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2 Extend your investigation, making clear the rules and the methods that you use. 2 The pony needs an area of 100 m 2 of grass each day. 1 The diagram below shows a rectangle which is 2 cm wide and 4 cm long. Grazing You may wish to use 5 mm or 1 cm squared paper to help you with this activity. (a) (b) What area of grass does the pony have when the rope is 4 m long? The first E is shown on the grid below All the numbers in the E are added together. 2 The E is moved one square to the right to create the second E. 3 Investigate the total of the numbers in the E for any position on the grid. Bella and Juan are arguing about the number of squares in the diagram.Contents 1 Introduction Engaging mathematics for all learners OCR s AO3 Problem Solving Guide OCR & The School Mathematics Project Support for Problem Solving About these investigations 4 2 The investigations 5 Dodgy Dice 5 Winning Lines 6 Winning Lines 2 7 Grazing 8 Pile em high 9 Spotty Roofs 10 Matchstick Models 11 Opposite Corners 12 Magic E 13 How Many? In order for learners to be successful, they should be given mathematical activities which allow them to experience working with others solving problems using technology and other resources mathematical modelling mathematics outside the classroom environment 1.1 Engaging mathematics for all learners OCR recommends that teachers read the QCA publication Engaging mathematics for all learners, which is available as a PDF from: The QCA publication gives practical advice for organising rich activities within the curriculum.
Depending on your own experience in using open-ended and richer tasks, we would recommend you read and use the activities in the AO3 Problem Solving Guide first before you use the tasks in this booklet.
1.3 OCR & The School Mathematics Project Support for Problem Solving A further set of tasks has been carefully developed and trialled by The School Mathematics Project in partnership with OCR.
This is not from the perspective simply of following the method intended, rather to ask open questions such as How many ways can you find to solve?
The idea is to change the emphasis of the question to finding as many methods as possible and to appreciate the interconnectedness of concepts.
Becky notices that there are some other squares that are never landed on.
1 What is the next square after square 3 that cannot be landed on?
The game is played on a square board, with squares numbered from one to one hundred.
GO The dice Pawel and Becky use only has the numbers 4 and 7 on it.
We hope you find these tasks interesting, useful and rewarding.
2 The investigations Dodgy Dice Pawel and Becky have invented a game.