Compare, order and continue patterns to 10000

What you will learn

• Compare, order and continue patterns to 10000

Models used: number sentences, stories, tables.

Before you start

• Read and write numbers to 10000

Look at the biggest groups first

Compare 32 and 28. Each long row represents a group of ten.

1. The number at the top of each column is the value of one counter in that column.

   Compare 32 and 28. Each long row represents a group of ten.

   A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.

2. The number at the top of each column is the value of one counter in that column.

   32 has three tens. 28 has only two tens. Those tens decide the comparison.

   A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.

3. Both bars use the same scale. Compare their lengths and read the names beside them.

   Even though 8 is more than 2, 28 is less than 32. Compare the tens before the ones.

   28 < 32

   3232

   2828

   Difference: 4

Worked example: A new example, together

Continue the sequence: 8084, 8094, 8104, 8114, …

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

   Line up the place-value columns. Find the first difference from the left.

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

   Equal changes

   Position	Value
   1	8084
   2	8094
   3	8104
   4	8114

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

   Compare neighbours: 8094 − 8084 = 10.

   Equal changes

   Position	Value
   1	8084
   2	8094
   3	8104
   4	8114

   Continue the sequence: 8084, 8094, 8104, 8114, …

   8124

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

   Check the same change at the next pairs.

   Equal changes

   Position	Value
   1	8084
   2	8094
   3	8104
   4	8114

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

   8114 + 10 = 8124.

   Equal changes

   Position	Value
   1	8084
   2	8094
   3	8104
   4	8114

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

   Check the result against the question we started with.

   8124 − 8114 = 10.

   We found 8124. A constant-step pattern repeats the same change between neighbours.

   Equal changes

   Position	Value
   1	8084
   2	8094
   3	8104
   4	8114

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

• Compare, order and continue patterns to 10000
• justify a comparison with place value
• 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.