Continue number patterns

What you will learn

• Continue number patterns

Models used: number sentences, stories, tables.

Before you start

• Compare and order numbers to 1000

Find the repeated change

Look at 20, 25, 30. What changes each time?

1. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   Look at 20, 25, 30. What changes each time?

   Many larger answers are possible. The repeated change tells us which one follows this pattern.

2. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   20 to 25 is a jump of 5. The next jump is also 5.

3. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   Repeat the same jump. The next number is 35.

   30 + 5 = 35

Worked example: A new example, together

Continue the sequence: 143, 153, 163, 173, …

1. Equal changes. Read each value with the heading above its column.

   Compare each neighbouring pair. Repeat the verified change once more.

   A constant-step pattern repeats the same change between neighbours.

   Equal changes

   Position	Value
   1	143
   2	153
   3	163
   4	173

2. Equal changes. Read each value with the heading above its column.

   Compare neighbours: 153 − 143 = 10.

   Equal changes

   Position	Value
   1	143
   2	153
   3	163
   4	173

   Continue the sequence: 143, 153, 163, 173, …

   183

3. Equal changes. Read each value with the heading above its column.

   Compare neighbours: 153 − 143 = 10.

   Equal changes

   Position	Value
   1	143
   2	153
   3	163
   4	173

4. Equal changes. Read each value with the heading above its column.

   Check the same change at the next pairs.

   Equal changes

   Position	Value
   1	143
   2	153
   3	163
   4	173

5. Equal changes. Read each value with the heading above its column.

   173 + 10 = 183.

   Equal changes

   Position	Value
   1	143
   2	153
   3	163
   4	173

6. Equal changes. Read each value with the heading above its column.

   Check the result against the question we started with.

   183 − 173 = 10.

   We found 183. A constant-step pattern repeats the same change between neighbours.

   Equal changes

   Position	Value
   1	143
   2	153
   3	163
   4	173

Common mistakes to discuss

• Testing one gap only. A rule must fit every neighbouring pair. 2, 4, 8 could add 2 then 4, or double; check a third term before deciding.

Check your understanding

• Continue number patterns
• explain a pattern using a repeated change
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.