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# Algebra and Real-life Linear Relationships

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• Published : August 17, 2013

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The CENTRE for EDUCATION in MATHEMATICS and COMPUTING

PATTERNING

AND

ALGEBRA: ALGEBRAIC EXPRESSIONS

This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo.

Play the Late Delivery game first! Levels 1 and 2 are recommended. Click on http://www.bbc.co.uk/education/mathsfile/shockwave/games/postie.html or go to www.wiredmath.ca for the link. 1. a. Write each of the following expression as a single number. i. 20 + 5 ii. 15 ÷ 3

iii. 11 × 9

b. For each question in (a) write 3 equivalent expressions using 3 different operations. 2. Match up the equivalent expressions below: 4+3 1+ 2 6×2+2 16 ÷ 2

55 − 52
2×2×2 49 ÷ 7 7×2

Did You Know?
A cheetah can run 76 km/h. The fastest human can only run about 37 km/h!

3.

The scale balances because the mass on the left side is equal to the mass on the right side. A number sentence can be written to describe the picture: 10 + 10 + 1 = 10 + 5 + 5 + 1 or 2 × 10 + 1 = 2 × 5 + 10 + 1 . a. Draw 3 different combinations of masses on a scale that would balance.

b. Write a number sentence to describe each of the 3 new combinations.

4.

a. Balance the scale using a combination of 10 g, 5 g and 1 g weights. Assume you have many different masses. Compare your solution with your classmates.

b. Write an equivalent expression, which is different than the masses in the picture, to describe the total mass in each pan.

Expectations: i) model real-life linear relationships graphically and algebraically; ii) solve simple algebraic equations using a variety of strategies, including inspection and guess and check. For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.

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5.

Simplify each expression. a. 3n + 4n − 2n d. 3b + 8 + 2b − 3 g. 4.04r × 2 + 6

b. 4w − 3w + 7w e. 8c ÷ 2 h. (7 + 5x − 2x) × 2

c. 2a + 10a + 5 f. i.

4z × 2 + 5

d + 2d + 3d × 2 + 9

6.

The sum of a number n and 20, is 25. Which equation below shows this relationship? a. 20 + n = 25 Solve for x . a. c. e. g. i. 1+ x = 3 7+x= 7 3x + 1 = 16

b. 25n = 25

c. 20 − n = 25

d. 25 + n = 20

7.

5x + 3x = 16
4x + 2 = 6x

b. d. f. h. j.

x − 12 = 3 4 x = 32 11x = 18 + 4

15 − x + 4 = 17
4 + x = 9 − 2x

8.

If Jim works for 4 hours and earns \$32, how long will he need to work to earn \$40?

9.

Tommy wants to buy a comic book that costs \$7. To earn money he decides to run a lemonade stand with his brother. Tommy and his brother earn \$10 and split the amount evenly between them. a. How much money did Tommy make? b. How much more money does Tommy need to earn to buy the comic book? c. Write an expression where x is the additional money Tommy needs.

10.

How many circles are needed to balance the square?

11.

If ∆ is an operation such that a∆ b = ab + a − b , what does 4∆8 equal?

Expectations: i) model real-life linear relationships graphically and algebraically; ii) solve simple algebraic equations using a variety of strategies, including inspection and guess and check. For more activities and resources from the University of Waterloo’s Faculty of Mathematics, please visit www.cemc.uwaterloo.ca.

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CHALLENGE YOURSELF!
12. 13. Two numbers are in the ratio 9 to 4. Their sum is 39. Find the smaller number. Three consecutive integers have a sum. When the sum is divided in half it is equal to 24. Determine the three numbers?

14.

The cafeteria charges \$2.25 for a hamburger, \$1.75 for fries, \$1.00 for a salad and \$1.25 for a drink. Dawn buys two hamburgers, one fry, one salad and two drinks. a. Write a mathematical expression to describe the situation. b. How much change does Dawn receive if she pays with a ten dollar bill?

15.

There are 30 players on the hockey team. If there are 8 more boys on the team than girls, how many girls...