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Chapter 10
Measurement and Geometry
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10
Measurement and Geometry
Lesson 10-1
Polygons
Lesson 10-2
Perimeter
Lesson 10-3
Measurement: Area
Lesson 10-4
Problem-Solving Strategy: Solve
a Simpler Problem
Lesson 10-5
Triangles and Angles
Lesson 10-6
Quadrilaterals
Lesson 10-7
Problem-Solving Investigation:
Choose a Strategy
Lesson 10-8
Solid Figures
Lesson 10-9
Complex Solid Figures
Lesson 10-10
Measurement: Volume
10-1
Polygons
Five-Minute Check (over Chapter 9)
Main Idea and Vocabulary
California Standards
Example 1: Classify Shapes
Example 2: Classify Shapes
10-1
Polygons
• I will identify, describe, and classify polygons.
• plane figure
• pentagon
• polygon
• hexagon
• triangle
• octagon
• quadrilateral
10-1
Polygons
Standard 3MG2.1 Identify, describe,
and classify polygons (including pentagons,
hexagons, and octagons).
10-1
Polygons
Classify the polygon.
A polygon has sides, and this figure does not
have sides.
Answer: This is not a polygon.
10-1
Polygons
Classify the polygon.
A. polygon; pentagon
B. polygon; hexagon
C. polygon; octagon
D. not a polygon
10-1
Polygons
Classify the polygon.
There are 6 sides and 6 angles.
Answer: So, it is a hexagon.
10-1
Polygons
Classify the polygon.
A. polygon; triangle
B. polygon; square
C. polygon; pentagon
D. polygon; hexagon
10-2
Perimeter
Five-Minute Check (over Lesson 10-1)
Main Idea and Vocabulary
California Standards
Key Concept: Find Perimeter
Example 1: Find Perimeter
Example 2: Find Perimeter
10-2
Perimeter
• I will find the perimeter of a polygon.
• perimeter
10-2
Perimeter
Standard 3MG1.3 Find the perimeter of
a polygon with integer sides.
10-2
Perimeter
10-2
Perimeter
Find the perimeter
of the triangle.
To find the perimeter, add
the lengths of the sides.
5 cm + 3 cm + 4 cm = 12 cm
Answer: So, the perimeter is 12 centimeters.
10-2
Perimeter
Find the perimeter of the square, if all its sides are
equal to 4 cm.
A. 16 cm
B. 20 cm
C. 18 cm
D. 8 cm
10-2
Perimeter
Find the perimeter of
the square.
To find the perimeter,
add the lengths of the
sides.
5 units + 5 units + 5 units + 5 units = 20 units
Answer: So, the perimeter is 20 units.
10-2
Perimeter
Find the perimeter of this rectangle.
A. 56 units
B. 40 units
C. 28 units
D. 30 units
10-3
Measurement: Area
Five-Minute Check (over Lesson 10-2)
Main Idea and Vocabulary
California Standards
Example 1: Determine Area
Example 2: Determine Area
Example 3: Determine Area
Measurement: Area
10-3
Measurement: Area
• I will determine area.
• area
10-3
Measurement: Area
Standard 3MG1.2 Estimate or determine
the area and volume of solid figures by covering
them with squares or by counting the number of
cubes that will fill them.
Standard 3MR2.1 Use estimation to verify the
reasonableness of calculated results.
10-3
Measurement: Area
Find the area of
the figure.
Count the number of
whole squares.
Answer: The area is 9 square units.
10-3
Measurement: Area
Find the area of the figure.
A. 20 square units
B. 18 square units
C. 21 square units
D. 14 square units
10-3
Measurement: Area
Find the area of the figure.
Count the number of squares.
Answer: The area of this figure is 6 square units.
10-3
Measurement: Area
Find the area of the figure.
A. 36 square units
B. 40 square units
C. 48 square units
D. 30 square units
10-3
Measurement: Area
The figure below shows the size of Filipa’s porch.
What is the area of the porch?
Step 1 Count the number of
whole squares. There
are 6 of them.
Step 2 Count the half squares.
There are 2 halves.
Two halves equal 1
whole square.
10-3
Measurement: Area
Step 3 Add.
6 square units + 1 square unit = 7 square units
Answer: The area of Filipa’s porch is 7 square units.
10-3
Measurement: Area
The figure below shows the top view of a land plot.
What is the area of the land plot?
A. 64 square units
B. 60 square units
C. 50 square units
D. 48 square units
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Five-Minute Check (over Lesson 10-3)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
10-4
Problem-Solving Strategy: Solve a Simpler Problem
• I will solve problems by working a simpler
problem.
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Standard 3MG1.3 Find the perimeter of a
polygon with integer sides.
Standard 3MR1.2 Determine when and how to
break a problem into simpler parts.
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Julianna is placing a border around a rectangular
bulletin board. The perimeter of the bulletin board
is 10 feet. One side measures 2 feet. What will be
the length of the border for each side?
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Understand
What facts do you know?
• The bulletin board is rectangular with a perimeter
of 10 feet.
• The length of one side is 2 feet.
What do you need to find?
• The length of the border for each side.
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Plan
Solve a simpler problem to find the length of the
border for each side.
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Solve
Two sides are 2 feet long.
2 feet + 2 feet = 4 feet
Find the total length of
the other two sides.
total of
2 sides
perimeter
10 feet
–
4 feet
total of
remaining sides
=
6 feet
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Solve
The two unknown sides add up to 6 feet. Since
both sides are the same length, divide by 2.
6 feet ÷ 2 feet = 3 feet
Answer: So, two pieces of border should be 2 feet
long, and the other two should be 3 feet
long each.
10-4
Problem-Solving Strategy: Solve a Simpler Problem
Check
Look back at the problem. Add up all of the sides.
2 feet + 2 feet + 3 feet + 3 feet = 10 feet
So, the answer is correct.
10-5
Triangles and Angles
Five-Minute Check (over Lesson 10-4)
Main Idea and Vocabulary
California Standards
Key Concept: Identify Triangles by its Sides
Example 1: Identify a Triangle
Example 2: Identify a Triangle
Example 3: Identify Angles
10-5
Triangles and Angles
• I will identify and classify different triangles and
compare angles.
• equilateral triangle
• scalene triangle
• isosceles triangle
• right triangle
10-5
Triangles and Angles
Standard 3MG2.2 Identify attributes of
triangles (e.g., two equal sides for the isosceles
triangle, three equal sides for the equilateral
triangle, right angle for the right triangle).
10-5
Triangles and Angles
Standard 3MG2.4 Identify right angles in
geometric figures and determine whether other
angles are greater or less than a right angle.
10-5
Triangles and Angles
10-5
Triangles and Angles
Identify the triangle
shown on the grid.
This triangle has
two sides of equal
length.
Answer: It is an isosceles triangle.
10-5
Triangles and Angles
Identify the triangle shown in the grid.
A. isosceles triangle
B. equilateral triangle
C. scalene triangle
10-5
Triangles and Angles
Identify the triangle.
This triangle has three sides of equal length.
Answer: It is an equilateral triangle.
10-5
Triangles and Angles
Identify the triangle shown below.
A. isosceles triangle
B. equilateral triangle
C. scalene triangle
10-5
Triangles and Angles
Identify the triangle. Tell if
each angle of the triangle
is a right angle, less than
a right angle, or greater
than a right angle.
This triangle has three sides that are equal.
Answer: It is an equilateral triangle. Every angle is
less than a right angle.
10-5
Triangles and Angles
Identify the triangles below. Tell if each triangle is a
right angle, less than a right angle, or greater than
a right angle.
A. scalene; right angle
B. isosceles; all angles
are less than a right
angle
C. equilateral; all angles
are less than a right
angle
D. right; right angle
10-6
Quadrilaterals
Five-Minute Check (over Lesson 10-5)
Main Idea and Vocabulary
California Standards
Key Concept: Types of Quadrilaterals
Example 1: Identify Quadrilaterals
Example 2: Identify Quadrilaterals
Example 3: Identify Angles
10-6
Quadrilaterals
• I will identify, describe, and classify different
quadrilaterals.
• parallel
• square
• rectangle
• parallelogram
10-6
Quadrilaterals
Standard 3MG2.3 Identify attributes of
quadrilaterals (e.g., parallel sides for the
parallelogram, right angles for the rectangle,
equal sides and right angles for the square).
10-6
Quadrilaterals
Standard 3MG2.4 Identify right angles in
geometric figures or in appropriate objects
and determine whether other angles are
greater or less than a right angle.
10-6
Quadrilaterals
10-6
Quadrilaterals
Identify the quadrilateral.
This quadrilateral has opposite sides that are the
same length and are parallel.
Answer: It is a parallelogram.
10-6
Quadrilaterals
Identify the quadrilateral.
A. square
B. parallelogram
C. rectangle
10-6
Quadrilaterals
Identify the quadrilateral.
This quadrilateral has 4 right angles, opposite sides
that are equal, and opposite sides that are parallel.
Answer: It is a rectangle.
10-6
Quadrilaterals
Identify the quadrilateral.
A. square
B. parallelogram
C. rectangle
10-6
Quadrilaterals
Identify the quadrilateral.
Tell if each angle shown is
a right angle, less than a
right angle, or greater than
a right angle.
This quadrilateral has opposite
sides that are parallel, 4 sides
that are the same length, and
4 right angles.
Answer: It is a square. All angles are right angles.
10-6
Quadrilaterals
Identify the quadrilateral. Tell if each angle shown
is a right angle, less than a right angle, or greater
than a right angle.
A. square; all angles are
right angles
B. parallelogram; two
angles are less than a
right angle, two angles
are greater than a right
C. rectangle; all angles
are right angles
10-7
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 10-6)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
10-7
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
10-7
Problem-Solving Investigation: Choose a Strategy
Standard 3MG1.2 Estimate or determine the
area and volume of solid figures by covering them
with squares or by counting the number of cubes
that will fill them.
10-7
Problem-Solving Investigation: Choose a Strategy
Standard 3MR1.1 Analyze problems by identifying
relationships, distinguishing relevant from
irrelevant information, sequencing and prioritizing
information, and observing patterns.
10-7
Problem-Solving Investigation: Choose a Strategy
CASSANDRA: My family is making a
sandbox. It has the shape of a
rectangle with a width of 4 feet
and a length of 6 feet. The plastic
that goes under the sand costs $2
for each square foot.
YOUR MISSION: Determine if $50 will
be enough to pay for the plastic.
10-7
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• You know the length and width of the sandbox.
• The cost of the plastic is $2 per square foot.
What do you need to find?
• Find the total cost of the plastic.
10-7
Problem-Solving Investigation: Choose a Strategy
Plan
Draw a picture to help you solve the problem.
10-7
Problem-Solving Investigation: Choose a Strategy
Solve
The drawing shows that
the area of the sandbox is
24 square feet. Multiply
24 square feet by $2 per
square foot to find the
total cost of the plastic.
24 × $2 = $48
$48 is less than $50.
Answer: So, $50 will be enough to pay for
the plastic.
10-7
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. Use addition to check.
$24 + $24 < $50
So, the answer is correct.
10-8
Solid Figures
Five-Minute Check (over Lesson 10-7)
Main Idea and Vocabulary
California Standards
Key Concept: Solid Figures
Example 1: Identify Solid Figures
Example 2: Identify Solid Figures
10-8
Solid Figures
• I will identify, describe, and classify solid figures.
• cube
• pyramid
• rectangular solid
• cylinder
• cone
• sphere
10-8
Solid Figures
Standard 3MG2.5 Identify, describe, and classify
common three-dimensional geometric objects
(e.g., cube, rectangular solid, sphere, prism,
pyramid, cone, cylinder).
10-8
Solid Figures
10-8
Solid Figures
Identify the solid figure.
Answer: cone
10-8
Solid Figures
Identify the figure.
A. cone
B. cube
C. cylinder
D. rectangular solid
10-8
Solid Figures
Identify the solid figure.
Answer: sphere
10-8
Solid Figures
Identify the figure.
A. cone
B. cube
C. cylinder
D. rectangular solid
10-9
Complex Solid Figures
Five-Minute Check (over Lesson 10-8)
Main Idea
California Standards
Example 1: Complex Solid Figures
Example 2: Complex Solid Figures
10-9
Complex Solid Figures
• I will identify common solid objects that make
more complex solid objects.
10-9
Complex Solid Figures
Standard 3MG2.6 Identify common solid
objects that are the components needed to
make a more complex solid object.
Standard 3MR1.2 Determine when and how to
break a problem into simpler parts.
10-9
Complex Solid Figures
Identify the figures that make the complex solid.
Answer: cone, cylinder
10-9
Complex Solid Figures
Identify the figures that make each complex solid.
Answer: rectangular solids
10-10 Measurement: Volume
Five-Minute Check (over Lesson 10-9)
Main Idea and Vocabulary
California Standards
Example 1: Find Volume
Example 2: Find Volume
Volume
10-10 Measurement: Volume
• I will determine the volume of solid figures.
• volume
• cubic unit
10-10 Measurement: Volume
Standard 3MG1.2 Estimate or determine
the area and volume of solid figures by covering
them with squares or by counting the number of
cubes that would fill them.
10-10 Measurement: Volume
How much sand does
the sand box hold?
There are 15 cubic units
on the bottom layer. The
sand box can hold two
layers.
15 + 15 = 30
Answer: The sand box can hold 30 cubic units
of sand.
10-10 Measurement: Volume
How much cement will the container hold?
A.
3 cubic units
B.
4 cubic units
C.
5 cubic units
D.
6 cubic units
10-10 Measurement: Volume
Estimate the volume of
the figure.
There are 16 cubic units
in each layer. The figure
has 4 layers.
16 + 16 + 16 + 16 = 64
Answer: The volume of the figure is 64 cubic units.
10-10 Measurement: Volume
Estimate the volume of the figure.
A.
48 cubic units
B.
36 cubic units
C.
12 cubic units
D.
24 cubic units
10
Measurement and Geometry
Five-Minute Checks
Math Tool Chest
Image Bank
Measurement: Area
Volume
10
Measurement and Geometry
To use the images that are on the
following four slides in your own
presentation:
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in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
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10
Measurement and Geometry
10
Measurement and Geometry
10
Measurement and Geometry
10
Measurement and Geometry
10
Measurement and Geometry
Lesson 10-1
(over Chapter 9)
Lesson 10-2
(over Lesson 10-1)
Lesson 10-3
(over Lesson 10-2)
Lesson 10-4
(over Lesson 10-3)
Lesson 10-5
(over Lesson 10-4)
Lesson 10-6
(over Lesson 10-5)
Lesson 10-7
(over Lesson 10-6)
Lesson 10-8
(over Lesson 10-7)
Lesson 10-9
(over Lesson 10-8)
Lesson 10-10 (over Lesson 10-9)
10
Measurement and Geometry
(over Chapter 9)
Convert to a smaller unit.
8 L = __ mL
A. 8,000
B. 80
C. 10
D. 120
10
Measurement and Geometry
(over Chapter 9)
Convert to a smaller unit.
3 km = __ m
A. 10
B. 33
C. 15
D. 3,000
10
Measurement and Geometry
(over Chapter 9)
Convert to a larger unit.
5,000 g = __ kg
A. 15
B. 5
C. 55
D. 120
10
Measurement and Geometry
(over Chapter 9)
Convert to a larger unit.
16,000 mL = __ L
A. 16
B. 140
C. 160
D. 320
10
Measurement and Geometry
(over Lesson 10-1)
Classify the polygon.
A. triangle
B. pentagon
C. square
D. hexagon
10
Measurement and Geometry
(over Lesson 10-1)
Classify the polygon.
A. triangle
B. pentagon
C. square
D. hexagon
10
Measurement and Geometry
(over Lesson 10-1)
Classify the polygon.
A. triangle
B. pentagon
C. square
D. hexagon
10
Measurement and Geometry
(over Lesson 10-1)
Classify the polygon.
A. triangle
B. pentagon
C. square
D. hexagon
10
Measurement and Geometry
(over Lesson 10-2)
Find the perimeter of the figure.
A. 26 cm
B. 12 cm
C. 24 cm
D. 36 cm
10
Measurement and Geometry
(over Lesson 10-2)
Find the perimeter of the figure.
A. 22 in.
B. 10 in.
C. 8 in.
D. 24 in.
10
Measurement and Geometry
(over Lesson 10-2)
Pascal wants to enclose his garden with a
small fence. If his garden is a rectangle 3 yards
by 2 yards, how many yards of fencing material
does he need?
A. 6 yards
B. 12 yards
C. 10 yards
D. 16 yards
10
Measurement and Geometry
(over Lesson 10-3)
Find the area of the figure.
A. 35 square units
B. 25 square units
C. 7 square units
D. 40 square units
10
Measurement and Geometry
(over Lesson 10-3)
Find the area of the figure.
A. 3 square units
B. 18 square units
C. 8 square units
D. 9 square units
10
Measurement and Geometry
(over Lesson 10-3)
Find the area and perimeter of the figure.
A. 14 units;
6 square units
B. 12 units;
6 square units
C. 10 units;
10 square units
10
Measurement and Geometry
(over Lesson 10-4)
Solve. Use the solve a simpler problem
strategy. Afua bought 8 red ribbons, 4 blue
ribbons, and 5 yellow ribbons from the fabric
store. Each piece of ribbon cost $1.00. How
much did she spend in all?
A. $12
B. $4
C. $8
D. $17
10
Measurement and Geometry
(over Lesson 10-5)
Identify the triangle. Write equilateral, isosceles,
or scalene.
A. isosceles
B. equilateral
C. scalene
10
Measurement and Geometry
(over Lesson 10-5)
Identify the triangle. Write equilateral, isosceles,
or scalene.
A. scalene
B. equilateral
C. isosceles
10
Measurement and Geometry
(over Lesson 10-5)
Identify the triangle. Write equilateral, isosceles,
or scalene.
A. scalene
B. equilateral
C. isosceles
10
Measurement and Geometry
(over Lesson 10-6)
Identify the quadrilateral.
A. rectangle
B. square
C. parallelogram
10
Measurement and Geometry
(over Lesson 10-6)
Identify the quadrilateral.
A. square
B. rectangle
C. parallelogram
10
Measurement and Geometry
(over Lesson 10-6)
Identify the quadrilateral.
A. square
B. rectangle
C. parallelogram
10
Measurement and Geometry
(over Lesson 10-7)
Solve. Indu has 27¢ in his pocket. If he has 6 coins
altogether, what coins does he have?
A. 1 quarter, 2 pennies, 2 dimes
B. 1 dime, 3 nickels, 2 pennies
C. 1 nickel, 2 dimes, 1 quarter
10
Measurement and Geometry
(over Lesson 10-8)
Identify the solid figure.
A. cylinder
B. cube
C. square
10
Measurement and Geometry
(over Lesson 10-8)
Identify the solid figure.
A. square
B. cylinder
C. cube
10
Measurement and Geometry
(over Lesson 10-8)
Identify the solid figure.
A. sphere
B. cube
C. square
10
Measurement and Geometry
(over Lesson 10-8)
Identify the solid figure.
A. square
B. cube
C. rectangular solid
10
Measurement and Geometry
(over Lesson 10-9)
Identify the figures that
make this complex solid.
A. cone, cylinder
B. sphere, cone
10
Measurement and Geometry
(over Lesson 10-9)
Identify the figures that make this complex solid.
A. square, cone
B. rectangular solid,
cylinders
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