PURPOSEPURPOSE1.1. Seated and Silent by 7:53.Seated and Silent by 7:53.

2.2. Have forms ready to turn in.Have forms ready to turn in.

3.3. Have Student Survey ready to turn in.Have Student Survey ready to turn in.

4.4. Complete All About Me Assignment or Time Capsule Complete All About Me Assignment or Time Capsule Activity if not completed yesterday.Activity if not completed yesterday.

5.5. All About Me and Time Capsule are on the back counter.All About Me and Time Capsule are on the back counter.

6.6. Today we will be discussing TCAP scores.Today we will be discussing TCAP scores.

Advisory – Silent Reading

If you do not have your own

reading material, take a

book, magazine, comic, or

graphic novel from my shelf.

Procedures ReviewProcedures Review

• Think of at least 3 procedures we talked Think of at least 3 procedures we talked about yesterday. about yesterday.

• Be prepared to share one of those Be prepared to share one of those procedures if your UNO card is drawn.procedures if your UNO card is drawn.

Square Roots, Cube Roots, and Irrational Numbers

8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Words to know…• Square root Square root • Perfect squarePerfect square• Irrational Irrational • Cube rootCube root

Individual Think Time:How can you turn two blocks

into a square?

2

2

2 x 2 = 4

3 x 3 = 9

3

3

4 x 4 = 16

4

4

5

5

5 x 5 = 25

The square root of 4 is 2

The square root of 9 is 3

The square root of 16 is 4

The square root of 25 is 5

Square numbers

Here are the first 10 square numbers:

12 = 1 × 1 = 1

22 = 2 × 2 = 4

32 = 3 × 3 = 9

42 = 4 × 4 = 16

52 = 5 × 5 = 25

62 = 6 × 6 = 36

72 = 7 × 7 = 49

82 = 8 × 8 = 64

92 = 9 × 9 = 81

102 = 10 × 10 = 100

Adding consecutive odd numbers

The first square number is 1.The second square number is 4.The third square number is 9. The fourth square number is 16.The fifth square number is 25. The sixth square number is 36. The seventh square number is 49. The eighth square number is 64. The ninth square number is 81. The tenth square number is 100.

1 + 3 = 41 + 3 + 5 = 91 + 3 + 5 + 7 = 161 + 3 + 5 + 7 + 9 = 251 + 3 + 5 + 7 + 9 + 11 = 361 + 3 + 5 + 7 + 9 + 11 + 13 = 491 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 641 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 811 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

Think about this…..

Could you figure out what the 11th square number would be?

Think about this…..

What about the 15th square number?

Finding the square root is the inverse of finding the square:

8

squared

64

square rooted

We write

64 = 8

The square root of 64 is 8.

Square roots

We can easily find the square root of a square number.

1 = 1

4 = 2

9 = 3

16 = 4

25 = 5

36 = 6

49 = 7

64 = 8

81 = 9

100 = 10

Square roots

Square numbers

When we multiply a number by itself we say that we are squaring the number.

To square a number we can write a small 2 after it.

For example, the number 3 multiplied by itself can be written as

3 × 3 or 32

Three squared

The value of three squared is 9.

The result of any whole number multiplied by itself is called a perfect square.

Think about this……

?9

4

?100

49

Think about this……

3

2

9

4

10

7

100

49

Remember

Square roots that are not perfect squares are called irrational. An irrational number in a non-repeating, non-terminating decimal. This means the decimal does not repeat, but it also doesn’t end.

Approximating Square Roots

Categorize the following square roots as rational or irrational.

For example, the is rational because 22 or

2 x 2 = 4. The is irrational because there is no whole number that can be multiplied by itself to result in 5.

4

5

140016028915

Think about this….

• What could be a square root that is irrational?

• How do you know?

1 23 4

5 67 8

Cubes

2

2

2

2 x 2 x 2 = 8

3 x 3 x 3 = 27

The index of a cube root is always 3.

The cube root of 64 is written as .3 64

Cube Roots

What does cube root mean?

The cube root of a number is…

…the value when multiplied by itself three times gives the original number.

Cube Root Vocabulary

n xindex

radicand

radical sign

If a number is a perfect cube, then you can find its exact cube root.A perfect cube is a number that can be written as the cube (raised to third power) of another number.

Perfect Cubes

What are Perfect Cubes?

• 13 = 1 x 1 x 1 = 1• 23 = 2 x 2 x 2 = 8• 33 = 3 x 3 x 3 = 27• 43 = 4 x 4 x 4 = 64• 53 = 5 x 5 x 5 = 125• What would the next perfect cube be?

Examples:

34 4 4 4 64

4643 because

Examples:

3327

3

5

4

125

64

36216

3273

5

4

125

643

62163