# What do they know?

### Differentiation and Place Value for Years 5 – 7

Recently a teacher showed me a page from her booklet on getting to know the students’ understanding of place value. It looked like this:

She was disappointed with the outcomes:

• wide range of maths ability – more than half could not read a 6-digit number while some even struggled with numbers in the 100s she discovered,
• although the questions allowed some student choice it was not enough to diﬀerentiate the task for all students,
• two students were quick to announce the task as way too easy and boring.

We all know the urgency to find out what our students do know and can do but this page did not allow the students to demonstrate anything but the mundane, confined information asked for.

“What to do?” was the question.

Well as far as I am concerned a problematized situation is never far away and usually elicits a lot of useful information.

Together, she and I created a problem about my next-door neighbour’s son. Yes I know he is now in his 20s, but he is still my most used character and he still thinks he’s a maths genius. So, here’s the problem.

Kai’s homework flipped him out last. He thinks it would flip you out even worse. I said to Kai:

”Oh no, my class is up for a challenge and won’t flip out.”

He doesn’t believe me, but I know you can rise to a challenge, so here it is.

#### What diﬀerent ways can you make one or more of these numbers without using a 7.

This is your chance to show oﬀ your place value knowledge. Use any of the 4 operators or fractions or brackets or decimals. Surprise me please!

Before the students begin put up the following sequence and ask students why they think you would not find that very acceptable or creative.

Be prepared to initiate an acceptable, creative list for the number 43 without using a 4.

Explain that you are hoping to surprise Kai with their brilliance.

Observe which numbers students try as well as the strategies used, and you will get a more realistic view of your class than might otherwise be the case. And by the way, if anyone doesn’t like your choice of numbers let them choose their own. Also … please share with us.

Problematized situations new to you? Go check out our online course!

Cheers