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Cleaning Coins

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BELL RINGERS – THE NUMBER SYSTEM – GRADE 8

Task 1 - Which of the following numbers are perfect squares? Explain your reasoning. 5, 9, 36 and 41

Task 2 - Which of the following numbers are perfect cubes? Explain your reasoning. 8, 12, 27 and 64

Task 3 - Problem: Represent the following rational number in fraction form 0.333?

Task 4 - Instructions: Decide whether each of the following numbers is rational or irrational.
1. 0.333 ______________________
2. √4 ______________________
3. √2 = 1.414213… ______________________
4. 2 ______________________
5. 11 ______________________
6. 12.3456565656 ______________________ Task 5 - Give possible coordinates for the following points. A. K’s x-coordinate is between B. L’s x-coordinate is between

j and j j and j

K’s y-coordinate is between L’s y-coordinate is between

j and j j and j

K’s coordinates could be ( j, j) L’s coordinates could be ( j, ___ )

Task 6

Look at Point F on the number line below.

a. Where are the points that are GREATER than Point F?

Task 7
Timothy, Adrienne, and Robert all started with 0 points. Timothy’s score is at 25, Adrienne’s score is at -30, and Robert’s score is at 10. a. Place Timothy, Adrienne, and Robert’s scores on the number line.

b. Which person has the greatest score? How do you know?

c.Who has the second greatest score? ______________________

d. Which person’s score is the greatest distance from 0 (has the greatest absolute value)? e. Whose score is the second greatest distance from 0 (has the second greatest absolute value)?

f. Explain why the answers to b and d are different.
Task 8
The numbers on the diagram represent inches above/below the top of the flower pot.

a. What distance would the spider have to climb from where she is to get to 0?

b. If the spider makes it up to 0, what distance would she have to climb from 0 to reach her web?

c. What is the total distance she would have to climb from her starting point, up past 0 and on up to her web? Explain how you found your answer.

Task 9

Look at the number line below.

a. Which two points are a distance of 8 units apart? _____ and _____ b. Which two points are a distance of 3 units apart? _____ and _____ c. Which two points are a distance of 6 units apart? _____ and _____

Task 10
Directions: On the dot grid below, you are going to create a right triangle. * Mark point A on the grid. * Draw horizontal AB that is 2 units in length. * Draw vertical AC that is 4 units in length. * Draw BC to form the hypotenuse of the right triangle. * Use the Pythagorean theorem to find the length of your hypotenuse. * Cut out your triangle * Place point C at the origin and place the hypotenuse along the x-axis * Mark point B on the x-axis * You have now graphed the length of the irrational side of a right triangle!

EXPRESSIONS AND EQUATIONS – GRADE 8

Task 1

Task 2
Which of the following shows the correct simplification of
67/63? Justify your choice and explain the mistake made in the other choices.
a. 14
b. 610
c. (6/6)4
d. 64

Task 3

TASK 4
Rewrite the first term in each of the following products as power to a power. Then simplify each expression using a single exponent. a. (9)3(35) b. (8)2(25) c. (252)(53) d. (72)(492)

Task 5
Choose the correct scientific notation form of the number 48,000,000
a. 4.8∙106 b. 48∙106 c. 48∙107 d. 4.8∙107
TASK 6
Match each number in column A to an equivalent number in column B Column A | Column B | a. 2.1∙105 | 1. 380,000 | b. 2.1∙10-7 | 2. 0.00000021 | c. 3.8∙105 | 3. 3,800,000 | d. 3.8∙106 | 4. 210,000 |

TASK 7
Bob has reduced the fractions below. Circle any that could be reduced more and tell how you know. a. 512 b. 66 c. 1520 d. 814

TASK 8
Simplify each of the following fractions. Explain how you know if it is completely simplified. a. 5∙5∙5∙5∙55∙5∙5 b. 9∙9∙99 c. 4∙4∙4∙44∙4∙4
Write each of the fractions above using exponents. Write the simplified form using exponents. What do you notice? Can you explain mathematically what is happening?
TASK 9
Choose the correct simplification of the product of 76and 72.
a. 495

b. 715

c. 78

TASK 10
Circle the correct simplification of 27239. Justify your choice using the Power properties. a. 9-7 b. 3-3
c. 271
d. 3-4

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