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# What Makes A Good Resource - What does it mean to know your tables

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Created on 08 September 2009 by ncetm_administrator
Updated on 03 September 2010 by ncetm_administrator

# What does it mean to know your tables

Resource description:
I used a multiplication grid as shown here:

This one is taken from the Collins frameworking for year 7, but it is fairly straightforward to create your own. The A4 sheet has a blank version of the table underneath.

Teacher comment:
The perennial complaint of maths teachers everywhere is that students do not know their tables and this holds back their understanding of more advanced maths ideas. In my department, one teacher has focussed exclusively on learning tables. He has given out laminated A4 sheets that are double sided and covered with tables. The students choose a table, write it out and are then tested on it. If they get it right they get a reward, wrong and they do it again.

This got me thinking about rote learning. Is it the most effective method? Is there a better way to get students practising and learning their tables? I started to consider whether connections might be a better way to do this. If a student can see the relationship between the 2, 4 and 8 times table will that enable them to remember multiplication ‘facts’?

What I did:
I played ‘Mission Impossible’ (available at www.goear.com as a live, free stream) and told them they had the length of the song to fill the grid in. Some students got excited and started dancing in their seats but most settled quickly to trying to complete the grid.

Most students started filling in from the first column and worked very methodically through the grid and so didn’t get very far. No-one succeeded in filling the whole grid in. I then arranged the students in pairs to discuss methods for which columns can be filled in quickly. I listened to the conversations and prompted where needed. Most groups came up with 1 and 10 being very easy to fill in and some added 2 and 5.

We then had a whole class discussion about why these were easy and this led naturally into discussions of strategies for completing the others. Some students pointed out that the music had distracted them or that it had made them panic and rush.

When this discussion was running out of steam, I tried some prompting questions such as:
“If I know the 2 times table, what other one can I work out?”
“If I know the 3 times table what other one can I work out?”

“The 4’s – you just double it”
“You can get 8 if you double that!”
“I can do my sixes now!”
“I can do nines on my hands.”
“For tens you just add a zero.”
“Half of tens gives you fives.”

This led to the students being able to work out all the tables (except possibly seven!).

I then directed the students to the blank copy of the grid and asked them to choose where to put the numbers: they could make the task a normal 10x10 table if they wished or something more interesting.  I played a different song (this time it was a slower paced longer song: Europe’s “The Final Countdown as we only had 5 minutes left!) and they had to fill in the sheet again.

Most students got much further second time round and left the room feeling much more positive about their times table.

Reflection:
There are many key elements to this lesson. Firstly the use of music is rare in my classroom, and so the lesson is immediately more interesting and engaging. Secondly the discussions about strategies all came from the students: I may have prompted, but at no point did I tell them what they should be doing. This led to methods being named after students who had suggested them, which helps to keep it fresh and relevant in the students eyes. I was careful with “add a zero” to work out tens as I didn’t want to create problems later, but equally I wanted the focus to be on methods that would help them learn their tables. In reflection I should have explored this in more detail at the time it came up. Thirdly, the students could choose how to fill in the bottom grid and they would naturally self differentiate.

I wasn’t expecting the conversation about the music causing panic and mistakes but this proved to be a key element of the lesson. Interestingly, no-one commented that the second piece of music was longer, although this was obviously a key element of the students completing more of the grid.

Obviously as a class we now revisit the grids regularly to keep them practising. My original goal was to have a more interesting way of practising and learning tables than ‘by rote’ and this definitely succeeds by that criteria.

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18 November 2009 18:18
Once they are getting more confident I like this game on the bbc website http://www.bbc.co.uk/skillswise/numbers/wholenumbers/multiplication/timestables/game.shtml
I enourage them to play game 2 with ALL the tables. They then compete against themself & aim to improve - ie filling in more of the grid before they lose all their lives or completing it more quickly. I often use this as a starter when we have the computers.

I like the game because, as you point out, learning the times tables is about far more than "knowing" what 4x7 is. To grasp later ideas they need to see relationships, find factors etc.

The other point to make re the grid - if they can do it in 3 mins encourage them to do this at the start of non-calculator tests as then they can concentrate on the questions and not need to worry about the multiplication. Especially important for any dyslexic students or others who get lost half way through a question because they forget why they were workig out 4x7...