1. Welcome: Please represent the number 𝟒 𝟓 in as many ways as you can!

2. Learning Target #2 I can convert repeating decimals into fractions.
At the end of this lesson, you will be writing a justification for the following question, SO PAY ATTENTION!
Are decimals rational or irrational numbers?

3. CLAIM: Are all square roots and cube roots irrational numbers?
Your claim is the statement that answers the question.
The claim is usually sentence in length.
It must be and answer the question.
What would a claim be for this question?
Square roots and cube roots are both irrational and rational numbers.
concluding
original 1
accurate,
specific,
completely

4. EVIDENCE: Are all square roots and cube roots irrational numbers?
Evidence is all the data that supports your claim.
Evidence must be and data from the problem.
Evidence also comes from:
It is important to have pieces of evidence to your claim, so you must the answer in ways!
MATHEMATICAL
SUFFICIENT,
RELEVANT,
SPECIFIC
MATHEMATICAL
EXAMPLES! class notes, personal experience, textbook, computer simulations, websites etc.
MANY
PROVE
REPRESENT
MANY

5. EVIDENCE: Are all square roots and cube roots irrational numbers?
What would make good evidence statements for the claim?
* When finding the square roots of 25, one will get 5 or The cube root of 27 is 3. According to the lesson given by Mrs. Fairbourn, square roots of perfect squares and perfect cubes are whole numbers that can be written as fractions. The square root of 26, however, is 5.099…, a decimal that never ends. The cube root of 4 is 1.587…, a decimal that never ends.

6. Reasoning: Are all square roots and cube roots irrational numbers?
Reasoning is the explanation that your claim to the that supports it.
Shows why the chosen counts as evidence and gives detailed of the math involved and uses correct vocabulary.
CONNECTS
EVIDIENCE
DATA
UNDERSTANDING
PRINCIPLES
MATHEMATICAL

7. Reasoning: Are all square roots and cube roots irrational numbers?
What would make good reasoning statements for this claim?
As illustrated by the evidence, not all square or cube roots are irrational numbers. 5, -5, and 3 are all square and cube roots, and they are not irrational numbers, but rational numbers. All four can be written as fractions. When finding the square roots of 25, one will get 5 or -5. There are an infinite amount of perfect squares and perfect cubes that result in square and cube roots that can be written as fractions, the very definition of rational numbers.
There are also square and cube roots that are irrational numbers. When finding the square root of an imperfect square, the decimal never ends. It is not possible to write a decimal that never ends as a fraction, so square and cube roots of imperfect squares are not rational.

8. Counterclaim: Are all square roots and cube roots irrational numbers?
The of your claim. with your claim.
Include the side as a counterclaim. Respond to the side of the claim with your own . Makes your justification and .
OPPOSITE
DISAGREES
OPPOSING
OTHER
ARGUMENT
STRONG
RELATABLE

9. Counterclaim: Are all square roots and cube roots irrational numbers?
What would make good counterclaim statements for this claim?
* Some may claim the square root or cube root of 15 is an irrational number, so all square and cube roots must be irrational. However, through more research and experimentation, one would discover several rational square and cube roots.

10. Final Justification
Square roots and cube roots are both irrational and rational numbers. When finding the square roots of 25, one will get 5 or -5. The cube root of 27 is 3 . According to the lesson given by Mrs. Fairbourn, square roots of perfect squares and perfect cubes are whole numbers that can be written as fractions. The square root of 26, however, is 5.099…, a decimal that never ends. The cube root of 4 is 1.587…, a decimal that never ends.
As illustrated by the evidence, not all square or cube roots are irrational numbers. 5, -5, and 3 are all square and cube roots, and they are not irrational numbers, but rational numbers. All four can be written as fractions. When finding the square roots of 25, one will get 5 or -5. There are an infinite amount of perfect squares and perfect cubes that result in square and cube roots that can be written as fractions, the very definition of rational numbers. There are also square and cube roots that are irrational numbers. When finding the square root of an imperfect square, the decimal never ends. It is not possible to write a decimal that never ends as a fraction, so square and cube roots of imperfect squares are not rational.
Some would say the square root or cube root of 15 is an irrational number, so all square and cube roots must be irrational. However, through more research and experimentation, one would discover several rational square and cube roots.

11. Change these fractions to decimals. What pattern do you notice?
5 2 9
52 99
1 3
= .2
= .52
= .411
= .3

12. Changing a fraction to a decimal:
Divide the by the !
“ in ”
NUMERATOR
1 3
DENOMINATOR
TOP
BOX
If decimal repeats, draw a over the repeating digits.
BAR
JUST
. 3

13. Based on the pattern you just saw, how can you convert these decimals to fractions?
.14
3 .45
.315
14 99

14. .2222222222222 = Mixed Numbers 5 5 2 9 5. 2 “Top in Box”
Then put the number in of the decimal.
Don’t forget the bar!
5 2 9
WHOLE
FRONT = 5
5. 2

15. Changing REPEATING DECIMAL to fraction
1. Repeating digit in the
2. Denominator: Put a
of 9’s matches the number of !
NUMERATOR
2 9
. 2
. 41
41 99 9
NUMBER
DIGITS

16. Time for a Walk About!!!
On a blank sheet of paper, write the numbers 1-12 vertically down the paper. (Make sure to write your name!) Around the room, there are different decimals, fractions, and statements. Change the repeating decimals to fractions, the fractions to decimals, and determine if each statement is a Claim, Evidence, Reasoning, or Counterclaim on your paper! Make sure you put the correct problem with the correct number.