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PRE-ALGEBRA
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Pre-Algebra
Coordinate System and Functions Ratios and Proportions Other Types of Numbers
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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)?
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Coordinate System and Functions
x Function x + 2 y
0 0 + 2 2
1 1 + 2 3
2 2 + 2 4
3
4
Next, students learn to complete a table with the function given:
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Coordinate System and Functions After completing the table, students plot
the points and draw the line for the function.
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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.
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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.
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Ratios and Proportions
What is the preskill for ratios and proportions?
How should problems be set up?
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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 = TVsRadios Radios
3 TVs = TVs 7 Radios 28 Radios
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Ratios and Proportions
3TVs = TVs7 Radios 28 Radios
3TVs (4 ) = TVs7 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
Classification Ratio Quantity
Cars 3
SUVs 5
Vehicles 1600
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?:
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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
Fraction
family
Ratios Quantity
Coffee 2/3
Tea 1/3
People 3/3
Students: 1) set up the ratio table and 2) complete the fraction family column:
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Ratios and Proportions
Fraction
family
Ratios Quantity
Coffee 2/3 2
Tea 1/3 1
People 3/3 3
3) Students use the numerator of the fraction to complete the ratio column.
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Ratios and Proportions
Fraction
family
Ratios Quantity
Coffee 2/3 2
Tea 1/3 1 15
People 3/3 3
4) Students fill in known quantities.
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Ratios and Proportions
5) Students write the ratio equation:
2 Coffee = Coffee 1 Tea 15 Tea
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Ratios and Proportions
Fraction
family
Ratios Quantity
Coffee 2/3 2 30
Tea 1/3 1 15
People 3/3 3
6) Students solve the ratio problem to answer questions.
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Ratios and Proportions
Fraction
family
Ratios Quantity
Coffee 2/3 2 30
Tea 1/3 1 15
People 3/3 3 45
7) Students use the number-family strategy to solve for unknowns. (See Format 20.2)
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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 + > 6/6
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Ratios and Proportions
Difference 1
Louise 5 1800
Boss 6
Students can then use the ratio table and ratio equation to solve for the unknown quantities.
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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?
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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%
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Ratios and Proportions
California 40%
Florida 60%
All 100% 170
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:
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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 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?
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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%
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Ratios and Proportions
Difference 25% 175
Women’s 75
Men’s 100
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:
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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?
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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?1. If the signs of the numbers are the
same, you add.2. If the signs of the numbers are different,
you subtract.3. When you subtract, you start with the
number that is farther from zero and subtract the other number.
4. 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 553 5 x 5 x 5