problem solving measurement year 2

Year 2 | Problem Solving with Length Worksheets

Year 2 measurement maths mastery resources

Aligned with the maths mastery approach,  these differentiated  Year 2 | Problem Solving with Length Worksheets  are designed to save you time whilst delivering high quality learning experiences for children.

Topic: Measurement: length and height

Combine with our lesson plan, maths activity cards, lesson presentations and revision mat for a complete maths lesson, complete with National Curriculum links, vocabulary, TAF statements, small steps, differentiation and ready to progress criteria.

Explore our year 2 summer block 1 resources.

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Problem Solving Measurement Year 2

Nur Anis Afifah Azliman

Problem Solving

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Problem-solving maths investigations for year 2.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 2 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 2 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 2:

• Individually, they are incorporated into every unit in our Year 2 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 2 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Year 2 Maths Worksheets UK Hub Page

Welcome to Math Salamanders Year 2 Maths Worksheets hub page.

In our Year 2 area, you will find a wide range of printable math worksheets and Maths activities for your child to enjoy.

Come and take a look at our dot-to-dot pages, or our maths games. Perhaps you would prefer our 2d shape worksheets, or learning about numbers using our number line worksheets?

Hopefully you will find something here to meet your child's maths requirements!

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 2 Maths Learning

Here are some of the key learning objectives for the end of Year 2:

• know and use Place value up to 100
• Compare and order numbers up to 100
• Counting on and back in 1s and 10s
• count in 2s, 5s and 10s
• Position numbers on a number line up to 1000
• use addition and subtraction facts to 20
• use related facts for addition and subtraction
• add or subtract 1 or 10 from a 2-digit number
• add and subtract 2-digit numbers
• number bonds to 100 using tens only
• add three single-digit numbers
• recognise and make equal groups
• use the x symbol to write multiplication sentences
• use arrays and pictures to represent multiplication sentences
• know multiplication facts for the 2, 5 and 10 times table
• recognise and find a half, a quarter and a third
• understand and use fraction notation
• understand the equivalence of a half and two-quarters
• count on in halves, thirds and quarters up to 10
• count in pence: 1p, 2p ,5p, 10p and 20p
• count in pounds: £1, £2, £5, £10 and £20
• find a simple total or difference between two money amounts
• find the change from simple amounts
• tell the time: o'clock, half-past, quarter-past and to
• understand and compare durations of time
• compare and measure length, mass, volume, capacity and temperature
• read a variety of scales going up in 1s, 2s, 5s and 10s
• recognise 2D and 3D shapes
• count sides and vertices on 2D shapes
• count faces, edges and vertices on 3D shapes
• sort and make patterns with 2D and 3D shapes
• describe movement and turns
• make tally charts
• draw and interpret pictograms
• understand and use block diagrams

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 2 is generally equivalent to 1st Grade in the US.

On this page you will find link to our range of math worksheets for Year 2.

Quicklinks to Year 2 ...

• Place Value Zone

Operations Zone

• Mental Math Zone

Word Problems Zone

• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 2 Place Value Charts

Here you will find a range of Free Printable Place Value Charts for Year 2.

These printable charts will help your child learn to read and write numbers.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Number Grid up to 200

Place Value and Counting Worksheets

Here you will find a range of Year 2 Place Value Worksheets.

These Year 2 maths worksheets will help your child learn their place value, reading, writing and ordering numbers up to 100.

There are also some money worksheets involving counting in dimes and pennies to support place value learning.

• learn to order numbers to 100;
• learn to count in dimes and pennies;
• learn to read and write numbers to 100.

Year 2 Place Value Worksheets

• Place Value to 20 Worksheets
• Math Place Value Worksheets Tens and Ones
• Ordering 2-digit numbers Worksheets
• Greater than Less than Worksheets - up to 2 digit numbers
• Printable Counting Worksheets to 50
• Missing Number Chart 1-100
• Counting by 2s Worksheets
• Math Worksheets Counting by 1s 5s and 10s

Number Line Worksheets

Here is our selection of free printable number line worksheets for Year 2 pupils.

These first grade math worksheets will give your child a good grasp of place value and number sequences up to 100.

• count on and back by ones;
• position numbers to 100 on a number line.
• Number lines to 20
• Number lines to 100

Year 2 Mental Maths Zone

Here you will find a range of printable mental math sheets designed especially for Year 2 children.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, solving word problems and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• Year 2 Printable Mental Maths

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Year 2 Addition Worksheets

Here you will find a range of Free Printable Addition Worksheets to support Year 2.

The following first grade math worksheets involve adding different amounts.

• learn their addition facts to 12+12;
• learn to solve an addition fact where one of the addends is missing;
• learn to add numbers in columns up to 100.
• Number Bonds to 10 and 12
• Addition Sentences to 12
• Addition Fact Practice to 12
• Addition Facts to 20 Worksheets
• Adding tens
• Addition Word Problems
• 2 Digit Addition Without Regrouping
• 2 Digit Addition Worksheets With Regrouping
• Free Addition Worksheets (randomly generated)

Year 2 Subtraction Worksheets

Here you will find a range of Year 2 Subtraction Worksheets.

The following worksheets involve using the Math skills of subtracting.

Using these Year 2 maths worksheets will help your child to:

• learn their addition and subtraction facts to 12;
• learn to subtract 2 digit numbers.
• Subtraction Facts to 12
• Subtracting tens
• Subtraction Word Problems
• Two Digit Subtraction Worksheets Without Regrouping
• 2 Digit Subtraction Worksheets With Regrouping
• Free Subtraction Worksheets (randomly generated)

Addition & Subtraction Worksheets

If you need to mix and match addition and subtraction fact questions within the same sheet, then use this section here.

The addition and subtraction worksheets involve counting on and back with numbers to 12.

• Math Activities Addition and Subtraction to 12
• Add and Subtract 10 Worksheets
• Addition Subtraction Worksheets (randomly generated)
• Addition and Subtraction Problems

Year 2 Maths Word Problems

Here you will find a range of math word problems aimed at Year 2 level. Each problem sheet is based on an interesting theme such as parties or the seaside.

• Add and subtract with numbers to 12;
• order numbers to 100;
• solve a range of math problems.
• Maths Problems for Year 2

Longer Math Problems

• Year 2 Maths Problems (1st Grade)

Year 2 Geometry Worksheets

Here is a range of free geometry worksheets for Year 2 pupils.

The following worksheets will help your child to:

• Identify and name a range of 2d and 3d shapes;
• Draw 2d shapes;
• Know some of the properties of 2d shapes.
• Year 2 Geometry Worksheets (1st Grade)

Measurement Zone, including Time & Money

Year 2 measurement worksheets.

Here is our selection of measurement worksheets for Year 2 pupils.

These sheets involve reading scales going up in ones to find the weight or liquid capacity.

Using these sheets will help children to consolidate their counting as well as learning to read a simple scale.

• Year 2 Measurement Worksheets (1st Grade)

Year 2 Money Worksheets

Here you will find a range of free printable First Grade Money Worksheets.

The following worksheets involve counting different amounts of money in pennies, nickels and dimes.

• learn the names and values of the US coins;
• learn to count up different amounts of money to £1 in coins.
• Free Counting Money Worksheets UK Coins (easier)
• Free Money Worksheets UK Coins up to £1

Printable Money Resources

• Printable Money Flashcards
• Kids Counting Money Dominoes

Telling the Time Worksheets

Here is our selection of telling the time worksheets for 1st grade.

• read o'clock and half-past times;
• convert o'clock and half-past times to digital;
• draw clock hands correctly to mark out o'clock and half-past.

The year 2 maths worksheets in this section will help your child learn to tell simple times on an analogue clock.

• Telling Time Worksheets o'clock and half-past
• Clock Worksheets - Quarter Past and Quarter To

Year 2 Bar Graph Worksheets

Here is our selection of bar graphs for first graders.

These Year 2 maths worksheets involve reading and interpreting a range of bar graphs and picture graphs with a scale going up in ones.

Using these sheets will help children to understand how bar graphs work.

• Year 2 Picture/Bar Graphs (First Grade)

Fun Zone: Puzzles, Games and Riddles

Year 2 Maths Games

Here you will find a range of free printable Math games. All children like to play Math games, and you will find a good range of Maths Games at a Year 2 level here for your child to play and enjoy.

• Year 2 Maths Games (First Grade)

Year 2 Maths Puzzles

Here you will find a range of printable Year 2 level math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition and subtraction facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• develop thinking and reasoning skills;
• develop perseverance.
• Year 2 Maths Puzzles (1st Grade)
• Dot to Dot up to 50

Math Salamanders Year 2 Maths Games Ebook

Our Year 2 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store - use the link below to find out more!

• Year 2 Maths Games Ebook

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

• National Curriculum Tool

Year 2 - Measurement

New curriculum.

choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

compare and order lengths, mass, volume/capacity and record the results using >, < and =

recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

find different combinations of coins that equal the same amounts of money

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

compare and sequence intervals of time

• tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times
• know the number of minutes in an hour and the number of hours in a day.

Non-Statutory Guidance

Pupils use standard units of measurement with increasing accuracy, using their knowledge of the number system. They use the appropriate language and record using standard abbreviations.

Comparing measures includes simple multiples such as ‘half as high’; ‘twice as wide’.

They become fluent in telling the time on analogue clocks and recording it.

Pupils become fluent in counting and recognising coins. They read and say amounts of money confidently and use the symbols £ and p accurately, recording pounds and pence separately.

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

Making connections to other topics within this year group.

Number and place value

Pupils should be taught to:

• count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
• recognise the place value of each digit in a two-digit number (tens, ones)
• identify, represent and estimate numbers using different representations, including the number line
• compare and order numbers from 0 up to 100; use <, > and = signs
• read and write numbers to at least 100 in numerals and in words
• use place value and number facts to solve problems.

Making connections to this topic in adjacent year groups

• lengths and heights (e.g. long/short, longer/shorter, tall/short, double/half)
• mass or weight (e.g. heavy/light, heavier than, lighter than)
• capacity/volume (full/empty, more than, less than, quarter)
• time (quicker, slower, earlier, later)
• lengths and heights
• mass/weight
• capacity and volume
• time (hours, minutes, seconds)
• recognise and know the value of different denominations of coins and notes
• sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening
• recognise and use language relating to dates, including days of the week, weeks, months and years
• tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

Non-statutory guidance

The pairs of terms: mass and weight, volume and capacity, are used interchangeably at this stage.

Pupils move from using and comparing different types of quantities and measures using non-standard units, including discrete (e.g. counting) and continuous (e.g. liquid) measurement, to using manageable common standard units.

In order to become familiar with standard measures, pupils begin to use measuring tools such as a ruler, weighing scales and containers.

Pupils use the language of time, including telling the time throughout the day, first using o’clock and then half past.

• measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
• measure the perimeter of simple 2-D shapes
• add and subtract amounts of money to give change, using both £ and p in practical contexts
• tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks
• estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, hours and o’clock; use vocabulary such as a.m./p.m., morning, afternoon, noon and midnight
• know the number of seconds in a minute and the number of days in each month, year and leap year
• compare durations of events, for example to calculate the time taken by particular events or tasks.

Non statutory guidance

Pupils continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (e.g. 1 kg and 200g) and simple equivalents of mixed units (e.g. 5m = 500cm).

The comparison of measures should also include simple scaling by integers (e.g. a given quantity or measure is twice as long or five times as high) and this should connect to multiplication.

Pupils continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units, and giving change using manageable amounts. They record £ and p separately. The decimal recording of money is introduced formally in year 4.

Pupils use both analogue and digital 12-hour clocks and record their times. In this way they become fluent in and prepared for using digital 24-hour clocks in year 4.

Cross-curricular and real life connections

Learners will encounter measurement in various ways in everyday life. Time, money, temperature, weighing ingredients are just some of them.

Time is a sequence of events that relates to our daily life. Clocks/watches and calendars are tools that measure time.

We use money to buy the things we need. Using money involves using different mathematics skills like counting, adding, and subtracting amounts of money.

Measurement skills are extensively used in every kitchen, every recipe. In school, opportunities arise in other subjects such as science – measuring plant growth and monitoring and recording temperatures, or P.E. – measuring long jumps, counting skips, timing races etc.

Take cross-curricular opportunities to deepen children’s understanding of units of measurement. For example, ask them to:

• find out what measures their parents use in their jobs or in the home;
• take measurements of jumps or throws in PE lessons;
• use measures in art, design and technology lessons, discussing degrees of accuracy.
• Money Problems? This Nrich article explains the skills that children need to understand ‘Money’ When first introduced to money in the classroom, many children find it difficult to distinguish between the value of a pile of coins and the number of coins in the pile. These children may go on to find the concepts of equivalent amounts of money and giving change difficult to grasp.
• Mooney, C., Briggs, M., Fletcher, M., Hansen, & McCullouch, J. (2012). Primary mathematics Teaching Theory and Practice : 6th ed. London: Sage. Chapter 10, Measures.
• The Maths4Life booklet, Measurement , is an overall guide to some of the complexities in teaching and learning measurements, including possible misconceptions. This booklet, created for teachers of adult learners contains a great deal of helpful background information and ideas that primary teachers will be able to use or adapt. It also includes some suggestions for classroom activities.

• Charlotte's Clock is a different route to teaching our children to tell the time. Learning to tell the time isn’t easy. For many children, and for a variety of reasons, it’s especially difficult

Activity Set A

Other questions to use as starting points;

• What could you use to find out how much water this container holds?
• Would it be better to use multilink cubes or peas to balance the weight of this shoe? Why?
• Would you measure the length of a book in centimetres or metres? Why?
• What units would you use to measure the width of the classroom?
• How about the weight of your teacher?
• Look at a mug. Which of these amounts would you choose to say how much water the mug holds? 1 metre, 1 litre, 1 centimetre, ¼ kilogram, ¼ litre

Possible contexts include:

• Estimating measures, e.g. give children a 1kg weight to hold. Then give them a range of everyday items and ask them to say whether they weigh more, less or about the same as 1kg.
• Estimate and then check how far you can jump from this line.
• Units used to measure everyday objects, e.g. look at food labels and find a big packet of food that weighs less than a small packet of food.
• Comparing objects using appropriate measurements, e.g. working with two or more objects to find the shortest, longest, heaviest, smallest capacity, etc. and explain how this was done and what units of measurement were used.

(NB The following three resources were produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resources have the potential to complement teaching in line with the new 2014 mathematics curriculum)

This Interactive Teaching Programme displays an on-screen ruler you can use to measure lines and the sides of shapes. There is a choice of rulers and five screens to use to demonstrate measuring length. You can draw your own lines and shapes or select those that are available on the ITP. The ITP can be used to demonstrate how to use measure using different rulers. The ITP can be used to compare lengths and the perimeters of shapes and to support children's understanding of scale. You can develop their ability to estimate length against a given scale and use the ruler to check the accuracy and demonstrate what to the nearest half and whole unit means.

This ITP allows you to add different masses to or from a scale pan. You can add masses of 1, 2, 5, 10, 50, 100 and 500 units. The pointer or hand shows the total mass. This can be hidden to promote children’s prediction skills. The maximum value of the circular scale can be changed together with the size of the interval. A digital readout can also be hidden or displayed. A red marker can be used to keep a track of previous values and to set target quantitiesp

This ITP allows you to control two taps that pour a liquid in and out of a measuring cylinder. You can set the scale on the cylinder to a maximum of 50, 100, 200, 500 or 1000 units and the scale interval to 1, 2, 5 or 10 units. You can simply turn the taps on and off and ask questions that involve prediction, addition and subtraction.

Activity Set B

• Order Order!

Both of these activities require the children to order various quantities from smallest to largest. A good activity to assess estimation skills and knowledge of units of measurement.

Activity Set C

In your bank, you have three types of coins. The number of spots shows how much they are worth. Match your coin values to those shown.

This activity from Nationwide Bank Education has three levels of difficulty, requiring children to share coins equally.

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

Change White Elephant is an activity about giving change.

Activity Set D

(NB This resource was produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resource has the potential to complement teaching in line with the new 2014 mathematics curriculum)

This ITP can be used to show analogue time, digital time or synchronised analogue and digital clocks. The program allows you to add or subtract a selected time interval.

Use a counting stick to practise counting in 5-minute, quarter-hour or half-hour intervals.

Since counting sticks usually have 10 intervals, you may wish to make a stick with 12 divisions.

• What Is the Time?  
• Provide plenty of opportunities to tell the time during the routine of the day. Put children in charge of letting everyone know when it is 10 minutes before assembly/lunch/break.Check that children can tell you how many minutes are in an hour and how many hours in a day. Have a detailed timetable for children to refer to, with times displayed as analogue clock faces as well as written times.
• Matching times to everyday events, e.g. match some pictures of daily events to some given clock faces showing their typical times.
• Comparing times, e.g. sort some given times into a sequence from earliest to latest and draw hands onto corresponding clock faces.
• Problems involving the duration of time, e.g. School starts at 9 o'clock; show this time on your clock. Now show what time it would be if you were half an hour late.
• I went out for a walk at half past 3 and walked for quarter of an hour. Show me on these two clock faces what time I started and what time I would then have finished.

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

• Suggest sensible units you might use to measure: the height of your table; how much water is in a cup; the weight of my reading book; how long it takes me to wash my hands.
• Choose a piece of equipment to help you measure: the weight of your shoe; how long the classroom is; how long this lesson lasts; how much water a cup holds.

How much water is in this measuring jug?

About how heavy do you think your pencil case is?

• If I programme my floor turtle to go forward three metres is there enough room in the classroom? How could you measure to find out?
• Megan and Jack are growing beans. Megan’s plant is 25 cm tall. Jack’s is 38 cm tall. Whose plant is the taller? By how much? Can you compare them using > or < ?

Harry has the same amount of money but has six coins. What are they? Is there only one possible answer?

• Jess has saved 62p. She spends 15p. How much money does she have left? She pays with a 50p piece. How much change does she get?

tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times.

• What time does this clock show?
• Draw a clock showing the time five minutes later.
• Show your school day on clock faces: when do you leave home, have breaks, go back home, etc.?
• Teachers TV: Primary Maths – Measures . Lesson Ideas on measures - children have to estimate the volume of puddles, make muffins and concoct magic potions!
• Bank of England. Part 1: What is money and how does it work? A useful support for teachers in helping children understand the importance and real life application of money.
• Piaget - conservation . This video shows young children having a conversation with their teacher about the amount of water in a container, the number of coins in a row and sharing biscuits equally. It clearly shows that young children judge an amount simply from what they see. Conservation, in terms of quantity, is an understanding that needs to be developed through practical experiences in the EYFS. Some children take longer than others to achieve this understanding. It is worth asking your colleagues to bear this in mind when they work on number, length, weight and capacity in KS1.

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Year 2, ordering measures, word problems, worksheet

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

2 September 2022

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Measure Length (m) Lesson

This Year 2 Measure Length (m) lesson covers the prior learning of measuring length in centimetres, before moving onto the main skill of measuring length in metres.

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 Objectives Mathematics Year 2: (2M2)  Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit using rulers, scales, thermometers and measuring vessels

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Lesson Slides

These lesson slides guide pupils through the prior learning of measuring length in centimetres, before moving onto the main skill of measure length (m). 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.

1 Prior Learning

This worksheet recaps prior learning of measuring length in centimetres, before moving onto the main skill of measuring length in metres.

Video Tutorial

In this Measure Lengths using Centimetres Video Tutorial, Katie explores measuring the length of objects using centimetres. Children can join in by using any objects and a ruler or tape measure. Throughout the video, there will be questions for the children to answer.

Interactive Activity

This Year 1 Measure Lengths Using Centimetres Game aims to support pupils' measurement skills.

2 Varied Fluency

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

This Year 2 Measure Length m activity checks pupils' understanding of measuring objects using metres.

2 Reasoning & Problem Solving

This measure length (m) extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the measure length (m) lesson.

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of measure length (m).

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

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.

Interactive Challenge Activity

This Year 2 Measure Length (m) Maths Challenge checks pupils' ability to measure in metres within a problem solving context.

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

2 Additional Activities

Consolidation Pack

These Length and Height worksheets are fantastic at helping your pupils practice their reasoning and problem solving skills. This pack contains two different question types for Year 2 Spring Block 5.

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This Summer week 1 Maths pack contains varied fluency, reasoning and problem solving worksheets

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Water Jug Problem in AI: An In-Depth Guide

Curious about the Water Jug Problem in AI? This classic puzzle involves measuring exact amounts of water using two jugs of different capacities. This blog will explore the Water Jug Problem in AI, its algorithmic solutions, practical examples, and how it's used to teach concepts in Artificial Intelligence. Let's dive in!

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Ever pondered the seemingly simple task of measuring exact quantities of water using just two jugs? This classic puzzle has been a staple in computer science, challenging minds for decades. Welcome to the intriguing world of the Water Jug Problem in AI. Beyond being a mere brain teaser, it’s a fundamental problem that has shaped the development of Artificial Intelligence algorithms.   

Imagine teaching a computer to solve puzzles, make decisions, and find optimal solutions – that’s where the Water Jug Problem comes in. In this blog, we’ll delve into the intricacies of this problem, exploring various solution approaches and understanding its significance in the broader context of AI. Get ready to quench your thirst for knowledge as we unravel the secrets of this classic puzzle!  

Table of Contents  

1) What is the Water Jug Problem in AI?   

2) Solving the Water Jug Problem  

a) Breadth-First Search (BFS)  

b) Depth-First Search (DFS)  

c) Pruning  

3) Conclusion  

What is the Water Jug Problem in AI?   

The Water Jug Problem in AI is a classic puzzle often used to illustrate problem-solving and search algorithms. It involves two jugs with known capacities and an unlimited water supply. The challenge is to measure a specific amount of water using these jugs. For example, given a 3-litre and a 5-litre jug, the goal might be to measure exactly 4 litres .   

The problem requires figuring out a sequence of actions (filling, emptying, and transferring water between jugs) to achieve the desired measurement. It's a practical example of how AI systems can be designed to explore possible states and actions to reach a solution, demonstrating concepts like state space, goal state, and operators. This problem helps understand the importance of planning and decision-making in AI.  

Solving the Water Jug Problem  

After understanding the basics of the Water Jug Problem in AI, it's time to explore the methods used to solve it. These methods include various search algorithms and optimisation techniques, each offering unique approaches to finding the solution.  

1) Breadth-First Search (BFS)  

Breadth-First Search (BFS) is a fundamental algorithm in computer science, particularly useful in solving the Water Jug Problem . BFS explores all possible moves level by level, starting from the initial state. In the context of the Water Jug Problem , this means systematically filling, emptying, and transferring water between jugs, considering every possible state that can be reached from the current state.  

To implement BFS, you use a queue to keep track of the current state and all potential subsequent states. The algorithm begins by enqueueing the initial state, then iteratively dequeues states to explore their neighbouring states. For example, if you have a 3-litre jug and a 5-litre jug, BFS would first consider the states where each jug is either filled to its capacity or emptied. It then explores transferring water between the jugs in various configurations.  

The main advantage of BFS is its ability to find the shortest path to the goal state, ensuring the minimum number of moves. However, BFS can be memory-intensive, as it needs to store all possible states . Despite this, BFS is particularly effective when the solution requires exploring all possibilities or when the search space is relatively small , making it a good fit for problems like the Water Jug Problem .  

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2) Depth-First Search (DFS)  

Depth-First Search (DFS) takes a different approach by exploring one potential path to its end before backtracking and trying alternative paths. In the Water Jug Problem , DFS starts from the initial state and continues to explore the deepest level of the state space before moving back to explore other branches. This is implemented using a stack, which helps in maintaining the sequence of states being explored.  

DFS is often more memory-efficient than BFS, as it only needs to store the current path and backtrack when necessary. However, one downside is that DFS does not guarantee finding the shortest path to the solution. In some cases, it may even explore paths that are far longer than necessary, particularly if the solution lies closer to the root of the search tree.  

In the water jug problem, DFS might fill one jug completely and then attempt to pour water into the other jug until it is full or empty before moving to another operation. This method can be advantageous when you need to explore deep solutions or when the search space is large, and the solution lies deep within it. However, care must be taken to avoid infinite loops or repeatedly visiting the same states, which can be mitigated by keeping track of visited states.  

3) Pruning  

Pruning is a technique used in search algorithms to eliminate paths that are unlikely to lead to a solution, thereby improving efficiency. In the context of the Water Jug Problem , pruning can significantly reduce the number of states that need to be explored, speeding up the search process.  

One common pruning method involves keeping track of visited states to prevent re-exploration. For instance, if you have already explored the state where the 3-litre jug is full, and the 5-litre jug is empty, there is no need to revisit this state. This prevents redundant calculations and helps the algorithm focus on new, unexplored paths.  

Another pruning strategy involves identifying and ignoring moves that do not contribute to reaching the goal. For example, if the goal is to measure 4 litres and you find yourself repeatedly filling and emptying the same jug without making progress, these actions can be pruned from consideration. Pruning is particularly useful in the water jug problem when combined with BFS or DFS, as it helps manage the search space more effectively. It can also be combined with heuristics to further refine the search process, making it faster and more efficient. By reducing the number of unnecessary or unproductive states, pruning helps in achieving the solution more quickly and with less computational effort.

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The Water Jug Problem in AI might seem simple, but it's a cornerstone in AI problem-solving. From search algorithms to constraint satisfaction, its applications are vast. By understanding this puzzle, you've taken a significant step into the world of AI. Keep exploring, experimenting, and pushing the boundaries of Artificial Intelligence!

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Frequently Asked Questions

The main constraints are the jug capacities , the initial and desired amounts of water, and the allowable actions (fill, empty, transfer). The problem must be solved within these limitations, ensuring exact measurements.  

The problem involves measuring a specific amount of water using two jugs with known capacities without measuring tools. The challenge is to find a sequence of actions (filling, emptying, transferring) to achieve the exact amount. 

The Water Jug Problem illustrates state space search in AI, exploring all possible states (amounts of water in jugs) and transitions (actions taken). It demonstrates problem-solving through algorithms like BFS, DFS, and pruning to find a solution efficiently.  

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Alongside our diverse Online Course Catalogue, encompassing 1 9 major categories, we go the extra mile by providing a plethora of free educational Online Resources like News updates, Blogs , videos, webinars, and interview questions. Tailoring learning experiences further, professionals can maximise value with customisable Course Bundles of TKA .       

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Our Data, Analytics & AI Blogs cover a range of topics related to Artificial Intelligence , offering valuable resources, best practices, and industry insights. Whether you are a beginner or looking to advance your Artificial Intelligence Skills, The Knowledge Academy's diverse courses and informative blogs have got you covered.  

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