Mathematics Developmental Continuum
Recall of Multiplication Facts: 3.0
Supporting materials
Indicator of Progress
Success depends on students having automatic recall of multiplication facts for all numbers from 0 to 10.
Earlier, students have automatic recall of simple number facts but do not recall all the multiplication facts up to 10 × 10. The challenge is filling the gaps for the more ‘unusual’ facts and developing speed and reliability.
Students can make very good use of a calculator as a support initially, but their mathematical progress will be hindered if they do not have fluent recall of multiplication facts.
Illustration 1: Detecting lack of recall
It is easy to identify when students do not have fluent recall of multiplication facts by direct questioning, but it is also evident in many other circumstances. For example, students without fluent recall of multiplication facts will find it difficult to carry out any computations that include multiplication facts (e.g. long multiplication), find factors of numbers, put fractions in lowest terms or work out areas etc.
Illustration 2
Examples of the types of tasks that would be illustrative of multiplication concepts, aligned from the Mathematics Online Interview:
- Question 32 - Multiplication tasks
Teaching Strategies
Learning mathematics involves some memorisation. There will be some drill-and-practice, but it should be on a basis of strong understanding of mathematical principles. Memorisation need not be a chore. As with other memory intensive tasks (e.g. spelling), set clear goals that are not too overwhelming, enlist the help of parents, develop students’ metacognition and make it fun with plenty of encouragement.
Activity 1: Set realistic goals provides advice on a good sequence to use, so that students are set realistic goals.
Activity 2: Stress number patterns and properties highlights multiplication patterns and properties, creates both understanding and confidence, and forms the basis for easy recall.
Activity 3: Enlist help of parents, Activity 4: Strengthen students' metacognition and Activity 5: Use games with a chance element list some of the more successful methods for overcoming memory 'hurdles'.
Activity 1: Set realistic goals
Expect students to learn their tables, but in stages. Set realistic goals so that students build competence in stages without ever being overwhelmed. Start with the easiest tables
2×, 5×, 10×,
then move onto
3×, 4×, 9×
and then
6×, 8×, 7×.
Don't forget 1× and 0×.
Make links where possible: e.g. relate 5× to reading the minute hand on a clock, 7× to days in weeks etc.
Activity 2: Stress number patterns and properties
Students need first to learn multiplication tables with understanding. This means that they can work out the answers in a variety of ways, such as:
- 4 × 6 is equal to 6 + 6 + 6 + 6 (i.e. I can add if needed, but it takes too long)
- 4 × 6 = 3 × 6 + 6 (i.e. I can work out an unknown result by building on a known near result)
- 4 × 6 = 6 × 4 (i.e. if I know one I already know the other)
- 4 × 6 = 2 × 12 (i.e. I can convert one I don’t know to one I do know)
- known characteristics, such as 4 x 6 will be an even number (so it is not 25)
NOTE: Fluency follows understanding, and is no substitute for it. If students learn multiplication tables with understanding and are aware of number patterns, then it is not a big step to attain fluency.
Using number patterns and number properties makes learning tables easier. For example, because of the commutative law, when it comes time to learn the 8× and 7× tables, the only new facts are 8 × 8 = 64, 8 × 7 = 56 and 7 × 7 = 49, because all the other facts are in previously learned tables. Teachers will have experienced that these are the three facts less likely to be known.
Examples of patterns include the sequences of digits: eg for the 9s, the ones digits are 9, 8, 7, 6, etc, whilst the tens digits are 0, 1, 2, 3, etc. The sum of the two digits is 9 (e.g. 5 × 9 = 45 and 4 + 5 = 9)
It is helpful to many students to see the patterns visually on a hundreds chart.
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This hundreds chart shows the multiples of 9 with decreasing digits in ones column.
Activity 3: Enlist help of parents
Time for individual practice at home is essential. Enlist help from parents to monitor their children’s practice and test them. Remind parents of the importance of encouragement and also the importance of feedback - students should not practise mistakes.
One piece of useful advice is to use simple flashcards, small scale, with only the facts that are being targeted. Don’t take much time on practising facts that are already known, but focus on missing skills.
Another useful strategy is to use the multiplication grid up to 10 × 10. See how quickly the student can find the facts on the grid. This reinforces correct answers.
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This multiplication chart can be used to highlight patterns in tables.
Activity 4: Strengthen students' metacognition
Pay attention to strengthening students’ metacognition. Teach students some basic strategies for memorising that can be applied to many school subjects including spelling etc, such as “Copy-cover-write-check”. Ensure that students know that if they do not frequently check their answers, they may practise mistakes.
Activity 5: Use games with a chance element
There are many classroom games to make practice of tables enjoyable (e.g. adaptations of Bingo, dominoes, card games, Multo (from Maths300) (http://www.curriculum.edu.au/maths300)), commercial computer programs). Again, make sure that there is a process for challenging wrong answers, so they are not practised.
If using competitions, include an element of chance, so that the winners are not predictable, and do not score only on speed of response. Avoid comparisons and simplistic ‘league tables’ or ‘tables races’ where the slower children are easily discouraged. Make sure children get credit when they achieve individually appropriate goals.
Challenge students to record and beat their 'personal best', rather than focusing on relative performance. Praise, and even rewards, for achievements works wonders. Encouragement is critical, particularly for those who are slower to achieve.
Accuracy is clearly far more important than speed, at any time. Do not over-emphasise speed of response and do not only play games that require speed to win. However, reasonable speed is a goal of attaining fluent response.
References
Curriculum Corporation (n.d.). Maths 300 (http://www.curriculum.edu.au/maths300) Retrieved 28th March 2006.