1. Name:________________________________________________________________________________Date:_____/_____/__________ A Point A is located at (-4, 3). Perform the following transformations: 1)Translate (5, -4):____________________________________________________ 2)Translate (-2, 3):____________________________________________________ 3)Reflect over the “x” axis: ____________________________________________ 4)Reflect over the “y” axis:_____________________________________________ 5)Rotate 90˚ clockwise:_________________________________________________ 6)Rotate 180˚ counter-clockwise:_____________________________________ 7)Rotate 270˚ clockwise:________________________________________________ 8)Dilate by a scale factor of 3:__________________________________________ 9)Dilate by a scale factor of ½: _________________________________________ Quiz Day

2. 10. A.Translation B.Rotation C.Dilation D.Reflection 11. Which numbered triangle is a 90˚ counter-clockwise rotation of the shaded triangle? A.Triangle 1 C. Triangle 3 B.Triangle2 D. Triangle 4 12.A.Translation B.Rotation C.Dilation D.Reflection 13. What is the scale factor of the dilation to the right?

3. Today’s Lesson: What: volume of prisms and cylinders Why: To calculate the volume of both rectangular prisms and cylinders. What: volume of prisms and cylinders Why: To calculate the volume of both rectangular prisms and cylinders.

4. Vocabulary: Rectangular Prism -- a 3-D figure that is comprised of six ____________faces (a “box”). Cube – a special type of ____________________ where each face is a ___________________. Cylinder – a 3-D figure with circular ____________ for both the top and the bottom. Radius -- refers to the line segment that __________________________ in the center and extends to the circumference line (edge). Diameter – refers to the line segment that extends the entire way _______________ a circle. The diameter splits the circle into two _____________ halves. Volume — the measure of ___________ occupied by a solid region, measured in __________ units. rectangular rectangular prism square faces begins across equal space cubic

5. Where is volume in real life ? (brainstorm) Key Words : Fill Hold Pour Filling a cup or bowl. Pouring sand into a sandbox. The amount of water an aquarium holds. How much cake batter a cake pan will hold. Etc., etc....

6. Volume of a PRISM: 1) V = lwh 12 cm 5 cm 4 cm 240 cm ³

7. Volume of a PRISM: 2) V = lwh 3.5 cm 14 cm 98 cm ³ 2 cm

8. Volume of a PRISM: 3) V = lwh 7 cm 343 cm ³

9. Word problem example: MaryBeth is filling a sandbox with sand. If the sandbox is seven feet in length, two feet in height, and four feet in width, how much sand can the sandbox hold? 56 ft ³

10. Volume of CYLINDERS: 1) V = r²h 10 cm 6 cm 282.6 cm ³

11. Volume of CYLINDERS: 2) V = r²h 4.5 cm 2.5 cm ≈ 88.3 cm ³

12. Volume of CYLINDERS: 3) V = r²h 15 cm 4 cm 188.4 cm ³

13. Word problem example: Joe is pouring coffee into his coffee mug. The mug is 7 in. tall, and its bottom has a diameter of 4 in. How much coffee does Joe’s mug hold? 87.92 in ³

14. Changing an attribute (length, width, or height) : If ONE (and only one) attribute of a figure is changed, then the resulting volume will change by the ________ amount! In other words, if ONE attribute doubles, the volume will also _____________ ! Or, if ONE attribute is decreased by half, then the volume will also ____________ by half! 12 cm 4 cm Example: If the volume of the first figure is 64 cm³ (and only the height is changed), then what is the volume of the second figure? 192 cm ³ same double decrease

15. Word problem example: Julie has a jewelry box that holds 60 in³ when filled. Stephanie’s jewelry box has the same dimensions– except that its length is half the length of Julie’s box. How much can Stephanie’s box hold? 30 in ³

16. END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow represent the homework assigned for that day.

17. Vocabulary: Rectangular Prism -- a 3-D figure that is comprised of six _____________ faces (a “box”). Cube – a special type of _______________________ where each face is a ___________________. Cylinder – a 3-D figure with circular __________________ for both the top and the bottom. Radius -- refers to the line segment that __________________________ in the center and extends to the circumference line (edge). Diameter – refers to the line segment that extends the entire way _______________ a circle. The diameter splits the circle into two _____________ halves. Volume — the measure of __________ occupied by a solid region, measured in _______ un.³ Volume of a PRISM: 1) 2) 3) Math-7 NOTES DATE: ______/_______/_______ What: volume of prisms and cylinders Why: To calculate the volume of both rectangular prisms and cylinders. What: volume of prisms and cylinders Why: To calculate the volume of both rectangular prisms and cylinders. NAME: Where is Volume in real-life? V = lwh 12 cm 7 cm 5 cm 4 cm 3.5 cm 14 cm 2 cm Word Problem Example : MaryBeth is filling a sandbox with sand. If the sandbox is seven feet in length, two feet in height, and four feet in width, how much sand can the sandbox hold? Key Words : Fill Hold Pour

18. Volume of CYLINDERS: 1) 2) 3) V = r²h 15 cm 4 cm 4.5 cm 2.5 cm 10 cm 6 cm Word problem example: Joe is pouring coffee into his coffee mug. The mug is 7 in. tall, and its bottom has a diameter of 4 in. How much coffee does Joe’s mug hold? Changing an attribute (length, width or height): o If ONE (and only one) attribute of a figure is changed, then the resulting volume will change by the ________ amount! o In other words, if ONE attribute doubles, the volume will also _____________ ! Or, if ONE attribute is decreased by half, then the volume will also ____________ by half! Word problem example: Julie has a jewelry box that holds 60 in³ when filled. Stephanie’s jewelry box has the same dimensions– except that its length is half the length of Julie’s box. How much can Stephanie’s box hold? 12 cm 4 cm Example: If the volume of the first figure is 64 cm³ (and only the height is changed), then what is the volume of the second figure? _____________________

19. NAME: _________________________________________________________________________________DATE: ______/_______/_______ “Volume of Prisms and Cylinders”

20. Changing Attributes: 5.Jen has a mug that holds 800 cubic cm of liquid. If Julie’s mug has a congruent base, but is half the height, what is the volume of Julie’s mug? 6.A pool that is 20 ft long, 8 ft wide, and 4 ft deep holds 640 ft³ of water. Another pool holds 1,280 ft³ of water. It is equal in size, but is a different depth. How deep must it be? 7.A jumbo sandbox holds 81 cubic ft of sand. Another sandbox is equal in size, but is 1/3 the length. How much sand does the smaller box hold?