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The times tables

There is a danger that if students learn times tables by rote they may not develop an understanding of the connections and patterns which are evident
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PAULA KELLY: We can divide numbers up into different families, depending on their properties. This week, we’re interested in one particular group, the positive integers or whole numbers. We can divide these numbers into even more specific groups. One simple way to do this is to sort them into even numbers and odd numbers. Numbers are in the evens group if we can divide them equally in two with no remainder. A number is odd if we have a remainder when we divide it by 2. Using these definitions, do you think 0 is an even, odd, or neither? Post your comments below.
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Even numbers are usually the first example of a certain type of number family. as they can all be divided by 2, all even numbers are in the 2 times table. This family of numbers is also known as the multiples of 2. The 2 times table starts with the number 2. And each subsequent term of the sequence is 2 more than the previous term. So we have 2, 4, 6, 8, and so on. Any number not in the 2 times table is not a multiple of 2. So 14 is a multiple of 2, but 15 is not. Likewise, the 3 times table starts with the number 3. Each subsequent term is three more than the last term.
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So we have 3, 6, 9, 12, and so on.
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So the 12 times table starts with the number 12. And each term goes up by 12 each time. We have 12, 24, 36, 48. It’s important for students to realise that times tables go on forever. Some students only ever see the 3 times table go up to 10 times 3 to get 30 or 12 times 3 to get 36 and think this is the complete times table. In primary school, great importance is placed upon students to learn their times tables. Knowing your times tables is very important. But hopefully, students are encouraged to consider the patterns within times tables and the mathematical structure of the times tables, not just learn them by rote or as a rhyme without any underlying understanding.
In this video, Paula discusses the link between even numbers and the two times table.
From an early age, students are required to learn their times tables. By the time students start secondary school, around age 11, they are expected to have instant recall of times tables. In England, students are expected to be fluent in times tables up to, and including the twelve times tables.
There is a danger that if students learn times tables by rote they may not develop an understanding of the connections and patterns which are evident in the times tables. It is a bit like learning the words to a song so that you can sing it but never consider what the words mean. I have experienced students being fluent in their eight times table, in that they can ‘chant’ the times table up to ten times eight is eighty, but thought the times table stopped at this point and did not realise the eight times table continues forever.
Students have also struggled to use their knowledge of the times tables, for example, to explain how that knowing \(7 \times 8\) or \(10 \times 8\) and \(4 \times 8\) can be used to calculate \(14 \times 8\). Being fluent in the eight times table is about more than just knowing the ‘words to the song’.

Discuss

Are the following numbers odd, even or neither? Don’t worry if you’re not sure, have a go and importantly, justify your answer:
a) 0
b) 1.6
c) 2.3

Weekly problems

Now complete questions 1 and 2 from this week’s worksheet.

Teaching resources

  • Multiplication pack one contains sixteen work cards with a wide variety of activities covering simple times tables including the two, three, five, ten, four, nine, eleven and the six times tables.
These times tables games involve children working in pairs using ‘target boards’ to practise multiplication facts.
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Maths Subject Knowledge: Understanding Numbers

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