Numeracy

Maths with Mr. Bigger

Part-Part Whole

A useful strategy for students is being able to manipulate numbers into smaller parts and understanding the relationship. This can happen from as early as Foundation and these skills can be useful for solving problems.

With part whole models, it is important to remember that the parts combine to make the whole. The parts and the whole should not be combined to create a new whole. Rather, the point of the part whole model is to look at what the other missing part would be when combined with the other part that makes the whole. To write this model as a number sentence it would be 2 + __ = 5 or 5 = 2 + __.

The below model is a great tool to use with younger students for Part-Part Whole

Multiplication

If a student is wanting to calculate 7X50, a useful strategy would be to apply their knowledge of the distributive property. 

They may break apart 7 and think of 5 x 50 and 2 x 50. Students who are fluent with the Part-Part Whole relationships for 7, can fluently recognise this as a logical step. So while the distributive property is something we may be teaching in Year 5 or 6, if our students are missing the critical fluency with PPW, considerable cognitive load with be taken up before they even get to thinking deeply about the distributive property. 

Try giving older students problems like above to test their knowledge of Part-Part Whole.