Number and Algebra: Patterns and relationships, Level 4
AO1: Generalise properties of multiplication and division with whole numbers. This means students will generalise, which means to establish properties that hold for all occurrences. This involves the ability to look at several examples, notice what changes (variables) and what does not, use appropriate mathematical terminology and symbols to describe the pattern, and apply the generalisation to other examples. At Level Four students should be able to describe and apply the properties of multiplication and division as these operations apply to whole numbers. These properties include commutativity, distributivity, associativity, inverse and identity. This includes the ability to express generalisations using words and symbols, e.g. 4 x 6 = 24 so 24 ÷ 6 = 4 and 24 ÷ 4 = 6 (example) leading to a x b = c so c ÷ b = a and c ÷ a = b. This is the inverse relationship of multiplication and division.
AO2: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns. This means students will describe the function rule for a linear relationship as well as recognise recursive relationships where more complex relationships are involved. For example, given the pattern of fish made with matchsticks and counters below, students should be able to represent the relationships in a table and graph and use these representations to predict the terms in the sequence:
|
|
Counters |
1 |
2 |
3 |
4 |
5 |
Matchsticks |
8 |
14 |
20 |
26 |
32 |
Level Four students should be able to:
- Give linear rules connecting the variables, e.g. "the number of matchsticks is the six times the number of counters plus two", or "take one off the number of fish, multiply that number by six then add eight".
- Extend the graph or table of a linear relationship to predict further co-ordinate pairs, recognising that constant difference (add six in the fish pattern) is associated with points that lay on a line.
- Use recursive methods to predict further members of a sequence where the relationship is non-linear, e.g. The sequence of triangular numbers:
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| +2 | +3 | +4 | +5 | ||||||||||||||||||
Recursive means finding what is added to or subtracted from one term to get the next.
Click to download a PDF of second-tier material relating to Level 4 Patterns and Relationships (282KB)
