teaching resource

Mixed Operations - Length Word Problems Worksheets

Updated: 12 Jul 2024

Solve multi-step length word problems with a printable pack of 3-act Maths Word Problem Worksheets.

Editable: Google Slides
Non-Editable: PDF
Pages: 8 Pages
Years: 5 - 6

Curriculum

VC2M5N06

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>
VC2M5N07

Solve problems involving division, choosing efficient mental and written strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction <ul> <li>interpreting and solving everyday division problems such as ‘How many buses are needed if there are 436 passengers and each bus carries 50 people?’, deciding whether to round up or down in order to accommodate the remainder and justifying choices</li> <li>solving division problems mentally, such as 72 divided by 9, 72 ÷ 9, by thinking, ‘How many nines make 72?’, □ x 9 = 72, or ‘Share 72 equally 9 ways’</li> <li>using the fact that equivalent division calculations result if both numbers are divided by the same factor</li> </ul>
VC2M5N09

Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation <ul> <li>modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem; formulating the situation as a number sentence; and justifying their choice of operations in relation to the situation</li> <li>modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved</li> <li>modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations</li> <li>investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples</li> </ul>
VC2M6N09

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>
VC2M6M02

Establish the formula for the area of a rectangle and use it to solve practical problems <ul> <li>using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides</li> <li>using one-centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area</li> <li>solving problems involving the comparison of lengths and areas using appropriate units</li> <li>investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter</li> </ul>

teaching resource

Mixed Operations - Length Word Problems Worksheets

Updated: 12 Jul 2024

Solve multi-step length word problems with a printable pack of 3-act Maths Word Problem Worksheets.

Editable: Google Slides
Non-Editable: PDF
Pages: 8 Pages
Years: 5 - 6

Solve multi-step length word problems with a printable pack of 3-act Maths Word Problem Worksheets.

What is a 3-Act Maths Task?

A 3-Act Maths Task is a way of teaching maths by telling a story or presenting a problem in three parts. First, students are hooked with an easy-to-solve problem. Next, they are presented with an additional problem requiring the previous answer. Finally, they are given a third problem using the previous answers and a new operation or task to complete using the information they’ve discovered during the last two acts.

Rigorous 3-Act Maths Word Problems for Measuring Length

With those high-stakes assessments looming, our job is to prepare our students for what they might encounter. Rigorous maths standards require students to apply their skills across multiple situations and be able to show their thinking and explain the mathematical reasoning behind their answers.

This collection of Three-Act Maths Tasks is designed to do just that. Modelled after multi-part questions commonly found on standardised tests, these tasks guide the student through three questions that require them to use information acquired in previous steps and apply that information to new scenarios. Each task consists of two purely mathematical questions and a third question that requires critical thinking and an explanation of answers.

This printable set of three-act maths tasks requires students to use their knowledge of length conversions and solving word problems with multiple operations.

Download, Print, and Use!

This resource is available as an easy-to-use Google Slides or Printable PDF Resource file. To get your copy, click the dropdown arrow on the download button to select your preferred file format. Make your copies, pass them out to your students, and you’re ready to begin!

This resource was created by Brittany Kellogg, a teacher and Teach Starter Collaborator.

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Curriculum

VC2M5N06

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>
VC2M5N07

Solve problems involving division, choosing efficient mental and written strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction <ul> <li>interpreting and solving everyday division problems such as ‘How many buses are needed if there are 436 passengers and each bus carries 50 people?’, deciding whether to round up or down in order to accommodate the remainder and justifying choices</li> <li>solving division problems mentally, such as 72 divided by 9, 72 ÷ 9, by thinking, ‘How many nines make 72?’, □ x 9 = 72, or ‘Share 72 equally 9 ways’</li> <li>using the fact that equivalent division calculations result if both numbers are divided by the same factor</li> </ul>
VC2M5N09

Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation <ul> <li>modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem; formulating the situation as a number sentence; and justifying their choice of operations in relation to the situation</li> <li>modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved</li> <li>modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations</li> <li>investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples</li> </ul>
VC2M6N09

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>
VC2M6M02

Establish the formula for the area of a rectangle and use it to solve practical problems <ul> <li>using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides</li> <li>using one-centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area</li> <li>solving problems involving the comparison of lengths and areas using appropriate units</li> <li>investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter</li> </ul>

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