Math Gr4 Ch11
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Math Gr4 Ch11

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Math Gr4 Ch11 Math Gr4 Ch11 Presentation Transcript

  • Chapter 11 Geometry and Measurement Click the mouse or press the space bar to continue.
  • Geometry and Measurement 11 Lesson 11-1 Geometry: Congruent Lesson 11-2 Geometry: Symmetry Lesson 11-3 Measurement: Perimeter Lesson 11-4 Problem-Solving Strategy: Solve a Simpler Problem Lesson 11-5 Measurement: Area Lesson 11-6 Problem-Solving Investigation: Choose a Strategy Lesson 11-7 Measurement: Area of Complex Figures
  • 11-1 Geometry: Congruent Five-Minute Check (over Chapter 10) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Geometry: Congruent
  • 11-1 Geometry: Congruent • I will identify congruent figures. • congruent
  • 11-1 Geometry: Congruent Standard 4MG3.3 Identify congruent figures.
  • 11-1 Geometry: Congruent Tell whether the figures are congruent. The figures have the same size and shape. Answer: Yes, the pentagons are congruent.
  • 11-1 Geometry: Congruent Tell whether the figures are congruent. A. Yes B. No
  • 11-1 Geometry: Congruent Tell whether the figures are congruent. The figures are the same shape, but they are not the same size. Answer: No, the triangles are not congruent.
  • 11-1 Geometry: Congruent Tell whether the figures are congruent. A. Yes B. No
  • 11-1 Geometry: Congruent Determine whether the gardens are congruent. Mr. Smith Mr. Bose 10 ft. 8 ft. 5 ft. 4 ft.
  • 11-1 Geometry: Congruent The diagrams show that both classrooms have the same shape. They are both rectangles. Mr. Smith’s garden has a larger length and a larger width. So, the gardens are not the same size. Answer: Since the gardens have different sizes, they are not congruent.
  • 11-1 Geometry: Congruent Determine whether the windows are congruent. 3 ft. 3 ft. 5 ft. 6 ft. A. Yes B. No
  • 11-2 Geometry: Symmetry Five-Minute Check (over Lesson 11-1) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3
  • 11-2 Geometry: Symmetry • I will identify figures that have bilateral and rotational symmetry. • line symmetry • bilateral symmetry • line of symmetry • rotational symmetry
  • 11-2 Geometry: Symmetry Standard 4MG3.4 Identify figures that have bilateral and rotational symmetry.
  • 11-2 Geometry: Symmetry 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.
  • 11-2 Geometry: Symmetry Tell whether the figure has line symmetry. Then tell how many lines of symmetry the figure has. A. Yes; 1 B. Yes; 2 C. Yes; 4 D. No
  • 11-2 Geometry: Symmetry Tell 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.
  • 11-2 Geometry: Symmetry Tell whether the figure has line symmetry. Then tell how many lines of symmetry the figure has. A. Yes; 1 B. Yes; 2 C. Yes; 3 D. No
  • 11-2 Geometry: Symmetry Tell whether the figure has rotational symmetry.
  • 11-2 Geometry: Symmetry Answer: The figure has rotational symmetry because it is the same after each rotation.
  • 11-2 Geometry: Symmetry Tell whether the figure has rotational symmetry. A. Yes B. No
  • 11-3 Measurement: Perimeter Five-Minute Check (over Lesson 11-2) Main Idea and Vocabulary California Standards Key Concept: Perimeter of a Rectangle Example 1 Example 2
  • 11-3 Measurement: Perimeter • I will find the perimeter of a polygon. • perimeter
  • 11-3 Measurement: Perimeter 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.
  • 11-3 Measurement: Perimeter Standard 4AF1.4 Use and interpret formulas to answer questions about quantities and their relationships.
  • 11-3 Measurement: Perimeter
  • 11-3 Measurement: Perimeter Meli is creating a pen for her puppy. The picture shows the layout for the pen. What is the perimeter of the pen? 36 in. 60 in.
  • 11-3 Measurement: Perimeter One Way: Use Addition Add the measures of all of the sides of the figure. P = 36 + 36 + 60 + 60 P = 192
  • 11-3 Measurement: Perimeter Another Way: Use Formula Multiply the length and the width by 2. Then add. P = (2 × ) + (2 × w) P = (2 × 60) + (2 × 36) P = 120 + 72 or 192 Answer: So, the perimeter of the pen is 192 inches.
  • 11-3 Measurement: Perimeter 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? A. 46 ft. B. 192 ft. 21 ft. C. 525 ft. D. 92 ft. 25 ft.
  • 11-3 Measurement: Perimeter 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.
  • 11-3 Measurement: Perimeter One Way: Use Addition Add the measures of all of the sides of the figure. P=7+7+7+7 P = 28
  • 11-3 Measurement: Perimeter Another Way: Use Formula Multiply the length of one side by 4 because there are 4 sides of equal length. P = 4 × side length P=4×7 P = 28 Answer: So, the perimeter of the square is 28.
  • 11-3 Measurement: Perimeter Find the perimeter of a square with a side of 11 centimeters. A. 11 cm B. 15 cm C. 44 cm D. 55 cm
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem Five-Minute Check (over Lesson 11-3) Main Idea California Standards Example 1: Problem-Solving Strategy
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem • I will solve problems by solving a simpler problem.
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem 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.
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem Pearl 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?
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem Understand What 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?
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem Plan Find 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.
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem Solve Find the area of one section of the backdrop. 10 × 12 = 120 square feet To find the area of the entire backdrop, multiply the area of one section of the backdrop by 3.
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem Solve So, 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. Answer: Since 720 < 800, there is enough paint.
  • 11-4 Problem-Solving Strategy: Solve a Simpler Problem Check The 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.
  • 11-5 Measurement: Area Five-Minute Check (over Lesson 11-4) Main Idea and Vocabulary California Standards Key Concept: Area of a Rectangle Key Concept: Area of a Square Example 1 Example 2 Perimeter and Area
  • 11-5 Measurement: Area • I will find the area of rectangles and squares. • area • square units
  • 11-5 Measurement: Area 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.
  • 11-5 Measurement: Area
  • 11-5 Measurement: Area
  • 11-5 Measurement: Area Write a formula to find the area of the rectangle.
  • 11-5 Measurement: Area One Way: Count the square units. Make a rectangle 4 by 7 square units. There are 28 square units.
  • 11-5 Measurement: Area Another Way: Multiply Multiply the length times the width to find the area. A = length × width A= ×w = 4 units × 7 units = 28 square units Answer: So, the area is 28 square units.
  • 11-5 Measurement: Area What is the area of a rectangle with a length of 3 cm and a width of 7 cm? A. 10 cm2 B. 20 cm2 C. 21 cm2 D. 42 cm2
  • 11-5 Measurement: Area What is the area of a square with sides that are 6 inches in length? A = side × side Formula A = 6 in. × 6 in. Replace s with 6. A = 36 square inches Multiply. Answer: So, the area of the square is 36 square inches.
  • 11-5 Measurement: Area What is the area of a square with sides that are 5 inches in length? A. 5 square inches B. 10 square inches C. 20 square inches D. 25 square inches
  • 11-6 Problem-Solving Investigation: Choose a Strategy Five-Minute Check (over Lesson 11-5) Main Idea California Standards Example 1: Problem-Solving Investigation
  • 11-6 Problem-Solving Investigation: Choose a Strategy • I will choose the best strategy to solve a problem.
  • 11-6 Problem-Solving Investigation: Choose a Strategy Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing, and prioritizing information, and observing patterns.
  • 11-6 Problem-Solving Investigation: Choose a Strategy Standard 4NS3.3 Solve problems involving multiplication of multi-digit numbers by two-digit numbers.
  • 11-6 Problem-Solving Investigation: Choose a Strategy 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.
  • 11-6 Problem-Solving Investigation: Choose a Strategy 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?
  • 11-6 Problem-Solving Investigation: Choose a Strategy Plan You can use the four-step plan and number sentences to solve the problem.
  • 11-6 Problem-Solving Investigation: Choose a Strategy 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 = 16 So, she jogs 16 blocks.
  • 11-6 Problem-Solving Investigation: Choose a Strategy Solve Use number sentences to find 4 minutes × 16 blocks. Answer: So, Lynn jogs for 64 minutes.
  • 11-6 Problem-Solving Investigation: Choose a Strategy Check To check your work estimate an answer: 4 × 20 = 80. Since 80 is close to 64, the answer is correct.
  • 11-7 Measurement: Area of Complex Figures Five-Minute Check (over Lesson 11-6) Main Idea and Vocabulary California Standards Example 1 Example 2
  • 11-7 Measurement: Area of Complex Figures • I will find the area of complex figures. • complex figure
  • 11-7 Measurement: Area of Complex Figures 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.
  • 11-7 Measurement: Area of Complex Figures 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.
  • 11-7 Measurement: Area of Complex Figures Step 2 Find the area of each part. Horizontal Rectangle A = length × width A = 10 ft × 4 ft A = 40 square feet
  • 11-7 Measurement: Area of Complex Figures Vertical Rectangle A = length × width A = 14 ft × 4 ft A = 56 square feet
  • 11-7 Measurement: Area of Complex Figures 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.
  • 11-7 Measurement: Area of Complex Figures Find the area of the figure. A. 97 square inches B. 132 square inches C. 127 square inches D. 39 square inches
  • 11-7 Measurement: Area of Complex Figures Find 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.
  • 11-7 Measurement: Area of Complex Figures Step 2 Find the area of each part. Rectangle A = length × width A = 9 in. × 2 in. A = 18 square inches
  • 11-7 Measurement: Area of Complex Figures Square A = side × side A = 2 in. × 2 in. A = 4 square inches
  • 11-7 Measurement: Area of Complex Figures Step 3 Add the areas. 18 square feet + 4 square feet + 4 square feet = 26 square feet Answer: So, the area is 26 square feet.
  • 11-7 Measurement: Area of Complex Figures Find the area of the complex figure. A. 26 square C. 9 square centimeters centimeters B. 14 square D. 6 square centimeters centimeters
  • Geometry and Measurement 11 Five-Minute Checks Geometry: Congruent Perimeter and Area
  • Geometry and Measurement 11 Lesson 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)
  • Geometry and Measurement 11 (over Chapter 10) If a circle has a radius of 4 meters, what is the length of the diameter? A. 2 meters B. 4 meters C. 8 meters D. 16 meters
  • Geometry and Measurement 11 (over Chapter 10) If a circle has a diameter of 12 inches, what is the radius? A. 2 inches B. 6 inches C. 12 inches D. 24 inches
  • Geometry and Measurement 11 (over Lesson 11-1) Tell whether the figures are congruent. A. Yes B. No
  • Geometry and Measurement 11 (over Lesson 11-1) Tell whether the figures are congruent. A. Yes B. No
  • Geometry and Measurement 11 (over Lesson 11-1) Tell whether the figures are congruent. A. Yes B. No
  • Geometry and Measurement 11 (over Lesson 11-1) Tell whether the figures are congruent. A. Yes B. No
  • Geometry and Measurement 11 (over Lesson 11-2) Tell whether the figure has line symmetry. Then tell how many lines of symmetry the figure has. A. yes, 4 B. no, 0 C. yes, 1 D. yes, 2
  • Geometry and Measurement 11 (over Lesson 11-2) Tell whether the figure has line symmetry. Then tell how many lines of symmetry the figure has. A. yes, 1 B. yes, 2 C. no, 0 D. yes, 0
  • Geometry and Measurement 11 (over Lesson 11-2) Tell whether the figure has rotational symmetry. A. yes B. no
  • Geometry and Measurement 11 (over Lesson 11-2) Tell whether the figure has rotational symmetry. A. yes B. no
  • Geometry and Measurement 11 (over Lesson 11-3) Find the perimeter of a rectangle that is 12 feet long and 3 feet wide. A. 27 feet B. 15 feet C. 30 feet D. 18 feet
  • Geometry and Measurement 11 (over Lesson 11-3) Find the perimeter of a square that is 9 yards on one side. A. 9 yards B. 18 yards C. 27 yards D. 36 yards
  • Geometry and Measurement 11 (over Lesson 11-4) 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? A. Sabrina spends more money; $0.05 B. Lavanya spends more money; $0.05 C. Lavanya spends more money; $0.03 D. Lavanya spends more money; $0.16
  • Geometry and Measurement 11 (over Lesson 11-5) Find the area of a rectangle that is 3 inches by 7 inches. A. 21 square inches B. 10 inches C. 21 inches D. 10 square inches
  • Geometry and Measurement 11 (over Lesson 11-5) Find the area of a rectangle that is 2 cm by 8 cm. A. 20 square centimeters B. 10 square centimeters C. 16 square centimeters D. 18 square centimeters
  • Geometry and Measurement 11 (over Lesson 11-5) Find the area of a square that has sides of 5 yards. A. 20 yards B. 25 square yards C. 20 square yards D. 10 square yards
  • Geometry and Measurement 11 (over Lesson 11-5) Find the area of a square with 9 feet per side. A. 18 square feet B. 36 square feet C. 72 square feet D. 81 square feet
  • Geometry and Measurement 11 (over Lesson 11-6) 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. A. 375 customers B. 525 customers C. 675 customers D. 1,050 customers
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