Mathematics Explained Student Workbook

First year sales have gone well for the Student Workbook that I wrote with my good friend and colleague Ralph Manning to go alongside the fourth edition of Mathematics Explained for Primary Teachers. I'm pleased about this partly because Ralph and I have been able to direct 20% of all the royalties through our church towards our support for a Christian charity for which we both are directors. This is the Dohnavur Fellowship in Tamil Nadu, South India. The Fellowship has a children's home, schools and a hospital, all on a beautiful site just to the East of the Western Ghats. Ralph has visited Dohnavur twice in the last couple of years and has been helping to develop their new English-medium teaching and learning in the primary schools.

I'm also delighted that so many primary trainee teachers seem to be using the workbook and finding it helpful. It contains a range of activities that give the reader the opportunity: (a) to reinforce the key ideas of the main text book; (b) to use and apply these ideas; and (c) to consider some aspects of teaching and learning of these ideas.

Here are examples of each of these activities.

Task 49: Checking understanding of mental strategies for multiplication and division

Do these calculations by mental strategies, using the given starting point:

(a) 23 × 19 (use 19 = 20 – 1)

(b) 41 × 23 (use 23 = 1 + 2 + 4 + 16 and doubling)

(c) 408 ÷ 24 (use 10 × 24 = 240, 5 × 24 = 120, …)

(d) 408 ÷ 24 (divide both numbers by 2 to get an equivalent ratio)

(e) 319 ÷ 11 (write 319 as 99 + …)

Task 53: Using and applying mental strategies for multiplication and division

Try to answer this question within 30 seconds of reading it! Do not write anything down.

A shop offers a TV for £480 or 24 monthly payments of £25.25. How much extra do you pay if you go for the monthly instalments?

Task 55: Learning and teaching of mental strategies for multiplication and division

(a) A class calculates that to tile a bathroom wall with 13 rows of 37 square tiles you would need 481 tiles in total. Suggest how this might be done using relationships suggested by the rectangular array of tiles.

(b) The teacher then asks how we use the previous answer to work out many tiles would be needed for 13 rows of 38 tiles? A child replies 482. Identify the error here and suggest how to use this situation to promote learning.