Imaginesis: printable Year 4 Addition and Subtraction maths worksheets for England (National Curriculum) — Checking answers with inverse operations, Adding and subtracting numbers with up to 4 digits in columns, Two-step word problems in context: word problems with hints, answers and worked solutions as PDF, also as a test in groups A–D.
Leo wrote down a total of 51 magic leaves in his potion book. He added 17 silver leaves to reach this sum. Leo checks his work with a subtraction. How many leaves were written down first?
51 - 17 = ?
Hint: Start with the whole number of 51 magic leaves and subtract the 17 silver leaves that Leo added.
Answer: 34
Work it out using the column method.
43,445 + 19,872 = □
Answer: 63,317
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 check an answer by reversing the calculation, such as adding to check a subtraction and dividing to check a multiplication.
KS3.N.6 recognise and use relationships between operations including inverse operationsY1.AS.2 represent and use number bonds and related subtraction facts within 20Y2.AS.5 recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.Y3.AS.3 estimate the answer to a calculation and use inverse operations to check answersY4.AS.2 estimate and use inverse operations to check answers to a calculation
In Year 4, children estimate an answer first, then use inverse operations (the opposite operation) to check whether the answer is right. The curriculum point for this grade is to estimate and use inverse operations to check answers to a calculation. Earlier stages build the groundwork: by the end of grades 1-3, children have recognised the inverse relationship between addition and subtraction and used it to check calculations and solve missing number problems. Year 4 number work includes four-digit numbers and multiplication facts up to 12 × 12, so checks may involve these numbers.
A common mistake is to check a sum by repeating the same calculation. If the first answer was wrong, the child often gets the same wrong answer again and feels the check has worked. The check only helps when it reverses the operation, so the child is testing the answer a different way.
Tasks on this skill are printed from the available templates. These include checking addition by subtraction, checking subtraction by adding, and checking subtraction: true or false, where the child decides whether a check holds. Other templates ask the child to find a missing starting number, such as what number was it subtracted from, or to fix a faulty check with checking subtraction: correct the mistake. For multiplication and division, the templates are multiplication and division: how many before sharing and multiplication and division: what it was multiplied by.
Task types: Checking addition by subtraction · Checking subtraction: by adding · Checking subtraction: correct the mistake · Checking subtraction: true or false · Multiplication and division: how many before sharing · Multiplication and division: what it was multiplied by · What number was it subtracted from? Choose
Your child learns to add and subtract numbers of up to four digits by lining them up in columns, ones under ones, tens under tens, and so on, and working from right to left.
Y4.AS.1 add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriateY5.AS.1 add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
In Year 4, children use the column method to add and subtract whole numbers with up to four digits. They write the numbers one under the other, keeping each place value in its own column, and carry or exchange when a column does not have enough. The curriculum asks for these formal written methods "where appropriate", so children are also expected to judge when a written method is the sensible choice.
A common mistake is misaligning the columns, for example writing 1,246 and 58 so that the 8 sits under the 2 instead of the 6. The sum then adds the wrong digits together and gives an answer that looks plausible. In subtraction, a frequent error is taking the smaller digit from the larger one in each column regardless of which is on top, or getting stuck when a zero sits in the middle of the number, as in 4,003 minus 1,378. Borrowing across zeros is a specific step that needs practice of its own.
Printable tasks for this skill include "Add using the column method" and "Subtract using the column method", where the child works through each sum on paper. "Column addition: choose the result" and "Column addition: true or false" ask the child to check or select answers, which helps them spot misaligned columns. "Written subtraction: borrowing across zeros" targets the zero-exchange step, and "Written subtraction: true or false" gives practice in checking whether a given answer is correct.
Task types: Add using the column method · Column addition: choose the result · Column addition: find the mistake · Column addition: true or false · Subtract using the column method · Written subtraction: find the mistake · Written subtraction: true or false · Numbers to a million: addition word problem · Numbers to a million: subtraction word problem · Written subtraction: borrowing across zeros
Solving two-step word problems with four-digit numbers, choosing the right addition or subtraction for each step.
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 4, a child is expected to solve two-step addition and subtraction problems in real contexts, deciding which operations and methods to use and why. The numbers are four-digit numbers, so a problem might involve a total of several thousand, such as working out how many items are left after two separate changes. The curriculum asks the child to explain their choice of operations, not only to find an answer.
A common mistake is to combine the first two numbers in the problem and stop, or to use the same operation for both steps without checking what each step is asking. A child may also work out the first step correctly and then lose track of what it represents when the second step begins. Reading the question one step at a time, and saying in words what each answer means, helps prevent this.
Tasks on this skill are printed from the two-step word problem (combine) template, which asks the child to join or change amounts across two steps. The stock and sets templates give practice in deciding how many groups or sets a total can make, and the word problem, three days templates present a short sequence of events where the child chooses the result or judges whether a statement is true or false. Children are usually asked to write down which operation they used at each step and why.
