Home → Curriculum Hub → Maths Lessons → Place Value → Working with Place Value
Ready-to-teach lesson. Includes a video tutorial, printable worksheets and GCSE exam-style practice with worked solutions.
Students learn working with place value by naming the column a digit sits in, then stating what that digit is worth. The lesson covers integers, decimals and digit card problems.
Most students arrive able to read three-digit numbers confidently. That confidence breaks down with decimals, because they read 0.45 and 0.305 as forty-five and three hundred and five.
This lesson underpins later place value work including standard form and bounds, so it is important students have a conceptual understanding throughout.
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The video works through the six teaching examples on the place value chart, then models the digit card problems. Use it for cover, revision or flipped learning.
Place value tells you the magnitude of a number. It is the reason 30 is 10 times larger than 3, which is 100 times larger than 0.03.
Roman numerals cannot do this. They have no decimal point and no zero, so there is no empty column to hold a place open.
Egyptian numerals went further than Roman numerals by including unit fractions. The hieroglyphs stayed complex though, so place value was still in its infancy.
In secondary school the place value table underpins far more than reading numbers aloud. I go back to it with Year 7 and Year 8 at the start of every school year.
With Year 7 we use it to:
With Year 8 we use it to:
At GCSE we use it to:
The worksheet runs from stating the value of a digit through to digit card problems, in 11 questions. Full solutions are included on the answer sheet.
Print it as a lesson follow-up or set it for homework. Questions 7 to 9 work well as a paired task with mini whiteboards.
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The starter is a crossword with every clue written in words. Students convert each clue into digits and fit the answer into the grid.
The grid marks the work for them. If seven thousand six hundred and forty one is written with the wrong number of digits, it will not fit.
Prompts / Questions to consider
The teaching examples give six numbers with a digit underscored. Students state what that digit is worth, using the chart on the right to place it.
Insist on the column name before the value. “Hundredths, so 0.04” is a stronger answer than “0.04” on its own.
Prompts / Questions to consider
Each student builds one number from the pink cards and one from the green cards. Every card in a set must be used, including the decimal point.
The question asks for the greatest possible difference. So students need the largest number one set can make, and the smallest the other can make.
The green cards make 931.0 at most. The pink cards make 3.456 at the least. The greatest difference is 927.544.
Prompts / Questions to consider
More able: ask for the smallest possible difference from the same cards. Students must now match the two numbers as closely as they can, which is 3.901 and 3.654, a difference of 0.247.
Less able: give a printed place value chart and ask students to write each card into a column before they read the number aloud.
| Phase | Focus | Time |
|---|---|---|
| Starter | Crossword converting words into digits | 10 min |
| Development | Value of an underscored digit on the chart | 15 min |
| Check | Ordering decimals with different numbers of decimal places | 10 min |
| Main / stretch | Digit card problems: largest, smallest, closest | 15 min |
| Plenary | Greatest possible difference challenge | 10 min |
Use this checklist after the lesson or as a revision self-check.
Try these GCSE-style questions on working with place value, then reveal the solutions to check your working. Select the image to view it full screen.
Write down the smallest four-digit even number, using each card only once.
The units digit must be even, so it is 2, 4 or 8. To keep the number small, put the smallest digits in the highest columns first.
Ordering the cards from smallest gives 2458, and the units digit 8 is already even. Answer: 2458.
Put one digit in each box to make the largest total, then write down that total.
A digit in the tens column is worth 10 times the same digit in the units column. So the two largest digits belong in the tens boxes.
Put 9 and 7 in the tens, and 5 and 1 in the units. Both 95 + 71 and 91 + 75 give the largest total. Answer: 166.
Use each digit once to complete the calculation.
Doubling has to produce a three-digit answer, so the two-digit number must be 50 or more. That leaves 6 or 8 in the tens column.
Testing those options, 64 × 2 = 128 and 82 × 2 = 164 both use all five digits once. Either answer is correct.
Use these cards to make the number closest to 0.7, then the number closest to 6.8.
Part a. Put 0 in the units and 6 in the tenths, then make the rest as large as possible. That gives 0.695, which is 0.005 below 0.7.
Part b. Put 6 in the units and 9 in the tenths, then make the rest as small as possible. That gives 6.905, which is 0.105 above 6.8.
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The value of a digit depends on the column it sits in. The 3 in 3091 is worth 3000. The 3 in 0.305 is worth three tenths, or 0.3.
They read the digits after the decimal point as a whole number, so 305 looks bigger than 45. Comparing the tenths column first fixes it, because 3 tenths is less than 4 tenths.
Put the two largest digits in the tens columns, because a tens digit is worth 10 times a units digit. With 5, 1, 7 and 9 that gives 95 + 71 or 91 + 75. Both total 166.
Seven thousandths, written 0.007. The columns after the decimal point run tenths, hundredths, thousandths, so the 7 sits in the third one. The zero in the tenths column holds that place open.
In standard form, percentage multipliers and recurring decimals. Upper and lower bounds also depend on knowing which column a measurement has been rounded to.
Move on to ordering decimals, then to multiplying and dividing by powers of 10. Both use the column language students have just practised. For the full topic hub, visit All Place Value Lessons.
Put the pink and green cards on the board for the last five minutes of a lesson. Ask for the greatest difference, then ask whether swapping which set makes the large number changes the answer.
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