X. Pensiliau a Rheolyddion

Introduction
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.

License

Gwersi PCAME a Dewch i Feddwl Mathemateg (9 i 11 oed) Copyright © by Ann Longfield, David Johnson, Jean Hindshaw, Linda Harvey, Jeremy Hodgen, Michael Shayer, Mundher Adhami, Rosemary Hafeez, Matt Davidson, Sally Dubben, Lynda Maple, and Sarah Seleznyov. All Rights Reserved.

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