Ratios+and+Rates

Overview:
 * Section A**: Students learn about unit rates by investigating contexts invloving the average number of people per car during various times of day and gas economy of different vehicles.
 * Section B**: Students learn the difference between making absolute comparisons and relative comparisons. For example, one state may produce more corn than another (absolute) but the state that produces less may use less land area and produce more corn per acre than the first state (relative).
 * Section C**: Students explore several contexts to make decisions based on ratios. They learn to write part-part and part-whole ratios using ratios and percents. For example, a class may be described using a ratio of boys to girls (15 to 10 -part to part) or as a percentage of the entire class (60% boys -part to whole).
 * Section D**: Students used various ratios to explore constant and variable relationships and solve problems based on their explorations. They collect data on the heights and shadows of various items at various times of the day to learn that the ratio of height to shadowlength is constant for various items at the same time of day but variable between the same item measured at different times of the day.
 * Section E**: This section explores the use of a scale factor to represent a proportional enlargement or reduction in size. This lesson connects and extends to the 6th grade unit "Models You Can Count On" and is a precursor to the 8th grade unit "It's All the Same". Acroos these three units, the students progress from the use of various models (ratio tables, double number lines) to the use of a scale factor to applying this scale factors to determine sizes of corresponding sides of similar figures.

Links to activities and resources: Interactive [|ratio table] [|Ratio table] game [|Rates]: Speed and distance Challenge: [|Miles per gallon] [|Challenge: Are you faster than a car?]