Place value chart

A place value chart for the projector: add discs to the ones, tens, hundreds and beyond (or tenths to thousandths), trade ten for one, and read the number aloud.

thousands

hundreds

tens

ones

How to use it

Press + under a column to add a disc, and − to take one away. The count of discs shows under each column, and the number appears at the side.
Press 10→1 under a column that has ten or more discs to trade them for one disc in the next column to the left, or 1→10 to break one into ten.
Choose how many whole-number columns and whether to include decimals, then type a number under Set a number to see it built with discs.

Ideas for class

Put 12 discs in the ones column. Ask what is odd about the chart (there is no digit for 12) and trade up to show 1 ten and 2 ones.
Type 4,305 and ask students to point to the column with no discs and say why the zero is needed.
Add one disc to the thousands column of 4,999 one at a time and watch trades ripple through every column.
Show 2.35 with decimals on and ask for the value of the 3 and the 5. Turn on Show it in words and read 2.35 as two and thirty-five hundredths.
Hide the number (press H) and put discs in several columns. Ask students to write the number, and reveal it.
Multiply by ten by moving every disc one column to the left, and divide by ten by moving every disc one column to the right.
Compare 3,450 and 3,405 by typing both and asking which has more in the hundreds column.

Questions

How many columns can the chart have?

From two to seven whole-number columns (up to the millions) and up to three decimal columns (tenths, hundredths and thousandths).

What does trading do?

10→1 takes ten discs from a column and puts one in the column to its left, the way ten ones become a ten. 1→10 does the reverse. The value of the number never changes, which the box at the side confirms.

Can a column hold more than nine discs?

Yes, up to 30, on purpose. Seeing a column with 12 discs is how students understand why we regroup: our digits stop at 9.

Is the number read aloud correctly for decimals?

The words follow the usual way of reading decimals: 2.35 is “two and thirty-five hundredths”, and 0.7 is “seven tenths”. They are built from exact integers, so there are no rounding errors.

Does it save my chart?

The chart and your column settings are remembered in this browser, and Share copies a link with them after the # sign, which our servers never see.

Is it suitable for the youngest students?

Two columns (ones and tens) work for first grade. Use the hide option and let students say the number before you reveal it.

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Using a place value chart in class

The chart shows that the value of a digit depends on its column. Discs make the zero visible (an empty column) and make trading concrete (ten discs out, one disc in).

Build a number from its expanded form: “2 thousands, 4 tens and 7 ones”.
Compare numbers column by column, left to right.
Show why we carry in addition and borrow in subtraction: they are trades.
Extend to decimals: tenths are to the right of the ones column, each ten times smaller.

Mistakes to listen for

Reading 4,305 as “four thousand three hundred and fifty”. Show the empty tens column.
Treating 0.35 as larger than 0.5 because 35 is larger than 5. Show them in tenths and hundredths.
Saying the digit is the value: “the 3 in 4,305 is 3”. It is 300.