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Grade 5 · Maths · Lessons
Two rules, one graph
📜rule A📜rule B📈graph🔗pairs
Two rules, one graph.
The big ideaMake a list from each rule. Match the lists, then plot each pair: across first, then up.

How it works

Make a list from each rule. Match the lists, then plot each pair: across first, then up.

If rule A adds 3 and rule B adds 6, B is always twice as big as A.

Terms line up by their place in the list.

Rule A: add 3• 3, 6, 9, 12Rule B: add 6• 6, 12, 18, 24
Two lists.

Example 1: Make lists

  1. Rule A starts at 0 and adds 3. Rule B starts at 0 and adds 6.
  2. A: 0, 3, 6, 9. B: 0, 6, 12, 18.
  3. Match them term by term.

Example 2: A pair

  1. The 3rd terms are 6 and 12.
  2. Plot 6 across and 12 up.
  3. Each pair is a point.

Example 3: A pattern

  1. B is always twice A.
  2. 6 is 2 × 3 and 12 is 2 × 6.
  3. The rules are linked.

Words to know

term
One number in a list or pattern.
ordered pair
Two numbers that name a point.

Watch out

Try it

  1. Rule A: add 2 from 0. Rule B: add 6 from 0. What is the 3rd pair?
  2. How many times as big is B as A in that case?
  3. Which number do you plot across first?
  4. What do you get when you plot every pair?
Answers: 1. 4 and 12 · 2. 3 · 3. the A term · 4. a line of points
For grown-upsMake a table of two rules, like pennies and nickels, and plot the pairs.
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