Ratio, rate, and speed (motion graphs)

Practice 5 items →

On a distance–time graph the slope is speed; on a speed–time graph the area is distance. Students handle changing ratios and compound rates, read both graph types, and compute average speed as total distance over total time — 48 km/h for an equal-distance out-and-back at 40 and 60, not 50.

Specification · for a parent or teacher

Part no.: speed-motion-graphs
Course: Advanced Math 7 · Unit 6
Realm: Applied
Difficulty: 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

changing ratios and constant-difference models; compound rates; distance–time and speed–time graphs; average speed as total $d$ / total $t$ .

Ready when

out at 40, back at 60, equal distances — they compute $48$ km/h, not $50$ .

Formulas

Average speed, equal distances

\bar v = \frac{2 v_1 v_2}{v_1 + v_2}

Watch for

averaging 40 km/h and 60 km/h for an out-and-back of equal distance (the answer is not 50).

Before · requires

Rate and speedrate-speed · Math 6
Coordinates and graphs (four quadrants)four-quadrant-plane · Math 6

After · used by

— none

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