PRE-ALGEBRA. Pre-Algebra Coordinate System and Functions Ratios and Proportions Other Types of...

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

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:

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 = TVsRadios Radios

3 TVs = TVs 7 Radios 28 Radios

Ratios and Proportions

3TVs = TVs7 Radios 28 Radios

3TVs (4 ) = TVs7 Radios (4 ) 28 Radios

Ratios and Proportions

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

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?:

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

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:

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.

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.

Ratios and Proportions

5) Students write the ratio equation:

2 Coffee = Coffee 1 Tea 15 Tea

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.

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)

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

Difference 1

Louise 5 1800

Boss 6

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

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

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:

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

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:

Other Types of Numbers

Primes and Factors Integers Exponents

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?

Other Types of NumbersPrimes and Factors

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

determined?

Other Types of NumbersPrimes and Factors

What are the prime factors of 30?

What are prime factors used for?

Other Types of NumbersIntegers What are integers? How do the authors recommend

introducing negative numbers? What is the rule?

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.

Other Types of NumbersIntegers What rules does Format 20.3 teach?

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.

Other Types of NumbersIntegers What rules do students need to know to

multiply integers?

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

Other Types of NumbersExponents What is used initially to help students

understand exponents? What is the base number? What is the exponent?

53

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

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