ILEARN Checkpoint 1 Review: Real Number System

CHECKPOINT 1 REVIEW
Unit 1
Rational/Irrational
Estimating Non-Perfect Square Roots
Real World Word Problems

What characteristics make a number rational vs irrational?

​

Rational or Irrational?

Categorize

Options (9)

positive whole numbers

negative whole numbers

terminating decimals

repeating decimals

fractions of any kind

square roots of perfect squares

square roots of non-perfect squares

non-terminating & non-repeating decimals

pi

Organize these statements into the right category based on whether they represent rational or irrational numbers.

RATIONAL

IRRATIONAL

Categorize

Options (12)

$$\frac{5}{2}$$  

$$0.75$$  

$$0.\overline{3}$$  

$$\sqrt[]{16}$$  

$$0$$  

$$-575$$  

$$\pi$$  

$$3.14$$  

$$3.14159...$$  

$$\sqrt[]{15}$$  

$$\sqrt[]{100+16}$$  

$$-0.12345...$$  

Organize these real numbers into the right categories based on whether they are rational or irrational.

RATIONAL

IRRATIONAL

STEPS:
1. Find the two closest ________ _______ on either side of your number.
2. Find those number's ________ ________.
3. Calculate the __________ between your number and the perfect squares to see what you will be closer to.

​4. Make a decimal estimate.

Estimating Non-Perfect Square Roots

Estimate to the nearest tenth.

​Lets use between 9-10 as our example.
9.1-9.2: Very close to 81
9.3-9.4: Closer to 81, but not very close.
9.5: Same difference between 81 and 100.
9.6-9.7: Closer to 100, but not very close.
9.8-9.9: Very close to 100.

​

WHEN estimating:

Hotspot

Click on the point that best answers the question.

Hotspot

Click on the point that best answers the question.

Miss Jane has a square rug. The area of the rug is 144ft. How long is each side?

Square Root Word Problems

Miss Jane has a square rug. The area of the rug is 65ft. Would the rug fit into a square room with side lengths of 7.5ft?

Square Root Word Problems

Multiple Choice

If I know the area of a square, how do I find the side length?

• I square the area.
• I divide the area by 2.
• I take the square root of the area.
• I divide the area by 4.

Multiple Choice

The area of a square is 117 square meters. Which best represents the length of a side of the square? 

• 10.8 m
• 11 m
• 10 m
• 11.2 m

Multiple Choice

Grandma's square garden has an area of 90 square feet. The length of one side of her garden would be between what two whole numbers? What is the length of this side to the nearest tenth of a foot?

• 9 and 5, 9.5

• 9 and 6, 9. 6

• 9 and 10, 9.5

• 9 and 10, 9.6

In math, there are words that hint at the 4 operations: addition, subtraction, multiplication, and division.

​

Real World Word Problems

​Jed made 1/4 of his weekly allowance by mowing lawns. If he made $106 that week, how much did he make just by mowing lawns?

Multiple Choice

The temperature on a cold winter day starts out at 10 degrees, but it drops rapidly 24 degrees due to a strong cold front moving in.  What is the current temperature?

• 14
• 34
• -14
• -34

Multiple Choice

Suppose $700 is being deducted each month to pay the mortgage. After six months, how much money has been taken out of the pay for the mortgage?

• $4200
• $-4,200
• $116.66
• $-166.66

Multiple Choice

Mrs. Borcherding can grade 5 ¼ tests in 30 minutes. She started grading tests at 5:30pm and finished at 9:30pm. How many tests did she grade in total?

• 32

• 20.5

• 21

• 42

Multiple Choice

 A florist sells a dozen roses for $29.88. What is the cost of one rose?

• $2.41
• $2.49
• $2.40
• $2.08