Pre-Algebra NWEA Review Day 1: Rational Numbers

NWEA/ILEARN REVEIW DAY ONE

Rational/Irrational

Estimating Square Roots

Exponents

Rational numbers can be turned into fractions, irrational cannot.

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REMEMBER: you can turn any postive OR negative number into a fraction by putting it over 1!

Rational = Fraction

​ALL perfect squares are rational, because when you take the square root you get an integer.

Non-perfect squares are irrational.

Repeating = Rational

EX: 0.333...

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Terminating = Rational

EX: 4.6547 (it ends)

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Non-repeating AND non-terminating = Irrational

EX: pi, 5.4692... 

You can turn any fraction into a decimal by doing numerator divided by the denominator.

​​RATIONAL OR IRRATIONAL? (screenshot to help!)

Perfect Squares

Decimals

REMINDER

Poll

If you answered 5 questions about what you just reviewed, how do you think you would do?

• I would get a 100%!

• I might miss one!

• I would miss 2 or 3.

• I would get more than half wrong.

Multiple Select

Select all of the numbers that are RATIONAL.

• $$-6$$

• $$0$$

• $$\frac{1}{7}$$

• $$-\frac{5}{4}$$

• $$100$$

Multiple Select

Select all of the numbers that are IRRATIONAL. (2)

• $$\sqrt[]{100}$$

• $$\sqrt[]{2}$$

• $$\sqrt[]{15}$$

• $$\sqrt[]{1}$$

• $$\sqrt[]{49}$$

Multiple Select

Select all of the numbers that are RATIONAL. (3)

• $$0.2348$$

• $$2.3333...$$

• $$1.23454...$$

• $$0.301121...$$

• $$0.\overline{12}$$

Multiple Select

Select all of the numbers that are IRRATIONAL. (2)

• $$0.23487...$$

• $$\frac{15}{3}$$

• $$\sqrt[]{25}$$

• $$0$$

• $$\pi$$

Multiple Select

Select all of the numbers that are RATIONAL.

• $$\sqrt[]{81}$$

• $$\frac{3}{4}$$

• $$0$$

• $$0.454545...$$

• $$2.5283$$

Poll

How did you do?

• All 5 right!

• Missed 1!

• Missed 2!

• Missed 3 or more.

Poll

Rate how you feel about what we just reviewed.

• Thumbs up

• Thumbs sideways

• Thumbs down

No need to go any further! Just find the square root :)

Step 1: Is it a perfect square?

The two perfect squares are NOT the two numbers right beside!

This will tell you what number the decimal answer starts with.

ex: between 3 and 4 means 3._

The perfect square number that your number is closer to will help you pick your decimal!

​​ESTIMATING NON-PERFECT SQUARES (screenshot to help!)

Step 2: Find the 2 perfect squares on either side.

Step 3: Take the square roots to find the integers (whole numbers).

Step 4: Use the differences to help you round.

Poll

If you answered 5 questions about what you just reviewed, how do you think you would do?

• I would get a 100%!

• I might miss one!

• I would miss 2 or 3.

• I would get more than half wrong.

Match

Match the following square root problems with the perfect squares on either side.

• $$\sqrt[]{17}$$

• $$\sqrt[]{86}$$

• $$\sqrt[]{80}$$

• $$\sqrt[]{3}$$

• $$\sqrt[]{14}$$

16, 25

81, 100

64, 81

1, 4

9, 16

• 16, 25

• 81, 100

• 64, 81

• 1, 4

• 9, 16

Match

Match the following square root problems with the integers they are between

• $$\sqrt[]{27}$$

• $$\sqrt[]{75}$$

• $$\sqrt[]{2}$$

• $$\sqrt[]{38}$$

• $$\sqrt[]{10}$$

5, 6

8, 9

1, 2

6, 7

3, 4

• 5, 6

• 8, 9

• 1, 2

• 6, 7

• 3, 4

Reorder

Order the steps to estimating $$\sqrt[]{55}$$ .

• Check if 55 is a perfect square or not.

• Find the 2 perfect squares on either side of 55, which are 49 and 64.

• Take the square roots of the perfect squares to get the integer, which are 7 and 8.

• Find the differences between 55 and the perfect squares to help estimate your decimal. 55 is 6 away from 49 and 9 away from 64.

• Since 55 is closer to 49 by a few, the decimal will be of the left side of 7.5, more like 7.3 or 7.4.

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Hotspot

Click the best decimal estimate for the following square root.

$$\sqrt[]{65}$$

BE ACCURATE!

Hotspot

Click the best decimal estimate for the following square root.

$$\sqrt[]{77}$$

BE ACCURATE!

Poll

How did you do?

• All 5 right!

• Missed 1!

• Missed 2!

• Missed 3 or more.

Draw

CHALLENGE: Identify which points on the number line match each square root given.

Poll

Rate how you feel about what we just reviewed.

• Thumbs up

• Thumbs sideways

• Thumbs down

Product Rule: same base, add the exponents.

Quotient Rule: same base, subtract exponents first - second.

PRODUCT & QUOTIENT RULE

Power Rule: when a power is raised to another power, multiply.

Fractions: when a fraction is raised to a power, do the power rule to bother the numerator and denominator.

Move ONLY the negative exponent and it's base to the opposite side of the fraction.

Anything to the power of zero is ONE!!!!!!

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THE NUMBER ONE!!!!!

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ONLY 1!!!!!!!!!!!!

​​EXPONENT RULES (screenshot to help!)

POWER RULE & FRACTIONS

NEGATIVE RULE

ZERO RULE

Poll

If you answered 5 questions about what you just reviewed, how do you think you would do?

• I would get a 100%!

• I might miss one!

• I would miss 2 or 3.

• I would get more than half wrong.

Multiple Choice

Choose the correct rule used to solve and answer.

$$t^7\times t^2$$

• Product Rule

  $$t^{14}$$

• Product Rule

  $$t^9$$

• Power Rule

  $$t^{14}$$

• Power Rule

  $$t^9$$

• Quotient Rule

  $$t^5$$

Multiple Choice

Choose the correct rule used to solve and answer.

$$\frac{5^5}{5^2}$$

• Product Rule

  $$5^3=125$$

• Product Rule

  $$5^7=78,125$$

• Power Rule

  $$5^3=125$$

• Quotient Rule

  $$5^3=15$$

• Quotient Rule

  $$5^3=125$$

Multiple Choice

Choose the correct rule used to solve and answer.

$$\left(\frac{x}{y}\right)^4$$

• Product Rule

  $$\frac{x^4}{y^4}$$

• Power Rule

  $$\frac{4x}{4y}$$

• Power Rule

  $$\frac{x^4}{y^4}$$

• Quotient Rule

  $$\frac{x^4}{y^4}$$

• Power Rule

  $$\frac{x^4}{y}$$

Math Response

Simplify the following.

HINT: Only the negative exponent and the base it's directly attached to move.

$$2x^{-2}$$

Type answer here

Correct Answer: \frac{2}{x^2}

Deg^°

Rad

Math Response

Simplify the following.

HINT: Treat whole numbers like normal! (If it says multiply, multiply them.)

$$2x^2\times4x^4y$$

Type answer here

Correct Answer: 8x^6y

Deg^°

Rad

Poll

How did you do?

• All 5 right!

• Missed 1!

• Missed 2!

• Missed 3 or more.

Poll

Rate how you feel about what we just reviewed.

• Thumbs up

• Thumbs sideways

• Thumbs down

Day One Review

COMPLETE

4 more review days until EOY NWEA