21st March 2017 - Lynne’s logic – Tables!
Hi there again, and – as promised – here’s something on tables. Firstly, always expect the unexpected; if you ask your learners to do a calculation without using tables, don’t be surprised if they end up working on the floor!
Now for some serious bits:
- No, it is not true that all adults knew all their tables by heart when they were at school. They are doing what we always do, looking back with rose-tinted specs!
- 2s, 5s and 10s tables should come first. But why? It is because they are of most use. We have 2p, 5p and 10p coins. We partition our clocks into 5-minute sections, so use 5s and 10s to tell the time. Also, 2, 5 and 10 will figure prominently on the scales of graphs, but that is probably a chicken and egg situation.
- Next should be 3s. If a learner can recall 2, 3, 5 and 10 as remembered facts, and understands the commutative law (that 6 x 3 = 3 x 6), then they are well on the way to fluency.
- To access the 4s, 6s and 8s tables easily, learners need to become confident using doubling, which is using factors. If they need 7 lots of 6, they should find 7 lots of 3 and double the answer; they will use factors - 7 x 6 = 7 x 3 x 2. In the same way, they can find the 4s table by doubling the 2s, so 7 x 4 = 7 x 2 x 2. To find the 8s table, they should double the 4s. So 7 x 8 = 7 x 2 x 2 x 2. It is important you prove why this method works, as it is such a useful strategy. Use apparatus or a pictorial method – I don’t think it is enough to simply tell your learner, they will not have the confidence in the method to use it. (I usually draw an array and reflect it horizontally so the learner can see why doubling works.)
- Teach 9s using the finger trick - children love it! Hands out straight in front of you and count from the left how many 9s you require, and fold that finger down. To the left of that finger are the tens, and to the right are the units. Try to find 4 sets of 9. Count and fold down the 4th finger. On the left are 3 fingers = 30, and on the right are 6 fingers (include 2 thumbs) = 6. Total of 4 lots of 9 is 36.
- That leaves us 7s. Sorry, no pattern except for odd x 7 = odd, and even x 7 = even. An effective strategy is to split it. So 6 lots of 7 is 5 lots of 7, plus 1 lot of 7. Again, if you support using an array, the learner should develop the confidence to use this strategy, which also has a posh name – the distributive law.
So what can we do in the numeracy activity to develop these remembered facts?
- Play a game against your learner, using what I call a target board. You need a bingo card-type grid with around 20 sections, counters in two colours and either a 0-9 die, or a set of playing cards with the picture cards removed, which will give you numbers 1 – 10 randomly. In each section, you will put a multiple of the table number you are working on, and this will depend on whether you are using 0-9, or 1-10. Player one rolls the die, multiplies that by the table number being worked on and covers the number on the grid with their counter. Player two then rolls the die and covers another section on the grid with their counter. Only one counter on each section on the grid. Winner has most of their coloured counters on the grid, or play first to get three in a row.
- Positives to this game are that the learner is given the correct numbers, and will begin to anticipate what they need to roll to be able to cover an empty section – the equivalent division fact. The most common negative is that the learner will probably not want to stop playing to do the linked recording!
- As with most games, you need to play more times than once, as the learner will then begin to use problem-solving skills.
- Play ‘Concentration’. On one side, face down the calculations for that table, e.g. 7 x 3, 4 x 3. On the other side, face down the answers for those calculations. The aim is to pick one card from each side that match. Keep the pair if they match and replace face down if they do not. The person with the most pairs wins. Do not have too many cards or the learner will not be able to memorise where they are.
- The calculation cards from the Concentration game can also be used as flash cards.
Tables knowledge is very useful, but you need to appreciate that some learners do not have the same capacity to remember facts as other learners. Keep this in mind when setting Catch Up®
targets, and that is why moving on to phase 2 uses the words “almost all” at Catch Up®
Numeracy level 6.