I create resources for mathematics teaching based on the Singapore and Shanghai curriculum models for best practice.
I will focus on the core principles of Intelligent Practice, Low-Threshold High-Ceiling tasks, fluency based activities and Problem Solving and Reasoning activities.

I create resources for mathematics teaching based on the Singapore and Shanghai curriculum models for best practice.
I will focus on the core principles of Intelligent Practice, Low-Threshold High-Ceiling tasks, fluency based activities and Problem Solving and Reasoning activities.

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

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.
In this pack there is one free sample activity from our full pack - Tricky Totals: Problem Solving ‘Start the Day’, 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 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 free sample of the Odd One Out: ‘Start the Day’ reasoning activity 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

A collection of 35 ‘Start the Day’ activities to support your children’s mathematics reasoning and problem solving skills whilst also developing their fluency in addition, subtraction, multiplication, properties of number, algebra, statistics and even compass directions.

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 you find it difficult to teach bridging method using visual resources? Look no further than the full set of fluency activities designed to allow children to develop the skills of bridging as an addition strategy using Numicon or Tens Frames.
The full sets include blank spaces for children to record, an answer pack for demonstrating on the IWB, and an example question to start the teaching. Each set is divided into a specific addition focus (either adding 6, 7, 8, 9, 16, 17, 18, or 19).
This activity is ideal for children in Key Stage 1 or 2.
How could I use this activity?
Our staff have used these fluency packs in two main ways:
As a whole class teaching input, using the Example page to show strategy of partitioning the add focus visually, followed by whole class work through of the questions whilst on the Interactive Whiteboard.
Individual booklets (printing 4 pages per sheet in the print settings) and allowing children to work through the booklet with at their own pace, or with a teacher or TA).
How are the activities useful?
In terms of developing real mastery amongst your students, it is important that they can:
Answer simple addition problems quickly from memory, or by using calculation strategies rather than counting. This pack allows children to develop a long term memory of addition facts through the visual nature, whilst helping them to calculate through a bridging strategy.
Manipulate numbers in different ways so that they can be confident in any addition scenario. This pack enables children to consider the most efficient methods of bridging.
How do children develop more efficient methods?
Encourage your children to recognise the different ways to manipulate the calculation. As an example, consider 6 + 7:
Some children will automatically change this to 7 + 6 because they have been drilled into “put the largest number first”. For true mastery, children must be able to recognise that addition involves the sum of two addends, and therefore it doesn’t matter which one goes first. So, how do we teach this? Ask them to calculate (not count) the answer both ways around. What do they notice?
For 6 + 7, we partition 7 into 4 and 3, because 6 + 4 = 10, and this is what we call bridging.
For 7 + 6, we partition 6 into 3 and 3, because 7 + 3 = 10.
In both examples the sum is still 13, but the partitions we created we different.
So, which one is more efficient?
The honest answer is, once we are fluent, they are both efficient. But, whilst we are still learning, most children will find it easier to do 6 + (4 + 3) for the simple reason that even numbers bonds to 10 are easier to remember. Your biggest challenge as a teacher using a mastery style, is to get the children to recognise this of their own accord through real reasoning in the classroom. That’s why these resources have been designed to visually show each calculation.

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 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.

Do you operate a ‘mastery’ classroom? Do you find it difficult to teach bridging method using visual resources? Look no further than the full set of fluency activities designed to allow children to develop the skills of bridging as an addition strategy using Numicon or Tens Frames.
The full sets include blank spaces for children to record, an answer pack for demonstrating on the IWB, and an example question to start the teaching. Each set is divided into a specific addition focus (either adding 6, 7, 8, 9, 16, 17, 18, or 19).
This activity is ideal for children in Key Stage 1 or 2.
How could I use this activity?
Our staff have used these fluency packs in two main ways:
As a whole class teaching input, using the Example page to show strategy of partitioning the add focus visually, followed by whole class work through of the questions whilst on the Interactive Whiteboard.
Individual booklets (printing 4 pages per sheet in the print settings) and allowing children to work through the booklet with at their own pace, or with a teacher or TA).
How are the activities useful?
In terms of developing real mastery amongst your students, it is important that they can:
Answer simple addition problems quickly from memory, or by using calculation strategies rather than counting. This pack allows children to develop a long term memory of addition facts through the visual nature, whilst helping them to calculate through a bridging strategy.
Manipulate numbers in different ways so that they can be confident in any addition scenario. This pack enables children to consider the most efficient methods of bridging.
How do children develop more efficient methods?
Encourage your children to recognise the different ways to manipulate the calculation. As an example, consider 6 + 7:
Some children will automatically change this to 7 + 6 because they have been drilled into “put the largest number first”. For true mastery, children must be able to recognise that addition involves the sum of two addends, and therefore it doesn’t matter which one goes first. So, how do we teach this? Ask them to calculate (not count) the answer both ways around. What do they notice?
For 6 + 7, we partition 7 into 4 and 3, because 6 + 4 = 10, and this is what we call bridging.
For 7 + 6, we partition 6 into 3 and 3, because 7 + 3 = 10.
In both examples the sum is still 13, but the partitions we created we different.
So, which one is more efficient?
The honest answer is, once we are fluent, they are both efficient. But, whilst we are still learning, most children will find it easier to do 6 + (4 + 3) for the simple reason that even numbers bonds to 10 are easier to remember. Your biggest challenge as a teacher using a mastery style, is to get the children to recognise this of their own accord through real reasoning in the classroom. That’s why these resources have been designed to visually show each calculation.

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.

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 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 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 - 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.

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 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.