Instructional Strategies MAP2D Quarter 3 Instructional Strategies Grade 6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Chapters 8 and 9 Geometry Grade 6 MAP2D Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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 are the angles opposite each other when 2 lines cross. a° b° Vertical angles are congruent. a = b Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Vertical Angles c° d° c = d Vertical angles are the angles opposite each other when 2 lines cross. c° d° Vertical angles are congruent. c = d Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Adjacent Angles “Adjacent” means “next to”. Adjacent angles are next to each other, sharing one side. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Complementary angles add up to 90°. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Supplementary angles add up to 180°. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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 xº 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. of a circle r = radius Area = r 2   3.14 Area is the space inside the circle. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

C = d   3.14 Circumference of a Circle d = diameter Circumference   3.14 Circumference is the distance around a circle or sphere. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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 ≈ 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679… 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 prism = Area of one Base  height V = B h height Area of the Base Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Volume of a Rectangular Prism area of the Base Volume = x height V = B h h V = h Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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 area of the Base Volume = x height h b V = B h h V = h Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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 height h V = B h V = h Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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 MAP2D Chapters 10 and 11 Probability and Statistics Grade 6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

Probability of an Event The probability of an event equals: yellow blocks (yellow) blocks in the bag 1 P(Y) = 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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?