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Pre-Algebra

Pre-Algebra. Pre-Algebra. Coordinate System and Functions Ratios and Proportions Other Types of Numbers. Coordinate System and Functions. Instruction begins in third or fourth grade. First students learn how to plot points on the coordinate system: X on horizontal axis

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Pre-Algebra

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  1. Pre-Algebra

  2. Pre-Algebra • Coordinate System and Functions • Ratios and Proportions • Other Types of Numbers

  3. Coordinate System and Functions • Instruction begins in third or fourth grade. • First students learn how to plot points on the coordinate system: • X on horizontal axis • Y on the vertical axis • Where is (7,6)?

  4. Next, students learn to complete a table with the function given: Coordinate System and Functions

  5. Coordinate System and Functions • After completing the table, students plot the points and draw the line for the function.

  6. Coordinate System and Functions • After several lessons completing a table with the function provided, students are shown how to derive the function when given two pairs of points—Format 20.1, page 453.

  7. Coordinate System and Functions • Finally, students can be taught to derive the function when given the points on the coordinate system with a line draw through them.

  8. Ratios and Proportions • What is the preskill for ratios and proportions? • How should problems be set up?

  9. Ratios and Proportions Example set up using equivalent fractions preskill to solve ratio problems: The store has 3 TVs for every 7 radios. If there are 28 radios in the store, how many TVs are there? TVs = TVs Radios Radios 3 TVs = TVs 7 Radios 28 Radios

  10. Ratios and Proportions 3TVs = TVs 7 Radios 28 Radios 3TVs (4 ) = TVs 7 Radios (4 ) 28 Radios

  11. Ratios and Proportions • After reviewing the use of equivalent fractions, one may introduce problem solving with a ratio table.

  12. A factory makes SUVs and cars. It makes 5 SUVs for every 3 cars. If the factory made 1600 vehicles last year, how many cars and how many SUVs did it make?: Ratios and Proportions

  13. Ratios and Proportions • After working with simple ratio tables, teachers may introduce tables for problems using fractions such as: Two-thirds of the people at Starbucks are drinking coffee. The rest are drinking tea. If 15 people are drinking tea, how many are drinking coffee? How many people are there in Starbucks? (p 449).

  14. Students: 1) set up the ratio table and 2) complete the fraction family column: Ratios and Proportions

  15. 3) Students use the numerator of the fraction to complete the ratio column. Ratios and Proportions

  16. 4) Students fill in known quantities. Ratios and Proportions

  17. Ratios and Proportions • Students write the ratio equation: 2 Coffee = Coffee 1 Tea 15 Tea

  18. 6) Students solve the ratio problem to answer questions. Ratios and Proportions

  19. 7) Students use the number-family strategy to solve for unknowns. (See Format 20.2) Ratios and Proportions

  20. Ratios and Proportions Ratio and proportions can also be used to solve comparison problems like: Louise was paid 5/6 of what her boss was paid. If Louise is paid $1800 per month, how much more does her boss get paid, and what does her boss get paid?

  21. Ratios and Proportions Students set up a number family using fractions: Difference Louise Boss 1/6 + > 6/6

  22. Students can then use the ratio table and ratio equation to solve for the unknown quantities. Ratios and Proportions

  23. Ratios and Proportions • Ratio and Proportions can also be used to solve percentage problems such as: A store got 40% of its oranges from California and the rest from Florida. If the store had 170 total oranges, how many were from California and how many from Florida?

  24. Ratio and Proportions A store got 40% of its oranges from California and the rest from Florida. If the store had 170 total oranges, how many were from California and how many from Florida? First students complete the number family: California Florida All 40% + % >100%

  25. A store got 40% of its oranges from California and the rest from Florida. If the store had 170 total oranges, how many were from California and how many from Florida? Students then put the information into a ratio table: Ratios and Proportions

  26. Ratios and Proportions Finally, students can use ratio tables to do comparison problems using percentages: A bike store sold 25% fewer women’s bicycles than men’s bicycles. If the store sold 175 fewer women’s bikes, how many men’s and women’s bikes did it sell?

  27. Ratios and Proportions A bike store sold 25% fewer women’s bicycles than men’s bicycles. If the store sold 175 fewer women’s bikes, how many men’s and women’s bikes did it sell? Again, students would start with the number family: Difference Women’s Men’s 25% + % > 100%

  28. A bike store sold 25% fewer women’s bicycles than men’s bicycles. If the store sold 175 fewer women’s bikes, how many men’s and women’s bikes did it sell? Then the information from the number family would into the ratio table: Ratios and Proportions

  29. Other Types of Numbers • Primes and Factors • Integers • Exponents

  30. Other Types of NumbersPrimes and Factors What are prime numbers? How do students “test” numbers to determine if they are prime? What examples should one use for this activity?

  31. Other Types of NumbersPrimes and Factors What are the prime factors of a number? How can the prime factors of a number be determined?

  32. Other Types of NumbersPrimes and Factors What are the prime factors of 30? What are prime factors used for?

  33. Other Types of NumbersIntegers • What are integers? • How do the authors recommend introducing negative numbers? • What is the rule?

  34. Other Types of NumbersIntegers • What is absolute value? How is this introduced to students? • Once students understand the concept, students can solve problems with positive and negative integers, Format 20.3, p. 458.

  35. Other Types of NumbersIntegers • What rules does Format 20.3 teach?

  36. Other Types of NumbersIntegers • What rules does Format 20.3 teach? • If the signs of the numbers are the same, you add. • If the signs of the numbers are different, you subtract. • When you subtract, you start with the number that is farther from zero and subtract the other number. • The sign in the answer is always the sign of the number that is farther from zero.

  37. Other Types of NumbersIntegers • What rules do students need to know to multiply integers?

  38. Other Types of NumbersIntegers • What rules do students need to know to multiply integers? Plus x plus = plus; Minus x plus = minus; Minus x minus = plus; Plus x minus = minus

  39. Other Types of NumbersExponents • What is used initially to help students understand exponents? • What is the base number? • What is the exponent? 53

  40. Other Types of NumbersExponents • How can multiplying numerals with exponents be shown? 4 x 4 x 4 x 4 x 4 43 x 42 = 45

  41. Other Types of NumbersExponents • How can simplifying exponents be shown? 55 = 5 x 5 x 5 x 5 x 5 53 5 x 5 x 5

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