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