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# Multiplication tables check - How to use shikaku puzzles to help pupils develop a secure understanding of multiplication facts

Help children practise the essential multiplication facts with this online game, suggests Steve Lomax

Here’s a question for you: is 7 x 8 a seven times table question or an eight times table question?

The DfE’s multiplication tables check assessment framework states that ‘when constructing tests, the first number in the question will denote the multiplication table the question is part of. For example, 4 x 12 would be considered part of the four multiplication table.’

Following this then, when considering 7 x 8, seven is the multiplicand (group size) and eight is the multiplier – it is a ‘seven times table’ question.

This is a downside of the multiplication tables check assessing multiplication facts in such a rigid fashion.

We really want pupils and teachers to have the flexibility to explore and understand the underlying structures represented by 7 x 8 – for example, ‘seven multiplied by eight’, ‘seven eight times’ and also ‘seven groups of eight’  – as well as understanding that 7 x 8 can be applied to represent contextual situations, such as the fact that a rectangle with dimensions of seven units and eight units has an area of 56 square units.

Shikaku is a wonderful mathematical puzzle which brings together factor/factor/product relationships, the commutative nature of multiplication and relating area to arrays and multiplication. Shikaku is played on a rectangular grid, with some of the squares containing a number. Pupils must solve the puzzle by dividing the grid into rectangles containing only one number. The number must represent the area of the rectangle. Try a tutorial and play online here.

While the 25 questions in the multiplication tables check assess only multiplication facts, solving a shikaku puzzle supports all pupils to develop a secure understanding of multiplication and division facts that are essential for future success in maths.

The DfE’s multiplication tables check notes state that the test ‘should not be detrimental to pupils’ self-esteem or confidence.’ Activities like shikaku help to put a stop to a ‘can do/can’t do’ attitude to mathematics that has been a problem in the UK for decades, as well as empowering pupils to say goodbye to learning 144 isolated facts and hello to learning just 30 factor/factor/product relationships.

In fact, once children know their two, five and ten times tables, there are only 21 more factor/factor/product relationships to learn up to 10 x 10.

These 21 relationships are essential knowledge for all pupils and usually the ones that are referred to when a child (or adult!) says that they don’t know their times tables.

They also play a significant role in the multiplication tables check, with the 25 questions having an emphasis on the six, seven, eight, nine and 12 multiplication tables, because these have been determined to be ‘the most difficult’.

This ‘can do/can’t do’ climate in UK mathematics has been cultivated by the dominance of electronic times tables tests that rank pupils’ speeds on a leaderboard.

If we are serious about ensuring that pupils can recall and use their times tables fluently, then now is the perfect time to stop using resources and strategies that foster a climate of being scared of ‘getting it wrong’.

It’s time to start embracing a culture of ‘the answer is only the beginning’, and teaching for relational understanding to support all pupils to have a secure, sustainable and flexible understanding of mathematical ideas.

Steve Lomax is the strategic mathematics lead of the Balcarras Teaching School, a nationally accredited NCETM professional development lead and teaching for mastery lead. He is the co-founder of Kangaroomaths and CanDoMaths and tweets at @MaxTheMaths. Download a poster displaying the 21 essential factor/factor/product relationships here.

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