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Engaging Frogs and Toads Activity: Exploring Strategies for Minimum Moves in Mathematics

This activity introduces an engaging mathematical challenge using frogs and toads. Participants will swap frogs and toads while following specific rules: sliding into an empty space or hopping over another to an empty square. The goal is to discover the rules governing the minimum number of moves required to solve the puzzle with varying counts of frogs and toads. Discussion points include analyzing solutions for different configurations and reflecting on the problem-solving process. This activity supports the primary mathematics curriculum through exploration, pattern recognition, and independent study.

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Engaging Frogs and Toads Activity: Exploring Strategies for Minimum Moves in Mathematics

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  1. Part time PGCE Introduction to Mathematics

  2. Frogs and toads • Activity: • To swap over the frogs and toads • Rules: • You may either: - slide one square into an empty space • hop one frog/toad over one other frog/toad into an empty space • Aim: • To find the rule for determine the minimum number of moves for any numbers of frogs and toads. • Possible steps: • What is the minimum for 2 frogs and 2 toads? How many slides & hops? • How about 3 of each/ 4 of each etc? • How about 2 frogs and 3 toads? • What patterns are there?

  3. For discussion • Have you solved the problem? • Have you finished the investigation or is there something else you could do? • What helped/hindered you in solving the problem?

  4. A Model for the Primary Mathematics Curriculum • Facts • Skills • Concepts • Processes • Situations • Attitudes Shuard,H. (1986) Primary mathematics today and tomorrow York:SCDC

  5. David Burghes Mathematics Enhancement Project 1997 In his survey, Year 7 / 8 pupils were asked: ‘What do you think are the good qualities of the best maths teacher you ever had? They gave answers such as: • Patience • Sense of humour • Give individual help • Does not move on too quickly • Checks and helps understanding • Approachable and caring • Makes mathematics enjoyable and fun • Strict and good control of the class • Doesn’t get cross if pupils do not understand • Listen • …..but, by far the most frequent response was gives clear explanations

  6. Independent Study Tasks Task 1 • Jennings, S.F. (2006) ‘Personal development plans and self-directed learning for healthcare professionals: are they evidence based?’ Postgraduate Medical Journal. 83 pp. 518-524. Available at http://pmj.bmj.com (Accessed: July 7th , 2010) • Wilcox, S.W. (1996) ‘Fostering self-directed learning in the university setting.’ Studies in Higher Education. 21(2) pp173-176 What are the key messages about independent study? Task 2 • Read extracts from:  Williams, P. (2008) Review of Mathematics Teaching in Early Years Settings and Primary Schools What are the key messages about attitudes towards mathematics?

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