E. Sgaffaldiau

Introduction
An activity to explore relationships in a table of numbers. Children learn that the relationship between columns is a more useful tool than looking down the columns. A second, visual, context is also used to demonstrate (implicitly) the use of ratio and proportion, again through organising numbers in columns.
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: Relationships within and between columns of numbers
Children give descriptions of how sets of numbers are generated in columns. They then look across the columns, linking elements in the same row. Children work together to identify the multiplicative relationships between A and B (double and half), A and C (three times, or A + B), A and D, B and C and B and D. They work on inverse relationships and use the letters as generalised number. Children use this notation while moving between columns independently of the order of the numbers within the column. They are challenged with the ‘one-and-a-half’ relationship, where they have to first halve B then add it to B.
Episode 2:
Children look at a visual, real life, context for similar number relationships. Theyare asked to find the correct numbers for the cells in a table. They have to interpret the questions, the diagram, the numbers and the table, in relation to one another. Children are challenged to find the fractional relationship (4 to 5, 4/5 or one-and-a-quarter) in the table with the aid of a diagram, using knowledge gained from earlier discussion of the ‘one-and-a-half’ relationship.
Reflection
Children look back on what they have done in the activity, noting the similarities in the mathematics of the two episodes.
BEFORE YOU TEACH
You need to have a pre-drawn large copy of both the table of figures and the scaffolding diagram. Plan the use of the flipchart so that the first table – the four columns A, B, C, and D – remains visible when the second table is made from the scaffolding diagram.

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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