Engaging Math Problems for Teachers' Discussion
A selection of math problems used in lessons designed with different research approaches is provided, including discussions on dog growth, teacher lunch portions, milkshake comparisons, and more. These problems are ideal for sparking meaningful discussions among teachers during department meetings or professional development sessions.
- Math Problems
- Teaching Strategies
- Professional Development
- Research Approaches
- Classroom Discussions
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A selection of problems used in the lessons The first slide (Discussion problem) may be useful as a starting point for discussion at a department meeting. The next set of slides display a problem (all from unit 1 lessons) chosen from each of the three different approaches* used in the design of the project lessons. These may generate useful discussion for teachers when considering the teaching of these topics or engaging with these PD materials *(The lessons have been designed to reflect three different research approaches and these are discussed in other sections of the microsite)
Discussion problem: Which Dog has grown the most? Caesar has grown from 5 kg to 8 kg Brutus has grown from 3 kg to 6 kg and Tiberius has grown from 4 kg to 7kg What might the issues/responses be from children? Explain your thinking What maths are you using?
Problem from a lesson representing design approach A (RME) Groups of trainee teachers are sent out to a check the suitability of venues for school trips. Large sandwiches are provided for lunch. Q1 a) Inwhich group do the teachers get the most to eat? Explain your thinking b) In which group do the teachers get the least to eat? Explain your thinking
Problem from a lesson representing design approach B (constructivist) B C A E D
Problem from a lesson representing design approach C (Enquiry/cognitive conflict) Comparing Milkshakes Comparing Milkshakes Two batches of milkshake are made by mixing cartons of juice with cartons of milk: Batch 1 Batch 2 Beth and Charlie can t agree on whether the two batches of milkshake will taste the same. Determine whether the two batches will taste the same, commenting on the two reasons given. Two batches of milkshake are made by mixing cartons of juice with cartons of milk: ! " # $% ! " # $% ! " # $% ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ ! " # $% ! " # $% ! " # $% ! " # $% ! " # $% ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ Determine whether the two batches will taste the same. Both batches have two more cartons of milk than juice so they will taste the same In Batch 1, of the milkshake is juice, whereas in Batch 2, of the milkshake is juice so they will taste different
Comparing Milkshakes Comparing Milkshakes Two batches of milkshake are made by mixing cartons of juice with cartons of milk: Batch 1 Batch 2 Beth and Charlie can t agree on whether the two batches of milkshake will taste the same. Determine whether the two batches will taste the same, commenting on the two reasons given. Two batches of milkshake are made by mixing cartons of juice with cartons of milk: Both batches have two more cartons of milk than juice so they will taste the same ! " # $% ! " # $% ! " # $% ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ 3 In Batch 1, of the milkshake is juice, 5 5 7 whereas in Batch 2, of the milkshake is ! " # $% ! " # $% ! " # $% ! " # $% ! " # $% juice so they will taste different ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ ! "#$ Beth and Charlie can t agree on whether the two batches of milkshake will taste the same. Determine whether the two batches will taste the same, commenting on the two reasons given. Both batches have two more cartons of milk than juice so they will taste the same In Batch 1, of the milkshake is juice, whereas in Batch 2, of the milkshake is juice so they will taste different
