G. Darlunio Rhifau
| Introduction |
|---|
| An activity to explore intuitive mental operations on numbers, linking them to use of the number line and to pencil and paper methods. The aim is for children to reconstruct the structure of the number system for themselves, and recognise the different meanings of operations such as subtraction and multiplication. |
| This activity has two episodes but each of these could be taught as two lessons (see the lesson abstract – addition and subtraction first, then multiplication and division). Leave time for reflection. |
| Episode 1: Mental, pictorial and on-paper addition and subtraction |
| The common mental methods in adding a pair of simple two-digit numbers are first listed on the board then demonstrated by children, using the vertical number line. These methods are then compared with the standard pencil and paper methods. The focus of the activity is discussion of the common features of mental, visual and formal written methods used in number operations. Calculations are ‘broken down’ to allow children to deal with simpler numbers that are easier to combine. Children then compare subtraction methods mentally and on the vertical number line, noting that subtraction means a difference between two numbers as well as ‘taking away’. Negative numbers can be discussed and linked to practical examples. |
| Episode 2: Multiplying and dividing numbers on the number line |
| Use a number line to show mental methods of multiplication of two-digit numbers by a single digit one, in different ways, focusing on the need for a ‘counter’ for how many times the number is added. The mental and visual methods are then compared to the pencil and paper mode, and the connections clarified by children. |
| Reflection |
| Children should look back and realise that 10s and 5s are the commonly used ‘easy numbers’ that will help them with addition and subtraction. Compare advantages, disadvantages, and preferences for each method of addition and subtraction (and multiplication if you reach Episode 2). |
| BEFORE YOU TEACH |
| Remember that this lesson is not for practising methods. It is an opportunity for children to elaborateon their informal strategies, making connections, and contrasting approaches. The teacher must judge by the level of interest and ideas generated when to move on and when to ‘linger’ and explore. |