A blog about teaching and learning in a maths classroom.

Sunday, 08 February 2015 | 4 Comments

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

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

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**Simon Job** — eleventh year of teaching maths in a public high school in Western Sydney, Australia.

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