Do you operate a ‘mastery’ classroom? Do you want to know how well your students really understand place value, number lines and the intervals found on them? Look no further than this full-lesson reasoning-based activity, complete with answers. There is also a complete set of mastery style questions after the initial task, which is aimed specifically at stretch and challenge for all children. This activity is ideal for children in Key Stage 2. How could I use this activity? As a pre-assessment and post-assessment of any unit you teach linked to number lines, intervals (marked and unmarked) and even measures; As a full-lesson activity related to those same areas of learning. Why is this activity useful? This activity has been specifically designed to develop children’s reasoning skills. They are given some limited information for each number line, with the only constant being the number they have to mark. Each number line represents a different scale, with different values for the intervals. Children will need to use all of their logic to establish the other intervals, and therefore where 564 can be marked. We have used this activity in a classroom, and found the knowledge we gain as teachers about each child’s true maths ability and understanding, is far greater than any test could provide. Which objectives in the UK National Curriculum does it match? Key Stage 2 Number and Place Value: recognise the place value of each digit in a three-digit number (hundreds, tens, ones) compare and order numbers up to 1000 identify, represent and estimate numbers using different representations solve number problems and practical problems that involve all of the above

LESSON TYPE: Investigation and Low-Threshold High Ceiling This is a full lesson PowerPoint for KS2 children. The lesson is a Low-Threshold High-Ceiling task as defined by nRich and the University of Cambridge. Included are some simple instructions for moving through the PowerPoint, and a main task page. From this page, students or teachers can navigate to two question ‘prompts’ for if they are stuck, and four ‘ready to’ stars, for if they need further challenge. The lesson is designed so that all children are able to access the content at their level, with multiple examples of self and teacher directed challenge evident throughout the activity. This lesson has been delivered during an OfSted Inspection, and received ‘Outstanding’ feedback for its focus on mastery skills, child-led learning and stretch and challenge for all students.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (upto 20+20) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (upto 200+200) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (upto 50+50) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

Do your children need practice solving problems and puzzles? Do you need activities that specifically practise reasoning about the properties of numbers? Then look no further than this ‘Start the Day’ activity pack. This is the full pack which has 5 similar activities (each with teacher answers) in PDF and PowerPoint form for easy printing and sharing with your children on an interactive whiteboard. The activity is designed to help children master properties of number, including (but not limited to): Recognising the multiples and factors of different numbers; Identifying similarities between numbers, such as number of tens and ones, place holders, odds and evens etc; Recognising prime, square, triangular and cube numbers; Considering more obscure areas of mathematics (Fibonacci sequence, mathematical language such as dozen, century etc). Note: Any of the numbers presented could be the ‘Odd One Out’. The purpose of this activity is to encourage children to think of as many reasons for this choice, and justifying their decisions. The answer pages provide some reasons to allow teacher and pupil discussion during the plenary. Tips on how to deliver these activities: On the first occasion you use these activities, allow children a free run at solving the puzzle, perhaps with some very minor discussion around the known numbers and how they might help; Allow children to talk through their strategies for finding solutions, encouraging pupil voice in both paired and whole-class discussions; If necessary (some children won’t find a way to solve the problem without a system), share a way to work backwards. How many of the numbers are odd/even? How many of them can be divided by 6? Etc; Encourage children to think about what they did to make the problem smaller; Ask children how they could adapt the problem to make it easier, or more challenging (for example through using more numbers in the set, or through forcing a key rule (e.g. the odd one out must be because of its factors); Use one activity per week over a half term to encourage regular revisiting of the content (justifying the ‘Odd One Out’) and strategies (working backwards/trial and improvement); Have children create their own versions and send them to us to challenge our followers - Twitter: @UKExceED

As featured in Andrew Jeffrey’s recent Puzzle and Games CPD Webinar in conjunction with Oxford University Press, this is the free pack of reasoning starter activities. You can find additional packs for a small cost by visiting our shop. In this pack, you will find: 5 addition based activities; 5 multiplication based activities; Answers to each challenge. In the addition based activities (Addends 1, Addends 2 etc), children are given the sum total of each column and each row. They are asked to work out where each of the digits 1-9 should go in order to make those sums correct. In the multiplication based activities (Factors 1, Factors 2 etc), children are given the product total of each column and each row. They are asked to work out where each of the digits 1-9 should go in order to make those products correct. Additional information: Each square is colour-coded green and yellow for odd and even digits respectively. You do not have to share this with the children, but can if you feel this would help children to overcome some barriers to starting on the problem.

Do you operate a ‘mastery’ classroom? Do your students need to practise their addition skills to improve their fluency? Look no further than this HexaSums - Addition Fluency Starter. How to use the Starters: Each question starter displays a randomised set of 36 hexagons, each with a value attached. One the left of the screen, students are given an instruction to find a set number of adjacent hexagons, and sum their value to reach the Target Total (or as close to it as possible) on the right of the screen. The adjacent hexagons needed will always range between 2 and 6. The Target Total as always based on the mean average of all 36 hexagons, multiplied by the adjacent hexagons needed value. This means children will usually be able to find the Target Total exactly, but will always be very close at the very least. Note: This is the full pack for addition. The full pack has a total of 8 PDF documents, each with 10 starter activities. The full pack includes: All 36 hexagons between 0 and 10; All 36 hexagons between 0 and 20; All 36 hexagons between 0 and 50; All 36 hexagons between 0 and 100; 18 hexagons up to 10, and 18 hexagons up to 20; 18 hexagons up to 10, and 18 hexagons between 10 and 20; 18 hexagons up to 20, and 18 hexagons between 10 and 20; 18 hexagons up to 20, and 18 hexagons upto 100. Embrace the power of small ‘Adjacent Hexagons Needed’ and 'Target Totals’ Try not to be tempted to skip the sessions with low numbers like 2 for the adjacent hexagons needed, and 11 for example for the Target Totals. You’ll be suprised how many different ways they will find to complete the task. This will also encourage that speed of recall (for example, in searching for number bonds to 11: 10 and 1, 9 and 2, 8 and 3 etc). Encourage the children to make their own rules Ok, so we all know they need to be fluent, and at times that requires speed. So what if you feel that they are already there? Encourage children to create their own rules. When we’ve led this with our children, they’ve come up with brilliant ways of adapting the game which still suit the aims of the teacher. Here are some of the best: ChiSir, can we use subtraction? Yes, of course. For best results: Display the Question Starter on an IWB, or print for pairs of students; Use a 3-minute timer to allow children to find the target number; If children find an answer, encourage the mastery approach where they try to find other ways to achieve the Target Total; Make a game/competition from the Starter to create an ‘edge’ to the activity; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Encourage discussion about number bonds and how they help. The power of this daily approach is truly remarkable, and will have your children recognising number bonds to support calculation in no time.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (Decimal + Decimal upto 20) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (upto 100+100) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (upto 500+500) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

This is the full Intelligent Practice programme developed for fractions, and comes complete with answers on separate pages. You can try the Intelligent Practice: Fractions - Quarters free sample before you buy. There are separate pages for each multiple of 4 (and corresponding 10x value) from 4 to 100, representing 25 pages of worksheets designed specifically for developing student confidence and deeper understanding. The visual representations (BAR models) of the fractions aim to help children understand the concept of four ‘parts’ to a ‘whole’. Intelligent practice guides them through calculating one quarter, two quarters, three quarters and four quarters of the amount. The second section enables children to repeat this process for an amount that is 10 times greater, helping to reinforce place value understanding, and its effect on the fraction parts. The final section encourages children to reflect on the patterns they have noticed. Skilful questioning from the teacher will enable the children to identify, for example: Why the whole amounts used are always multiples of 4; Why the ‘parts’ in each section increase by the same amount each time; Why the ‘parts’ between sections are also 10x greater; Why every time the ‘whole’ increases by 4, each part increases by 1, etc.

This is the full Intelligent Practice programme developed for fractions, and comes complete with answers on separate pages. You can try the Intelligent Practice: Fractions - Thirds free sample before you buy. There are separate pages for each multiple of 3 (and corresponding 10x value) from 3 to 99, representing 33 pages of worksheets designed specifically for developing student confidence and deeper understanding. The visual representations (BAR models) of the fractions aim to help children understand the concept of three ‘parts’ to a ‘whole’. Intelligent practice guides them through calculating one third, two third, and three thirds of the amount. The second section enables children to repeat this process for an amount that is 10 times greater, helping to reinforce place value understanding, and its effect on the fraction parts. The final section encourages children to reflect on the patterns they have noticed. Skilful questioning from the teacher will enable the children to identify, for example: Why the whole amounts used are always multiples of 3; Why the ‘parts’ in each section increase by the same amount each time; Why the ‘parts’ between sections are also 10x greater; Why every time the ‘whole’ increases by 3, each part increases by 1, etc.

Do your children need practice solving problems and puzzles? Do you need activities that specifically practise reasoning with addition and subtraction? Then look no further than this ‘Start the Day’ activity pack. This is the full pack which has 5 similar activities (each with teacher answers) in PDF form for easy printing and sharing with your children on an interactive whiteboard. The activity is designed to encourage children to work systematically to find the correct totals. The 3 x 3 grid uses the digits 1-9 only once. Three different sections are colour-coded to represent a sum total of that colour, and the smaller sum totals represent the 4 touching squares around it. Children are forced to reason throughout, for example that if two blue squares total 8, the paired numbers must be either 1 + 7, 2 + 6, 3 + 5 but not 4 + 4 because the digit 4 cannot be used twice. Tips on how to deliver these activities: On the first occasion you use these activities, allow children a free run at solving the puzzle, perhaps with some very minor discussion around the sum totals and how they might help; Allow children to use the digit cards 1-9 to physically manipulate their puzzle; Allow children to talk through their strategies for finding solutions, encouraging pupil voice in both paired and whole-class discussions; If necessary (some children won’t find a way to solve the problem without a system), share a way to work backwards. For example, what piece of information helps us the most. Can we start from there? Why can’t a 5 go here? Etc; Encourage children to think about what they did to make the problem smaller; Ask children how they could adapt the puzzle to make it easier, or more challenging (for example through fewer clues, or being able to use digits more than once); Use one activity per week over a half term to encourage regular revisiting of the content (addition and subtraction) and strategies (working backwards/trial and improvement); Have children create their own versions and send them to us to challenge our followers - Twitter: @UKExceED

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (Decimal + Decimal upto 100) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (Decimal + Whole upto 20) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

Do you operate a ‘mastery’ classroom? Do your students take too long to recognise the benefit of inverse operations between addition and subtraction facts, or worse, cannot recognise them at all? Look no further than this Fact Families: Fluency with Calculations booklet. Note: This is the Addition (upto 999+999) which includes 5 randomised PDF packs. Click here to find the full pack for addition (Fact Families Addition Bundle) which has a total of 9 different sets, each with 5 different randomised PDFs, and each of those with an example, five questions and seperate answer pages. The full pack includes: Upto 20+20 Upto 50+50 Upto 100+100 Upto 200+200 Upto 500+500 Upto 999+999 Decimal + Whole (Upto 20) Decimal + Decimal (Upto 20) Decimal + Decimal (Upto 100) This resource has been developed through a proven research-based approach. The sessions each have an example set, and 5 follow up questions which helps children to build upon common techniques of calculation. All session use the same format, and provide colour coded visuals to help children make the links between the operations and their inverse. For best results: Use the PDF file to create an small booklet; Teach the main strategy for each session using a whole class approach, and the example calculation provided; Use a 3-minute timer to allow children to complete the page; Allow children to call out their name when they have finished, and tell them their time; Allow children to call out the answers in order afterwards as you mark as a whole class, discussing any difficulties or interesting patterns; Allow children to discuss their strategies for each question; Allow children to create Bar models to represent their understanding of each question; The power of this daily approach is truly remarkable, and will have your children recognising inverse operations to support calculation in no time. You will know your children have made good progress when they start recognising that 126 - 97 can be calculated by using 97 + ___ = 126. This is what the fact families are perfect for! Avoid those unnecessary exchanges in error-prone compact subtraction methods! Also supplied is a full answers booklet for you to check students answers when they call them out.

This is the free sample version of the full Intelligent Practice programme developed for fractions, and comes complete with answers on a separate page. You can buy the full version of the Intelligent Practice: Fractions - Thirds booklet, complete with 33 pages, plus answers. The visual representations (BAR models) of the fractions aim to help children understand the concept of three ‘parts’ to a ‘whole’. Intelligent practice guides them through calculating one third, two thirds, and three thirds of the amount. The second section enables children to repeat this process for an amount that is 10 times greater, helping to reinforce place value understanding, and its effect on the fraction parts. The final section encourages children to reflect on the patterns they have noticed. Skilful questioning from the teacher will enable the children to identify, for example: Why the whole amounts used are always multiples of 3; Why the ‘parts’ in each section increase by the same amount each time; Why the ‘parts’ between sections are also 10x greater; Why every time the ‘whole’ increases by 3, each part increases by 1, etc.