Instructional Strategies

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Instructional Strategies

Chapters 8 and 9 Geometry Grade 6 MAP2D

Grade 6 MAP2D Quarter 3 Instructional Strategies
Adjacent and Vertical Angles Adjacent Angles : angles that are next to each other. 1 2 3  1 and 2 are adjacent angles. Vertical Angles : angles that are opposite of one another.  1 and 3 are vertical angles. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Vertical Angles a° b° a = b

Vertical Angles c° d° c = d

Complementary angles add up to 90°.

Supplementary angles add up to 180°.

Triangle Sum Property 1 2 3 For any triangle, the sum of the measures of the interior angles is always 180º. 1 3 2 1 2 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Solve for a Missing Angle in a Triangle
73º 1. Write the equation: m1 + m2 + m3 = 180º m1 + m2 + m3 = 180º 90º 73º x 2. Fill in the angle measures 163º + x = 180º 3. Solve the equation for the missing value. 163º+x –163º= 180º–163º x = 17º Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Area is the space inside the circle.

C = d   3.14 Circumference of a Circle

Leaving Answers in Terms of Pi
Instead of multiplying by 3.14, leave the π symbol. Like a variable, it should appear after a coefficient. C = πd A = πr 2 8 C = π  2r A = π  82 C = π  2  8 A = π  64 C = 16π A = 64π Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Estimating with Pi π ≈ … JUST USE 3  C = πd A = πr 2 8 C = π  2r A = π  82 C = π  2  8 A = π  64 C = 16π A = 64π C ≈ 16  3 A ≈ 64  3 C ≈ 48 A ≈ 192 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Area vs. Volume Remember, area is the space inside a flat figure. It is measured using square units. Volume is the amount of space inside a prism. It is measured using cubic units. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Finding The Volume Any Prism

Volume of a Rectangular Prism

Find the Volume of a Rectangular Prism
Remember B is the area of the base. In this case, the area of the rectangle!! Step 1: Use the formula for the volume of a prism 4 m 6 m 11 m Step 2: Identify B and h. Step 3: Substitute 24 for B, and 11 for h. Area of a rectangle: Step 4: Simplify Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Volume of a Triangular Prism

Find the Volume of a Triangular Prism
Remember B is the area of the base. In this case, the area of the triangle!! Step 1: Use the formula for the volume of a prism Step 2: Identify B and h. Step 3: Substitute 35 for B, and 50 for h. Area of a triangle: Step 4: Simplify Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Volume of a Cylinder r h V = B h V = h area of the Base Volume = x

Find the Volume of a Cylinder
Remember B is the area of the base. In this case, the area of the circle!! Step 1: Use the formula for the volume of a cylinder 5 mm Step 2: Identify B and h. 12 mm Step 3: Substitute 25π for B, and 12 for h. Area of a circle: Step 4: Simplify Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Find the Area of a Shaded Region
5 2 13 9 Think of putting wallpaper on a wall… 5 2 With a window Find the area of the wall And subtract out the window l  w l  w 13  9 5  2 117 10 = 107 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Perimeter and Area of Rectangles
8 ft 4 ft Perimeter is the sum of all sides Area is the number of square units in a region. 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6 3 m

Area of a rectangle is bh.
Area of a Triangle The FORMULA for finding the area of a triangle is because a triangle is half of a rectangle. 5 in. 4 in. Area of a rectangle is bh. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Probability and Statistics

Probability of an Event

Representing Outcomes
1st Die 2nd Die Outcome You can use a tree diagram, a list, or a table to list the outcomes of compound events. 1 2 3 4 5 6 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 36 Outcomes 1 1 2 3 4 5 6 2 1 2 3 4 5 6 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 3 1 2 3 4 5 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 What are all the possible outcomes when 2 dice are rolled? 4 1 2 3 4 5 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 5 1 2 3 4 5 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 6

Representing Outcomes
You can use a tree diagram, a list, or a table to list the outcomes of compound events. 36 Outcomes (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) What are all the possible outcomes when 2 dice are rolled? (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Representing Outcomes
You can use a tree diagram, a list, or a table to list the outcomes of compound events. (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) 1 2 3 4 5 6 What are all the possible outcomes when 2 dice are rolled?

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