How did you learn your times tables? Many adults today, recall having learnt all of them ‘off by heart’, through rote memorization, but there is a strong argument to support that a more ‘meaningful’ approach will have greater long-term benefits.
Rote learning is simply a way for the brain to store data short-term and does not require a deep understanding of a concept. In order to commit all 144 times tables to long-term memory, they must be accessed, repeated, and tested frequently.
What we have learnt over the years, is that learning in meaningful ways, is far more effective.
At NumberWorks’nWords, we know that true mastery of a concept (the times tables in this instance), requires a higher order thinking, which in turn leads to the formation of new neural pathways. The brain’s ability to make connections in this way is referred to as neuroplasticity.
A highly effective approach to the teaching of mathematics is called Cognitive Guided Instruction (CGI). Like Bloom’s Taxomony (Benjamin Bloom 1956), it focuses on ‘conceptual understanding’ over ‘process’ and suggests learning without understanding, limits a child’s ability to problem solve and apply what they have learnt to new situations.
So let’s return to the task of learning the Times Tables and explain how, at NumberWorks’nWords, we do this in a more meaningful way.
Our program incorporates a range of strategies when learning the times tables, so children are afforded the opportunities to make connections in their understanding of number and number properties, patterns, place value, operations and more.
Our comprehensive visual and interactive resources, used in conjunction with concrete materials, written representations and most importantly, explicit teaching, empower our students to make connections in real and relevant ways.
When something ’clicks’ for a child, it is like it is locked in. Suddenly, the steps make sense and the new piece of information is literally attached or connected to something permanent in the brain.
Recalling and using this information becomes fluid and purposeful, and enables the child to understand the concept, rather than simply following a process that has no meaning.
When teaching the Times Tables, we always start with the easiest patterns (x1, x2, x10, x5) then move onto the progressively more difficult (x3, x4, x9, x11, x6, x7, x8, x12). The accepted standard of fluid recall is to be able to solve each table in 3 seconds or less.
Below are some strategies that you may find helpful, as your child masters each of the times tables.
1X
The number always stays the same. Explaining this as ‘one group of’ something, helps the child to see that there is a conservation of number and that the ‘one group’ does not change.
2X
Some children may not initially see that the 2 times table is the same as the addition doubles strategy. Once this connection is made, the 2x process is often understood in a different perspective and it alters the way the brain arranges the numbers.
Using visualisation also helps, eg 2×3 or 2 groups of 3 is like an insect’s legs (3 on each side), 2×4 is a spider’s legs, 2×6 is a carton of 12 eggs in 2 rows.
3X
Children learn to skip count in 3s and also learn an addition strategy called ‘count on’ which means you put the large number in your head and count on up to 3 steps forward, eg if you know 3×3 =9, then 4×3= 9 count on 3 more, hence 9 (big number in your head) count on 10…11…12 (the answer).
4X
Once a child masters the 2X tables, then the 4X is simply double the 2X. eg. 2×7=14, so 4×7= double 14 which is 28. This is particularly easy when there is no need to bridge the tens.
If the child does need to bridge the tens, the connection to place value and partitioning become important eg 2×8 can be considered as 5+3+5+3 which the child could then put the ‘friendly’ numbers together and mentally arrange them as 5+5+3+3 = 10+6.
5X
Children learn to skip count in 5s orally because they can quickly learn the pattern of the words. Reciting the pattern is actually a quick and efficient way to get an answer to a 5X table, so this is an easy connection for children to make.
X6, X7, and X8
I group these together because it allows children to see that they are not as difficult as they may have first thought. Once the child masters the earlier tables (x1, x2, x3, x4, x5, x9, x10, x11), it means they can turn them all around to solve any table that includes a 6, a 7 or an 8.
Making this connection straight away, means children will more readily apply the learnt strategy, now in a meaningful way to the more ‘difficult’ tables.
I often explain to students who are learning their tables with us, that there is a useful strategy, or pattern to almost all of them.
However, there is a small list of specific tables that I recommend they do commit to memory. When children realise that the list is so small, it makes the overwhelming task of learning (memorising) ‘all’ of the tables, seem very easy indeed.
6×6=36
6×7=42
6×8=48
7×7=49
7×8=56
8×8=64
9X
Not everyone is aware of the many strategies and patterns that exist in the 9 time tables. Firstly, the 2 digit answers in every instance (1-10) always appear as the same combinations of digits ie 2 and 7 go together to make 3×9=27 as well as 8×9=72, 3and 6 go together as 36 and 63 etc. The added clue is that the 2 digit combinations actually add to make 9, so this helps the child to remember which ones go together.
When presented with a 9 times table, eg 9×8 the child can think that 10 x 8 would be 80, so 9×8 will start with a 7 and the number that goes together with 7 is 2. The answer is 72.
Then of course there is always the ‘using the fingers’ strategy. By counting off the 10 fingers 1 to 10, simply curl over the finger represented in the 9x fact. (See image below)
10X
It is important for children to understand why the zero goes on the end of any number that is being multiplied by 10. The pattern of simply ‘adding’ a zero is easy, but again the risk is that children will simply follow a process without really attaching any meaning to it. Using language like ‘adding’ can actually confuse many children with the process of addition and of course that is not what is happening here.
When children make the connection to the changing place value of the digits, they will realise that the original number is now 10 times bigger! When learning to multiply by ten, children need opportunities to manipulate and arrange concrete materials and to see the process visually, before they can understand what is happening.
The learning of concepts such as fractions, decimals will be so much easier once children have this fundamental understanding of the 10 times tables.
11X
The obvious pattern in the repeated digit makes the 11s easy to recall, but again, it is important to develop this understanding through cognitive guided instruction (so the child knows the answer is the combination of the already learnt 10x fact plus the 1x fact)
12X
Like the 11s, the 12 times tables are the combination of the already learnt 10x fact and 2x fact.
At NumberWorks’nWords we know that mastery of the Times Tables is a fundamental core skill. We focus on core skills and the teaching of meaningful strategies, because it is proven that the more connections children make as they learn each table, the more readily they will be able to apply their understanding to each new mathematical problem in the future.
