Imaginesis: printable Year 5 Multiplication and Division maths worksheets for England (National Curriculum) — Solving Equations with a Missing Number, Two-Step Calculations and Order of Operations, Finding the Greatest Common Factor: word problems with hints, answers and worked solutions as PDF, also as an A/B test.
Ada fills 25 cups with orange juice using the first machine on the cafeteria counter. She starts the second machine to squeeze more juice until she fills 39 cups in all. How many cups did Ada fill with the second machine?
Hint: Think about how many cups you need to add to 25 to reach 39. What can you take away from 39 to find that missing part?
Answer: 14
The kitchen counter holds 7 rows of muffins with 4 muffins in each row. Another 14 muffins sit on a plate next to the counter. How many muffins are there in all?
Hint: First find how many muffins are in the 7 rows by multiplying 7 by 4. Then add the 14 muffins from the plate.
Answer: 42
At an animal shelter, 20 dog biscuits and 55 chew toys are to be packed into identical gift bags for new owners. Every bag gets the same number of biscuits and the same number of toys, and nothing is left over. What is the greatest number of gift bags that can be made?
Hint: Try a number of bags and check whether both the biscuits and the toys share out with nothing left over.
Answer: 5
Children find the unknown value in a calculation by using inverse operations and treating the equals sign as a balance between both sides.
Y1.AS.4 solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = □ – 9.Y2.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.4 solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.Y3.MD.3 solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.Y5.MD.10 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
In Year 5, children solve missing number problems across addition, subtraction, multiplication, and division, including calculations that combine these operations. Instead of simply computing a total at the right-hand side of a page, they use their knowledge of place value and inverse operations to determine the value of a missing box placed anywhere in the sentence—such as finding a missing starting number or balancing two sides of an equation.
A common difficulty arises when children treat the equals sign as an instruction to "do the sum" rather than a symbol of balance. For example, when finding what number was taken from in a subtraction equation, a child might mistakenly subtract the two visible numbers instead of adding them together to find the original total.
Worksheet tasks build this understanding through concrete and visual layouts:
Task types: Missing addend (box equation) · Put the sign between the sum and the number · A balanced scale: how much does the hidden block weigh · A box in subtraction: what number was it taken from? · How many more to make the sides equal · Which number hides in the box · A box in a sum of three numbers · Fill in both boxes in turn
Children learn to solve two-step problems combining addition, subtraction, multiplication, and division, while working out which calculation to do first.
Y5.MD.10 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
Children learn to solve problems that combine two operations across addition, subtraction, multiplication, and division. At this stage, they learn to determine which step must be completed first to find the correct total, while reinforcing their understanding that the equals sign shows that the values on both sides are equivalent.
A common error is working through calculations strictly from left to right. When faced with mixed operations, children often carry out the first operation they see rather than completing the multiplication or division step first. In word problems, children also struggle when they calculate an intermediate total but forget to apply the second step, such as subtracting items that were lost or shared out.
Worksheet tasks build this skill through both written expressions and practical problem solving. Children evaluate calculations in order of operations (two steps) exercises, select the right answer in choose the correct result tasks, and decide whether equations are true or false. They also solve contextual problems, such as finding two kinds of groups, one total, calculating how many are left after giving out the same to each, or determining what remains when so many groups of so many, and then some were lost.
Task types: Order of operations (two steps) · Order of operations: choose the correct result · Order of operations: true or false · First how many in one, then how many in all · How many are left after giving out the same to each · So many groups of so many, and then some were lost · Two kinds of groups, one total
Children learn to list factor pairs for two numbers and identify the largest factor that divides evenly into both.
KS3.N.3 use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation propertyY5.MD.1 identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbersY6.ASMD.5 identify common factors, common multiples and prime numbers
In Year 5, children build on basic multiplication facts to find all the factor pairs of a number. They compare the factor lists of two given numbers to identify their common factors and determine the greatest common factor—the largest whole number that divides into both with no remainder.
A common stumbling block is confusing factors with multiples, causing children to list numbers that are larger than the given values instead of breaking the numbers down. Another typical issue is missing factor pairs in larger numbers (such as overlooking 3 and 12 when listing factors of 36), which leads them to select a smaller shared factor instead of the greatest one.
Practice tasks generally take two forms:
Children learn to use division to calculate the value, cost, or measurement of a single item from a known total.
KS3.R.10 use compound units such as speed, unit pricing and density to solve problems.Y5.MD.11 solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.
In Year 5, children solve problems involving simple rates by using division to calculate the value for one. While multi-step compound units like speed and density are introduced later in Key Stage 3, Year 5 focuses on the foundational step: taking a shared total and dividing it equally by the number of items to find the unit rate.
A common mistake is dividing the wrong way around. Children often divide the number of items by the total amount rather than dividing the total amount by the number of items, or they mistake the problem for a multiplication task. This happens when they rush to calculate with the numbers given instead of visualizing the quantities being shared out.
Tasks using the Find the value for one template provide concrete, everyday scenarios. For example, a question might state that four identical notebooks cost £12, or that five bottles hold 750 ml altogether, asking the child to carry out a single division step to determine the price or volume of just one.
