lesson 33 introduction symmetry - fourth grade rocks! · 2020. 5. 11. · introduction 362...

Introduction

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Lesson 33 Symmetry

Lesson 33Symmetry

You have learned about shapes and lines. Now you will learn about a line with a particular purpose called a line of symmetry. Take a look at this problem.

a. Trace the square, including the dashed line. Cut out the square and fold it on the

dashed line. Do the two parts fit exactly on top of each other?

b. Now trace and cut out the rectangle. Make sure you include the dashed line. When you fold on the dashed line, do the two parts fit exactly on top of each other? Why or why not?

c. Which other shape(s) are divided into two parts that fit exactly on top of each other?

d. Which other shape(s) are divided into two parts that do not fit exactly on top of

each other?

e. Describe what parts that fit exactly on top of each other look like and what parts

that don’t fit look like.

Each of the figures below has a dashed line drawn across it. Imagine folding each shape along the dotted line. If the two parts would fit exactly on top of each other when the shape is folded, draw a star on that shape.

4.G.1.3

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Lesson 33 Symmetry

In the problem on the previous page, you tested folding each figure along a line to see if the two parts fit exactly on top of each other. When you can fold a shape on a line and the parts line up with each other, the line is called a line of symmetry. Lines of symmetry were shown on the square, the isosceles triangle, and the circle.

Shapes can have more than one line of symmetry.

All of the lines of symmetry for a square are shown on the square at the right. Notice that all 4 lines of symmetry pass through the center point of the square.

This scalene triangle has no lines of symmetry. If you try drawing lines in the triangle so the parts fit exactly on top of each other, you’ll see you can’t.

To the right are two different quadrilaterals. The rectangle has two lines of symmetry which go through the center point. The other quadrilateral has no lines of symmetry.

Reflect1 Describe a shape in your classroom that has at least one line of symmetry.

Modeled and Guided Instruction

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Lesson 33

Lesson 33 Symmetry

Finding a Line of Symmetry

Read the problem below. Then explore different ways to find lines of symmetry.

Which of these shapes has at least one line of symmetry?

Model It You can trace and cut out the shapes. Then try folding the shapes in half.

The shaded parts show where one part is folded over the other part.

Picture It You can try drawing different lines in the shapes to find lines of symmetry.

The lines drawn show all of the places you could fold each shape to make parts that fit exactly on top of each other.

©Curriculum Associates, LLC Copying is not permitted. 365Lesson 33 Symmetry

Connect It Now you will describe the lines of symmetry you found to solve the problem from the previous page.

2 Does the parallelogram have any lines of symmetry? Why or why not?

3 How many lines of symmetry are shown on the pentagon?

4 Does the pentagon have any other lines of symmetry? How do you know?

5 The hexagon has 6 equal sides, 6 equal angles, and 6 lines of symmetry.

Explain why you think this is true.

6 Explain how you can figure out whether or not a line that divides a shape into two parts is a line of symmetry.

Try It Use what you just learned to solve this problem.

7 Circle the figure below that has the greater number of lines of symmetry.

Modeled and Guided Instruction

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Lesson 33

Lesson 33 Symmetry

Read the problem below. Then explore different ways to draw lines of symmetry.

Draw all of the lines of symmetry for these shapes. How many lines of symmetry does each shape have?

Picture It You can use drawings to help draw lines of symmetry.

The top and bottom of the oval match, so this shows a line of symmetry.

Another line can be drawn so that the left and right sides match.

Picture It You can imagine folding the shape in different ways to draw lines of symmetry.

Look at the plus sign. The lines show everywhere it could be folded to form parts that fit on top of each other.

Drawing a Line of Symmetry


Connect It Now you will describe and draw lines of symmetry to solve the problem from the previous page.

8 On a separate piece of paper, trace the oval and show all lines of symmetry. What do you notice about the place where all lines of symmetry cross?

9 Now trace the plus sign and show all lines of symmetry. Where do the lines cross?

How does this compare with the oval?

10 How many lines of symmetry does the oval have?

11 How many lines of symmetry does the plus sign have?

12 Explain how you can decide when you have found all of the lines of symmetry in

a figure.

Try It Use what you just learned to solve this problem.

13 Draw all of the lines of symmetry on the hexagon below. All the sides of the figure have the same length.

Guided Practice

Practice


Lesson 33

Finding and Drawing Lines of Symmetry

Lesson 33 Symmetry

Pair/ShareWhy do you think that squares and rectangles have different numbersof lines of symmetry?

Pair/ShareWhat’s different about the triangle that has aline of symmetry and the one that doesn’t have a line of symmetry?

Example

14 Name a kind of triangle that has a line of symmetry. Name another kind of triangle that doesn’t have a line of symmetry.

Show your work.

Solution

Which of the figures below has fewer lines of symmetry?

Look at how you could explain your work.

The square has lines of symmetry connecting the corners and connecting both pairs of opposite sides.

The rectangle only has lines of symmetry connecting opposite sides, not opposite corners. So the rectangle has fewer lines of symmetry.

Solution

Study the example below. Then solve problems 14–16.

rectangle

The student thought about folding the figures to decide where the lines of symmetry are!

What are the kinds of triangles that are named by their sides?


Pair/ShareDiscuss why the lines of symmetry that areincorrect don’t work.

Pair/ShareDraw the figure on a piece of grid paper and cut it out to check the lines of symmetry.

15 Draw all of the lines of symmetry on the figure. How many lines of symmetry are there?

Solution

16 Which figure shows the correct line(s) of symmetry? Circle the letter of the correct answer.

A C

B D

Michael chose D as the correct answer. How did he get that answer?

What point in a figure do all lines of symmetry pass through?

Imagine folding the figures in half along the lines.

Independent Practice

Practice


Lesson 33

Finding and Drawing Lines of Symmetry

Lesson 33 Symmetry

Solve the problems.

1 Which shape always has 4 lines of symmetry?

A an isosceles triangle

B a rhombus

C a square

D a rectangle

2 Each shape below has side lengths labeled in units. Determine the number of lines of symmetry for each shape. Draw each shape in the correct box. Some boxes may have more than one shape. Some boxes may not have any shapes.

7 7

4

6

3

5 5

3

3

3

3

3

3

2 2

5

5

4 4

4 4

Number ofLines of

Symmetry0

Exactly1

Exactly2

Exactly3

Exactly4

Morethan

4

Shape

Self Check


3 Part of a figure is shaded on the grid below. Complete the figure by shading squares. Lines r and s are lines of symmetry for the completed figure.

r

s

4 Draw all of the lines of symmetry on the figure below. Then draw a different quadrilateral that has more lines of symmetry than this figure. Show the lines of symmetry.

Explain your work.

Go back and see what you can check off on the Self Check on page 337.

lesson 33 introduction symmetry - fourth grade rocks! · 2020. 5. 11. · introduction 362...

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