Mathematics K–6 · Years 3–4
How many in the jar: estimating a collection by sampling
Number and algebra
The idea
A large collection can be estimated by counting one scoop, counting how many scoops fill the container and multiplying, then checked against a full count.
What you need
- a clear jar holding about 400 dried beans
- a 60 mL scoop
- an egg carton or ten-frames for counting in tens
- a recording sheet
How to do it
- Look at the jar and write down a first estimate of the number of beans.
- Take one level scoop of beans and count them in tens using the egg carton. Record the count.
- Count how many level scoops empty the jar, keeping the beans from each scoop in a separate pile. Multiply the scoop count by the beans per scoop for a second estimate.
- Count every bean in tens and record the true total. Compare both estimates with the total and work out the difference for each.
- Repeat with a jar of pasta pieces and see whether the second estimate is again closer than the first.
What you should see
If one level scoop holds 48 beans and the jar empties in 8 scoops, the estimate is 8 times 48, which is 384, and the full count is compared with it; the scoop estimate is off by however much the scoops differ from the one that was counted. The difference column shows which estimate, the first look or the scoop estimate, came closer. Counting in tens with the carton lets a second child check each ten of the full count.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The only way to know how many is to count every one.
- A bigger jar always has more beans than a smaller jar however full each is.
Safety card
Hazards
- dried beans and pasta are a choking hazard for small children
Controls
- no eating; sweep up dropped beans
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.