Children should know all times tables by the end of year 4, but there are children that slip through the net, taking much longer to learn them. There are also children that may seem to have learned times tables by the end of year 4, but forget and have to work into upper key stage 2 to relearn.
This post describes a plan to get children who are in years 3 and 4 and who are not on track to understand times tables by the end of year 4. The plan is also for children in years 5 and 6 who still do not know their timetables.
A fact a day for a term
The basic structure of the plan is to work on one fact per day. Working with commutative facts such as 3 x 4 and 4 x 3 together, and taking into account that familiarity with tasks should accelerate the work the longer it goes, a term is a sensible time frame to work in. This will be systematic, working from x10 to x5, then x2, x4 and x8, then x3, x6 and x9, finishing with x7, x11 and x12. This is to enable links to be made between times tables. Within each times table, we’ll work in increasing order of times tables (i.e., 10 x 1, 10 x 2, 10 x 3 etc.). Of course, different children will have different starting points, not all starting with 10 x 1. As days pass, children will consolidate their understanding of a timetable through repetition, multiple representations, counting and low stakes testing.
Multiple representations
For times tables to stick and to be useful in other areas of maths, they need to be rooted in secure understanding. To allow this to happen, each fact will be represented in different ways, in the first instance by the teacher but increasingly by the child. The first representation is Numicon, using the example of 4 x 5:
Using this we can explain that 4 x 5 means 5 lots of 4 and that by counting in multiples, we can find out that 4 x 5 = 20. Children will have done this for 4 x 1, 4 x 2, 4 x 3 and 4 x 4 in the preceding days so they should be able to count in 4s. However, they may need to do some skip counting, where they whisper or say in their head each number except for the last on each Numicon piece (1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12…). The Numicon also helps to lead into other representations:
Repeated addition: 4 + 4 + 4 + 4 + 4 = 20
Bar model:
Number line:
All the while, the child is practising counting in 4s, and thinking about how 4 x 5 = 20.
Commutativity
One more representation can lead the child into working on the related commutative fact. An array gives a little further practice seeing how 4 x 5 =20:
Rotating the array shows how 5 x 4 has the same product:
This can lead into counting in 5s to get to 20 and showing that 5 + 5 + 5 + 5 = 20. Then, repeating the representations of Numicon, a bar model and a number line will help to internalise the commutative fact.
Low stakes testing
Having worked on this new fact (and its commutative relative), the child can then work on remembering facts that have been previously worked on in days gone by. Practising recalling times tables is of course a great way of ensuring that they come to mind immediately when needed. Quick, effortless recall means that little cognitive effort is required to summon the knowledge, thereby keeping as much working memory as possible freed up to solve a problem that needs the timestable fact in the first place.
There are two ways of working on quick recall of times tables. The first is if the child has a reliably secure understanding of multiplication. In this case, simple testing such as asking ‘What is 3 x 5?’ or the use of individual flashcards will be fine. However, if a child is still not quite there with conceptual understanding, testing by using objects or images can help to get them to think mathematically instead of guessing. The teacher shows any of the pictorial representations already described to prompt thinking about the number of groups, the size of each group and ultimately quick recall of the whole.
This is a re-blog post originally posted by Nick Hart and published with kind permission.
The original post can be found here.
Featured Image: Tiger Pixel on Flickr via (CC BY-NC-ND 2.0)
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