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Grades 6–7MathRatio and ProportionLesson 4 of 4Ages 11–13

Years 7–8 in England and Wales · Cambridge Lower Secondary Stages 7–8 · IB MYP 1 to MYP 2, ages 11–13

Does twice the time mean twice the distance?

A walker moves at a steady pace while teammates mark where they are every 5 seconds, then the class graphs distance against time. A steady walker's points make a straight line through zero, but a walker with a head start doesn't. Students identify proportional relationships from tables and graphs, find the constant of proportionality and write it as an equation.

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First page of the Does twice the time mean twice the distance? teacher guide
A walker moving along a measured line on the playground with red beanbags dropped at even spacing behind them, a teammate watching, and a large stopwatch in the sky.Preview · the opening mission

Read this to the class:

A sports company is making a pace app for school walking clubs. The app assumes that if you walk for twice as long, you go twice as far. One tester said, "That's only true if you walk at a steady pace from the start line." Another said, "What if you start a few metres ahead?" Your team's job: collect real data on a walker, graph it, and find out when "twice the time means twice the distance" is true and when it isn't.

Teams of three, with jobs that rotate after each walk: Walker (walks at a steady pace), Timer (calls out "5, 10, 15, 20" seconds), Marker (drops a beanbag beside the line at the walker's front foot at each call).

Look inside the PDF

Sample pages, stamped “preview”. The download is the clean, full lesson.

Teacher guide, page 1
Inside: the lesson steps
Student sheet, ready to copy

In the full lesson PDF

8 printable pages

  • Predict (5–10 min)
  • Hunt (20 min)
  • Reveal (10–15 min)
  • Act (10 min)
  • Background for the teacher
  • Assessment
  • Student sheet
  • Worksheet: Label it
  • Worksheet: Try it at home

On the student sheet

  • My prediction
  • Walk 1, from zero
  • Walk 2, head start at 5 m
  • Graph both walks
  • What did we find?
  • Our note to the app company
  • Exit ticket
  • Label it
  • Try it at home

US Letter, prints cleanly in black and white. The student sheet is on its own page, ready to photocopy.

Free with an account (any 3 lessons), or US$19 for all 4 lessons in this unit.

What students show by the end

  • Collects and tabulates data
  • Tests for proportionality
  • Finds and uses k

From the lesson’s rubric, which scores each one as not yet, getting there or got it.

Questions teachers ask

How long does “Does twice the time mean twice the distance?” take?

50–60 min. Group size: teams of 3, or 4 with an extra marker.

How much prep does it need?

15 minutes: on a playground or long hallway, mark a straight line 30 m (about 98 ft) long with a 0 at one end. Each team needs a stopwatch or timer, 4 beanbags or pieces of chalk to mark positions, and a measuring tape or metre stick. Print graph paper or use the grid on the Student sheet.

What materials do I need?

Measuring tape, 30 m, or metre sticks; stopwatch or timer; beanbags, chalk or small cones to mark positions; graph paper. Cost: free with chalk, a measuring tape and a timer you already have.

Which curriculum standards does it cover?

Common Core Math (US): 6.RP.A.3 and 7.RP.A.2.

What’s in the lesson PDF?

A teacher guide that walks you through predict, hunt, reveal, act, background for the teacher and assessment, then a student sheet (“My prediction”; “Walk 1, from zero”; “Walk 2, head start at 5 m”; “Graph both walks”; “What did we find?”; “Our note to the app company”; “Exit ticket”; “Label it” and “Try it at home”) on its own page, ready to photocopy. It’s US Letter and prints cleanly in black and white.

Can I try it for free?

Yes. A free account includes any 3 full lessons of your choice, and this can be one of them. After that, this unit is US$19 for all 4 lessons, yours to keep, or every lesson is US$199 a year.