X. Pensiliau a Rheolyddion
Introduction |
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An activity on dealing simultaneously with two additive relations in a table. Each cell of the table is in fact the solution to the equation: 10x + 15y = cost, where x is the number of pencils, and y the number of rulers. |
By using the structure of a ready reckoner, children realise that the table is an alternative way of arriving at the total. On the second notesheet they use what they have learnt about the properties of this type of table to get from three given values of total cost to what each pencil and ruler must have cost. This contributes to the development of a foundation for later work in algebra. This activity has two episodes. Each episode consists of an introduction, paired or group work and whole class sharing. The session must finish with a whole class reflection phase, regardless of how far the class has got. |
Episode 1: |
Children map ordinary multiplication sums onto a two-way table. By using their own strategies to find an isolated missing number and then sharing these strategies, they recognise the flexibility involved in the use of the relation table, in other words, the possibility of going in any direction, including diagonally. |
Episode 2: |
Having understood the way a relation table is used, children work on two extensions. They construct the operations needed to fit all the given values, and use multiplication as shorthand. The strategies are likely to include the special value of the zero column and zero row to find intermediate values. |
Reflection |
Children recognise the specific use of a table in this lesson ¬– distinct from both a times table and a table that incorporates data under various headings. They talk about how to find missing values or operations given sufficient data. |
BEFORE YOU TEACH |
The simultaneous equations involved can be found informally by trial and improvement for positive whole numbers, but even that involves coordinating two multiplications. Solving by formal algebra is not intended. Use your own judgement on who to ask to work on this, and how much time to give them to try to explain what they have done to the rest of the class. High-achieving children may extend the activity, devising their own questions and grids for each other. This will involve deciding the minimum amount of data needed to do so. |