Express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
<ul>
<li>using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, 12 blocks can form the following rectangles: 1 × 12, 2 × 6 and 3 × 4</li>
<li>researching divisibility tests and explaining each rule using materials; for example, using base-10 blocks to test if numbers are divisible by 2, 5 and 10</li>
<li>using divisibility tests to determine if larger numbers are multiples of one-digit numbers; for example, testing if 89 472 is divisible by 3 using 8 + 9 + 4 + 7 + 2 = 30, as 30 is divisible by 3 then 89 472 is a multiple of 3</li>
<li>demonstrating and reasoning that all multiples can be formed by combining or regrouping; for example, multiples of 7 can be formed by combining a multiple of 2 with the corresponding multiple of 5: 3 × 7 = 3 × 2 + 3 × 5, and 4 × 7 = 4 × 2 + 4 × 5</li>
</ul>
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient mental and written calculation strategies and using digital tools where appropriate; check the reasonableness of answers
<ul>
<li>solving multiplication problems such as 253 × 4 using a doubling strategy, for example, 2 × 253 = 506 and 2 × 506 = 1012</li>
<li>solving multiplication problems like 15 × 16 by thinking of factors of both numbers, 15 = 3 × 5, 16 = 2 × 8, and rearranging the factors to make the calculation easier, 5 × 2 = 10, 3 × 8 = 24 and 10 × 24 = 240</li>
<li>using an array to show place value partitioning to solve multiplication, such as 324 × 8, thinking 300 × 8 = 2400, 20 × 8 = 160, 4 × 8 = 32 then adding the parts, 2400 + 160 + 32 = 2592; and connecting the parts of the array to a standard written algorithm</li>
<li>using different strategies used to multiply numbers, and explaining how they work and if they have any limitations; for example, discussing how the Japanese visual method for multiplication is not effective for multiplying larger numbers</li>
</ul>
Find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations
<ul>
<li>using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3 × 5 = 15 and 30 ÷ 2 = 15, then 3 × 5 = 30 ÷ 2, and therefore the solution to 3 × 5 = 30 ÷ □ is 2</li>
<li>using relational thinking, and an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6</li>
<li>using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not – for example, using arrays to demonstrate that 2 × 3 = 3 × 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 × 2 × 3 = 12 and 2 × 3 × 2 = 12 and 3 × 2 × 2 = 12; and understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8</li>
<li>using materials, diagrams or arrays to recognise and explain the distributive property, for example, where 4 × 13 = 4 × 10 + 4 × 3</li>
<li>constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 × 4 = 12 and knowing 2 × 2 = 4, then 3 × 4 can be written as 3 × (2 × 2) and, using the associative property, (3 × 2) × 2 so 3 × 4 = 6 × 2 and so 6 is the solution to 3 × 4 = □ × 2</li>
</ul>
Solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies with and without digital tools
<ul>
<li>explaining how 1/3 of a quantity can be achieved by dividing by 3, and how knowledge of 1/3 of a quantity can be used to find 2/3 or 4/3 of the same quantity, using situations involving money, length, duration, mass or capacity</li>
<li>investigating percentage discounts of 10%, 25% and 50% in an online toy sale, using their equivalent decimal representations of 0.10, 0.25 and 0.50 to calculate the amount of discount on sale items, with and without digital tools</li>
<li>linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding a 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%</li>
<li>explaining the equivalence between percentages and fractions, for example,33 1/3% and 1/3, keeping to percentages that are equivalent to fractions with small denominators such as 66 2/3% and 12.5%</li>
<li>representing a situation with a mathematical expression, for example, numbers and symbols such as 1/4 × 24, that involves finding a familiar fraction or percentage of a quantity; and using mental strategies or a calculator and explaining the result in terms of the situation in question</li>
</ul>
Use mathematical modelling to solve practical problems involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and using efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made
<ul>
<li>modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation, for example, purchasing items during a sale</li>
<li>modelling situations involving earning money and budgeting, asking questions such as ‘Can I afford it?’, ‘Do I need it?’ and ‘How much do I need to save for it?’ and developing a savings plan or budget for an upcoming event or personal purchase</li>
<li>modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals</li>
</ul>
Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies
Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division
Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
Solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate
Use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in te
teaching resource
Multi-Step Word Problem Cards (Division and Multiplication) - Year 5-6
Updated: 15 Apr 2024
Solve multi-step multiplication and long division word problems with a set of printable maths task cards.
Solve multi-step multiplication and long division word problems with a set of printable maths task cards.
Add Multi-Step Word Problems to Your Year 6 Maths Rotation
Teachers around the world agree… word problems are tough! But multi-step word problems are even tougher! Why do students struggle so much with multi-step word problems? There are a few reasons why they’re so hard and even more reasons to build in additional practise.
Multi-step word problems require comprehension! Students must understand the problem statement, find relevant information, and determine the correct operation to solve the problem. Some students need help comprehending the problem or may get overwhelmed by the amount of information presented.
Problem-solving skills need some work! Multi-step word problems involve many steps and multiple operations. Students must identify the appropriate operations, use mathematical reasoning, and arrive at the final answer. Weak problem-solving skills can make it challenging for students to break down the problem into smaller, manageable steps.
Multi-Step Multiplication and Long Division Word Problems on Deck!
We have the perfect practise activity to add to your maths group rotations. Use these task cards to practise one and two-step word problems that involve multiplication and long division. They work great as an independent or group activity during maths rotations.
Included with this teaching resource are:
24 multi-step multiplication and long division word problem task cards
a recording sheet
an answer key.
Download Your Year 6 Maths Word Problems Today!
Use the dropdown icon on the Download button to choose between the PDF or editable Google Slides version of this resource. A recording sheet and answer key are also included with this download.
Print on heavy card for added durability and longevity.
Lindsey Phillips, a teacher and Teach Starter collaborator, contributed to this resource.
Don’t stop there! We’ve got more activities and resources that cut down on lesson planning time:
Express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
<ul>
<li>using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, 12 blocks can form the following rectangles: 1 × 12, 2 × 6 and 3 × 4</li>
<li>researching divisibility tests and explaining each rule using materials; for example, using base-10 blocks to test if numbers are divisible by 2, 5 and 10</li>
<li>using divisibility tests to determine if larger numbers are multiples of one-digit numbers; for example, testing if 89 472 is divisible by 3 using 8 + 9 + 4 + 7 + 2 = 30, as 30 is divisible by 3 then 89 472 is a multiple of 3</li>
<li>demonstrating and reasoning that all multiples can be formed by combining or regrouping; for example, multiples of 7 can be formed by combining a multiple of 2 with the corresponding multiple of 5: 3 × 7 = 3 × 2 + 3 × 5, and 4 × 7 = 4 × 2 + 4 × 5</li>
</ul>
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient mental and written calculation strategies and using digital tools where appropriate; check the reasonableness of answers
<ul>
<li>solving multiplication problems such as 253 × 4 using a doubling strategy, for example, 2 × 253 = 506 and 2 × 506 = 1012</li>
<li>solving multiplication problems like 15 × 16 by thinking of factors of both numbers, 15 = 3 × 5, 16 = 2 × 8, and rearranging the factors to make the calculation easier, 5 × 2 = 10, 3 × 8 = 24 and 10 × 24 = 240</li>
<li>using an array to show place value partitioning to solve multiplication, such as 324 × 8, thinking 300 × 8 = 2400, 20 × 8 = 160, 4 × 8 = 32 then adding the parts, 2400 + 160 + 32 = 2592; and connecting the parts of the array to a standard written algorithm</li>
<li>using different strategies used to multiply numbers, and explaining how they work and if they have any limitations; for example, discussing how the Japanese visual method for multiplication is not effective for multiplying larger numbers</li>
</ul>
Find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations
<ul>
<li>using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3 × 5 = 15 and 30 ÷ 2 = 15, then 3 × 5 = 30 ÷ 2, and therefore the solution to 3 × 5 = 30 ÷ □ is 2</li>
<li>using relational thinking, and an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6</li>
<li>using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not – for example, using arrays to demonstrate that 2 × 3 = 3 × 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 × 2 × 3 = 12 and 2 × 3 × 2 = 12 and 3 × 2 × 2 = 12; and understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8</li>
<li>using materials, diagrams or arrays to recognise and explain the distributive property, for example, where 4 × 13 = 4 × 10 + 4 × 3</li>
<li>constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 × 4 = 12 and knowing 2 × 2 = 4, then 3 × 4 can be written as 3 × (2 × 2) and, using the associative property, (3 × 2) × 2 so 3 × 4 = 6 × 2 and so 6 is the solution to 3 × 4 = □ × 2</li>
</ul>
Solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies with and without digital tools
<ul>
<li>explaining how 1/3 of a quantity can be achieved by dividing by 3, and how knowledge of 1/3 of a quantity can be used to find 2/3 or 4/3 of the same quantity, using situations involving money, length, duration, mass or capacity</li>
<li>investigating percentage discounts of 10%, 25% and 50% in an online toy sale, using their equivalent decimal representations of 0.10, 0.25 and 0.50 to calculate the amount of discount on sale items, with and without digital tools</li>
<li>linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding a 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%</li>
<li>explaining the equivalence between percentages and fractions, for example,33 1/3% and 1/3, keeping to percentages that are equivalent to fractions with small denominators such as 66 2/3% and 12.5%</li>
<li>representing a situation with a mathematical expression, for example, numbers and symbols such as 1/4 × 24, that involves finding a familiar fraction or percentage of a quantity; and using mental strategies or a calculator and explaining the result in terms of the situation in question</li>
</ul>
Use mathematical modelling to solve practical problems involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and using efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made
<ul>
<li>modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation, for example, purchasing items during a sale</li>
<li>modelling situations involving earning money and budgeting, asking questions such as ‘Can I afford it?’, ‘Do I need it?’ and ‘How much do I need to save for it?’ and developing a savings plan or budget for an upcoming event or personal purchase</li>
<li>modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals</li>
</ul>
Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies
Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division
Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
Solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate
Use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in te
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