Imaginesis: printable Year 5 Place Value maths worksheets for England (National Curriculum) — Counting Forwards and Backwards in Powers of 10, Solving Multi-Step Word Problems, Using Positive and Negative Numbers in Context: word problems with hints, answers and worked solutions as PDF, also as an A/B test.
Mia saves for a garden swing: after the first week her jar holds £12, after the second £19, and after the third £26. She puts in the same amount every week. How much money will the jar hold after the fifth week?
Hint: How much does Mia add each week? Keep going until the fifth week.
Answer: 40
The prep table holds 22 bowls of chopped carrots. Another 16 bowls of chopped carrots were brought from the fridge, and 24 more bowls were filled from the counter. How many bowls of chopped carrots are on the prep table in all?
Hint: First, add the 22 bowls of chopped carrots to the 16 bowls from the fridge, and then add the last 24 bowls.
Answer: 62
Children learn to count forwards and backwards in steps of 10, 100, 1,000, 10,000, and 100,000 starting from any whole number up to 1,000,000.
Y1.NPV.1 count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given numberY1.NPV.2 count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tensY2.NPV.1 count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backwardY3.NPV.1 count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given numberY4.NPV.1 count in multiples of 6, 7, 9, 25 and 1000Y5.NPV.2 count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
In Year 5, children build on earlier counting to count forwards and backwards in steps of powers of 10—such as 10, 100, 1,000, 10,000, or 100,000—for any given number up to 1,000,000. Rather than always starting from zero or a round multiple, pupils work from irregular starting values (such as counting up in ten-thousands from 432,650).
Errors most often occur when a step crosses a place value boundary, particularly when counting backwards across zeros. For example, when counting back in thousands from 300,450, children may hesitate or miscalculate the transition to 299,450, often changing only the thousands digit and neglecting the regrouping needed in the ten-thousands and hundred-thousands columns.
Tasks provide structured practice through sequences where children keep counting forwards or backwards by the same step, or select the correct next number from options. Other worksheets challenge them to spot and correct an error within an equal-step sequence, or determine how many times they must count on by a specific power of 10 to reach a target value.
Children learn to break down and solve multi-step addition and subtraction word problems using numbers up to one million.
Y3.AS.4 solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.Y4.AS.3 solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.Y4.NPV.8 solve number and practical problems that involve all of the above and with increasingly large positive numbersY5.AS.4 solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.Y5.NPV.5 solve number problems and practical problems that involve all of the aboveY6.ASMD.7 solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and whyY6.ASMD.8 solve problems involving addition, subtraction, multiplication and divisionY6.NPV.4 solve number and practical problems that involve all of the above.
In Year 5, children tackle contextual problems that require more than one calculation to reach an answer, working with numbers up to one million. Rather than being told which calculation to carry out, pupils must read a scenario, decide whether to use addition or subtraction at each stage, and choose an efficient written or mental method to complete the steps.
A common difficulty is carrying out a single calculation and stopping too early, mistaking the first intermediate answer for the final solution. Children also frequently misinterpret the context, such as adding values together when the scenario actually describes comparing amounts or finding a remaining difference.
Worksheet tasks present these challenges through realistic scenarios. For example, a two-step word problem (combine) asks pupils to join multiple groups before finding a total or working out what remains. Another task type, most sets you can make from the stock, requires children to calculate totals from available supplies to determine how many complete sets can be assembled.
Children learn to count forwards and backwards through zero using whole numbers and make sense of negative values in everyday situations.
Y5.NPV.3 interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zeroY6.NPV.3 use negative numbers in context, and calculate intervals across zero
In Year 5, children learn to interpret negative whole numbers in practical contexts and count forwards and backwards through zero. They explore how values move below zero, building an understanding of how positive and negative whole numbers order along a continuous line.
A frequent stumbling block occurs when crossing zero. Children often omit zero entirely when counting backwards, jumping straight from 1 to -1. It is also common for pupils to treat negative numbers as if they were positive, mistakenly believing that -5 is greater than -2 because 5 is bigger than 2.
Practice activities bring this to life through tasks such as Negative points in a game. Children track players' scores as they gain points or receive penalties that push their totals below zero, calculating new scores and seeing how adding or losing points moves a total forwards or backwards through zero.
