Patterns and Relations / Algebraic Thinking - Grade 6 Numeracy
Patterns and Relations tests how you describe change, write rules, use variables, and solve simple equations. Questions may use number patterns, input–output tables, expressions, balanced equations, and ordered pairs on a coordinate grid.
Core rules
- A pattern rule describes how to get from one term to the next, or from position number to term value.
- In an input–output table, test whether the rule is “add the same amount,” “multiply,” or a combination such as multiply then add.
- A variable is a letter or symbol that stands for an unknown or changing number.
- An expression has numbers, variables, and operations but no equals sign; an equation states that two expressions are equal.
- Keep equations balanced: whatever you do to one side, do to the other. Use inverse operations to isolate the variable.
- Substitute to check a solution: replace the variable with your answer and evaluate both sides.
- Ordered pairs (x, y) can show a relation on a coordinate grid; the first number is horizontal, the second vertical.
Worked example
Pattern: 5, 8, 11, 14, … Reasoning: The terms increase by 3 each time. For position n, start with 3n. When n = 1, 3n = 3, but the term is 5, so add 2. Rule: 3n + 2. Check: n = 2 gives 6 + 2 = 8, and n = 3 gives 9 + 2 = 11. The 20th term is 3(20) + 2 = 62.
Traps that cost marks
- Using the term value as the position number.
- Assuming “add 3” answers a question about the nth term; 20 + 3 is not the 20th term.
- Treating an expression as if it can be “solved” without an equals sign.
- Applying an inverse operation to only one side of an equation.
- Ignoring order of operations when substituting a value.
- Reversing x and y when plotting an ordered pair.