partition decimals problem solving

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Decimal Partitioning Problems (Year 4)

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This resource is suitable for the White Rose Maths Scheme of Learning, covering Summer Term Block 4 (Decimals B), Step 3 (Partition Decimals).

Children can practise spotting the ones, tenths and hundredths in a decimal using part-whole models, number cards and place value charts.

An answer sheet is included.

This worksheet is available in different levels. Please see the drop-down menu to select another level.

This resource is also available in a handy Lesson Pack, containing a selection of brilliant worksheets for this small step.

View Lesson Pack    See all Year 4 White Rose

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: White Rose Maths | Summer Term: Decimals B | Small Step 3
• Topic Group: Fractions, Decimals and Percentages
• Year(s): Year 4
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 12/03/2024
• Resource Code: M2WAT16787
• Curriculum Point(s): Recognise and write decimal equivalents of any number of tenths or hundredths. Solve simple measure and money problems involving fractions and decimals to two decimal places.

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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

• National Curriculum Tool

Year 5 - Fractions (including decimals and percentages)

New curriculum.

compare and order fractions whose denominators are all multiples of the same number

• identify, name and write equivalent fractions of a given fraction, represented visually,including tenths and hundredths
• recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number[for example, 2 ⁄ 5 + 4 ⁄ 5 = 6 ⁄ 5 = 1 1 ⁄ 5 ]
• add and subtract fractions with the same denominator and denominators that are multiples of the same number
• multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
• read and write decimal numbers as fractions [for example, 0.71 = 71 ⁄ 100 ]

recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

• round decimals with two decimal places to the nearest whole number and to one decimal place

read, write, order and compare numbers with up to three decimal places

• solve problems involving number up to three decimal places
• recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
• solve problems which require knowing percentage and decimal equivalents of 1 ⁄ 2 , 1 ⁄ 4 , 1 ⁄ 5 , 2 ⁄ 5 and those fractions with a denominator of a multiple of 10 or 25.

Non-Statutory Guidance

Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions.

They extend their knowledge of fractions to thousandths and connect to decimals and measures.

Pupils connect equivalent fractions > 1 that simplify to integers with division and other fractions > 1 to division with remainders, using the number line and other models, and hence move from these to improper and mixed fractions.

Pupils connect multiplication by a fraction to using fractions as operators (fractions of), and to division, building on work from previous years. This relates to scaling by simple fractions, including fractions > 1.

Pupils practise adding and subtracting fractions to become fluent through a variety of increasingly complex problems. They extend their understanding of adding and subtracting fractions to calculations that exceed 1 as a mixed number.

Pupils continue to practise counting forwards and backwards in simple fractions.

Pupils continue to develop their understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities.

Pupils extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line.

Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems.

They mentally add and subtract tenths, and one-digit whole numbers and tenths.

They practise adding and subtracting decimals, including a mix of whole numbers and decimals, decimals with different numbers of decimal places, and complements of 1 ( for example, 0.83 + 0.17 = 1).

Pupils should go beyond the measurement and money models of decimals, for example, by solving puzzles involving decimals.

Pupils should make connections between percentages, fractions and decimals(for example, 100% represents a whole quantity and 1% is 1 ⁄ 100 , 50% is 50 ⁄ 100 , 25% is 25 ⁄ 100 ) and relate this to finding ‘fractions of’.

Links and Resources

• Making connections
• Exemplification

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.

Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

– National Curriculum in England Framework Document, September 2013, p10

Connections within Mathematics

Fractions, decimals and percentages are used in many other areas of mathematics.

When converting units of measure, children need a good understanding of decimals, e.g. converting cm to m, g to kg etc.

Children should also be required to use fractions and percentages when interpreting and evaluating data.

Fractions may be used when describing turns.

Making connections to this topic in adjacent year groups

Pupils should be taught to:

• recognise and show, using diagrams, families of common equivalent fractions
• count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
• add and subtract fractions with the same denominator
• recognise and write decimal equivalents of any number of tenths or hundredths
• recognise and write decimal equivalents to ¼, ½, ¾
• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
• round decimals with one decimal place to the nearest whole number
• compare numbers with the same number of decimal places up to two decimal places
• solve simple measure and money problems involving fractions and decimals to two decimal places
• use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• compare and order fractions, including fractions > 1
• add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
• multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ½, × ¼, = ⅛,]
• divide proper fractions by whole numbers [for example, ⅓ ÷ 2 = ⅙]
• associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ⅜ ]
• identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
• multiply one-digit numbers with up to two decimal places by whole numbers
• use written division methods in cases where the answer has up to two decimal places
• solve problems which require answers to be rounded to specified degrees of accuracy
• recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Cross-curricular and real life connections

Learners will encounter fractions, decimals and percentages in:

Measurement – when calculating measures for recipes, calculating journey times and fuel consumption

Money – working out the result of sales offers, tips/gratuities on bills, comparing prices

Statistics – interpreting and evaluating data e.g. 19% of the world’s population lives in China

• Teaching fractions with understanding: Part- whole concept

This article hosted by Nrich explores how children see fractions from an early age and the implications this can have for teaching practices. It includes ideas and images that can be used when presenting children with fractions work to build and extend their understanding of the part – whole relationship.

• History of Fractions

A fun article on the history of fractions that links well to the historical topic of Ancient Egypt.

• Math4life Fractions booklet (pdf)

A booklet that explains fractions, their uses and how they can be classified. There are some teaching and learning activities along with possible errors and misconceptions.

Maths4Life was written for those teaching adults but teachers of children will also find it very helpful.

• Fractions : difficult but crucial in mathematics learning (pdf) Nunes T. (2006) Teaching and Learning research briefing, no 13, London, The Institute of Education

An article exploring children’s intuitions about fractions and likely misconceptions that hinder progress through Key Stage 2 and beyond.

Activity A - Fractions ITP

An interactive program that allows you to model part-whole relationships using a strip divided in to equal parts. Relationships can be shown as fractions, decimals (to three places) or percentages.

Activity B - Fractions Jigsaw

A jigsaw-based activity that requires children to add and subtract fractions with the same and different denominators. Pieces must be matched to an answer that may be expressed in equivalent forms. It also includes multiplying fractions by a whole number.

Activity C - Peaches today, Peaches tomorrow…

A problem solving activity that requires children to find fractions of whole numbers. It provides plenty of practice and has many extension opportunities.

Activity D - Metre sticks and metre strips

Use classroom metre sticks/rulers and I metre long strips of paper to model relationships between a whole, tenths, hundreds and thousandths. Children can explore the size of 1, 2 and 3 decimal places and how they link to units of measurement. Labelling points with decimal, fraction and percentage equivalents can help to reinforce links between all three.

Activity E - Matching fractions, decimals and percentages

A pelmanism-style activity matching pairs of equivalent fractions, decimals and percentages. Points are awarded for correct answers and deducted for turning over cards without success.

Activity F - Using blank hundred squares

Use blank hundred squares to model and explore percentages, tenths and hundredths. Decimals, fractions and percentages can be represented by colouring in blank hundred squares which children can use to support addition and subtraction.

Useful Resources

• Moving digits ITP
• Clock faces to model different fractions
• Fractions ITP

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

Children should be able to circle the two fractions that have the same value, or choose which one is the odd one out and justify their decision. 6 ⁄ 10 , 3 ⁄ 5 , 18 ⁄ 20 , 9 ⁄ 15  

recognise mixed numbers and improper fractions and convert from one form to the other. Write mathematical statements >1 as a mixed number

Put the correct symbol, < or >, in each box.

3.03 ☐ 3.3 0.37 ☐ 0.327 Order these numbers: 0.27 0.207 0.027 2.07 2.7

(e.g. ⅖ + ⅘ = 6 ⁄ 5 = 1⅕)

How many halves in: 1 ½ 3 ½ 9 ½ …?

How many quarters in 1 ¼ 2 ¼ 5 ¼ ….?

multiply proper fractions and mixed numbers by whole numbers

What is 3 ⁄ 10 of: 50, 20, 100…?

What is ⅘ of 50, 35, 100….?

read and write decimal numbers as fractions (e.g. 0.71 = 71 ⁄ 100 )

What decimal is equal to 25 hundredths?

Write the total as a decimal:

4 + 6 ⁄ 10 + 2 ⁄ 100 =

Children partition decimals using both decimal and fraction notation, for example, recording 6.38 as 6 + 3 ⁄ 10 + 8 ⁄ 100 and as 6 + 0.3 + 0.08.

Recognise that: 0.007 is equivalent to 7 ⁄ 1000 6.305 is equivalent to 6305 ⁄ 1000

Write these numbers in order of size, starting with the smallest. 1.01, 1.001, 1.101, 0.11

solve problems involving numbers with up to three decimal places

8 tenths add 6 tenths makes 14 tenths, or 1 whole and 4 tenths. The 1 whole is 'carried' into the units column and the 4 tenths is written in the tenths column

recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’

Write in the missing numbers. 30% of ☐ is 60

write percentages as a fraction with denominator 100, and as a decimal

Shade 10% of this grid.

Which is bigger: 65% or ¾? How do you know?

What percentage is the same as 7 ⁄ 10 ? Explain how you know?

What is 31 ⁄ 100 as a percentage?

Which is a better mark in a test: 61% , or 30 out of 50? How do you know?

Year 4 and 5 extending their fractions work (NCETM video on Youtube)

A video demonstrating how children can use rods to explore which fractions, decimals and percentages are represented when compared to one whole.

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{{item.title}}, my essentials, ask for help, contact edconnect, directory a to z, how to guides, literacy and numeracy, flexible additive strategies - decimals.

This resource has been developed in partnership with the NSW Mathematics Strategy Professional Learning team, Curriculum Early Years and Primary Learners, and Literacy and Numeracy.

Using the resource

This resource is the last section of a four-part resource supporting additive thinking. Use this resource in conjunction with the other resources in this series in order to support a connected network of critical mathematical concepts, skills and understanding.

Supporting tasks

Full instructions on how to use each of these tasks - including materials, related tasks and learning intentions - are included in the resource available for download on this page .

Task 1: Decimals on a number line

Students visualise fractional quantities using an unmarked one-metre strip of paper

Variation 1: Students match fractional notation, word cards and images to the number line

Task 2: Making tenths and hundredths

Students partition paper into equal-sized parts to understand tenths and hundredths.

Variation 1: Students identify a part of their whole and record the fractions in a range of ways

Variation 2: Order the various fractions on a number line, comparing their models and counting forwards and backwards, naming and renaming

Variation 3: Make connections to metric units of measurement

Variation 4: Make connections to percentages

Task 3: Get your balance: tenths and hundredths

Students use a balance scale and weights to work out different ways of creating one kilogram.

Variation 1: Student use an unbalanced scale

Task 4: I’ll race you to zero: decimal place value

Students use mental strategies to subtract decimals using a 12 chart and dice.

Variation 1: Students make a number roll by cutting their 12 chart into strips and joining them into one number strip. Students can roll it up when out of use

Variation 2: Students use a 1 and 2-tenths chart

Task 5: More than or less than?

Students estimate and determine which of a set of problems are approximately equivalent to 250.

Variation 1: Student sort problems into less than and greater than categories

Variation 2: Change the target number and problems

Task 6: Roll 5 dice: decimal version

Students work out how many ways one number can be related to another using any operation.

Task 7: What can you say?

Students flexibly rename decimal fractions.

Task 8: How does knowing…?

Students adapt flexible strategies used with whole numbers to add and subtract decimal numbers.

Task 9: Red or black: decimals

Students adapt mental strategies used with whole numbers to add and subtract decimal numbers.

Task 10: Subtraction face-off: thousandths, hundredths and tenths

Students use an Explanation spinner and share the strategies used to work out differences.

Task 11: Number sentence battle

Students build number sentences using dice.

Task 12: Which would you work out in your head? Place value system

Students use mental, written and digital strategies to solve problems.

Variation 1: Change the questions examined by students

Download part 4 of the additive thinking series

• Flexible strategies with decimals (PDF 798 KB)
• Flexible strategies with decimals (DOCX 915 KB)

Related additive thinking resources

Part 1: Flexible strategies with combinations to 10

Part 2: Flexible strategies with 2-digit numbers

Part 3: Flexible strategies with 3-digit numbers

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Partitioning Explained For Primary School

Sophie Bartlett

Partitioning is a phrase that even the youngest primary school child will probably know. Here we show you how Year 2 children are taught this skill to help them break down any number into its component parts. We also show how this skill is related to other areas of maths.

This article is part of our series designed for teachers to inform mathematical subject knowledge, and for parents to help support children with home learning . More free home learning resources are also available on this website.

What is partitioning?

Partitioning is a way of splitting numbers into smaller parts to make them easier to work with. Partitioning links closely to place value: a child will be taught to recognise that the number 54 represents 5 tens and 4 ones, which shows how the number can be partitioned into 50 and 4. By moving tens and ones between the two parts, the number can be partitioned in many other ways:

When shown a number (up to 7+ digits by Year 6), children should be able to partition them independently to show good understanding of place value. For example, 5,202,086 = 5,000,000 + 200,000 + 2,000 + 80 + 6.

See also: Division Worksheets

FREE Partioning Numbers Worksheet

This time-saving worksheet is for Year 1 partioning numbers and includes 4 arithmetic questions, 9 consolidation questions, and 1 challenge question.

When will my child learn about partitioning in primary school?

Partitioning is taught very early on in pupils’ maths lessons, but it is first mentioned in the national curriculum as non-statutory guidance for Year 2:

Pupils should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two-digit numbers. They begin to understand zero as a place holder .

In Year 3, the non-statutory guidance advises that children use larger numbers to at least 1000, applying partitioning related to place value using varied and increasingly complex problems, building on work in year 2 (for example, 146 = 100 + 40 and 6, 146 = 130 + 16).

How does partitioning relate to other areas of maths?

Children will use partitioning in many other areas of maths:

• Introducing column addition: 56 + 78 may be first calculated as (50 + 70) + (6 + 8)
• Introducing column subtraction : 56 – 22 may be first calculated as (50 – 20) + (6 – 2)
• Understanding exchanging in column subtraction: 32 – 18 may be first calculated as (30 – 10) + (2 – 8) until children realise that they can’t subtract 8 from 2 without reaching a minus number. Partitioning is important here in understanding why exchanging works. 32 can be partitioned into 20 + 12, so this subtraction can be recalculated as (20 – 10) + (12 – 8)
• Introducing multiplication: 34 x 6 may be first calculated as (30 x 6) + (4 x 6)
• Introducing division methods with multi-digit divisors, including long division , short division and bus stop method , which require pupils to use multiples of the divisor and to calculate division with remainders

See also: Division Questions

Wondering about how to explain other key maths vocabulary to children? Check out our Primary Maths Dictionary , or try these other terms:

• What Is Division ?
• What Is BODMAS (and BIDMAS)?
• Division For Kids: How To Teach Short Division (Bus Stop Method) And Long Division To Children
• How To Teach Division KS2: Maths Bootcamp [7]
• What We’ve Learnt From Teaching Our Long Division Lesson 2,968 Times

Practice questions

1) Write the missing numbers. 361 = ___ + 60 + 1 300 945 = 900 + __ + 5     40

Write the value of each diagram. ( 1 st = 1,231)    (2 nd = 2,013)

3) Match the sums that have the same answer.

(2nd box to 1st box; 3rd box to 2nd box; 4th box to 4th box)

4) 700 + 20 + 3 =             ( 723) 3,000 + 40 + 2 =         ( 3,042) 2,000 + 300 =             ( 2,300)

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How to Perform Operations of Decimals: Word Problems

Greetings, budding mathematicians! Today, we're going to jump into an adventure with decimals. Working with decimals is a fundamental math skill that you'll use in many aspects of life, from managing money to measuring distances.

Introduction to Decimal Operations

First things first, let’s talk about decimals. A decimal is a way of representing a number that’s less than one, or a number that’s a whole and a fraction together. When you work with decimals, the same rules apply as when you’re working with whole numbers, but the decimal point plays a crucial role.

There are four major operations that you can perform on decimals:

• Subtraction
• Multiplication

Now, let’s tackle some word problems involving decimal operations.

Step-By-Step Guide to Solving Word Problems with Decimal Operations

Step 1: understand the problem.

First and foremost, carefully read through the problem. Identify what you know and what you need to find out.

Step 2: Plan the Solution

Next, decide which operation (addition, subtraction, multiplication, or division) will help you solve the problem. This will depend on what the problem is asking.

Step 3: Carry Out the Operation

Perform the operation on the decimals. Remember to align the decimal points when you’re adding or subtracting, and apply the rules for multiplication and division of decimals correctly.

Step 4: Check the Answer

Finally, check if your answer makes sense in the context of the problem.

Consider this problem: Laura bought \(2.3\) kilograms of apples and \(1.5\) kilograms of grapes. How many kilograms of fruit did she buy in total?

Step 1: Understand that you know the weight of apples and grapes separately, and you need to find the total weight.

Step 2: Realize that to find the total, you need to add the weights together.

Step 3: Add the weights: \(2.3\ kg + 1.5\ kg = 3.8\ kg\).

Step 4: Check that the answer makes sense. Laura bought \(2.3\ kg\) of apples and \(1.5\ kg\) of grapes, so it makes sense that she bought \(3.8\ kg\) in total.

Keep practicing with different word problems, and you’ll get the hang of decimal operations in no time. Remember, the more you practice, the better you’ll get. Happy calculating!

by: Effortless Math Team about 9 months ago (category: Articles )

Effortless Math Team

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Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

Mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 7 math word problems the ultimate guide to tackling 7th grade math word problems, mastering grade 2 math word problems the ultimate guide to tackling 2nd grade math word problems, mastering grade 8 math word problems the ultimate guide to tackling 8th grade math word problems, mastering grade 4 math word problems the ultimate guide to tackling 4th grade math word problems, mastering grade 3 math word problems the ultimate guide to tackling 3rd grade math word problems.

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Partitioning Lesson

This Year 4 Partitioning lesson covers the prior learning of place value in 3-digit numbers, before moving onto the main skill of partitioning numbers into thousands, hundreds, tens and ones, including unconventional partitioning.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

National Curriculum Objective

Mathematics Year 4: (4N4a) Identify, represent and estimate numbers using different representations

Mathematics Year 4: (4N6) Solve number and practical problems that involve 4N1 – 4N5 and with increasingly large positive numbers

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Lesson Slides

These lesson slides guide pupils through the prior learning of place value in 3-digit numbers, before moving onto the main skill of partitioning. There are a number of questions to check pupils' understanding throughout.

Modelling Powerpoint

This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this lesson.

These are the same as the lesson slides on Classroom Secrets. You can assign this as an activity for pupils to access individually in school or remotely from home.

Video Tutorial

Aaron shows pupils how to use a part-whole model to partition numbers in this Partitioning 2-Digit Numbers Video Tutorial.

1 Prior Learning

This worksheet recaps place value in 3-digit numbers, before moving onto the main skill of partitioning numbers into thousands, hundreds, tens and ones, including unconventional partitioning.

In this Tens and Ones Partitioning Video Tutorial, Katie shows pupils how to partition a 2-digit number into tens and ones.

Interactive Challenge Activity

This Year 1 Partitioning Numbers Maths Challenge checks pupils' understanding of partitioning numbers within 100.

2 Varied Fluency

This worksheet includes varied fluency questions for pupils to practise the main skill for this lesson.

Interactive Activity

This Year 4 Partitioning Numbers Game checks pupils’ understanding of partitioning 4-digit numbers into thousands, hundreds, tens and ones.

2 Reasoning & Problem Solving

This differentiated worksheet includes reasoning and problem solving questions to support the teaching of this step.

This partitioning extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the partitioning.

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of partitioning.

Discussion Problem

This worksheet includes two discussion problems which can be used in pairs or small groups to further pupils' understanding of the concepts taught in this lesson.

This Year 4 Partitioning Maths Challenge is designed to check pupils' ability to partition a number in to 1s, 10s, 100s and 1000s.

This differentiated worksheet includes varied fluency and reasoning and problem solving questions to support the teaching of this step.

2 Additional Activities

Home Learning Pack

This Autumn week 2 Maths pack contains varied fluency, reasoning and problem solving worksheets.

Consolidation Pack

This Place Value Consolidation Year 4 Autumn Block 1 resource is aimed at Year 4 Secure and has been designed to give children the opportunity to consolidate the skills they have learned in Block 1 – Place Value.

Learning Video Clip

Allegra is a tour guide who works in Rome. Today she is organising tours and exhibits in Vatican City, and she needs your knowledge of partitioning to help her.

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Operating with Decimals

Mathematics

Level 5 Level 6 Level 7

What is this sequence about?

This learning sequence aims to develop student proficiency when adding, subtracting, multiplying and dividing with decimals. A well-developed understanding of place value and number sense is critical for students to flexibly and intuitively operate with decimals. This sequence provides opportunities for students to consolidate their understanding of the continuous nature of the base 10 system and deepen their conceptual understanding about the role of estimation and efficient strategies when adding, subtracting, multiplying and dividing with decimals.

The sequence has been written by teachers for teachers. It has been designed to provide students with rich, engaging learning experiences that address the Victorian Curriculum. The sequence consists of four flexible stages, including suggested learning intentions.

Overview of stages

1. Decimal Number Sense

Suggested Learning Intentions

• To understand decimal place value to the thousandths
• To understand the relative size of decimals

3. Multiplying and Dividing by Powers of 10

• To understand that scientific notation can be used to describe infinitely large and infinitely small numbers
• To learn how to multiply and divide decimals using knowledge of place value in a base-10 system

2. Adding and Subtracting Decimals

• To solve decimal problems using rounding and estimation 
• To use my understanding of place value to solve decimal problems

4. Multiplying and Dividing Decimals

• To recognise the appropriate operation when solving decimal problems in context
• To use my number sense when multiplying and dividing decimal problems

Prior knowledge

Before you commence this sequence, it is suggested that you ensure your students are familiar with terms and concepts of place value, tenths and hundredths ( VCMNA159 ) and the connection between fractions and decimals. Students should also have had experience using intuitive and flexible computation strategies for whole number ( VCMNA156 ), which includes rounding and estimation.

It will be helpful for students to have first explored the concepts contained in the ‘Fractions to decimals’ and ‘Colour in decimats’ stages of the Keeping it in Proportion: Fractions and Decimals sequence, that focus on comparing and ordering decimals ( VCMNA187 ; VCMNA190 ) as well as decimal place value ( VCMNA189 ).

You can find support for building students’ understanding of these concepts in the Mathematics Curriculum Companion . The Teaching Context and Teaching Ideas related to content descriptions VCMNA159 ;  VCMNA189 and VCMNA190 may be particularly useful.

Teaching strategies

The Mathematics Curriculum Companion provides teachers with content knowledge, suggested teaching and learning ideas as well as links to other resources. Resources are organised by Mathematics strands and sub-strands and incorporate the proficiencies: Understanding, Fluency, Problem Solving and Reasoning. The Companion is an additional resource that you could refer to when you are planning how you might use the sequence in your school.

The sequence highlights opportunities to apply the  High Impact Teaching Strategies (HITS) , which are a component of the Victorian Teaching and Learning Model . 

The sequence highlights the use of a variety of scaffolding practices to help support students in the learning process, in particular:

• Collaborating
• Convince Me

Students should be able to understand and use the following concepts and terms by the end of the learning sequence:

You can find definitions of some of these terms in the F-10 Victorian Curriculum Mathematics Glossary . It is recommended that the explicit teaching of vocabulary occur throughout the learning sequence.

The Literacy in Mathematics section of the Literacy Teaching Toolkit provides several teaching strategies with worked examples demonstrating how teachers can use literacy to support student understanding of mathematical language. A further set of strategies demonstrate how teachers can develop students' literacy skills to support their mathematical problem solving.

Opportunities for formative and summative assessment are identified at different stages of the learning sequence. Look for the 'Assessment Opportunity' icon.

You may want to develop a rubric to assess students’ progress. A range of Formative Assessment resources are available from the Victorian Curriculum and Assessment Authority. This includes a Guide to Formative Assessment Rubrics , a series of modules to support you to develop your own formative assessment rubrics, and sample rubrics across six curriculum areas that demonstrate how you can put formative assessment rubrics into practice in the classroom.

In developing a rubric, you may wish to co-construct assessment criteria with your students. Each stage of the sequence provides sample success criteria for students working at Level 6.

The Victorian Curriculum and Assessment Authority has published annotated work samples that provide teachers with examples of student learning achievement at multiple levels for each strand of the Mathematics curriculum.

Victorian Curriculum connections

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 6, but also addresses the following content descriptions from Level 5:

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 5:

• Students solve simple problems involving the four operations using a range of strategies including digital technology
• Students estimate to check the reasonableness of answers and approximate answers by rounding
• Students order decimals and unit fractions and locate them on a number line
• Students continue patterns by adding or subtracting fractions and decimals.

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 6, addressing the following content descriptions:

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 6:

• Students make connections between the powers of 10 and the multiplication and division of decimals
• Students add, subtract and multiply decimals and divide decimals where the result is rational.

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 6, but also addresses the following content descriptions from Level 7:

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 7:

• Students solve problems involving all four operations with fractions, decimals, percentages and their equivalences
• Students make simple estimates to judge the reasonableness of results.

Learning Progressions

The Numeracy Learning Progressions support teachers to develop a comprehensive view of how numeracy develops over time. You can use the numeracy learning progressions to:

• identify the numeracy capability of your students
• plan targeted teaching strategies, especially for students achieving above or below the age-equivalent expected level in the Victorian Curriculum: Mathematics
• provide targeted feedback to students about their learning within and across the progressions.

The sequence is related to the following progressions:

Click on the Learning Progression to access more detailed descriptions of student learning at each level.

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Decimals Reasoning and Problem Solving

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 April 2022

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These problems will give your Year 6 pupils the opportunity to reason and solve problems with decimals.

This is a sample resource.

For a full year’s worth of reasoning and problem solving for Year 6 please see:

https://www.tes.com/teaching-resource/reasoning-and-problem-solving-for-year-6-12201133

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