Math Gr4 Ch11

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Chapter 11Geometry and MeasurementClick the mouse or press the space bar to continue.

Chapter Menu

Lesson 11-1Geometry: CongruentLesson 11-2Geometry: SymmetryLesson 11-3Measurement: PerimeterLesson 11-4Problem-Solving Strategy: Solve a Simpler ProblemLesson 11-5Measurement: AreaLesson 11-6Problem-Solving Investigation: Choose a StrategyLesson 11-7Measurement: Area of Complex Figures

11

Geometry and Measurement

Lesson 1 Menu

Five-Minute Check (over Chapter 10)Main Idea and VocabularyCalifornia StandardsExample 1Example 2Example 3

11-1Geometry: Congruent

Geometry: Congruent

Lesson 1 MI/Vocab


I will identify congruent figures.congruent

Lesson 1 Standard 1


Standard 4MG3.3 Identify congruent figures.

Lesson 1 Ex1

Tell whether the figures are congruent.

11-1Geometry: CongruentAnswer: Yes, the pentagons are congruent.

The figures have the same size and shape.

Lesson 1 CYP1

11-1Geometry: CongruentYes

No


Lesson 1 Ex2Tell whether the figures are congruent.

Answer: No, the triangles are not congruent.


The figures are the same shape, but they are not the same size.

Lesson 1 CYP2


Tell whether the figures are congruent.Yes

No

Lesson 1 Ex3Determine whether the gardens are congruent.


Mr. Smith10 ft.5 ft.

Mr. Bose8 ft.4 ft.

Lesson 1 Ex3The diagrams show that both classrooms have the same shape. They are both rectangles. Answer: Since the gardens have different sizes, they are not congruent.


Mr. Smiths garden has a larger length and a larger width. So, the gardens are not the same size.

Lesson 1 CYP3


Yes

No

Determine whether the windows are congruent.

6 ft.3 ft.

5 ft.3 ft.

End of Lesson 1

Lesson 2 Menu

Five-Minute Check (over Lesson 11-1)Main Idea and VocabularyCalifornia StandardsExample 1Example 2Example 3

11-2Geometry: Symmetry

Lesson 2 MI/Vocab


I will identify figures that have bilateral and rotational symmetry.line symmetryline of symmetry

bilateral symmetryrotational symmetry

Lesson 2 Standard 1


Standard 4MG3.4 Identify figures that have bilateral and rotational symmetry.

Lesson 2 Ex1

Tell whether the figure has line symmetry. Then tell how many lines of symmetry the figure has.Answer: Yes; the figure has 1 line of symmetry.


Lesson 2 CYP1


Yes; 1

Yes; 2

Yes; 4

No

Tell whether the figure has line symmetry. Then tell how many lines of symmetry the figure has.

Lesson 2 Ex2

11-2Geometry: SymmetryTell whether the figure has line symmetry. Then tell how many lines of symmetry the figure has.Answer: Yes; the figure has 2 lines of symmetry.

Lesson 2 CYP2


Yes; 1

Yes; 2

Yes; 3

No


Lesson 2 Ex3Tell whether the figure has rotational symmetry.


Lesson 2 Ex3Answer: The figure has rotational symmetry because it is the same after each rotation.


Lesson 2 CYP3


Yes

No

Tell whether the figure has rotational symmetry.

End of Lesson 2

Lesson 3 Menu

Five-Minute Check (over Lesson 11-2)Main Idea and VocabularyCalifornia StandardsKey Concept: Perimeter of a RectangleExample 1Example 2

11-3Measurement: Perimeter

Lesson 3 MI/Vocab


I will find the perimeter of a polygon.perimeter

Lesson 3 Standard 1


Standard 4MG1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

Lesson 3 Standard 2


Standard 4AF1.4 Use and interpret formulas to answer questions about quantities and their relationships.

Lesson 3 Key Concept 1


Lesson 3 Ex1


Meli is creating a pen for her puppy. The picture shows the layout for the pen. What is the perimeter of the pen?

60 in.36 in.

Lesson 3 Ex1


One Way: Use Addition Add the measures of all of the sides of the figure. P = 36 + 36 + 60 + 60 P = 192

Lesson 3 Ex1

11-3Measurement: PerimeterAnother Way: Use FormulaMultiply the length and the width by 2. Then add.P = (2 60) + (2 36) P = 120 + 72 or 192 Answer: So, the perimeter of the pen is 192 inches.

P = (2 ) + (2 w)

Lesson 3 CYP1


46 ft.

192 ft.

525 ft.

92 ft.

Surgie wants to build a fence for her yard. The picture shows the layout of her fence around the yard. What is the perimeter of the fence?

21 ft.25 ft.

Lesson 3 Ex2

Find the perimeter of a square with a side of 7 centimeters.


There is more than one way to find the perimeter of a square.

One Way: Use AdditionLesson 3 Ex2Add the measures of all of the sides of the figure.

11-3Measurement: PerimeterP = 7 + 7 + 7 + 7P = 28

Another Way: Use FormulaLesson 3 Ex2Multiply the length of one side by 4 because there are 4 sides of equal length.

11-3Measurement: PerimeterP = 4 side lengthP = 4 7

Answer: So, the perimeter of the square is 28.P = 28

Lesson 3 CYP2


11 cm

15 cm

44 cm

55 cm

Find the perimeter of a square with a side of 11 centimeters.

End of Lesson 3

Lesson 4 Menu

Five-Minute Check (over Lesson 11-3)Main IdeaCalifornia StandardsExample 1: Problem-Solving Strategy

11-4Problem-Solving Strategy: Solve a Simpler Problem

Lesson 4 MI/Vocab


I will solve problems by solving a simpler problem.

Lesson 4 Standard 1


Standard 4MR1.2 Determine when and how to break a problem into simpler parts.

Standard 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.

Lesson 4 Ex1Pearl is painting a backdrop that is 30 feet long and 12 feet wide for her school play. The backdrop needs two coats of paint. She has two cans of paint. Each can of paint covers 400 square feet of backdrop. Does Pearl have enough paint?


Lesson 4 Ex1UnderstandWhat facts do you know?The 30 foot by 12 foot backdrop needs two coats of paint.Pearl has two cans of paint.Each can of paint covers 400 square feet of the backdrop.What do you need to find?Does Pearl have enough paint?


Lesson 4 Ex1PlanFind how much paint is needed to paint the backdrop twice. Then find the total area the two cans of paint will cover and compare. You can solve a simpler problem to find the answer.


Lesson 4 Ex1SolveFind the area of one section of the backdrop.

11-4Problem-Solving Strategy: Solve a Simpler Problem10 12 = 120 square feetTo find the area of the entire backdrop, multiply the area of one section of the backdrop by 3.

Lesson 4 Ex1SolveSo, the area of the backdrop equals 120 3 or 360 square feet.

Since the backdrop needs to be painted twice, you need 360 + 360 or 720 square feet of paint.

11-4Problem-Solving Strategy: Solve a Simpler ProblemAnswer: Since 720 < 800, there is enough paint.

Lesson 4 Ex1CheckThe area of the backdrop is 30 12 or 360 square feet. Two coats of paint would need to cover 720 square feet. Since Pearl has enough paint to cover 800 square feet, the answer is correct.


End of Lesson 4

Lesson 5 Menu

Five-Minute Check (over Lesson 11-4)Main Idea and VocabularyCalifornia StandardsKey Concept: Area of a RectangleKey Concept: Area of a SquareExample 1Example 2

11-5Measurement: Area

Perimeter and Area

Lesson 5 MI/Vocab


I will find the area of rectangles and squares.areasquare units

Lesson 5 Standard 1







Lesson 5 Ex1

Write a formula to find the area of the rectangle.


Lesson 5 Ex1


Make a rectangle 4 by 7 square units. There are 28 square units.

One Way: Count the square units.

Lesson 5 Ex1


Another Way: MultiplyMultiply the length times the width to find the area.A = length width= 4 units 7 units= 28 square unitsAnswer: So, the area is 28 square units.

A = w

Lesson 5 CYP1


10 cm2

20 cm2

21 cm2

42 cm2

What is the area of a rectangle with a length of 3 cm and a width of 7 cm?

Lesson 5 Ex2What is the area of a square with sides that are 6 inches in length?

A = side side

11-5Measurement: AreaA = 6 in. 6 in.A = 36 square inchesFormulaReplace s with 6.Multiply.Answer: So, the area of the square is 36 square inches.

Lesson 5 CYP2


5 square inches

10 square inches

20 square inches

25 square inches

What is the area of a square with sides that are 5 inches in length?

End of Lesson 5

Lesson 6 Menu

Five-Minute Check (over Lesson 11-5)Main IdeaCalifornia StandardsExample 1: Problem-Solving Investigation

11-6Problem-Solving Investigation: Choose a Strategy

Lesson 6 MI/Vocab


I will choose the best strategy to solve a problem.

Lesson 6 Standard 1


Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing, and prioritizing information, and observing patterns.

Lesson 6 Standard 1


Standard 4NS3.3 Solve problems involving multiplication of multi-digit numbers by two-digit numbers.

Lesson 6 Ex1


LYNN: It takes me 4 minutes to jog one block in my neighborhood.

YOUR MISSION: Find how long it takes Lynn to jog the route in her neighborhood that is shown.

Lesson 6 Ex1


Understand

What facts do you know?It takes Lynn 4 minutes to jog one block.A map is given of her jogging route.What do you need to find?How many minutes does it take her to jog the route shown?

Lesson 6 Ex1


PlanYou can use the four-step plan and number sentences to solve the problem.

Lesson 6 Ex1


Solve

First find the total number of blocks Lynn jogs. Use the information given to find any measures that are missing.2 + 2 + 2 + 2 + 4 + 4 = 16So, she jogs 16 blocks.

Lesson 6 Ex1


Solve

Use number sentences to find 4 minutes 16 blocks.Answer: So, Lynn jogs for 64 minutes.

Lesson 6 Ex1


CheckTo check your work estimate an answer: 4 20 = 80. Since 80 is close to 64, the answer is correct.

End of Lesson 6

Lesson 7 Menu

Five-Minute Check (over Lesson 11-6)Main Idea and VocabularyCalifornia StandardsExample 1Example 2

11-7Measurement: Area of Complex Figures

Lesson 7 MI/Vocab/Standard 1


I will find the area of complex figures.complex figure

Lesson 7 MI/Vocab/Standard 2



Lesson 7 Ex1


Find the area of the baseball stands.Step 1 Break up the figure into smaller parts. The figure is already broken up into two rectangles that are easy to work with.

Lesson 7 Ex1


Step 2 Find the area of each part.Horizontal RectangleA = length widthA = 10 ft 4 ftA = 40 square feet

Lesson 7 Ex1


Vertical RectangleA = length widthA = 14 ft 4 ftA = 56 square feet

Lesson 7 Ex1


Step 3 Add the areas.40 square feet + 56 square feet = 96 square feet.Answer: The area of the baseball stands is 96 square feet.

Lesson 7 CYP1


97 square inches

132 square inches

127 square inches

39 square inches

Find the area of the figure.

Lesson 7 Ex2

11-7Measurement: Area of Complex FiguresFind the area of the complex figure.

Step 1 Break up the figure into smaller parts. Look for rectangles and squares. This figure can be broken up into 1 rectangle and 2 squares.

Lesson 7 Ex2


Step 2 Find the area of each part.RectangleA = length widthA = 9 in. 2 in.A = 18 square inches

Lesson 7 Ex2


SquareA = side sideA = 2 in. 2 in.A = 4 square inches

Lesson 7 Ex2


Step 3 Add the areas.18 square feet + 4 square feet + 4 square feet = 26 square feetAnswer: So, the area is 26 square feet.

Lesson 7 CYP2


26 square centimeters

14 square centimetersFind the area of the complex figure.



End of Lesson 7

CR Menu

Five-Minute Checks

Geometry: CongruentPerimeter and Area

11Geometry and Measurement5Min MenuLesson 11-1(over Chapter 10)Lesson 11-2(over Lesson 11-1)Lesson 11-3(over Lesson 11-2)Lesson 11-4(over Lesson 11-3)Lesson 11-5(over Lesson 11-4)Lesson 11-6(over Lesson 11-5)Lesson 11-7(over Lesson 11-6)

11Geometry and Measurement5Min 1-1

(over Chapter 10)2 meters

4 meters

8 meters

16 meters

If a circle has a radius of 4 meters, what is the length of the diameter?

11Geometry and Measurement

5Min 1-2

(over Chapter 10)2 inches

6 inches

12 inches

24 inches

If a circle has a diameter of 12 inches, what is the radius?


(over Lesson 11-1)Yes

No



5Min 2-2


No



5Min 2-3


NoTell whether the figures are congruent.


5Min 2-4


No



(over Lesson 11-2)yes, 4

no, 0

yes, 1

yes, 2



5Min 3-2

(over Lesson 11-2)yes, 1

yes, 2

no, 0

yes, 0



5Min 3-3

(over Lesson 11-2)yes

no

Tell whether the figure has rotational symmetry.


5Min 3-4

(over Lesson 11-2)Tell whether the figure has rotational symmetry.yes

no


(over Lesson 11-3)27 feet

15 feet

30 feet

18 feet

Find the perimeter of a rectangle that is 12 feet long and 3 feet wide.


5Min 4-2

(over Lesson 11-3)9 yards

18 yards

27 yards

36 yards

Find the perimeter of a square that is 9 yards on one side.


(over Lesson 11-4)Sabrina spends more money; $0.05

Lavanya spends more money; $0.05



Solve. Lavanya buys a 5 pound watermelon for 41 per pound. Sabrina buys an 8 pound watermelon for 25 per pound. Who spends more money, and how much more?


(over Lesson 11-5)21 square inches

10 inches

21 inches

10 square inches

Find the area of a rectangle that is 3 inches by 7 inches.


5Min 6-2

(over Lesson 11-5)20 square centimeters




Find the area of a rectangle that is 2 cm by 8 cm.


5Min 6-3

(over Lesson 11-5)20 yards

25 square yards

20 square yards

10 square yards

Find the area of a square that has sides of 5 yards.


5Min 6-4

(over Lesson 11-5)

18 square feet

36 square feet

72 square feet

81 square feet

Find the area of a square with 9 feet per side.


(over Lesson 11-6)375 customers

525 customers

675 customers

1,050 customers

Solve. On weekdays, a restaurant serves 25 customers for lunch and 50 for dinner. On Saturday and Sunday, the number of customers doubles. Find the number of customers the restaurant serves in one week.

11Geometry and MeasurementEnd of Custom ShowsThis slide is intentionally blank.

Education

Math Gr4 Ch11