The document provides examples and explanations of key concepts related to rates, expressions, and order of operations in mathematics: 1) It gives an example of calculating rate using the equation r = d/t, showing how to find the rate of a person running 100 meters in 40 seconds. 2) It lists two "number tricks" involving multiple steps of operations on a chosen number, but notes that only one trick allows determining the original number. 3) It discusses combining like terms in expressions and the rules of arithmetic for expressions. 4) Finally, it reviews the proper order of operations to simplify expressions.

1. 2.4 Opener
You can find a person's speed by dividing how far the
person travels by the time spent traveling. The equation
r = d/t shows the relationship, where r is the rate (or
speed), d is the distance, and t is the time.
1.) Anh runs 100 meters in 40 seconds. What is his rate in
meters per second?
2.) Rosario jogs at a rate of 6 miles per hour. How far does
she run in 30 minutes?
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2. 2.3 Homework Questions
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4. Number Tricks & Variables
Trick One Trick Two
1. Choose a # 1. Choose a #
2. Add 6 2. Multiply by 2
3. Multiply by 3 3. Subtract 6
4. Subtract 4 4. Multiply by 50
5. Multiply by 2 5. Add 50
6. Add 2 6. Divide by 10
7. Divide by 6 7. Subtract starting #
8. What is your number?
a.) Using one of these tricks, Spiro the Spectacular can
find your starting number. Which trick can he use? How
does he find your starting number?
b.) Even Spiro the Spectacular cannot find your starting
number using the other trick. Explain why not.
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5. Expressions & the Rules of Arithmetic
1.) x + 7 = 7 + x
2.) (a + 8) + z = a + (8 + z)
3.) 2(x + 3) = 2(x) + 2(3)
4.) 2(x) + 2 (3) = 2 (x+3)
5.) x(1) = x and x + 0 = x
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6. Like Terms
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7. Combining Like Terms
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8. Review of Order of Operations
1.
2.
3.
4.
5.
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9. Simplify Each Expression
1.) 3(x+2) + 5x
2.) 2z + 7z - z + 5
3.) 3a + 4b + 5a + 6
4.) 4(x-1) - 3(x+2)
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