Grade 6 · Read a unit rate · 486 of 750
Read a unit rate · practice 50
An object moves at a constant 8 distance units per time unit for 4 time units, starting with zero accumulated distance. How far does it travel? Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
An object moves at a constant 8 distance units per time unit for 4 time units, starting with zero accumulated distance. How far does it travel?
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Distance is rate multiplied by elapsed time.
Work through the reasoning
Step 1
Translate the givens
The rate is 8 distance/time and elapsed time is 4; the units tell us to multiply.
Step 2
Calculate with the model
Distance = 8 × 4 = 32.
Step 3
Check and interpret
Divide back: 32 ÷ 4 = 8. Equal time intervals add equal distances under a constant-rate assumption.
The answer
32 distance units.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
The mathematical idea
A constant rate links an elapsed input to an accumulated output by multiplication. The origin represents zero elapsed time and zero new distance. The rate is the slope, with output units per input unit; it is not the total distance. Starting quantities: Rate: distance/time = 8; Final time = 4.
distance = rate × time
03 · Reflect and transfer
Explain what changes and why.
What would change in the graph if the object started with a nonzero recorded distance?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.