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```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
 Y on the vertical axis

Where is (7,6)?
Coordinate System and Functions
Next, students learn to complete a table with the
function given:
x
0
Function x + 2
0+2
y
2
1
1+2
3
2
3
4
2+2
4
Coordinate System and Functions

After completing the table, students plot the points
and draw the line for the function.
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.
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.
Ratios and Proportions


What is the preskill for ratios and proportions?
How should problems be set up?
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
3 TVs =
TVs
Ratios and Proportions
3TVs
=
TVs
3TVs
(4 ) =
TVs
Ratios and Proportions

After reviewing the use of equivalent fractions, one
may introduce problem solving with a ratio table.
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
Cars
SUVs
Vehicles
Ratio
3
5
Quantity
1600
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).
Ratios and Proportions
Students: 1) set up the ratio table and 2) complete
the fraction family column:
Coffee
Fraction
family
2/3
Tea
1/3
People
3/3
Ratios
Quantity
Ratios and Proportions
3) Students use the numerator of the fraction to
complete the ratio column.
Coffee
Fraction
family
2/3
Ratios
Tea
1/3
1
People
3/3
3
2
Quantity
Ratios and Proportions
4) Students fill in known quantities.
Coffee
Fraction
family
2/3
Ratios
Tea
1/3
1
People
3/3
3
Quantity
2
15
Ratios and Proportions
5)
Students write the ratio equation:
2 Coffee
1 Tea
=
Coffee
15 Tea
Ratios and Proportions
6) Students solve the ratio problem to answer
questions.
Coffee
Fraction
family
2/3
Tea
People
Ratios
Quantity
2
30
1/3
1
15
3/3
3
Ratios and Proportions
7) Students use the number-family strategy to solve
for unknowns. (See Format 20.2)
Coffee
Fraction
family
2/3
Tea
People
Ratios
Quantity
2
30
1/3
1
15
3/3
3
45
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?
Ratios and Proportions
Students set up a number family using fractions:
Difference
Louise
Boss
1/6
+
>
6/6
Ratios and Proportions
Students can then use the ratio table and ratio
equation to solve for the unknown quantities.
Difference
Louise
1
5
Boss
6
1800
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?
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%
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
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?
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%
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?
Then the information from the number family would
into the ratio table:
Difference
25%
Women’s
75
Men’s
100
175
Other Types of Numbers
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

Primes and Factors
Integers
Exponents
Other Types of Numbers
Primes 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?
Other Types of Numbers
Primes and Factors
What are the prime factors of a number?
How can the prime factors of a number be
determined?
Other Types of Numbers
Primes and Factors
What are the prime factors of 30?
What are prime factors used for?
Other Types of Numbers
Integers
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What are integers?
How do the authors recommend introducing
negative numbers?
What is the rule?
Other Types of Numbers
Integers
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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.
Other Types of Numbers
Integers

What rules does Format 20.3 teach?
Other Types of Numbers
Integers

1.
2.
3.
4.
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.
Other Types of Numbers
Integers

What rules do students need to know to multiply
integers?
Other Types of Numbers
Integers
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

Other Types of Numbers
Exponents



What is used initially to help students understand
exponents?
What is the base number?
What is the exponent?
53
Other Types of Numbers
Exponents

How can multiplying numerals with exponents be
shown?
4x4x4x4x4
43 x 42 = 45
Other Types of Numbers
Exponents

How can simplifying exponents be shown?
55
53
=
5x5x5x5x5
5x5x5
```