English

Place Value

Primary schoolMathematicsBase-ten blocks: each column is worth ten times the column to its right

About this experiment

The digit 3 can mean three, thirty, three hundred or three thousand. What it is worth depends on its place in the number. Base-ten blocks make this easy to see: a ten is a rod of ten ones, a hundred is a flat of ten tens and a thousand is a cube of ten hundreds. Build numbers with blocks, trade ten blocks for one bigger block and break a block into ten smaller ones, and see how the digits and the expanded form change.

Learning goals

  • Say what each digit in a number up to 9999 is worth
  • Build and read numbers using thousands, hundreds, tens and ones
  • Write a number in expanded form, such as 3000 + 400 + 20 + 5
  • Exchange ten of one block for one of the next block, and the other way round
  • Understand the role of zero as a place holder

How to use it

  1. 1Read the number made by the blocks. What is each digit worth?
  2. 2Add ones until there are 12 of them. What is the number now? Press Trade 10 and see what changes and what stays the same.
  3. 3Break one hundred into tens. Is the number bigger, smaller or the same?
  4. 4Make 305. Why do you need the zero? What number would you get without it?
  5. 5Choose Make the number and build each target. Try to use as few blocks as you can.
  6. 6Make 1000 using only hundreds. How many do you need?

The model

Each digit is multiplied by the value of its place
Ten of one block can be traded for one of the next
The same amount can be shown in different ways

Assumptions

  • Each column can hold up to 19 blocks (thousands up to 9), so pupils can see that 12 tens is still a number before they trade.
  • Challenge numbers come from a fixed sequence, so every class gets the same targets in the same order. Every third target with three or more digits has a zero in the tens place.
  • Blocks are drawn in proportion: a ten is the length of ten ones and a hundred is ten tens side by side.

Try this in class

  1. Q1What is the value of the digit 7 in 4725?
  2. Q2Write 6000 + 30 + 8 as a number.
  3. Q3A number has 2 thousands, 14 hundreds and 3 ones. What is the number?
  4. Q4Which is bigger: 45 tens or 4 hundreds? Explain how you know.
  5. Q5Why do we need the zero in 507, but not at the start of 0507?

Frequently asked questions

Why let a column hold more than nine blocks?

Seeing 12 tens on the board and then trading 10 of them for a hundred is exactly the regrouping that pupils need for written addition and subtraction. The number itself does not change when you trade.

How does this help with column subtraction?

When there are not enough ones to take away, you break a ten into ten ones. Practising Break 1 with blocks first makes the written method of exchanging much easier to understand.

Can I use this with the whole class?

Yes. Project it and ask pupils to tell you which buttons to press, or let them use mini whiteboards to write the number and its expanded form before you reveal it.