Division problems

Sunday, 08 February 2015 | 4 Comments

My Year 7s do not have a good grounding in division.

Divide ... and conquer !

Divide ... and conquer ! | Flickr - Photo Sharing! : taken from - Author: Laura Bell CC BY-NC-ND

As we reviewed division on Friday, they showed me various models of division, grouping, sharing, we were bopping along through problems that used multiplication facts like 48 ÷ 4 – although many students are still referring to printed times tables.

Nearly all of them are relying on Stage 2 (school years 3 and 4) skills,

use mental strategies to divide a two-digit number by a one-digit number where there is no remainder, including: using the inverse relationship of multiplication and division

NSW Syllabus for the Australian Curriculum, Mathematics, MA2-6NA

Then we hit 310 ÷ 5. Stuck. Only 4 students felt they had a strategy to solve this problem.

Stage 3 (school years 5 and 6) presents a number of strategies:

dividing the hundreds, then the tens, and then the ones
using the formal algorithm

From Stage 3, the strategy they saw would have been:

300 ÷ 5	=	60
10 ÷ 5	=	2

So, 310 ÷ 5 = 62.

From what I saw, though, many of them would not have recognised 300 ÷ 5 = 60.

Instead of a review, I moved into teaching time. The class generally seemed more comfortable with using multiplication, the times tables in particular, so we moved forward with that strategy, for now.

310 ÷ 5

Breaking up 310, into 300 + 10.
From the 5 times table, is there a multiplication fact that gives an answer similar to 300?
There's 5 × 6 = 30. This is ten times smaller than 300.
Let's, instead, multiply 5 by 60.
5 × 60 = 300.
What do we have left over? 10.
5 × 2 = 10.
From this, 5 × 62 = 310.
So, 310 ÷ 5 = 62.

Next, 336 ÷ 8,

From the 8 times table, is there a multiplication fact that gives an answer similar to 336?
What if we multiply all the answers in the 8 times table by 10?
I'm trying to have them visualise the times table as:
8 × 30 = 240
8 × 40 = 320
8 × 50 = 400
Let's use
8 × 40 = 320 that leaves 16 (because 336 − 320 = 16)
and 8 × 2 = 16
So, 336 ÷ 8 = 42.

Looks like we'll be doing lots of division in the next few weeks.

Posted in • Lesson Idea • Number | Short URL: http://mths.co/4018

Comments

Ken Ellis on 08 February 15 at 11:30 PM #

Why would you want students to learn how to divide by anything larger than the limits of their 'times tables'? And why not teach the algorithm of short division? This lends itself to estimation then and I believe develops as much understanding as what you are currently battling with.

author

Simon Job on 09 February 15 at 12:28 AM #

bq. Why would you want students to learn how to divide by anything larger than the limits of their ‘times tables’? If you mean, why am I asking them to divide 310 by 5? Because when they sit the National numeracy tests without a calculator they will need to know division beyond straight times table facts. bq. And why not teach the algorithm of short division? Oh, I will. However, at this point, I was relying on their knowledge to drive the lesson. I was trying to develop the concept of division through what they were comfortable with, multiplication. Thanks for your thoughts.

Don Clark on 09 February 15 at 08:50 PM #

I feel some of out students struggle with division because they lack skills in place value and recognising that a number is the sum of its parts. I also think best results can occur when the problem is put into context such as sharing money...

Vincent Conlan on 18 February 15 at 10:53 PM #

I concur with Don Clark - the issue is student understaning of place value - a concept largely ignored but actually one of the functional foundation stones of our number system.

Get updates…

Email newsletter Subscribe to blog

Twitter Facebook Pinterest

About

Simon Job — eleventh year of teaching maths in a public high school in Western Sydney, Australia.
MathsClass is about teaching and learning in a maths classroom. more→

Elsewhere

@simonjob
updates via @mathslinks

MathsClass