A lesson you can
picture in your classroom.
Original teaching examples presented directly on the page: prompts, models, supported practice and independent transfer.
Finding three quarters
of a quantity.
Target: learners explain how to find ¾ of 20 with equal groups, then move towards calculation and a new independent problem.
Three groups make fifteen.
01Discover prior knowledge5 min
Show twelve counters. Ask: “Can you divide them into four equal groups? How many are in one group?” Listen before correcting. Look for equal sharing.
02Explore with objects8 min
Give the learner twenty counters. Organise into four equal groups. Ask what one group represents, connecting the group to a quarter.
03Guide the reasoning10 min
Ask: “If one quarter is five, how could you find three quarters?” Use three groups of five and write 20 ÷ 4 = 5; 5 × 3 = 15.
04Practise and fade help10 min
Begin together on ¾ of 16. Then ask learners to model ¾ of 24 and explain without the same prompts. Reduce help only if understanding is secure.
05Check independent transfer7 min
Exit ticket: “Find ⅖ of 30 independently, using words, a diagram or a number sentence.” Check the denominator, equal groups and reasoning.
This preview is educational illustration, not a validated curriculum or a downloadable teacher pack.
Concrete → visual
→ abstract.
Start with objects that can be counted, regrouped and discussed. Represent the relationship with diagrams or number lines. Only then ask the learner to express the same relationship using efficient symbolic methods.
The representation changes. The relationship stays.A useful lesson also
makes thinking visible.
Preview the kind of observation a teacher could record during a Proximal Math lesson. This is an illustrative on-page example, not a completed learner record or a diagnostic instrument.
Teachers should check not only whether the answer is correct, but whether the learner can explain the relationship and apply it again when the numbers change.