Multiplication Exploded - Easy Peasy
When I was at school multiplication was based multiplying pairs of numbers, putting the results in columns and adding those columns to get a right answer. At no stage did I question the value of the numbers. However, with Multiplication Exploded the concept of place value can be explored from the simplest multiplication question involving single digits to those using three digits multiplied by three digits. The program enables the user to explore multiplication using the 'array or the ‘standard written’ methods.
The program is ideal for use in the interactive classroom, a suite of computers or a single laptop. For whole class teaching the program lends itself superbly to a range of different numeracy skills based around previously learnt concepts and as a stand-alone resource to reinforce and extend ideas taught in the main lesson. A great advantage is that children can experiment with different ways of tacking the same question and discussing which is the most efficient and effective.
The introductory page is straightforward and allows easy access into the relevant program. Initially, the children need to be shown how enter a particular question but, with practice, numbers can be entered without difficulty and the children have the chance to offer estimations before trying a particular method.
Initially, I used the program with the most able mathematicians; children who had experience of different methods for solving multiplication questions. It was a valuable learning curve to watch as they discovered ways to apply principles learnt for written calculations whilst using a computer program (a process to which they quickly adapted).
Initially, the children could use single digits to work with doubling and halving before using the strategy of breaking numbers down to their simplest form, using a novel idea of a hammer in the array method. Then, using a hand icon as their guide they could reconstruct the starting question in any way they chose.
As a simple example, 6 x 8 can be broken down to (2x2x2x2x3), and by moving the numbers around, which is one of many great assets of the program, the children can double 3 then double the answer three times more or they can double four times then multiply by three etc. The children were absorbed in the different ways of reconstructing such a simple question and a competitive element soon developed.
Using the hammer tool within the array application children quickly and easily broke down larger multiplication questions into more manageable parts. Again, they were delighted with the numerous ways of regrouping the numbers.
The arrays of spherical objects (dot icon) helped less able children build up their knowledge of tables by dragging the mouse across the array to select multiples. This visual representation helped them to understand the concept of multiplication as equal addition and they worked with the most basic facts through to 10 x 10. The array option enabled more able children to visualise larger groups of numbers.
The array method follows the example set out in the Numeracy Strategy and as children develop their understanding answers can be entered using the standard pencil and paper procedure. A reward of a green tick is given to correct answers.
The nature of the program allows the children to bring their answers down from the grid in any order. Initially, I encouraged children to try different orders for adding answers. They enjoyed experimenting with different orders for finding totals. It was interesting to watch how the implementation of the Numeracy Strategy has made many children more confident with place value for addition, although the less able had to be directed towards the most obvious pattern for bringing answers down.
By unlocking a key icon children can see clearly each individual column for addition. However, the program requires children to store mentally any numbers needing to be carried into the next column. Certainly the less confident children made errors in their final addition because of the need to recall numbers to be carried.
The program clearly demonstrates that multiplication can be solved in different ways. This gives children confidence to be independent in their approach to multiplication and encourages them to choose a method they feel comfortable with.
The second way to use the program is through the standard written method, which is more suited to the more competent mathematicians and those children whose knowledge of known multiplication facts is sound to 10 x 10. Partitioning numbers is the main feature of this method. Children can experiment with partitioning the numbers from a question in any way they choose and the program allows numbers to be moved until users are happy with the order. The calculation is not affected and does not hinder the children’s own working process. However, I found that encouraging children to order the numbers logically was an interesting teaching point and it helped develop an understanding there is an order that makes the final addition easier.
At first tt was necessary to remind children about multiples of tens and hundreds. This allows them to work out more complex questions whilst retaining a true understanding of the numbers being multiplied. The program enhances this knowledge so the introductory teacher input for the more able children is minimal, although it needs to be slightly longer for children who struggle to understand multiples.
The whole program lends itself superbly to interactive whiteboard teaching and children who could see their answers emblazoned on the board felt a real sense of pride. This subsequently inspired other children to match their answers, as well as try to find more complex solutions.
Overall, the program tackles the difficult topic of multiplication in a clear, informative and fun way, something I believe is essential in Mathematics. I know from comments made by the children that the program went down really well and was very motivational. My laptop is now in constant demand from children for checking their own written calculations using the program.
Marc Bennett
Deputy Headteacher, Overton Church of England Primary School, Basingstoke
Title: Multiplication Exploded
Publisher: Easy Peasy
Contact: John McCormack
Official orders to: Easy Peasy, 1 Winder Gate, Frizington, Cumbria, CA26 3QS
Telephone: 01946 813065
Single User (CD has to be in the drive): £39.50 (plus VAT)
Site Licence plus CD (CD not required in drive, unlimited use on all computers and networks, no annual fee): £120 (Ex. Vat)
PC only.
The program is registered for Curriculum Online.
<< Email john@easypeasy.co.uk
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