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# Place the integers –3, – 2, – 1, 0, 1, 2, 3, 4, and 5 in the circles so that the three numbers in any line add up to

Place the integers –3, – 2, – 1, 0, 1, 2, 3, 4, and 5 in the circles so that the three numbers in any line add up to +3. Complete the pattern, then use your results to make the indicated prediction. 5 1 = ______ 5 2 = ______ 5 3 = ______ 5 4 = ______

## Place the integers –3, – 2, – 1, 0, 1, 2, 3, 4, and 5 in the circles so that the three numbers in any line add up to

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1. Place the integers –3, –2, –1, 0, 1, 2, 3, 4, and 5 in the circles so that the three numbers in any line add up to +3.

2. Complete the pattern, then use your results to make the indicated prediction. 51 = ______ 52 = ______ 53 = ______ 54 = ______ Predict: the ones’ digit of 543 ______ the tens’ digit of 574 ______ _

3. Complete the pattern, then use your results to make the indicated prediction. 61 = ______ 62 = ______ 63 = ______ 64 = ______ Predict the ones’ digit of 6113 ______

4. Complete the pattern, then use your results to make the indicated prediction. 41 = ______ 42 = ______ 43 = ______ 44 = ______ Predict the ones’ digit of 429 ______ Predict the ones’ digit of 482 ______

5. Complete the pattern, then use your results to make the indicated prediction. 21= _____ 12 = _____ 22 = _____ 112 = _____ 23 = _____ 1112 = _____ 24 = _____ 11112 = _____ Predict: ones’ digit of 284 = ? 11,1112 = ? ones’ digit of 243 = ? 111,1112 = ? _____

6. Study the pattern of the ones’ digits in the powers of 3 and the powers of 7. Then predict the ones’ digit of each number. • 350 b. 7101 • c. 381 d. 744

7. True or False? • y² • x³ = (xy)5 • 46 = 64 • z² • z6 = z3 • z4 • (312)0 = (123)0

8. True or False? • (33)4 = 312 • 36 + 36 = 312 • 34 • 33 = 312 • 39• 33 = 312

9. True or False? • All integers are negative. • The absolute value of every integer is its opposite. • Two integers that are opposites have the same absolute value. • The absolute value of an integer is always positive.

10. True or False? • The opposite of an integer is always negative. • The absolute value of a positive integer is the integer • The absolute value of an integer is always greater than the integer. • A positive and negative integer will always add to zero.

11. Teri made up a game of darts. Everyone was given a chance to throw 3 darts. If all 3 darts hit the target, list all possible scores that could result. -5 1 10

12. In each row, choose the item that does not belong. Be prepared to give the reason for your answer. • A B C D • (-2)(-3)(-7)(4)(-7)(-5) -(-4)(5) (-2)(-3)(5) • 2. -(-49) |-49| (-7)2 -72 • 3. 3a2b2 x3 abc 22y3

13. Study this pattern: 3, 4, 7, 11, 18, 29, 47, 76 • Note that 3 + 4 = 7 • 4 + 7 = 11 • 7 + 11 = 18 • Use the same rule to complete the patterns below: • 4, 5, _, , , 37 • 1, 2, , , , , 21 • 2, 1, , , , , 18 • 6, 10, , , , , 110

14. Study this pattern: 3, 4, 7, 11, 18, 29, 47, 76 • Note that 3 + 4 = 7, 4 + 7 = 11, and 7 + 11 = 18 • Use the same rule to complete the patterns below: • 2, , 10, , , , 74 • 3, , , 7, , , , 50 • 5, , , 5, , , , , 65 • 6, , , 4, , , , 35

15. Study this pattern: 3, 4, 7, 11, 18, 29, 47, 76 • Note that 3 + 4 = 7, 4 + 7 = 11, and 7 + 11 = 18 • Use the same rule to complete the patterns below: • 8, , , , 7, , , , 41 • , , , , 15, 20 • , , , , , , , ,10, 16 • 4. 10, , , , , 0, , , , ,10

16. In the 15th century, European flour merchants used positive and negative numbers. On a flour barrel +5 meant that it was 5 pounds overweight; –5 meant that it was 5 pounds underweight. The following numbers were on 100-pound barrels. Did the five barrels contain more or less than 500 pounds? How much more or less? –3 –2 +6 +3 –6

17. Tank is a football fullback. Sometimes he gains yardage (+5 means a five-yard gain). Sometimes he loses yardage (–8 means an eight-yard loss). Determine Tank’s total yardage in each of the following games. Game 1: +3, +5, +6, +1, +13 Game 2: –2, –6, –1, –2, –4 Game 3: –4, +4, –3, +3, +10, –13 Game 4: –5, +3, +6, –2, +8, –6, +9, –1 Game 5: +6, –7, –5, +10, –3, –8, +5, –10, +8, +3, +7, –11, –6

18. Fill in the missing squares. Each column, row and diagonal should have the same sum. Find the sum. 5 -9 ? Sum = ____ -1 -3 -7

19. Arrange the integers {-4, -3, -2, -1, 0, 1, 2, 3, 4} in the square so that each column, row and diagonal gives the same sum.

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