Represent and compare numbers to 100000

What you will learn

• Represent and compare numbers to 100000

Models used: number sentences, stories, tables.

Before you start

• Compare, order and continue patterns 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.

   One extra large unit can outweigh several smaller units. Equal large places make us look at the next place.

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

Choose the correct relation: 49251 □ 69567.

1. Compare largest place first. Read each value with the heading above its column.

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

   Comparing the largest differing place decides the order.

   Compare largest place first

   First number	Second number
   49251	69567

2. Compare largest place first. Read each value with the heading above its column.

   Line up equal place-value columns.

   Compare largest place first

   First number	Second number
   49251	69567

   Choose the correct relation: 49251 □ 69567.

   <

3. Compare largest place first. Read each value with the heading above its column.

   Line up equal place-value columns.

   Compare largest place first

   First number	Second number
   49251	69567

4. Compare largest place first. Read each value with the heading above its column.

   Compare from the greatest place; the first different digits decide.

   Compare largest place first

   First number	Second number
   49251	69567

5. Compare largest place first. Read each value with the heading above its column.

   49251 < 69567.

   Compare largest place first

   First number	Second number
   49251	69567

6. Compare largest place first. Read each value with the heading above its column.

   Check the result against the question we started with.

   The greater number comes later when counting forward.

   We found <. Comparing the largest differing place decides the order.

   Compare largest place first

   First number	Second number
   49251	69567

Common mistakes to discuss

• Longer looks larger. Compare the greatest place first, not the number of digits on the page. 0 thousands beats nothing: 998 is less than 1002 because the thousands differ.

Check your understanding

• Represent and compare numbers to 100000
• 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.