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## Well not much if you put fences up between them.

But what if you only have 3 fences – can they all have a paddock of their own?
The Chickens and the Foxes is a great example of how you can take one concept and differentiate to make it a task suitable for Prep through to Year 9.

Prep – Year 2. Read the Mem Fox’s Hattie and the Fox. Why is Hattie worried? How could you keep Hattie safe? What would a farmer do? Introduce the concept of creating two smaller paddocks from one large paddock by putting up a fence. Can you put up two fences? Etc.

Students in Year 3 – 4 should be given the opportunity to explore the number of paddocks that can be made with one fence, then with two and onto 3 fences rather than starting with the original problem. This will enable them to gain familiarity with the problem with small numbers.

Discuss the different paddocks that students make: Is it the same solution if 2 rulers create 4 paddocks but the solutions look different? (eg if you create square paddocks versus triangular paddocks)
Was one student able to make more paddocks out of the same number of fences? How did they do it? Point out the number of times the rulers overlap.
Are we sure we have the most number of paddocks for that number of fences? How could you find out?
Students in Year 5 – 6 should be given the problem as stated and asked to investigate in pairs or small groups. How are they tracking their attempts to create paddocks? Are they making predictions, testing and reflecting or randomly guessing? For example, do they place rulers parallel or perpendicular or a combination of both? Does this work? Why? Why not?
How many overlaps are possible with 3 rulers? How do you know? Does more overlaps create more paddocks?
Students in Year 7 – 9 should be encouraged to investigate patterns by recording in tables the number of fences and the number of paddocks. Investigating 1, 2, 3, 4 and 5 rulers will provide the foundations for a pattern. Is there a relationship?

What is the rule?

You can download a powerpoint and instructions for using this in the classroom in the following link.

Enjoy!