8.NSA.2-Chasing the Unreachable: Approximating Irrational Numbers-Slides/Student Notes

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fraction

terminates

repeats

fraction

never ends

repeat

IRRATIONAL

​Rational Numbers

CAN BE WRITTEN IN FRACTION FORM

​Irrational Numbers Include

• ​Numbers that DO NOT REPEAT and DO NOT TERMINATE

• ​They are decimals that GO ON & ON with RANDOM Numbers

Multiple Choice

Classify the number: -23

• natural, whole, integer, rational, real

• integer, rational, real

• integer, irrational, real

• whole, integer, rational, real

Multiple Choice

Classify the number: 3

• natural, whole, integer, rational, real

• whole, integer, rational, real

• natural, whole, integer, irrational, real

• natural,integer, rational

Multiple Choice

Classify the number: 0

• natural, whole, integer, rational, real

• integer, irrational, real

• irrational, real

• whole, integer, rational, real

Multiple Choice

A non-repeating or non-terminating decimal is classified as ________________.

• rational, real

• irrational, real

• integer, rational, real

• whole, integer, irrational, real

Multiple Choice

A repeating or terminating decimal is classified as ___________?

• rational, real

• integer, rational, real

• irrational, real

• whole, integer, irrational, real

Multiple Choice

Classify the number:

• rational, real

• whole, Integer, rational, real

• integer, irrational, real

• irrational, real

Multiple Choice

An example of a whole number is:

• 4/9

• -9

• 5.2

• 17

Multiple Choice

Classify the Number: 2.587

• irrational, real

• rational, real

• integer, rational, real

• integer, irrational, real

​Non-Perfect square

a perfect square is the product of a rational number multiplied by itself.

For example:

5² = 25 so √25 is 5

*they are "nice, neat" whole numbers*

Perfect squares are RATIONAL NUMBERS

​Perfect Square

But first, let's review

a non-perfect square is an integer whose square is not a whole number.

For example:

√7 = 2.645751....

*goes on forever without repeating*

Non-perfect squares are IRRATIONAL NUMBERS

Match

Match the following

• perfect squares are...

• non-perfect squares are...

• rational numbers are...

• irrational numbers are...

rational numbers

irrational numbers

able to be written as fractions

not able to be written as fractions

• rational numbers

• irrational numbers

• able to be written as fractions

• not able to be written as fractions

Multiple Choice

non-repeating and non-terminating (goes on forever without repeating) decimals are...

• rational

• irrational

Multiple Choice

terminating decimals (have an end) are...

• rational

• irrational

Multiple Select

select all the perfect squares

• $$\sqrt[]{81}$$

• $$\sqrt[]{27}$$

• $$\sqrt[]{64}$$

• $$\sqrt[]{121}$$

• $$\sqrt[]{65}$$

rational

close

truncating (see next slide)

2

squared

1

2

1

4

Multiple Choice

The √20 is between which two integers?

• 2 & 3

• 3 & 4

• 4 & 5

• 5 & 6

Multiple Choice

The √40 is between which two consecutive whole numbers?

• 7 & 8

• 4 & 5

• 5 & 6

• 6 & 7

Multiple Choice

Estimate the square root.

• 4

• 5

• 6

• 7

Multiple Choice

Estimate the square root.

• 3

• 4

• 5

• 6

Multiple Choice

Level 3: Estimate the square root.

• Between 7 and 8 and closer to 8

• Between 8 and 9 and closer to 9

• Between 9 and 10 and closer to 9

• Between 9 and 11 and closer to 10

1

2

1.4

1.5

1.96

2.25

1.96

2.25

1.4

1.5

better

Labelling

Between which two consecutive numbers does $$\sqrt[]{45}$$ lie?

Drag labels to their correct position on the image

6

8

5

4

3

7

Drag and Drop

What two whole numbers would the following square root be between?​

Placeholder

​and

Placeholder

Drag these tiles and drop them in the correct blank above

11

12

134

136

10

14

13

Math Response

Estimate the square root to the nearest tenth.

Type answer here

Correct Answer: 4.2

Deg^°

Rad

Math Response

Estimate the square root to the nearest tenth.

Type answer here

Correct Answer: 9.3

Deg^°

Rad

increasing

approximately

1

2

1.4

1.141

Multiple Choice

HINT: Convert Number to a decimal

• A

• B

• C

• D

Multiple Choice

Point B could represent which of the following numbers?

• √24

• √30

• √35

• √42

Multiple Choice

Which is the best approximation of point P?

• √8

• √2.8

• 17/5

• 2 1/4

Multiple Choice

Which best represents the position of  $$\sqrt{8}$$  on the number line below?

• Point P

• Point Q

• Point R

• Point S

Multiple Choice

• Point M

• Point N

• Point R

• Point S

Multiple Choice

Which best represents the position of $$$$

• Point P

• Point Q

• Point R

• Point S

Multiple Choice

The longest side of a right triangle measures  $$\sqrt{17}$$  inches. Which point in the number line most closely represents the value of  $$\sqrt{17}$$  ?

• Point W

• Point X

• Point Y

• Point Z

Multiple Choice

Which point most closely corresponds to the √8 on the number line below? (Click the question to see the picture)

• P

• Q

• R

• S

Multiple Choice

Which point most closely corresponds to the √8 on the number line below? (Click the question to see the picture)

• P
• Q
• R
• S

Multiple Choice

Which point on the number line best represents  $$\sqrt{8}$$  ?

• Point M

• Point N

• Point P

• Point Q

3.14

3.14

3.14

3.14

9.86

compare

Labelling

Approximate the location of each number square root on the number line.

Drag labels to their correct position on the image

Reorder

Order the following from least to greatest.

• $$\frac{4\pi}{3}$$

• $$\sqrt[]{21}$$

• 5.1

• $$2\sqrt[]{8}$$

1

2

3

4

• 1
• 2
• 3
• 4

Reorder

Reorder the following from least to greatest

• 9

• $$\sqrt[]{82}$$

• $$3\pi$$

• $$\pi^2$$

1

2

3

4

• 1
• 2
• 3
• 4

Math Response

Although pi is an ongoing number, which numbers will you need to use for pi ?

Type answer here

Correct Answer: 3.14

Deg^°

Rad

Drag and Drop

The symbol for pi on a calculator is

Placeholder

Drag these tiles and drop them in the correct blank above

π

θ

Σ

∞

Multiple Select

what is the definition of pi

select ALL that apply

• it is the sixteenth letter in the greek alphabet

• it has a represented value of 3.14

• it has a represented value of 22/7.

• Its something you eat...