Unit Summary 1
Class : Algebra 1
Unit: Operations in Algebra and Solving Equations – Chapters 1, 2, 3
I. Big Ideas:
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Students will understand how algebraic expressions are transformed into equivalent expressions.
Students will understand the concept of algebraic properties of equality and how they are applied to
solve equations.
Students will understand how to set up and solve equations to help determine the answers to real-life
problems.
II. Topics that will be covered:
1. Applying the order of operations
2. Combining like terms
3. Operations with integers
4. Adding and subtracting expressions
5. Using the distributing property
6. Evaluating expressions
7. Multiplying and dividing expressions
8. Solving one-step equations
9. Solving multi-step equations
10. Solving literal equations
11. Using the distributive property in equations
12. Using vocabulary related to the unit
13. Clearing an equations of fractions or decimals
14. Determining whether an equation has no, one, or infinitely many solutions
III.
Essential Questions:
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Why is it important to use the correct order of operations?
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How can I use the distributive property to write equivalent expressions?
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How can I clear an equation of fraction or decimals?
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What does it mean when an equation has one, none, or many solutions?
IV.
Sample questions to answer by the end of the unit:
1. George is in charge of supplies for a mountain climbing guide company. He is trying to locate
carabineers for four climbing teams. George’s preferred brand of carabiners are available at three outfitters
as follows: Outfitter A has 4 boxes plus 6 loose carabineers, outfitter B has 6 boxes but one box is missing
3 carabineers, outfitter C has 10 boxes plus 5 loose carabineers. Assuming each box contains an equal
number of carabiners, write an expression describing the total number of carabineers available. Write
another expression describing the number of carabiners available for each team if the carabineers are
divided equally among the teams.
2. Orange County has a population of 25,000 people and is increasing by 3500 people each year.
Hunterdon County has a population of 36,000 people and is increasing by 2700 people each year. At this
rate, when would the two counties have the same number of people residing there?
3. Which equation has no solution?
A) 2x + 4 = 2(x + 4)
C) 3x + 5 = 2(x + 3)
B) 2x + 4 = 2(x + 1)
D) both A and B
4. The solution to the equation 3x + 9 = 8 is the same as the solution to the equation:
A) 3x = 17
B) 3x + 1 = 0
C) 3x = 1
D) x + 3 = 8
5. Which of the following expressions is equivalent to the expression (5x – 2) – (3x – 5)?
A) 2x – 3
B) 2x + 7
C) 2x – 7
D) 2x + 3
E) None of the above
6. If 5w + 2 = 30, then
4
A) 20w = 112
C) 5w = 118
E) 5w = 112
7. If 5(2x + 8) = 9x – 11, what does 5x =?
8. Solve for y. 9x + 3y = 18
B) 5w = 120
D) 5w = 7
F) None of the above
Solve for x.
9. –5x = 30
10. 7 – 2(x + 1) = 8x – 3
11. 6x + 1.5 = 2.4x – 7
12. 4(2x + 11) = 10x + 44 – 2x
Write an equation to match the following statements.
13. The cost of 15 pens plus tax of $0.15 is $3.15. What equation models the situation?
How much would one pen cost?
14. Don buys a tennis racket that costs $62 and 12 tennis balls. His total bill was $71. How much was each
tennis ball? Write and solve an equation to match.
Simplify.
15. 11x + x – 6 + 2x
16. x3 – 4x + 8x3 + 16x