1. Write down some statements about the shape you see. Be specific as possible. CUBE ROOTS

2. A number is a perfect cube if you can take that many 1 x 1 x 1 unit cubes and form them into a cube. So how many perfect cubes could you make given 1000 blocks that are 1 x 1 x 1? Perfect Cubes and Cube Roots

3. Side Length Volume Operation VolumePerfect Cube 1 unit1 x 1 x 11 units³1 2 units2 x 2 x 22 units³8

4. Perfect Cubes and Cube Roots Side Length Volume Operation VolumePerfect Cube 1 unit1313 1 units 3 1 2 units2323 8 units 3 8 3 units3 27 units 3 27

5. Perfect Cubes and Cube Roots Side Length Volume Operation VolumePerfect Cube 1 unit1313 1 units 3 1 2 units2323 8 units 3 8 3 units3 27 units 3 27 4 units

6. Perfect Cubes and Cube Roots Side Length Volume Operation VolumePerfect Cube 1 unit1313 1 units 3 1 2 units2323 8 units 3 8 3 units3 27 units 3 27 4 units4343

7. Perfect Cubes and Cube Roots Side Length Volume Operation VolumePerfect Cube 1 unit1313 1 units 3 1 2 units2323 8 units 3 8 3 units3 27 units 3 27 4 units4343 64 units 3

8. Perfect Cubes and Cube Roots Side Length Volume Operation VolumePerfect Cube 1 unit1313 1 units 3 1 2 units2323 8 units 3 8 3 units3 27 units 3 27 4 units4343 64 units 3 64

9. Perfect Cubes and Cube Roots Side Length of cube Volume Operation Volume of cube Perfect Cube 1 unit1313 1 units 3 1 2 units2323 8 units 3 8 3 units3 27 units 3 27 4 units4343 64 units 3 64 x unitsx3x3 p units 3 So, x³= p

10. Common Core #4 Evaluate perfect cube roots in the form of x³ = p and estimate non-perfect cube roots to the nearest tenth.

11. Perfect Cubes and Cube Roots

12. Find the cube root of a given number, p. For example what is the cube root of 9,261? Answer is 21 because 21³=9,261 Find the cube root for the following: (1)x³ = 2197 (2) b³ = 4913(3) Answers are 13, 17, and 12 SAMPLE QUESTIONS

13. Estimate cube roots. For example, to the nearest tenth, what is the cube root of 3? We know 1³ = 1 and 2³ = 8 so the answer lies somewhere between 1 and 2. You must pick a number say 1.4 and multiply it three times and see how close it is to the number 3. 1.4³ = 2.744 Close but we need to now check 1.5….. 1.5³ = 3.375 So 1.4 is the best answer since it is closer to 3 than 1.5 SAMPLE HARDER QUESTIONS

14. Estimate the cube root to the nearest tenth by finding x. (1) x³ = 11(2) (3) x³ = 562 Answers are (1) 2.2 and (2) 4.6 And (3) 8.3 YOU TRY THESE