Pre-Algebra

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
Coordinate System and Functions

• Next, students learn to complete a table with the
  function given

x Function x 2 y
0 0 2 2
1 1 2 3
2 2 2 4
3
4
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
  pointsFormat 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

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Ratios and Proportions

• 3TVs TVs
• 7 Radios 28 Radios
• 3TVs (4 ) TVs
• 7 Radios (4 ) 28 Radios

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Ratios and Proportions

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

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Ratios and Proportions

• 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?

Classification Ratio Quantity
Cars 3
SUVs 5
Vehicles 1600
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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).

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Ratios and Proportions

• Students 1) set up the ratio table and 2)
  complete the fraction family column

Fraction family Ratios Quantity
Coffee 2/3
Tea 1/3
People 3/3
15
Ratios and Proportions

• 3) Students use the numerator of the fraction to
  complete the ratio column.

Fraction family Ratios Quantity
Coffee 2/3 2
Tea 1/3 1
People 3/3 3
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Ratios and Proportions

• 4) Students fill in known quantities.

Fraction family Ratios Quantity
Coffee 2/3 2
Tea 1/3 1 15
People 3/3 3
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Ratios and Proportions

• Students write the ratio equation
• 2 Coffee Coffee
• 1 Tea 15 Tea

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Ratios and Proportions

• 6) Students solve the ratio problem to answer
  questions.

Fraction family Ratios Quantity
Coffee 2/3 2 30
Tea 1/3 1 15
People 3/3 3
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Ratios and Proportions

• 7) Students use the number-family strategy to
  solve for unknowns. (See Format 20.2)

Fraction family Ratios Quantity
Coffee 2/3 2 30
Tea 1/3 1 15
People 3/3 3 45
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?

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Ratios and Proportions

• Students set up a number family using fractions
• Difference Louise Boss
• 1/6 gt 6/6
  

22
Ratios and Proportions

• Students can then use the ratio table and ratio
  equation to solve for the unknown quantities.

Difference 1
Louise 5 1800
Boss 6
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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 gt100

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Ratios 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?
• Students then put the information into a ratio
  table

California 40
Florida 60
All 100 170
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Ratios and Proportions

• Finally, students can use ratio tables to do
  comparison problems using percentages
• A bike store sold 25 fewer womens bicycles
  than mens bicycles. If the store sold 175 fewer
  womens bikes, how many mens and womens bikes
  did it sell?

27
Ratios and Proportions

• A bike store sold 25 fewer womens bicycles
  than mens bicycles. If the store sold 175 fewer
  womens bikes, how many mens and womens bikes
  did it sell?
• Again, students would start with the number
  family
• Difference Womens Mens
• 25 gt 100

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Ratios and Proportions

• A bike store sold 25 fewer womens bicycles
  than mens bicycles. If the store sold 175 fewer
  womens bikes, how many mens and womens bikes
  did it sell?
• Then the information from the number family would
  into the ratio table

Difference 25 175
Womens 75
Mens 100
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Other Types of Numbers

• Primes and Factors
• Integers
• Exponents

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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?

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Other Types of NumbersPrimes and Factors

• What are the prime factors of a number?
• How can the prime factors of a number be
  determined?

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Other Types of NumbersPrimes and Factors

• What are the prime factors of 30?
• What are prime factors used for?

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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.

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Other Types of NumbersIntegers

• What rules does Format 20.3 teach?

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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.

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Other Types of NumbersIntegers

• What rules do students need to know to multiply
  integers?

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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

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Other Types of NumbersExponents

• What is used initially to help students
  understand exponents?
• What is the base number?
• What is the exponent?
• 53

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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

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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