pair of perpendicular number lines, called axes, to define a coordinate
system, with the intersection of the lines (the origin) arranged to coincide with
the 0 on each line and a given point in the plane located by using an ordered
pair of numbers, called its coordinates. Understand that the first number
indicates how far to travel from the origin in the direction of one axis and the
second number indicates how far to travel in the direction of the second axis,
with the convention that the names of the two axes and the coordinates
correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
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2. Represent real-world and mathematical problems by graphing points in the
first quadrant of the coordinate plane, and interpret coordinate values of
points in the context of the situation.
5.G—Classify two-dimensional figures into categories based on their
properties
3. Understand that attributes belonging to a category of two-dimensional
figures also belong to all subcategories of that category.
4. Classify two-dimensional figures in a hierarchy based on properties.
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
20
© ECS Learning Systems, Inc.
99
TestSMART® Common Core Sample Booklet
Section II—Geometry
Mathematics, Grade 5—Book III
Standard 5.G.1 (L–M)
It’s a plane!
You know how to use a number line to measure distances between two points. Now, you will
use two number lines at once to measure distances. A coordinate plane is a grid system
used to describe a point’s location in relation to two intersecting and perpendicular lines.
Let’s begin with a horizontal line. Remember, a horizontal line runs side to side forever.
On a grid, the horizontal line is called the x-axis. The x-axis will always run from left to right,
or east to west, just like lines of latitude on a globe.
Now, we add a vertical line. Remember, a vertical line runs up and down forever.
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On a grid, the vertical line is called the y-axis. The y-axis will always run up and down, or
north to south, just like lines of longitude on a globe.
continue to next page
100
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© ECS Learning Systems, Inc.
21
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Section II—Geometry
Standard 5.G.1 (L–M)
What’s the point?
A. Directions: Determine the coordinates for each point on the coordinate plane. Write the
coordinates as an ordered pair. The first one is completed for you.
(2, 3)
1. Point A: ________________
2. Point B: ________________
3. Point C: ________________
4. Point D: ________________
y
10
7. Point G: ________________
B
7
5
I
F
G
4
A
3
C
2
1
H
8. Point H: ________________
1 2
D
3 4
5
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6. Point F: ________________
J
8
6
5. Point E: ________________
E
9
x
6
7
8
9 10
9. Point I: ________________
10. Point J: ________________
B. Directions: Determine which point on the coordinate plane matches each ordered pair.
The first one is completed for you.
y
Point M
11. (3, 0): ________________
10
12. (9, 4): ________________
9
13. (1, 6): ________________
7
R
8
L
6
14. (4, 9): ________________
15. (5, 6): ________________
16. (0, 3): ________________
P
K
5
4
3
O
N
2
Q
1
M
17. (6, 1): ________________
1 2
3 4
x
5
6
7
8
9 10
18. (6, 5): ________________
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
22
© ECS Learning Systems, Inc.
105
TestSMART® Common Core Sample Booklet
Section II—Geometry
Mathematics, Grade 5—Book III
Standard 5.G.2 (L–M)
Line Graphs
A line graph is another real-world use of a coordinate plane. A line graph shows the
relationship between two sets of data. Let’s look at an example.
JMS Fifth Graders
y
300
270
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210
180
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Number of Fifth Graders
240
150
120
90
60
30
x
2009
2010
2011
2012
2013
Year
This line graph shows the number of fifth-grade students at Jefferson Middle School from
2009 to 2013.
• The x-axis represents time in years.
• The y-axis represents the number of fifth graders at the school.
Talk About It: Use the line graph above to answer the following questions.
1. How many fifth-grade students were at Jefferson Middle School in 2010?
2. How many fifth-grade students were at Jefferson Middle School in 2012?
3. How many more fifth-grade students were at Jefferson Middle School in 2013 than
in 2009?
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TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
© ECS Learning Systems, Inc.
23
TestSMART® Common Core Sample Booklet
Section II—Geometry
Mathematics, Grade 5—Book III
Standard 5.G.3 (M)
The Haves & the Have Nots
Directions: Look at the shapes in each box below. Determine the shape represented by the
figures in the “Haves” category. Then, fill in the blanks with information about the attributes
of that shape. The first one is started for you.
3
4
2
1
7
6
8
5
Haves: 1, 2, 5, 8
rectangle
Have Nots: 3, 4, 6, 7
1. Shape: _______________________
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This page may not be reproduced.
Attributes:
4
a. _______________________ sides
b. 2 pairs of _______________________ lines
c. has 4 _______________________ angles
d. Each corner forms _______________________ lines.
1
3
2
5
7
6
Haves: 2, 5, 7, 8
4
8
Have Nots: 1, 3, 4, 6
2. Shape: _______________________
Attributes:
a. _______________________ sides
b. 1 pair of _______________________ lines
continue to next page
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TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
24
© ECS Learning Systems, Inc.
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Section II—Geometry
Standard 5.G.3 (M)
Problem Solving XI
Directions: Think about the attributes of each shape below. If a shape has the attribute listed
on the left, place a checkmark in the correct box in the chart. Write the name of the shape
that has all 3 attributes on the answer line.
Attribute
Kite
Rhombus
Square
Quadrilateral
Parallelogram
Rectangle
Acute Isosceles
Triangle
Obtuse Isosceles
Triangle
4 sides
must have parallel lines
must have right angles
1. Answer: ____________________________
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This page may not be reproduced.
Attribute
4 sides
must have 2 pairs of parallel lines
can have an acute angle
2. Answer: ____________________________
Attribute
Right Scalene
Triangle
3 sides
has 2 equal sides
has an angle greater than 90˚
3. Answer: ____________________________
continue to next page
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
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© ECS Learning Systems, Inc.
25
TestSMART® Common Core Sample Booklet
Mathematics, Grade 5—Book III
Section II—Geometry
Standard 5.G.4 (L–M)
What is a hierarchy?
A hierarchy is a system of ordered categories and subcategories. A hierarchy begins with
a large group that has a broad set of attributes. To divide the category into smaller
subcategories, we consider more specific attributes. This process can continue, allowing
the subcategories to become smaller and smaller, as well as more specific. Let’s look at an
example.
We begin with a very large category.
Animals
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This page may not be reproduced.
All living creatures belong to a group called “animals.” We can separate animals into smaller
subcategories composed of creatures with more specific attributes. Look at the diagram
below.
Animals
Mammals
Birds
Reptiles
Fish
Amphibians
Talk About It: What attributes might the animals in each subcategory above have?
If we want even smaller subcategories, we can consider even more specific attributes. For
example, we can divide the subcategory of mammals into mammals that live on land and
mammals that live in water. Look at the diagram below for more examples.
Animals
Mammals
Live on
land
Live in
water
Birds
Fly
Don’t
fly
Reptiles
Have
legs
Don’t
have legs
Fish
Have
teeth
Amphibians
Don’t
have
teeth
Have
a tail
Don’t
have
a tail
continue to next page
© ECS Learning Systems, Inc.
TestSMART® Common Core Student Work Text
TestSMART® Common Core Student Work Text—Mathematics, Grade 5—Book III
26
© ECS Learning Systems, Inc.
135
It’s On The Test
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Close Reading • Mathematics
Student Work Texts
Grades 3–8
Value-Priced to provide each student a copy.
Reading
Close Reading, Grade 5
Close Reading, Grade 5
Close Reading, Grade 5
Close Reading, Grade 6
Close Reading, Grade 7
Close Reading, Grade 8
Mathematics
Mathematics, Grade 5
Mathematics, Grade 5
Mathematics, Grade 5
Mathematics, Grade 6
Mathematics, Grade 7
Mathematics, Grade 8
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