Multiplication, Subtraction, Factors and Multiples
Key Stage: 3 ★★
On a hundred square board, you start on 42, and can either multiply by 2 or subtract 5 at each stage. What numbers is it possible to reach?
This problem offers all students opportunities to explore fundamental ideas about number theory in a simple context. They are encouraged to explore, conjecture, generalise and justify. There are opportunities for older students who are familiar with algebraic manipulation or modulo arithmetic to produce rigorous proofs.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
Key Stage: 3 ★★
On a hundred square board, you start on 42, and can either multiply by 2 or subtract 5 at each stage. What numbers is it possible to reach?
This problem offers all students opportunities to explore fundamental ideas about number theory in a simple context. They are encouraged to explore, conjecture, generalise and justify. There are opportunities for older students who are familiar with algebraic manipulation or modulo arithmetic to produce rigorous proofs.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
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Another nice lesson idea from n-rich, this link is on the topic of integers, factors and multiples. I like these lesson ideas as they teach the topic in an interesting and different way and come with a full set of teacher notes, hints for pupils and solutions for ease of planning. Would make an ideal investigation lesson as a paired or group work task.
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