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MAP 2 D

MAP 2 D. Quarter 4 Instructional Strategies Grade 6. MAP 2 D. Chapter 10 Measurement Chapter 2 Integers Chapter 11 Multi-Step Equations Inequalities. MAP 2 D. Instructional Strategies Chapter 10 Measurement. D. F. Let's Identify Parts of a Circle.

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MAP 2 D

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  1. MAP2D Quarter 4 Instructional Strategies Grade 6

  2. MAP2D Chapter 10Measurement Chapter 2Integers Chapter 11Multi-Step Equations Inequalities

  3. MAP2D Instructional StrategiesChapter 10Measurement

  4. D F Let's Identify Parts of a Circle First identify the radius as any line segment that joins a point on the circle to the center of the circle.

  5. G D F Let's Identify Parts of a Circle Introduce the diameter as any line segment that passes through the center of the circle and has its endpoints on the circle.

  6. G D E F Let's Identify Parts of a Circle A chord is a line segment that connects two points on a circle. Hint: The diameter is also a chord.

  7. G D E F Let's Identify Parts of a Circle radius diameter (also called a chord) chord

  8. AREA of a circle r = radius Area = r 2  3.14 Area is the space inside the circle.

  9. Circumference d = diameter Circumference of a Circle C = d  3.14 Circumference is the distance around a circle or sphere.

  10. 8 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 = πr2 C = π2r A = π82 C = π2 8 A = π64 C = 16π A = 64π

  11. 8 C ≈ 16 3 A ≈ 64 3 Estimating with Pi π ≈ 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679… JUST USE 3  C = πd A = πr2 C = π2r A = π82 C = π2 8 A = π64 C = 16π A = 64π C ≈ 48 A ≈ 192

  12. 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.

  13. height Area of the Base Finding The Volume Any Prism Volume of a prism = Area of one Base  height V = Bh

  14. h V = h Volume of a Rectangular Prism area of the Base Volume = x height V = B h

  15. 11 m Area of a rectangle: 4 m 6 m 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 Step 2: Identify B and h. Step 3: Substitute 24 for B, and 11 for h. Step 4: Simplify

  16. h b h V = h Volume of a Triangular Prism area of the Base Volume = x height V = B h

  17. Area of a triangle: 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. Step 4: Simplify

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

  19. Area of a circle: 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. Step 4: Simplify

  20. 5 2 13 5 2 l  w 9 5  2 Find the Area of a Shaded Region Think of putting wallpaper on a wall… …with a window Find the area of the wall And subtract out the window l  w = 107 sq. units 13  9 117 10

  21. 4 ft 8 ft Perimeter and Area of Rectangles Perimeter is the sum of all sides Area is the number of square units in a region. 4 3 m

  22. 4 in. 5 in. Area of a Triangle The FORMULA for finding the area of a triangle is because a triangle is half of a rectangle. Area of a rectangle is bh.

  23. MAP2D Instructional StrategiesChapter 10Measurement (After State Testing)

  24. 10 cm 8 cm 20 cm Let's Find the Area of a Parallelogram! Identify the base Identify the height Hint: The dotted line is an indicator of the height

  25. Let's Find the Area of a Parallelogram! Hint: The dotted line is an indicator of the height

  26. 4 in 5 in Let's Find the Area of a Triangle ! The FORMULA for finding the area of a triangle is because a triangle is half of the rectangle. Area of a rectangle is bh. Ch 21 L 6

  27. Plan A Plan B 4 in 5 in Ch 21 L 6

  28. Let's Find the Area of Complex Figures! 8 in ? ? 16 in 8 in 20 in Find the length of the missing sides Ch 21 L 2

  29. Complex Figures 8 in 12 in 8 in 16 in 8 in 20 in Find the area of the large rectangle Find the area of the small rectangle Subtract the areas Ch 21 L 2

  30. MAP2D Instructional StrategiesChapter 2Integers

  31. Let's Learn How to Find Lengths on a Coordinate Plane ! Y To find the length of a segment, compare the ordered pairs. ( 1, 2 ) ( 3, 2 ) X Cross out the common coordinate and find the difference of the other ones. EXAMPLE: (3, 2) and (1, 2) 3 – 1 = 2

  32. 2 2 Solving Two-Step Equations 6x – 2 = 10 Step 1 + 2 + 2 Add 2 to both sides of the equation 6x = 12 Step 2 Then divide both sides by 6 Step 3 x = 2 Simplify

  33. Solving Two-Step Equations Step 1 Subtract 5 from both sides of the equation -5 -5 Step 2 Then multiply both sides by 6 Step 3 x = 48 Simplify

  34. Let's Graph an Equation Rewrite the equation on the side of the function table Substitute the given value for the known variable

  35. 8 7 6 5 y = x + 2 4 3 x y 2 2 0 1 3 0 1 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 -1 4 2 -2 -3 -4 -5 -6 -7 -8 Let's Graph an Equation y = x + 2

  36. 8 7 6 5 y = x + 2 4 3 x y 2 2 0 1 3 0 1 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 -1 4 2 -2 -3 -4 -5 -6 -7 -8 Now we will graph the ordered pairs. y = x + 2 ( , ) ( , ) ( , ) Draw a line through the points. Label the line with the equation. Ch 19 L 5

  37. MAP2D Instructional StrategiesChapter 11Multi-Step Equations And Inequalities

  38. Let's Learn How to Find Lengths on a Coordinate Plane ! Y To find the length of a segment, compare the ordered pairs. ( 1, 2 ) ( 3, 2 ) X Cross out the common coordinate and find the difference of the other ones. EXAMPLE: (3, 2) and (1, 2) 3 – 1 = 2

  39. b x x b Simplifying Algebraic Expressions b b b b + = x x x x x x 1b + 2x + 2b + 2x = 3b+ 4x • A term can be a number, a variable, or a product of numbers and variables • Combine like terms

  40. Evaluating Algebraic Expressions Evaluate x + 5 for x = 11 Step 1: Substitute 11 for x. 11 + 5 Step 2: 16 Add. Section 1.1 Evaluating Algebraic Expressions

  41. Evaluating Algebraic Expressions Evaluate 2y + 3 for y = 4 Step 1: 2(4) + 3 Substitute 4 for y. Step 2: 8 + 3 Multiply. Step 3: 11 Add. Section 1.1 Evaluating Algebraic Expressions

  42. Evaluating Algebraic Expressions Evaluate 5x + 2y for x = 13 and y = 11 Step 1: 5(13) + 2(11) Substitute 13 for x and 11 for y. Step 2: 65 + 22 Multiply. Step 3: 11 Add. Section 1.1 Evaluating Algebraic Expressions

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