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CurriculumFocal Points

Common Core State Standards

426 Unit 6 Geometry

Advance PreparationEach child will need 16 twist-ties and 16 straws—4 straws each of the following four lengths: 2", 4", 6", and 8". Place these materials in

4 separate containers near the Math Message. For the optional Readiness activity in Part 3, make 2 copies of Math Masters, page 467

on cardstock paper. Cut out the shapes and place one set in a paper bag.

Teacher’s Reference Manual, Grades 1–3 pp. 136 –138

QuadranglesObjective To provide opportunities to explore various types

of quadrangles.o

Key Concepts and Skills• Identify right angles and parallel and

intersecting sides of quadrangles. 

[Geometry Goal 1]

• Draw and name quadrangles. [Geometry Goal 2]

• Use straws and twist-ties to model and

compare quadrangles. [Geometry Goal 2]

• Identify the sides, vertices, and adjacent

sides of quadrangles. [Geometry Goal 2]

• Measure the sides of a quadrangle. 

[Measurement and Reference Frames Goal 2]

Key ActivitiesChildren construct quadrangles and observe

their properties. They measure the sides of

a quadrangle to the nearest 1

_ 2 inch and

estimate the perimeter.

Ongoing Assessment: Recognizing Student Achievement Use journal page 136. [Geometry Goal 1]

Ongoing Assessment: Informing Instruction See pages 428 and 429.

Key Vocabularyquadrangle � square � rhombus � parallelogram

� rectangle � trapezoid � adjacent sides � kite

MaterialsMath Journal 1, p. 136

Student Reference Book, pp. 108 and 109

Home Link 6�4

Differentiation Handbook, p. 139 (optional)

straws and twist-ties � straightedge � ruler

Playing Name That Number Student Reference Book, pp. 299

and 300

per partnership: 4 each of number

cards 0–10 and 1 each of number

cards 11–20 (from the Everything Math

Deck, if available)

Children practice finding equivalent

names for numbers.

Math Boxes 6�5Math Journal 1, p. 137

Children practice and maintain skills

through Math Box problems.

Home Link 6�5Math Masters, p. 177

Children practice and maintain skills

through Home Link activities.

READINESS

Playing Touch-and-Match QuadranglesMath Masters, p. 467 (copied onto cardstock

or cardboard)

paper bag or box

Children identify similarities and differences

among quadrangles.

ENRICHMENTPlaying Shading ShapesMath Masters, pp. 457 and 458

Children explore the properties of

quadrangles.

ELL SUPPORT

Adding to the Vocabulary ChartDifferentiation Handbook, p. 133 (optional);

2 copies per child

Vocabulary Chart (from Part 3, Lesson 6 �1)

Children add the terms rectangle,

rhombus, square, trapezoid, and kite to

the Vocabulary Chart.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

�������

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Adjusting the Activity �Exploring Quadrangles

LESSON

6� 5

Date Time

Part 1

Use a straightedge. Connect points to form

a quadrangle.

Part 2

Write all 4-letter names that are possible

for your quadrangle. The first letter of each

name is given below.

A A B B

C C D D

Part 3

Work in a group.

Make quadrangles with straws and twist-ties. Make at least one of

each of the following kinds of quadrangles.

� all 4 sides equal in length

� 2 pairs of equal-length sides, but opposite sides not equal in length

� 2 pairs of equal-length opposite sides

� only 2 parallel opposite sides

� only 1 pair of equal-length opposite sides

Part 4

Measure each side of the quadrangle you drew in Part 1 to the nearest

�1

2� centimeter.

side AB cm side BC cm side CD cm side DA cm

The perimeter of my quadrangle is about centimeters.18

26�12�45�12�

CBAABCDABBADADCCDADCBBCD

D

A

B

C

Try This

Math Journal 1, p. 136

Student Page

Lesson 6�5 427

E

G

H

Quadrangle EFGH

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 1, p. 136)

Discuss Part 1 on journal page 136.

Draw and label a quadrangle on the board. Label it EFGH. Point out that another name for quadrangle is quadrilateral. Referring to the diagram on the board, review the characteristics of quadrangles.

� All quadrangles are 2-dimensional.

� All quadrangles have 4 vertices.

� All quadrangles have 4 sides.

� All quadrangles have 4 angles.

Remind children that the meaning of the prefix quad- is four. Ask for

other words that use the prefix. Quadruplets, quadruple, quadrupled, quadrant,

and quadrilateral (as another name for quadrangle) Draw or show pictures of a

few of the objects children might suggest that have the prefix quad.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

Ongoing Assessment: Journal

page 136 �Part 1Recognizing Student Achievement

Use journal page 136, part 1 to assess children’s progress toward identifying

points and drawing line segments to form a quadrangle. Children are making

adequate progress if they are able to successfully complete Part 1. Some

children may be able to identify the vertices of the quadrangle.

[Geometry Goal 1]

ELL

Getting Started

Math MessageTake 4 straws of each size and 16 twist-ties. Complete Part 1 on page 136 of your journal.

Home Link 6�4 Follow-Up Ask partners to explain how they found the right angle in Problem 4.

Mental Math and ReflexesHave children stand facing you to perform turn calisthenics.

Make a half-turn clockwise. Make a half-turn counterclockwise. Ask: What do you notice? Children are back in the starting position.

Make a three-quarter turn counterclockwise. Make a half-turn counterclockwise. Make a quarter-turn clockwise. Ask: What do you notice? Children are back in the starting position.

Have girls make a three-quarter turn clockwise and boys make a quarter-turn counterclockwise. Ask: What do you notice? Girls and boys are facing in the same direction.

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428 Unit 6 Geometry

NOTE Unlike triangles, quadrangles are not

rigid. Their shapes and areas may easily be

changed. But for any given quadrangle, the

perimeter does not change and, for any given

parallelogram, opposite sides remain parallel

in spite of the changes to their inner angles.

Name the parts of the quadrangle.

The sides are RS, ST, TU, and UR.The vertices are R, S, T, and U.The angles are R, S, T, and U.

QuadranglesA quadrangle is a polygon that has 4 sides. Another name for quadrangleis quadrilateral. The prefix “quad-” means four. All quadrangles have 4 sides, 4 vertices, and 4 angles.

Some quadrangles have 2 pairs of parallel sides.These quadrangles are called parallelograms.

Two sides are parallel if they are parts of lines that are parallel (never cross).

Geometry

Figures That Are NOT Parallelograms

A quadricycle is a vehiclesimilar to the bicycle andtricycle but having 4 wheels.

no parallel sides only 1 pair of parallel sides 3 pairs of parallel sides, but a parallelogrammust have 4 sides

Figures That Are Parallelograms

Opposite sides are parallel in each figure.

Student Reference Book, p. 108

Student Page

Some quadrangles have special names.Some of them are parallelograms.Others are not parallelograms.

Geometry

Quadrangles That Are Parallelograms

Rectangles are parallelograms. They have 4 right angles (square corners).

The sides of a rectangle do not all have to bethe same length.

Rhombuses are parallelograms. Their 4 sides are all the same length.

Squares are parallelograms. They have 4 right angles (square corners). Their 4 sides are all the same length.

All squares are rectangles. All squares are rhombuses.

Quadrangles That Are NOT Parallelograms

Trapezoids have exactly 1 pair of parallel sides. Their 4 sides can all be different lengths.

Kites are 4-sided polygons with 2 pairs of equal sides. The equal sides are next to each other. Their 4 sides cannot all be the same length. A rhombus is not a kite because all 4 sides of therhombus are the same length.

others Any polygon with 4 sides that is not aparallelogram, a trapezoid, or a kite

Student Reference Book, p. 109

Student Page

� Naming Quadrangles WHOLE-CLASSDISCUSSION

(Math Journal 1, p. 136)

Explain that the name of a quadrangle can begin with the letter at any vertex and can be read either clockwise or counterclockwise. Vertices must be named consecutively. For example, the quadrangle on the board can be named HEFG, EFGH, FGHE, and so on—but not HFGE.

Have children complete Part 2 on journal page 136.

Ongoing Assessment: Informing Instruction

Watch for children who have difficulty naming the quadrangle. Emphasize the

importance of naming the vertices in order. Suggest that children trace the

quadrangle with their fingers in order to determine the correct sequences.

� Constructing Quadrangles SMALL-GROUP ACTIVITY

(Math Journal 1, p. 136; Student Reference Book,

pp. 108 and 109)

Children construct the quadrangles listed in Part 3 on journal page 136. Have children make their constructions on flat surfaces and keep them (approximately) in a plane as they pick them up to show them.

When most of the groups have completed their constructions, bring them together to share observations about quadrangles. Children hold up quadrangles in each category as you and the class discuss their properties. To support English language learners as the geometric terms are introduced, write the terms on the board next to a picture or a straw model. Suggestions for discussion:

� Ask one person in each group to hold up any quadrangle with four sides of equal length and four right angles. Ask: How are all these quadrangles alike? They are all squares; their angles are all right angles. How are they different? They are not all the same size.

� Have children tug gently on two corners opposite each other. Ask: What happens when you do this? The shape and area change; the angles are not right angles, but the opposite sides are still parallel. Does the perimeter change? No What is the name of this shape? rhombus

� Have children make one angle a right angle. Ask: What happens when you do this? All angles become right angles. What is the name of this kind of shape? square

Note that squares and rhombuses are examples of parallelograms.

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ELL

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Lesson 6�5 429

Adjusting the Activity

Use a Venn diagram, Differentiation Handbook,

page 139, to organize information about similarities and differences between 2 quadrangles.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

Properties of

a RectangleProperties of

a Square

Properties ofa Rhombus

4 square

corners

4 equal sides

and4 square

corners

4 equalsides

K

L

M

N

Kite

Ongoing Assessment: Informing Instruction

Watch for children who believe that squares are only squares and not rectangles

or rhombuses. You may wish to make an analogy to address this misconception.

For example, the girls in the classroom are students, daughters, citizens, and

neighbors; they may also be sisters, granddaughters, or nieces. Likewise, the

square also belongs to several groups.

Have children hold up quadrangles having two pairs of equal sides. Kites and rectangles From those quadrangles, find the ones that have right angles. Rectangles The quadrangles with two pairs of equal sides and 4 right angles are called rectangles.

Have children hold up quadrangles having only two parallel opposite sides. Trapezoids, which include those with one pair of equal-length sides Those quadrangles are called trapezoids.

● Can you make a trapezoid that has a right angle? Yes

● Can you make a trapezoid with exactly one right angle? Try it. No. If a trapezoid has one right angle, it must have a second right angle as well because opposite sides must be parallel.

● Can you make a trapezoid with four right angles? No. If a trapezoid had four right angles, it would be a rectangle. There would be two pairs of parallel sides instead of one.

Sides that meet at a vertex are called adjacent sides. Have children hold up one of their quadrangles and trace its adjacent sides with their fingers. To support English language learners, write adjacent sides and draw some pictures illustrating adjacent sides on the board. Ask children in each group to hold up all quadrangles in which some or all adjacent sides are the same length. Have them set aside all the quadrangles in which all sides are the same length. Next, have them hold up any quadrangles in which there are just two pairs of equal adjacent sides. Such quadrangles are called kites. A kite is a quadrangle that has two pairs of equal adjacent sides and opposite sides that are not equal. To support English language learners, discuss the everyday meaning of the word kite as well as its meaning in this context.

Finally, have children hold up straw constructions that do not have four right angles or two pairs of parallel sides. Trapezoids and kites

Add one straw construction of each kind of quadrangle and its description to the Polygon Museum. Children can read more about quadrangles on pages 108 and 109 of the Student Reference Book.

� Finding the Perimeter of INDEPENDENTACTIVITY

a Quadrangle(Math Journal 1, p. 136)

Children complete Part 4 on journal page 136.

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430 Unit 6 Geometry

Name Date Time

QuadranglesHOME LINK

6�5

Help your child complete the statements. A right angle is a square corner. Parallel sides are the same distance apart and will never meet. Opposite sides are directly across from each other. Adjacent sides meet at a vertex (corner).

Please return this Home Link to school tomorrow.

Family Note

Fill in the blanks using the following terms: equal parallel right angles

1. Rectangle (Squares are special rectangles.)

All angles are right angles .

Pairs of opposite sides are equal in

length and parallel to each other.

2. Rhombus (Squares are also rhombuses.)

All sides are equal in length.

Opposite sides are parallel to each other.

3. Parallelogram (Squares and rhombuses are

also parallelograms.)

Opposite sides are equal in length.

Opposite sides are parallel to each other.

4. Kite

Opposite sides are not equal in length.

Solve.

5. 6 × 3 = 6. = 3 × 4 7. 6 × 6 = 361218

Practice

108 109

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Math Masters, p. 177

Home Link Master

5. Draw a shape with 4 sides that are

all equal in length.

This shape is a square .

or rhombus

Date Time

2. Circle the pair of lines that are

parallel.

4. Draw a ray, � DO . Draw a line

segment, _

RE . Draw a line, � � MI .

1. The grid is ONE. Shade 0.41 of

the grid.

Write the fraction

that shows how

much is shaded.

0.41 = 41

_

100

Math BoxesLESSON

6�5

34

167 168

99

100

109

D OR EM I

�4 �2

6

48

1224

192 96

48

24200 201

6. Complete.

3. Fill in the oval for the best answer.

The turn of the angle is

less than a 1 _ 2 turn.

less than a 1 _ 4 turn.

greater than a 1 _ 2 turn.

a full turn.

any square or rhombus

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Math Journal 1, p. 137

Student Page

2 Ongoing Learning & Practice

� Playing Name That Number SMALL-GROUP ACTIVITY

(Student Reference Book, pp. 299 and 300)

Children play Name That Number. See pages 299 and 300 in the Student Reference Book or Lesson 1-6 for directions. Encourage children to use as many cards and operations as they can to name the target number.

� Math Boxes 6�5 INDEPENDENTACTIVITY

(Math Journal 1, p. 137)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-7. The skill in Problem 6 previews Unit 7 content.

� Home Link 6�5 INDEPENDENTACTIVITY

(Math Masters, p. 177)

Home Connection Children identify characteristics of familiar quadrangles using the terms equal, parallel, and right angles in their answers.

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Playing Touch-and-Match 5–15 Min

Quadrangles(Math Masters, p. 467)

To provide experience with identifying similarities and differences among quadrangles, make two copies of Math Masters, page 467 on cardboard or cardstock paper. Cut out all of the quadrangles and place one set in full view on a table. Without children seeing, place one of the quadrangles from the other set in a bag or box. A child reaches inside the container, feels the shape without looking, and tries to find the matching shape from those on the table.

Ask children to explain how they made their matches. Expect responses like the following: “The shape I was holding had four square corners, but I knew it was the square and not the rectangle because all of the sides were the same length.”

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457

Materials □ gameboard and Shading Shapes Reference Page

(Math Masters, p. 458)

Object To claim the most quadrangles

Directions

Players take turns.

1. Shade one small triangle on the gameboard.

2. Players shade triangles to make quadrangles they see on the reference page.

3. When a player shades the final triangle of a quadrangle from the reference

page, that player claims the quadrangle by tracing the shape with a finger

and saying the name of the quadrangle. When a player claims a quadrangle,

he or she scores a point and that quadrangle is no longer available to claim.

4. Finished quadrangles may overlap each other (the same small triangle may

be colored twice), but no one can shade exactly the same quadrangle once

it has been claimed.

5. The game ends when time runs out or when the gameboard is completely

shaded. The winner is the player with the most points.

Name Date Time

Shading Shapes

EM3MM_G3_U06_167-205.indd 457 2/10/10 2:25 PM

Math Masters, p. 457

Game Masterpy

gg

p

Shade triangles on the gameboard to make the following quadrangles:

Rectangle

Square

Parallelogram Trapezoid

Trapezoid

Name Date Time

Shading Shapes Reference Page

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Math Masters, p. 458

Game Master

Lesson 6�5 431

Quadrangles (Quadrilaterals)

parallelogram 2 pairs of

parallel sides

rectangle 2 pairs of equal

sides;

4 right angles

rhombus 4 equal sides;

opposite sides

parallel

square 4 equal sides;

4 right angles

trapezoid only 2 sides

parallel;

parallel sides

not equal

kite 2 pairs of

adjacent equal

sides;

opposite sides

not equal

ENRICHMENT PARTNER ACTIVITY

� Playing Shading Shapes 15–30 Min

(Math Masters, pp. 457 and 458)

To further explore properties of quadrangles, have children play Shading Shapes. Directions are on Math Masters, page 457.When children have finished, have them share their strategies.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Adding to the 5–15 Min

Vocabulary Chart(Differentiation Handbook, p. 133)

To provide language support for geometry terms, have children add the terms rectangle, rhombus, square, trapezoid, and kite to the Vocabulary Chart. Children may also add the terms to their Math Word Banks using the template on Differentiation Handbook, page 133. See the Differentiation Handbook for more information.

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