This lesson is optional. In this lesson, students apply what they have learned about scale drawings to solve problems involving constant speed (MP1, MP2). Students are given a map with scale as well as a starting and ending point. In addition, they are either given the time the trip takes and are asked to estimate the speed or they are given the speed and asked to estimate how long the trip takes. In both cases, they need to make strategic use of the map and scale and they will need to estimate distances because the roads are not straight.
In the sixth grade, students have examined many contexts involving travel at constant speed. If a car travels at 30 mph, there is a ratio between the time of travel and the distance traveled. This can be represented in a ratio table, or on a graph, or with an equation. If \(d\) is the distance traveled in miles, and \(t\) is the amount of time in hours, then traveling at 30 mph can be represented by the equation \(d = 30t\). Students may or may not use this representation as they work on the activities in this lesson. But they will gain further familiarity with this important context which they will examine in greater depth when they study ratios and proportional reasoning in grade 7, starting in the next unit.
- Justify (orally and in writing) which of two objects was moving faster.
- Use a scale drawing to estimate the distance an object traveled, as well as its speed or elapsed time, and explain (orally and in writing) the solution method.
Let’s use scale drawings to solve problems.
Ensure students have access to geometry toolkits.
- I can use a map and its scale to solve problems about traveling.
A scale tells how the measurements in a scale drawing represent the actual measurements of the object.
For example, the scale on this floor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches would represent 16 feet, and \(\frac12\) inch would represent 4 feet.
A scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.