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Units for Seventh Grade
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Two-Dimensional Geometry
Student Activity Workbook
Shapes and Designs
Accentuate the Negative
Integers and Rational Numbers
Stretching and Shrinking
Understanding Similarity
Comparing and Scaling
Ratios, Rates, Percents, and Proportions
Moving Straight Ahead
Linear Relationships
What Do You Expect?
Probability and Expected Value
Filling and Wrapping
Three-Dimensional Measurement
Samples and Populations
Making Comparisons and Predictions
Grade 7
ISBN-13: 978-1-269-69460-5
ISBN-10:
1-269-69460-X
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ISBN 13: 978-1-269-69460-5
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Table of Contents
1. Shapes and Designs: Two-Dimensional Geometry
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
1
2. Accentuate the Negative: Integers and Rational Numbers
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
37
3. Stretching and Shrinking: Understanding Similarity
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
59
4. Comparing and Scaling: Ratios, Rates, Percents, and Proportions
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
103
5. Moving Straight Ahead: Linear Relationships
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
139
6. What Do You Expect?: Probability and Expected Value
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
181
7. Filling and Wrapping: Three-Dimensional Measurement
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
225
8. Samples and Populations: Making Comparisons and Predictions
Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel
Sample only - not for classroom use
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279
I
Shapes and Designs
Two-Dimensional Geometry
Parent Letter
Parent Letter in English
Labsheets
1.2 Four in a Row
1.3 Question A Angles
1.4 Question E Angles
1ACE Exercise 1
1ACE Exercise 2
1ACE Exercise 29
1ACE Exercise 30
1ACE Exercise 31
1ACE Exercise 64
1ACE Exercise 69
2.2A Trevor’s and Casey’s Methods
2.4A Question A
2.4B Question D
2ACE Exercise 2
3.1 Building Triangles
3.2 Question B
3.3 Building Quadrilaterals
3.4A Parallelograms
3.4B Questions A–E
3.5 Quadrilateral Game Grid
3ACE Exercise 18
Assessments
SampleCheck
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Up - not for classroom use
Partner Quiz
Self Assessment
Notebook Checklist
From Unit 1 of Connected Mathematics®3: Grade 7. Copyright © 2014 by Michigan State University,
Glenda Lappan, Elizabeth Difanis Phillips, James T. Fey, and Susan N. Friel. Published by Pearson Education, Inc.,
publishing as Pearson Prentice Hall. All rights reserved.
© Pearson Education, Inc. Not for distribution.
1
Dear
Querida
Family,
Familia:
This
Unit is Shapes
andlaDesigns:
Students
willprimos:
recognize,
La primera
unidad en
clase de Two-Dimensional
matematicas de suGeometry.
hijo(a) es La
hora los
Factores y
analyze,
measure,
and
reason
about
the
shapes
and
visual
patterns
that
are
important
multiplos. Esta es la primera unidad sobre el tema de numeros de Connected Mathematics.
features of our world. Students analyze the properties that make certain shapes special
and useful.
Unit Goals
The goal of Shapes and Designs is to have students discover and analyze many of the key
properties of polygonal shapes that make them useful and attractive.
This Unit focuses on polygons and develops two basic sub-themes:
tHow do the measures of angles in a polygon determine its possible shapes and uses?
tHow do the lengths of edges in a polygon determine its possible shapes and uses?
While some attention is given to naming familiar figures, each Investigation focuses on particular
key properties of figures and the importance of those properties in applications. For example,
students are asked to examine what properties of triangles make them useful in construction and
design, and why triangles are preferred over quadrilaterals. Students also examine and evaluate
angle properties of polygons that make some able to tile a surface whereas others cannot. We
frequently ask students to find and describe places where they see polygons of particular types
and to puzzle over why those particular shapes are used.
Homework and Having Conversations About The Mathematics
In your child’s notebook, you can find worked-out examples, notes on the mathematics of the
Unit, and descriptions of the vocabulary words.
You can help your child with homework and encourage sound mathematical habits during this
Unit by asking questions such as:
tWhat kinds of shapes/polygons will cover a flat surface?
tWhat do these shapes have in common?
tHow do simple polygons work together to make more complex shapes?
tHow can angle measures be estimated?
tHow can angles be measured with more accuracy?
You can help your child with his or her work for this Unit in several ways:
tPoint out different shapes you see, and ask your child to find other shapes.
Sample only - not for classroom use
tWhenever you notice an interesting shape in a newspaper or a magazine, discuss with your
child whether it is one of the polygons mentioned in the Unit, and suggest that it might be
cut out and saved for the Shapes and Designs Unit Project.
Common Core State Standards
While all of the Standards of Mathematical Practice are developed and used by students
throughout the curriculum, particular attention is paid to constructing viable arguments and
critiquing the reasoning of others as students make conjectures about the construction of
geometric shapes (angles and side lengths) and justify their responses to others. Shapes and
Designs focuses largely on the Geometry domain.
A few important mathematical ideas that your child will learn in Shapes and Designs are on
the next page. As always, if you have any questions or concerns about this Unit or your child’s
progress in class, please feel free to call.
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Important Concepts
Examples
Polygon
A shape formed by line segments
so that each of the segments
meets exactly two other segments,
and all of the points where the
segments meet are end points of
the segments.
Polygon Names
Examples of Polygons
Non-Examples
Triangle: 3 sides and 3 angles
Quadrilateral: 4 sides and 4 angles
Pentagon: 5 sides and 5 angles
Hexagon: 6 sides and 6 angles
Heptagon: 7 sides and 7 angles
Octagon: 8 sides and 8 angles
Nonagon: 9 sides and 9 angles
Decagon: 10 sides and 10 angles
Dodecagon: 12 sides and 12 angles
Regular polygon: Polygons whose side lengths are equal and
interior angle measures are equal.
Irregular polygon: A polygon which either
has two sides with different lengths or
two angles with different measures.
Line (or mirror) Symmetry
If the polygon is folded over the line of symmetry, the
two halves of the shape will match exactly.
Rotational (or turn) Symmetry
A polygon with turn symmetry
can be turned around its center
point less than a full turn and still
look the same at certain angles
of rotation.
Angles
Angles are figures formed by two rays or line segments that have a common vertex.
The vertex of an angle is the point where the two rays meet or intersect.
Angles are measured in degrees.
Angle Measures
Work is done to relate angles to right
angles, to develop students’ estimation
skills. Combinations and partitions
of 90° are used. 30°, 45°, 60°, 90°,
120°, 180°, 270°, and 360° are used as
benchmarks to estimate angle size.
The need for more precision requires
techniques for measuring angles.
Students use an angle ruler or
protractor to measure angles.
ray
vertex
ray
270°
30°
45°
60°
180°
120°
90°
Angles and Parallel Lines
Students explore the angles created when two parallel lines are cut by a line. The line that
cuts (intersects) the parallel lines is called a transversal. Angles 1 and 5, angles 2 and 6,
angles 3 and 7, and angles 4 and 8 are called corresponding angles. Angles 4 and 5 and
angles 3 and 6 are called alternate interior angles. Parallel lines cut by a transversal create
equal corresponding angles and equal alternate interior angles.
Sample only - not for classroom use1
2
3
4
5
6
7 8
Parallel lines and transversals help explain some special features of parallelograms such as the
opposite angles have equal measures or that the sum of the measures of two adjacent angles is 180°.
Polygons that Tile a Plane
For regular polygons to tile a plane,
the angle measure of an interior angle
must be a factor of 360˚.
Only three regular polygons can tile a plane: an equilateral triangle
(60° angles), a square (90° angles) and a regular hexagon (120° angles).
There are also combinations of regular polygons that will tile, such as
2 octagons and a square.
Triangle Inequality Theorem
The sum of two side lengths of a
triangle must be greater than the
3rd side length.
If the side lengths are a, b, and c, then the sum of any two sides
is greater than the third: a + b 7 c, b + c 7 a, c + a 7 b a
b
c
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Name
Date
Labsheet 1.2
Class
Four in a Row
60°
45°
30°
0
1
2
3
0°
0
1
2
0°
3
60°
45°
30°
0°
Sample
0
0 use
1 2 3only - not for classroom
1 2
0°
Investigation 1
Shapes and Designs
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3
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Name
Date
Labsheet 1.3
Class
Question A Angles
Estimate the measure of each angle in degrees. Name each angle with the
1.
∠ symbol.
2.
A
A
V
V
B
B
3.
A
4.
V
V
A
B
B
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Investigation 1
Shapes and Designs
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Name
Date
Labsheet 1.4
Class
Question E Angles
Find the measures of the angles. Use an angle ruler or a protractor.
1.
2.
3.
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4.
Investigation 1
Shapes and Designs
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Name
Date
Labsheet 1ACE
Class
Exercise 1
1. Tell whether each figure is a polygon. Explain how you know.
a.
b.
c.
d.
e.
Sample only - not
for classroom use
f.
Investigation 1
Shapes and Designs
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Name
Date
Labsheet 1ACE
Class
Exercise 2
Common Polygons
Number of Sides
and Angles
Polygon Name
3
triangle
4
quadrilateral
5
pentagon
6
hexagon
7
heptagon
8
octagon
9
nonagon
10
decagon
12
dodecagon
Examples in the
Shapes Set
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Investigation 1
Shapes and Designs
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Name
Date
Labsheet 1ACE
Class
Exercise 29
29. Without measuring, decide whether the angles in each pair have the same measure. If they
do not, tell which angle has the greater measure. Then find the measure of the angles with an
angle ruler or protractor to check your work.
a.
1
2
b.
1
c.
2
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1
2
Investigation 1
Shapes and Designs
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