Place Value Slider
Number · Year 4–Year 6
Worksheets for this ↓Multiply and divide by 10, 100 and 1,000. The digits move, the point does not.
Use this on paper
Powers of 10, on paper, for Year 5.
Powers of 10 · £1.50 a sheet, or any 5 for £5 · No subscription.
About the place value slider
A place value chart from millions down to thousandths, with a number on it. Press × 10 and every digit slides one place to the left; press ÷ 100 and every digit slides two places to the right. The decimal point stays exactly where it is.
That is the whole lesson, and it is the one the old rule gets wrong. Told to multiply by ten by adding a nought, a class writes 3.40 for 3.4 × 10. What really happens is that each digit becomes worth ten times as much, which is the same as moving one place to the left, and the point is a fixed mark the digits slide past.
The noughts that only hold a place are drawn in gold, so a class can see which digits they started with and which noughts appeared because a column would otherwise be empty. 34 × 100 is 3,400 with two of them; 34 ÷ 1,000 is 0.034 with two more, either side of the point.
The sum is written out underneath, and it waits until the digits have landed before it gives the answer, so there is a moment to ask the class where they think the digits will go.
How to use it on your whiteboard
- 1Tap the arrows above and below a digit to change it, or press New for a fresh number. The Digits buttons choose how many it has.
- 2Ask the class what will happen, then press × 10, × 100 or × 1,000.
- 3Watch the digits slide, and read the sum underneath.
- 4Divide to send the digits back the other way, or keep going into the decimals.
- 5Undo takes back one press at a time. A button greys out when a digit would fall off the end of the chart.
Questions
- Why do the digits move and not the decimal point?
- Because that is what multiplying by ten does: every digit becomes worth ten times as much, so it belongs one column to the left. The point marks where the ones end and the tenths begin, and that never changes. Moving the point instead gives the right answer for the wrong reason, and it stops making sense with whole numbers.
- What are the gold noughts?
- Placeholders. When 34 is multiplied by 100 the ones and tens columns are left empty, and a nought goes in each so that the 3 and the 4 stay in the right places. They are a different colour so the class can tell them apart from the digits the number started with.
- How far can it go?
- From millions to thousandths, which covers Years 4 to 6. A button greys out rather than letting a digit slide off the edge of the chart, because a number with a digit missing is a different number.
- Do I need an account?
- No. Trove Tools is free with no login, no subscription and no limits.