# Making Extension Manageable

Key 1: Make the maths weirder rather than making the numbers harder

• Give the starting and ending numbers and ask, “What happened?”
• Work backwards from the end point to the start.
• Have a gap in the question.
• Ask “What if…?” and then make a change to the circumstances. See what happens to the answer. Look for patterns.
• Add in extra steps, preferably in non-standard ways
• Give a non-standard format (e.g. Fraction in a 3D or group, irregular shapes)
• The Manipulation and Backwards questions in the Back-to-Front Maths Journals and Blasts will give you some guidance on how to get started.

Key 2: Make the maths applicable to a real life situation

• Find something of interest to the student. Consider, (1) how would this be someone’s job in real life? Create a task based on that job. Consider, (2) how does this apply directly to the student’s life? Create a task based on that application
• Lots of multi-year investigations on www.backtofrontmaths.com.au You will need to adapt these into kid-friendly language. See example below.
• Consider, why do we do that job in that way? What is the reason for it? Look for patterns then model and investigate what you find. Prove it mathematically.

Example: You have been given a budget of \$80. You need to plan a meal for eight people, make a shopping list, and work out the total cost for the meal.

Key 3: Make them prove it

• For students who “just know” the answer, try getting them to prove why a wrong answer is wrong. NB – proving the teacher wrong is heaps of fun for kids!
• Ask, “how are these all kind of the same?”

Key 4: Make an extension box

• Rather than making extension student do all of the low level drill and skill tasks, create an extension box and put in it an investigation as well as all the things needed to do that task in real life. Get 2 or 3 kids to work on the task together while other students work on skills practice.
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