units for seventh grade - pearson education · 2016. 6. 14. · isbn-13: isbn-10: 978-1-269-69460-5...

ISBN-13:ISBN-10:

978-1-269-69460-51-269-69460-X

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units for Seventh Grade

• Shapes and Designs Two-Dimensional Geometry

• 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

000200010271895795_CV.indd 1 4/25/14 2:25 PM

Sample only - not for classroom use

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MATHEMATICS

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Printed in the United States of America.

ISBN 10: 1-269-69460-XISBN 13: 978-1-269-69460-5

ISBN 10: 1-269-69460-XISBN 13: 978-1-269-69460-5



Table of Contents

P E A R S O N C U S T O M L I B R A R Y

I

1. Shapes and Designs: Two-Dimensional Geometry

1

1Glenda Lappan/Elizabeth Difanis Phillips/James T. Fey/Susan N. Friel

2. Accentuate the Negative: Integers and Rational Numbers

37


3. Stretching and Shrinking: Understanding Similarity

59


4. Comparing and Scaling: Ratios, Rates, Percents, and Proportions

103


5. Moving Straight Ahead: Linear Relationships

139


6. What Do You Expect?: Probability and Expected Value

181


7. Filling and Wrapping: Three-Dimensional Measurement

225


8. Samples and Populations: Making Comparisons and Predictions

279




Shapes and DesignsTwo-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

Check Up Partner Quiz

Self Assessment Notebook Checklist

From Unit 1 of Connected Mathematics®3: Grade 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.

7. Copyright © 2014 by Michigan State University,

1© Pearson Education, Inc. Not for distribution.


Querida Familia:La primera unidad en la clase de matematicas de su hijo(a) es La hora los primos: Factores y multiplos. Esta es la primera unidad sobre el tema de numeros de Connected Mathematics.

Querida Familia:La primera unidad en la clase de matematicas de su hijo(a) es La hora los primos: Factores y multiplos. Esta es la primera unidad sobre el tema de numeros de Connected Mathematics.

Dear Family,

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:

How do the measures of angles in a polygon determine its possible shapes and uses?

How 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:

What kinds of shapes/polygons will cover a flat surface?

What do these shapes have in common?

How do simple polygons work together to make more complex shapes?

How can angle measures be estimated?

How can angles be measured with more accuracy?

You can help your child with his or her work for this Unit in several ways:

Point out different shapes you see, and ask your child to find other shapes.

Whenever 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.

This Unit is Geometry. Students will recognize, analyze, measure, and reason about the shapes and visual patterns that are important features of our world. Students analyze the properties that make certain shapes special and useful.

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Shapes and Designs: Two-Dimensional



Important Concepts Examples

PolygonA 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

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) SymmetryIf the polygon is folded over the line of symmetry, the two halves of the shape will match exactly.

Rotational (or turn) SymmetryA 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.

AnglesAngles are figures formed by two rays or line segments that have a common vertex.

ray

rayvertex

The vertex of an angle is the point where the two rays meet or intersect. Angles are measured in degrees.

Angle MeasuresWork 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.

30° 60°

45°

90°

180°

270°

120°

Angles and Parallel LinesStudents 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.

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 PlaneFor 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 TheoremThe 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

Examples of Polygons Non-Examples

1 2

7 8

3 4

5 6

a b

c




Name Date Class

Labsheet 1.2 Four in a Row

0 21 3 0 21 3

45°

0° 0°

30°

60°

0 21 3 0 21 3

45°

0° 0°

30°

60°


Investigation 1Shapes and Designs



Name Date Class

Estimate the measure of each angle in degrees. Name each angle with the ∠ symbol.

1. A

V

B

2.

V

A

B

3.

V

A

B

4. V

A B

Labsheet 1.3 Question A Angles





Name Date Class

Find the measures of the angles. Use an angle ruler or a protractor.

1.

2.

3.

4.

Labsheet 1.4 Question E Angles





Name Date Class

Labsheet 1ACE Exercise 1

1. Tell whether each figure is a polygon. Explain how you know.

a. b.

c. d.

e. f.





Name Date Class


Number of Sidesand Angles

3

4

5

6

7

8

9

10

12

Polygon Name

triangle

Common Polygons

quadrilateral

pentagon

hexagon

heptagon

octagon

nonagon

decagon

dodecagon

Examples in theShapes Set





Name Date Class


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 2

c.

1

2





units for seventh grade - pearson education · 2016. 6. 14. · isbn-13: isbn-10: 978-1-269-69460-5...

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