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Unit 10 Algebra

Unit 10 Algebra. Lesson 1. Pan Balance Problems with Two Balances. Now let’s try it with stuff. Using Expressions in Algebra. Joe is two inches taller than Maria. How tall is Joe? What information do we need to solve this problem? What expression could we use to represent our problem?

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Unit 10 Algebra

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  1. Unit 10 Algebra Lesson 1

  2. Pan Balance Problems with Two Balances

  3. Now let’s try it with stuff.

  4. Using Expressions in Algebra Joe is two inches taller than Maria. How tall is Joe? What information do we need to solve this problem? What expression could we use to represent our problem? Maria + 2 in. = Joe M + 2 in. = J

  5. Using Expressions in Algebra We can use the algebraic expression M + 2 in. to solve this problem. If Maria is 55 in. Joe is 57 in. If Maria is 4’ 2”, Joe is 4’4”

  6. Expressions • Variables can be used to express relationships between quantities • An algebraic expression uses operation symbols (+, -, *, ÷) to combine variables and numbers. Claude earns $6 an hour. Use a variable to express the relationship between Claude’s earnings and the amount of time he worked.

  7. Use Expressions to Represent these Problems • Sue weighs 10 pounds less than Jamal. • Isaac collected twice as many cans as Alex. • There are half as many problems in today’s assignments as there were yesterday’s. To evaluate something is to find out what it is worth. To evaluate algebraic expressions, first replace each variable with its value.

  8. Open your math journal Page 350

  9. What’s My Rule? in out 5 50 3 32 1.4 17.6 1 x .5 y x = 14 y = 9.5 Rule = * 9 + 5

  10. What’s My Rule? in out 36 2 54 5 102 13 114 x 204 y x = 15 y = 30 Rule = ÷ 6 - 4

  11. Rules, Tables, and Graphs – Oh My! Rate describes a relationship between two quantities. It tells how many of one type of thing there are for a certain number of another type of thing. Speed tells how many units of distance there are of a given unit of time.

  12. Rules, Tables, and Graphs – Oh My! 60 mph is a rate that says that a distance of 60 miles is travelled for every 1 hour of time. Rates are expressed in phrases that include the word per: • miles per hour • dollars per pound • rainy days per month

  13. Rules, Tables, and Graphs – Oh My! Rates can also be expressed as fractions: 3 apples 89¢ or 12 inches 24 hours different units different units

  14. Open Your Math Journal • Open your math journal to page 354. • Complete the Math Message on the top of the page.

  15. Open Your Math Journal to page 354 Using the rate 8 miles per minute, • how far will the plane travel in 10 minutes? • how far will the plane travel in 2 ½ minutes. What rule can you write for these problems? distance traveled = 8 * number of minutes or d= 8t or 8 * t The rule is the formula. d and t are variables.

  16. Math Journal page 354 • Use the formula to complete the table on page 354. • Then display these values on a line graph on page 355. • Don’t forget, a line graph connects the ordered pairs with a line to show the change over time.

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