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NameHome-School Connection
Topic 6Connect Area to Multiplication and Addition
Dear Family,
Your child is learning about area. In addition to learning about the area of simple rectangular shapes, he or she will also learn how to find the area of irregular shapes. Your child will use both nonstandard and standard units to calculate areas with and without grid paper.
Here is an activity you can use to help your child understand area.
Changing Area
Materials grid paper and pencil
Step 1 Draw a rectangle on the grid paper, and have your child count the unit squares to find the area. Draw another rectangle with different dimensions. Have your child find the area of this rectangle.
Step 2 Draw an irregular figure, such as the outline of a house using a square and a triangle. Have your child count the unit squares to find the area. Work with your child to determine how to estimate area when only a portion of the unit square is filled. For example, 2 half unit squares is equal to 1 whole unit square.
Observe Your ChildChallenge your child to find two rectangles with different dimensions but with the same area. Ask your child to explain how he or she found the solution.
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De la escuela al hogar (en español)
Tema 6Nombre
Relacionar el área con la multiplicación y la suma
Estimada familia:
Su niño(a) está aprendiendo a hallar el área. Además de aprender sobre el área de figuras rectangulares simples, también aprenderá a hallar el área de figuras irregulares. Su niño(a) usará unidades no convencionales y unidades estándar para calcular áreas con y sin papel cuadriculado.
Pruebe esta actividad con su niño(a) para ayudarlo(a) a entender el área.
Cambiar el área
Materiales papel cuadriculado y lápiz
Paso 1 Dibuje un rectángulo en el papel cuadriculado y pida a su niño(a) que cuente las unidades cuadradas para hallar el área. Dibuje otro rectángulo con otras dimensiones. Pida a su niño(a) que halle el área de ese rectángulo.
Paso 2 Dibuje una figura irregular, como el contorno de una casa usando un cuadrado y un triángulo. Pida a su niño(a) que cuente las unidades cuadradas para hallar el área. Trabaje con su niño(a) para determinar cómo se puede estimar el área cuando solo una parte de la unidad cuadrada está sombreada. Por ejemplo, 2 mitades de unidades cuadradas son iguales a 1 unidad cuadrada entera.
Observe a su niño(a)Pídale que halle dos rectángulos con distintas dimensiones pero con la misma área y que explique cómo halló la solución.
Vocabulary
unit
unit square
unit
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Name Reteach to Build Understanding
6-1
1. A unit square is a square with sides that are 1 unit long. Write the missing side lengths.
A unit square has an area of square unit.
2. Area is the number of unit squares needed to cover a region with no gaps or overlaps.
About unit squares cover the shape.
3. Count the unit squares that cover the shape.
unit squares
The area of the shape is square units.
Is the area exact or an estimate?
4. Count the unit squares that are completely filled.
unit squares
Count the unit squares that are partially filled.
Combine the partially filled squares to make full squares.
The area of the shape is square units.
On the Back!
5. Count to find the area of the shape. Tell if the area is exact or an estimate.
R 6•1
C
A
D
B
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Name Math and Science Activity6-1
Landslides
Did You Know? A landslide is the movement of rocks, earth, or other materials down a slope. Landslides vary in size. Some are so small that no one knows they have happened. Others are very large and destructive. They damage property and harm living things.
Rainfall, earthquakes, and volcanoes can cause landslides. Man-made activities can cause landslides too. Cutting down too many trees, building roads, and using explosives are just a few examples.
One way to prevent landslides is to build a retaining wall. Leon built a retaining wall in parts.
➊ Leon builds sections A and B first. Count the unit squares to find the total area of sections A and B.
➋ Leon then built sections C and D. What is the area of each of these sections?
➌ How can you find the area of the entire retaining wall? What is the area? Is the area exact or an estimate?
➍ Extension Describe another way to find the area of the entire wall.
6•1Math and Science Activity
Vocabulary
5 1 square unit
5 1 square unit
= 1 square unit 5 1 square unit
5 1 square unit
5 1 square unit
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Name Reteach to Build Understanding
6-2
1. A unit square is a square with sides that are each 1 unit long.
Unit squares can be different sizes. The size of the unit square you use determines the area of the figure.
Count the unit squares that cover each figure.
Finish drawing unit squares to cover the figures and find the area. Use the unit squares shown.
2.
There are unit squares.
There are unit squares.
Area: square units Area: square units
Area: square units Area: square units
On the Back!
4. Draw a figure and cover it with unit squares to find the area. Draw the same figure. Use a unit square with a different size to find the area.
3.
R 6•2
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PartnerTalk
1 2 3 4
Teamwork
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If you have more time
Use grid paper. Choose one of the figures on this page. Draw a different figure that has the same area.
1 Count the squares. Begin at the bottom of the figure.
2 Count the squares. Begin at the top of the figure.
3 Count the squares. Begin on the left side of the figure.
4 Count the squares. Begin on the right side of the figure.
a cb
d e
f g
h
i
j
one square unit
Get Started or
Put in a bag.Get grid paper and a pencil.
Repeat for Each Round
Choose a, b, c, d, e, f, g, h, i, or j. Pick a tile. Pick two tiles if your group has only two students. Take turns finding the area of the figure in square units.Use the method next to your tile number.
6•2
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PartnerTalk
0 1 2 3 4 5 6 7 8 9
Teamwork
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0 9 square units 1 15 square
units 2 12 square units 3 8 square
units 4 23 square units
5 18 square units 6 14 square
units 7 8 square units 8 20 square
units 9 16 square units
If you have more time
Use grid paper. Choose one of the figures on this page. Draw a different figure that has the same area.
a b c
de
g
f j
hi
one square unit
Get Started
Put in a bag.Get grid paper and a pencil.
Repeat for Each Round
Pick a tile. Look at the bottom of the page. Find the area next to your tile number. Find a figure with that area. Explain your choice. Place your tile on that figure. Repeat until the bag of tiles is empty.
6•2
Vocabulary
= 1 square foot
3 ft
4 ft
5 1 square inch
3 m
6 m
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Name Reteach to Build Understanding
6-3
1. Standard units are used to measure the side lengths of a figure and the area of a figure. Some standard units of length are centimeters, inches, feet, meters, kilometers, and miles.
Write the square units for area for each standard unit.
Unit: inch (in.) Square Unit: square inch
Unit: foot (ft) Square Unit: foot
Unit: centimeter (cm) Square Unit:
Unit: meter (m) Square Unit:
2. The length of this figure is 6 meters.
The width of this figure is meters.
What square unit will you use to measure the area?
square units cover this figure.
The area of the figure is .
3. Mia painted this picture in art class.
Each unit square equals .
square units cover the painting.
What is the area of the painting?
On the Back!
4. Each unit square represents a standard unit. Count the shaded unit squares to find the area. Then draw another rectangle with the same area.
R 6•3
Vocabulary
5 ft
4 ft
9 ft
? ft
2 cm
7 cm
6 ft
6 ft
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Name Reteach to Build Understanding
6-4
1. One way to find the area of the rectangle is to count the number of unit squares that cover the figure.
There are 36 unit squares.
The area of the rectangle is square feet.
2. Another way to find the area of the rectangle is to multiply the number of rows by the number of squares in each row.
There are 6 rows and squares in each row.
6 × =
The area of the rectangle is square feet.
The picture shows the length and width of Karen’s bedroom window.
3. Use multiplication to find the area of the window.
There are rows.
There are squares in each row.
4 × 5 =
The area of the window is square feet.
4. The area of Joey’s ramp is 27 square feet.
The ramp is 9 feet long. How wide is the ramp?
Joey’s ramp is wide.
On the Back!
5. Find the area of the figure in two ways. Show your work.
R 6•4
Vocabulary
6 ft
9 ft
5 ft 4 ft
6 ft
6
5
4 2
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Name Reteach to Build Understanding
6-5
1. You can use the Distributive Property to break apart a multiplication fact into the sum of two other multiplication facts.
Write the multiplication fact as a sum of two multiplication facts.
6 × 7 = 6 × (5 + 2) = ( × 5) + ( × 2)
2. You can apply the Distributive Property to find the area of a shape.
Write the multiplication fact that represents the area of the large rectangle.
6 × 9 =
Complete the equations to show that the area of the large rectangle is equal to the sum of the areas of the smaller rectangles.
6 × 9 = 6 × (5 + 4)
6 × 9 = (6 × 5) + (6 × 4)
6 × 9 = +
6 × 9 =
3. Complete the equations to represent the picture.
5 × = × (4 + )
5 × = (5 × ) + ( × 2)
5 × = +
5 × 6 =
On the Back!
4. Draw a rectangle on grid paper. Divide your rectangle into two smaller rectangles. Use the Distributive Property to solve the equation that represents the area of your rectangle.
R 6•5
SouthNorth
5 1 square meter
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Name Math and Science Activity6-5
Floods
Did You Know? Floodwater only 2 feet deep can move a car! Rainstorms, hurricanes, and melting ice and snow can all cause flooding. Floods damage crops and harm plant and animal environments.
Floods can be beneficial too. Soil is improved by floodwaters. Better soil means new plants can grow. Floods can also wash away invasive weeds that harm an ecosystem.
Volunteers are using sandbags to build a levee along the side of a river. A levee can help control flooding. To make the building easier, the group splits the levee into parts.
➊ Team 1 starts on the North side and builds a levee that is 2 meters high and 7 meters long. Draw the levee on the grid and find the area.
➋ Team 2 builds their levee to the right of Team 1’s levee. There is no space between the two levees. Team 2’s levee is 2 meters high and 10 meters long. Draw the levee on the grid and find the area.
➌ Team 3 and Team 4 finish the levee to the South side. The area of Team 3’s levee is 12 square meters. The area of Team 4’s levee is 10 square meters. Complete the drawing of Team 3 and Team 4’s levees.
➍ Extension Use the Distributive Property to find the total area of Team 1 and Team 2’s levees.
6•5Math and Science Activity
7
6
2 2
2
5 1 square unit
Vocabulary
7 ft
6 ft
2 ft 2 ft
2 ft
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Name Reteach to Build Understanding
6-6
1. To find the area of an irregular shape, you can count unit squares. A unit square has 1 square unit of area.
Find the area of the irregular shape by counting unit squares.
The area of the irregular shape is square units.
2. To find the area of an irregular shape, you can also divide the shape into rectangles, find the area of each rectangle, and then add the areas.
First, draw lines to separate the shape into one rectangle and two squares.
Next, find the area of the rectangle and the areas of the squares.
Rectangle: 4 × = square feet
Squares: 2 × = square feet
2 × = square feet
Add the areas together to find the total area of the shape.
+ + = square feet
The area of the irregular shape is square feet.
On the Back!
3. Find the area of the irregular shape by counting unit squares. Then find the area of the irregular shape by dividing the shape into rectangles. Find the area of each rectangle, and add the areas together. Show your work.
R 6•6
Vocabulary
5 ft
8 ft
� 1 square ft
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Name Reteach to Build Understanding
6-7
1. When asked to find the area of an irregular shape, look at the structure of the figure.
To find the area of the shaded region, find the area of the large rectangle first.
5 × 8 = square feet
Next, find the area of the small rectangle.
3 × 4 = square feet
Then, subtract to find the area of the shaded region.
40 - 12 = square feet
The area of the shaded region is square feet.
2. Find the area of the shaded region of the figure by breaking the problem into simpler parts.
9 in.
5 in.2 in.
4 in.
Find the area of the large rectangle. × = square inches
Find the area of the small rectangle. × = square inches
Subtract to find the area of the shaded region. - = square inches
The area of the shaded part is square inches.
On the Back!
3. Use grid paper to draw a shaded rectangle with a smaller, unshaded rectangle in it. Find the area of the shaded region. Explain how you can use structure to solve the problem.
R 6•7
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Display the Digits
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Get Started or
Explain how to find the area of the shaded part in each rectangle. Find which tile completes the missing digit for the Area of the Shaded Part. Display each 0 – 9 tile exactly once. If you have a partner, take turns.
If you have more time
Make up other shaded region puzzles.Ask your partner to display the answers with 0–9 tiles.
Rectangle A B C D E F G H I JArea of
Shaded Part (square inches)
1 a 2 b 1 c d 1 e 1 f 1 g 1 h 1 i 1 j
a b
c d
e f
g h
i j
H
C
G
B
F
A
D
E
I J
1 square inch
6•7
Share your thinking while you work.
PartnerTalk
Display the Digits
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3Center Game ★★
Get Started or
Put the tiles in a bag. Pick a tile. Read the area under that tile number.Find a figure with that area in its shaded part. Explain how to solve a simpler problem to find the area of the shaded part. Use your tile to cover the letter that matches your shape. Display each 0 – 9 tile exactly once. If you have a partner, take turns.
If you have more time
Make up other shaded region puzzles.Ask your partner to display the answers with 0–9 tiles.
a b
c d
e f
g h
i j
a b c
g
d e f
hi j
0 1 2 3 4 5 6 7 8 9
Area of Shaded Part
(square inches)20 18 15 17 14 16 12 19 1 13
1 square inch
6•7
