Chapter 11

Rational Equations and Functions

11.1 Ratio and Proportion

• Review expressions and equations by having students create a Double Bubble Map.

Expressions and Equations

• Put student example here

Ratios

• What do students already know/remember about ratios?– Have students create a circle map

• Framework– Definition– Numerical examples– Real world examples

Ratios

Definition

Numerical

examples

Real world

examples

Proportions

• Start proportion Circle Map.

• Have students add to map as more examples are found

Proportions

Definition

Numerical

examples

Real world

examples

ratio

ratio

=

• Class will create a Flow Map detailing steps to solve proportion word problems.

• Students will create Double Flow Maps while solving homework problems.

Percents

• Review percents by having students complete a Circle Map.

12%

Framework—what do you do to get other forms?

You divide percentage by 100 to get decimal forms.

You place percentage over 100 to get a fraction.

Solving percent word problems.

• Refer back to the proportion Brace Map. Percent word problems are a specific type of proportion problem.

ratio

ratio

=

Numerator--Part of a whole

Denominator--Whole amount

Numerator--Percentage

Denominator--100

Student Activity

• Have students complete brace maps for percent word problems substituting the values from the problems for the verbal description of parts.

234

424

x

100

234

424

=

X

100

234 = X 424 100

There are 234 boys at Parry McCluer High School. If there are 424 students at PMHS, what percent of the students are boys?

Direct and Inverse Variation

• Introduce topic using a Tree Map to compare and contrast direct and inverse variations. Include formulas, definitions, and examples.

(Add example here)

• Use Bridge Maps to give examples of direct and indirect variation. Have students add their own examples to create a bulletin board display.

Direct and Inverse Variation

• On the second day, as part of the class warm-up, have students create a Double Bubble Map comparing and contrasting direct and inverse variations.

(Add student example here)

Simplify Rational Expressions

• Students will create circle map and will continue to add to it as new examples of rational expressions are found.– Framework

• What makes it a rational expression

Rational

Expressions

Examples of rational expressions

What makes it a rational expression

Multiplying and DividingRational Expressions

• Have students create flow map explaining process as teacher works examples.

4x . x-3 . 2 2x - 9 8x + 12x

4x . x - 3 .(x +3)(x – 3) 4x(x + 3)

1 × 1(x + 3)(x + 3)

1 2(x + 3)

Multiply Rational Expressions

4x ÷ x-3 . 2 2x - 9 8x + 12x

4x . x - 3 .(x +3)(x – 3) 4x(x + 3)

1 × 1(x + 3)(x + 3)

1 2(x + 3)

Divide Rational Expressions