The Efficient Learning of Multiplication Tables

1. The Efficient Learning of Multiplication Tables Elizabeth Anderson Glenavon School

2. Principles • The Twos: If child knows doubles from addition the two times tables are at hand • The Fives: May know from telling the minutes on a clock for time May know multiply even number by 5 and is half the even number with a 0 added Or may know a x 5 = ½ (a x 10)

3. The nines – a x 9 where a is a single digit the answer always adds up to 9. • The first digit in the answer is a – 1 • Display fingers with a finger folded – on left of finger tens, on right of finger ones.

4. Skip counting • Skip counting in 2’s, 3’s, 4’s and 5’s helps with those tables

5. Easy Parts • If chn know easier parts can breakdown more difficult parts, eg 6 x 6 = 36 may be used to work out 8 x 6 by noting • 8 x 6 = 2 x 6 + 6 x 6 = 12 + 36 = 48

6. Twice as much • Finding facts that are 2ce as much as a known fact eg 2 x 8 = 16 • leads to 4 x 8 = twice 16 = 32

7. The Ones • Chn learn y x 1 = y for any y

8. The noughts • Chn learn that y x 0 = 0 for any y

9. Cummutative principle • Chn learn that a x b = b x a • This shows reflective symmetry along the diagonal axis

10. Method • Chn sit a pre-test of all tables 0x – 9x – 100 Multiplication facts • Make a chart of known facts expected to learn and then coloured when covered and learnt to show rapid progress • Work in pairs to share solution methods and explain their ideas • Ideas reported back to class • At end of lesson child wrote in journal to share learning with a friend

11. Following each lesson the squares learnt were coloured in to show learning • Chn learn 64 out of 100 facts by end of 0x, 1x, 2x, and 5x covered in 1 or 2 lessons depending on capability of class • Focus on remaining ‘difficult’ facts

12. Lesson One • Focus Question: The zero times table – is there anything special about the zero times table. How would you explain it to a friend. • Same for 1 and 2 times tables • Focus question: What can you find out about the 5 times table? • Next test on 64 facts, 0, 1, 2 and 5 times

13. Lesson Two • Elicit reactions to test on 64 facts • Focus question: 24 is our special number. Make up number sentences that give an answer of 24. • This was repeated for 48 and 12 • Add to chart; 6x4, 4x6, 8x3,3x8, plus 6x8, 8x6 and 3x4, 4x3 • Chn put these facts in journal and learn overnight

14. Lesson Three • Focus Task: Think about 9 and represent it in a number of ways. Can you think of ways to explain how you would describe 9 to others?

15. Lesson Four • Focus Task: Explore the answers to the 9 times table to find strategies to help you remember this table • Discuss hand strategy

16. Lesson Five • Complete 3x and 4x on chart. • Discuss 3x – skip counting in 3’s • Discuss patterns found in 4x – twice the 2x tables

17. Lesson Six • Focus Question: How would a person who did not know 6x7 and 7x6 work it out? • Eg. If you know your 3 times tables you can work it out. 3x7 =21 so 6x7 = 21+21=42

18. Lesson Seven • Focus Task: Work out 7x8 – this being the fact people find the hardest to remember. Do not use repeated addition. • Eg.7x7 = 49 + 7 = 56

19. Post test • Test and chart on 100 multiplication facts • Compare results!!!

20. Borrowed from Vivienne Morrison • St Margarets College • 2002