Practice 1
Answer and teaching response
1 3/4 · Seven quarter-inch intervals separate the two marks.
Measure a length when the ruler does not start at zero
Use quarter-inch intervals to read the distance between two marks, then record measurements independently of where an object starts.
Get the student and teacher materialsPrepare the group
Learning goal: Produce a measurement record with start mark, end mark and actual length, supported by counted equal intervals.
You will need: A drawn ruler marked in quarter inches and a pencil. Use stated marks for the questions; screen and print scale are not calibrated rulers.
Start with this question
A paper strip starts at the 1 1/4-inch mark and ends at the 3-inch mark. How long is it?
1 3/4 inches. Seven quarter-inch intervals connect the start to the end; the end reading alone is not the strip length.
- Locate both ends of the strip. The left end sits at 1 1/4 inches, so the first 1 1/4 inches of the ruler are outside the strip.
- Count equal quarter-inch intervals from 1 1/4 to 3. Count the spaces traversed, not both endpoint marks as extra pieces.
- Group four quarter-inch intervals into one inch. The seven intervals give one inch and three quarters of another inch.
- Check by moving the strip's left end to zero on a drawing without stretching it. Its right end would be at 1 3/4, showing that changing the starting position does not change its length.
Run the 15-minute workshop
- 3 minutes. Present two identical strips starting at different ruler marks. Ask whether their lengths should differ.
- 4 minutes. Count the highlighted intervals and record start, finish and distance as separate quantities.
- 5 minutes. Use the first three measurement cards. Have partners check each other's interval counts.
- 3 minutes. Complete the independent card and explain why the endpoint reading is not the answer.
A useful error to discuss
A learner might say: The end mark reads 3, so the strip is 3 inches long.
Ask whether the strip includes the part of the ruler from zero to its starting mark. Trace only the intervals covered by the strip.
Practise, then check independently
Try the first three tasks with the worked model. Try the final task without help. Enter a number, fraction or mixed number, such as 3/4 or 1 1/4. The number check does not assess your drawing or explanation.
Practice 2
Answer and teaching response
2 1/2 · The distance includes two full inches and one half inch.
Practice 3
Answer and teaching response
3/4 · Three quarter-inch intervals separate the marks.
Independent check
Answer and teaching response
2 1/4 · Nine quarter-inch intervals make two inches and one quarter.
Transfer the idea
An object measured from 2 inches to 5 inches is moved so its left end is at 1 inch. Where should its right end be?
Discuss a possible response
At 4 inches. The object is 3 inches long; moving both ends one inch left preserves that distance.
Choose the next teaching step
Look for:
- Records a distance rather than a coordinate.
- Counts equal intervals and keeps inch units.
If the idea is not secure: Mark each covered quarter-inch space with a small arc before counting; start the count after the left endpoint.
If the learner is ready: Draw two different start-and-end pairs for a strip of length 1 1/2 inches and explain the agreement.
Materials for your group
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