Area
Objectives To guide children as they develop the concept of area,
demonstrate
the measure of area by using 1-foot and 1-yard squares,
d
and find areas by counting squares.
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EM Facts
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Teaching the Lesson
Key Concepts and Skills
• Use arrays to find the areas of rectangles. [Operations and Computation Goal 6]
• Estimate and then measure the areas
of surfaces with foot and yard square
templates. [Measurement and Reference Frames Goal 2]
• Find the area of a rectangular region
divided into square units. [Measurement and Reference Frames Goal 2]
• Describe the relationship between square
feet and square yards. [Measurement and Reference Frames Goal 3]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Subtraction Top-It
Key Vocabulary
area square feet square yards
Differentiation Options
READINESS
Exploring Cube Configurations
Ongoing Assessment:
Recognizing Student Achievement
Math Masters, p. 73
scissors tape
Children cut a rectangle into pieces and
rearrange the pieces to make a new shape.
They compare the area of the rectangle with
the area of the new shape.
Use the Top-It Games Record Sheet.
[Operations and Computation Goal 1]
Children review the meaning of area and the
use of square units. They measure areas
using models of a square foot and a square
yard. They find the areas of rectangles by
counting squares.
Math Masters, p. 416
per partnership: 10 centimeter cubes, crayons
Children find all possible ways to cover
4 square centimeters.
ENRICHMENT
Exploring Area
Math Journal 1, p. 73
Children practice and maintain skills
through Math Box problems.
Home Link 3 7
Math Masters, p. 72
Children practice and maintain skills
through Home Link activities.
Materials
Math Journal 1, pp. 68 and 72
Student Reference Book, pp. 154 and 155
Home Link 36
per group: 1-yard square piece of paper slate scissors ruler or yardstick supply
of newspaper, or other large paper a piece
of cardboard, at least 1-foot square
Advance Preparation
For Part 1, each small group will need a 1-yard square piece of paper. A 1-yard square can be taped together
from 3 sheets of newspaper (about 27 in. by 22 in. per full sheet). Each small group will need 5 sheets of
newspaper to cut out nine 1-foot squares. Make a 1-foot square template from a large, disassembled cereal box.
Tape a 1-yard square to the board for the Math Message.
Teacher’s Reference Manual, Grades 1–3 pp. 158, 159
206
Unit 3
Linear Measures and Area
Interactive
Teacher’s
Lesson Guide
Student Reference Book, pp. 310
and 311
Math Masters, p. 440
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 subtraction facts.
Math Boxes 3 7
Key Activities
Curriculum
Focal Points
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6
Getting Started
Content Standards
3.MD.5, 3.MD.5a, 3.MD.5b, 3.MD.6, 3.MD.7a
Mental Math and Reflexes
Math Message
Pose fact extensions similar to the following:
Look at the square piece of paper on the board.
Estimate the length of a side. Record your estimate on
your slate.
20 + 30 = 50
40 - 20 = 20
400 - 200 = 200
30 + 90 = 120
60 + 80 = 140
600 + 800 = 1,400
900 + 400 = 1,300
150 - 60 = 90
170 + 80 = 250
170 - 80 = 90
1,600 - 500 = 1,100
2,500 - 1,800 = 700
Home Link 3 6 Follow-Up
Children share their results and drawings. Some
children might want to add the length of their pace
to their personal references, with the understanding
that their pace will change as they grow.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Have someone measure a side of the paper square. Children
compare the measurement to their estimates.
Making Squares with
SMALL-GROUP
ACTIVITY
1-Foot Sides
Divide the class into groups of three or four. Each group needs a
1-yard paper square, scissors, a ruler or yardstick, a supply of
newspaper, and cardboard to make a 1-foot square template.
Children will need 1-foot and 1-yard squares for this lesson and
the next.
Ask each group to cut out enough 1-foot squares to cover the
1-yard square without gaps or overlaps. Suggest that children first
cut out a cardboard 1-foot square and use it as a template to draw
other 1-foot squares on newspaper.
Bring the class together and have children describe how they
measured and cut out their 1-foot squares. Ask: How many 1-foot
squares did it take to cover the 1-yard square? Nine 1-foot squares
The area of the 1-yard square is nine 1-foot squares.
NOTE Sometimes people think there are only 3 square feet in a square yard,
because there are 3 feet in a yard.
Lesson 3 7
207
Student Page
Date
Reviewing the Concept
Time
LESSON
Tiling with Pattern Blocks
36
Materials
□
□
of Area
pattern blocks: square, triangle, narrow rhombus
crayons
Work with a partner.
1. Use square pattern blocks. Look at the top rectangle on the next page. Cover as
much of the rectangle as you can, placing all of the blocks inside it. There may
be uncovered spaces at the edges. Do not overlap the blocks. Line them up so
that there are no gaps. This is called tiling.
2. Count and record the number of blocks you used.
3. Trace around the edges of each block. Then color any spaces not covered by
blocks. Estimate how many blocks would be needed to cover the colored spaces.
4. Record how many blocks are needed to cover the whole rectangle.
5. Tile the second rectangle with triangles. Repeat Steps 2–4 above.
6. Tile the third rectangle with narrow rhombuses. Repeat Steps 2–4 above.
Follow-Up
7. The area of a shape is a measure of the space inside the shape. You measured
the area of a rectangle three ways: with squares, triangles, and narrow
rhombuses. Record the areas below.
The area of the rectangle is about
The area of the rectangle is about
The area of the rectangle is about
12 squares.
30 triangles.
22 narrow rhombuses.
square
triangle
Fewer squares are needed to
How did you decide?
cover the rectangle.
8. Which of the three pattern blocks has the largest area?
Which has the smallest area?
ELL
(Math Journal 1, p. 68; Student Reference Book,
pp. 154 and 155)
Ask children to briefly share the ways they used pattern blocks to
measure area in the preceding lesson. Area is a measure of the
size of the surface inside a 2-dimensional closed boundary. Write
area on the board. Explain that area is a word with everyday
meanings, but it also has a mathematical meaning. It is used to
measure the space inside a shape. As children discuss the key
ideas related to area, list them on the board to support English
language learners. If you haven’t done so, discuss the Follow-Up
questions on journal page 68.
Because they were not able to cover surfaces completely using sets
of identical blocks, ask children to describe how they estimated the
spaces that were not covered. Ask: Which of the three blocks was
the easiest to use? squares
Math Journal 1, p. 68
EM3MJ1_G3_U03_55-78.indd 68
WHOLE-CLASS
DISCUSSION
1/3/11 11:01 AM
Discuss some advantages of using square shapes for measuring
area. Many surfaces have square corners. It is easier to cover a
rectangular surface without gaps or overlaps when using
square shapes.
Area can be measured in standard square units, such as square
inches—squares that measure 1 inch on each side. Other area
units include square feet, square yards, square centimeters,
and square meters. To support English language learners,
draw and label a square centimeter, square meter, square inch,
square foot, and square yard on the board. Ask children to
compare the different sizes. Use pages 154 and 155 in the
Student Reference Book to summarize these concepts.
Estimating and Measuring
Student Page
Measurement
Areas in the Classroom
SMALL-GROUP
ACTIVITY
PROBLEM
PRO
P
ROB EM
RO
SO
SO
SOLVING
G
Working in groups of 3 or 4, children estimate the areas of
surfaces in the classroom, such as desktops, tabletops, and bulletin
boards. Then they measure by tiling the surfaces with 1-foot
squares or by repeatedly laying down a 1-foot or 1-yard square
unit. Remind children that squares should be laid down as
carefully as possible without gaps or overlaps. Bring the class
together to share results.
Count the square units to find the areas
of these shapes.
Each square is 1 square inch.
18 squares cover the rectangle.
The area of the rectangle
is 18 square inches.
Each square is 1 square foot.
14 squares cover the shape.
The area of the shape is
14 square feet.
NOTE The 1-yard squares will be used again in Lessons 3-8 and 4-1. The
1-foot squares will be used again in Lesson 4-1. Make both available to children
so that they can continue to estimate and measure area during spare moments.
Remember: Perimeter is the distance around a shape.
Area is the amount of surface inside a shape.
Perimeter is the
distance around.
Area is the amount of
surface inside.
Student Reference Book, p. 155
131_168_EMCS_S_G3_SRB_MeA_577260.indd 155
208
Unit 3 Linear Measures and Area
2/12/11 2:18 PM
Student Page
Finding the Areas of
WHOLE-CLASS
ACTIVITY
Rectangles by Counting Squares
Date
Time
LESSON
Areas of Rectangles
37
Draw each rectangle on the grid. Make a dot inside each small square in
your rectangle.
1.
(Math Journal 1, p. 72; Student Reference Book, p. 155)
Do the first problem on journal page 72 with the class. Remind
children that a 3-by-5 rectangle is a rectangle with two sides
measuring 3 units each and two sides measuring 5 units each.
The units can be any linear units—inches, centimeters, feet,
meters, and so on—but must be the same for all sides.
2. Draw a 6-by-8
3. Draw a 9-by-5
rectangle.
rectangle.
or
Area =
15
Area =
square
units
48
Area =
square
units
45
square
units
Fill in the blanks.
4.
5.
Go over the answers after children have completed the page. Call
their attention to the example of counting squares to find areas on
page 155 of the Student Reference Book. Use the page to discuss
the difference between perimeter and area.
NOTE This lesson develops the concept of area. The next lesson develops a
Draw a 3-by-5
rectangle.
This is a
Area =
3
21
-by-
7
rectangle.
square units
9 -by- 4 rectangle.
36 square units
This is a
Area =
6.
7.
method for calculating areas of rectangles.
In Everyday Mathematics, an illustration of an x-by-y rectangle is
shown by a rectangle with x rows and y columns. However, not
everyone observes this convention. What is important is that an
x-by-y rectangle has two opposite sides x units long and two
opposite sides y units long.
This is a
Area =
6 -by- 6 rectangle.
36 square units
This is a
Area =
6
54
9
-by-
rectangle.
square units
Math Journal 1, p. 72
055-078_EMCS_S_SMJ_G3_U03_576353.indd 72
5/24/11 1:33 PM
2 Ongoing Learning & Practice
Playing Subtraction Top-It
PARTNER
ACTIVITY
(Student Reference Book, pp. 310 and 311,
Math Masters, p. 440)
Children practice subtraction facts by playing Subtraction Top-It.
If necessary, have children review the rules for the game on pages
310 and 311 in the Student Reference Book. Have partners play six
rounds, each recording the results on a Top-It Games Record Sheet
(Math Masters, page 440). Children circle the facts for which they
have fact power.
Student Page
Date
Time
LESSON
37
1.
Math Boxes
2.
Measure to the nearest
centimeter.
about
6
cm
Sample
answer:
Draw a line segment
4 centimeters long.
Ongoing Assessment:
Recognizing Student Achievement
Math Masters
Page 440
154 155
137–139
3. Write the equivalent lengths. Use a
4.
tape measure to help.
Use the Top-It Games Record Sheet to assess children’s knowledge of basic
subtraction facts. Children are making adequate progress if they correctly record
12 subtraction number sentences generated during the game.
[Operations and Computation Goal 1]
Draw a shape with an area of 9
square centimeters.
3 yards =
72
9
feet
3 meters =
5
940 − 400 = 540
centimeters
943
−409
300 centimeters
534
60–63
192
140 146
5. Solve.
Math Boxes 3 7
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 73)
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 3-5 and 3-9. The skill in Problem
6 previews Unit 4 content.
26
6.
Unit
8+3+2+2=
Unit
Ballpark estimate:
Sample answer:
inches = 2 yards
50 millimeters =
Subtract. Show your
work.
Solve.
1×2=
15
4
= 9 + 14 + 1 + 2
5×1=
24
85 + 16 + 4 + 15 = 120
4 + 3 + 11 + 6 =
2
=1×4
8×1=
5
8
52 53
56
50 51
Math Journal 1, p. 73
055-078_EMCS_S_SMJ_G3_U03_576353.indd 73
2/4/11 10:10 AM
Lesson 3 7
209
Home Link Master
Name
Date
HOME LINK
37
䉬
Family
Note
Time
Areas of Rectangles
Today we discussed the concept of area. Area is a measure of the amount of surface inside a
2-dimensional shape. One way to find area is by counting same-size units inside a shape. For
more information, see pages 154–156 in the Student Reference Book. In the next lesson, we
will look at ways to calculate area.
154–156
Please return this Home Link to school tomorrow.
Show someone at home how to find the area of each rectangle. Make a dot in
each square as you count the squares inside the rectangle.
Writing/Reasoning Ask children to write an answer to
the following: Explain what area means in Problem 2.
Area means the number of centimeter squares that are
inside the shape.
1. Draw a 4-by-6 rectangle on the grid. 2. Draw a 3-by-9 rectangle.
Home Link 3 7
INDEPENDENT
ACTIVITY
(Math Masters, p. 72)
Fill in the blanks.
3.
4.
This is a
Area ⫽
2
12
-by-
6
rectangle.
This is a
Area ⫽
square units
5
20
-by-
4
rectangle.
Home Connection Children show someone at home how
to determine area by counting squares. You might want to
send home the Student Reference Book.
square units
Practice
Write these problems on the back of this page. Fill in a unit box.
Use any method you wish to solve each problem. Write a number
model for your ballpark estimate. Show your work.
5.
600
⫺ 300
307
300
571
⫺ 264
6.
Unit
800
⫺ 700
119
100
805
⫺ 686
3 Differentiation Options
Math Masters, p. 72
READINESS
Exploring Cube Configurations
PARTNER
ACTIVITY
15–30 Min
(Math Masters, p. 416)
Teaching Aid Master
Name
Date
Time
Centimeter Grid Paper
To provide concrete experience with area concepts, have children
use centimeter cubes to find all the possible ways to cover 4
square centimeters so that the centimeters are connected on at
least one side. There are five possible configurations. (See below.)
Help children compare their configurations to see which ones are
duplicates. When children have found all five configurations, have
them record their figures by coloring the square centimeters on
the grid paper. Review the concept that each configuration covers
4 square centimeters or has an area of 4. If interest and time
permit, repeat the activity with 5 square centimeters. (See
solutions below.)
Possible combinations for 4 cm cubes
Twelve possible combinations for 5 cm cubes
Math Masters, p. 416
210
Unit 3 Linear Measures and Area
Teaching Master
ENRICHMENT
Exploring Area
INDEPENDENT
ACTIVITY
15–30 Min
(Math Masters, p. 73)
To further explore the concept of area, have children cut apart and
reassemble the pieces of a rectangle into a new polygon with the
same area. Discuss how shapes that look different might have the
same area.
Name
LESSON
37
䉬
Date
Exploring Area
1. Rectangle A is drawn on centimeter
grid paper. Find its area.
Area ⫽
24
square centimeters
A
2. Rectangle B has the same area as
Rectangle A. Cut out Rectangle B.
Then cut it into 5 pieces, any way you want.
B
Rearrange the pieces into a new shape
that is not a rectangle. Then tape the
pieces together in the space below.
What is the area of the new shape?
24
Sample answer:
Area of new shape ⫽
Planning Ahead
Time
square centimeters
In Lesson 3-8, you will need enough 1-yard squares to lay on the
floor the entire length of one classroom wall.
For Lesson 3-9, you will need about 15 food cans (with labels
still attached) or other cylinders—one per partnership. Gather a
variety of sizes from about 2 to 5 centimeters in diameter (about
the size of a D battery or a small can of tomato paste) to about
20 centimeters (1-gallon paint can). Unopened cans are preferable.
Use a permanent marker to label each can with a letter (A, B, C,
and so on) on the lid, and also make a mark on the rim.
3. Explain how you found the area of your new shape.
Sample answer: I counted the squares inside
the shape. Then I counted every 2 triangles
as 1 square.
Math Masters, p. 73
Lesson 3 7
211