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 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 a free sample set to show you how they are laid out and organised. 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 mean average to help your children master the content? Then look no further than this ‘Start the Day’ activity pack.
This is the free sample of the That’s Mean: Mean Average ‘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 mean averages by giving them three styles of practise problems:
Calculating the mean from a set of numbers;
Using the known mean and the known numbers in a set, to find one missing number from the same set;
Using observed patterns in each mean, to predict a the unknown mean, and then calculate the missing number from this mean and the known numbers.
Children might choose to use a trial and improvement method for finding this unknown number, reasoning out their others answers based on their choices. Otherwise, children might use algebra to replace this unknown number with x. The answer pages the answer, to enable teacher follow up during plenary or mini-plenary discussions.
Note: It is possible that the children will find different answers for part 3 above. This does not make them wrong, and teachers should be prepared to challenge children to justify why they made the choices they did.
Tips on how to deliver these activities:
These activities are best delivered after the children have learnt about the mean average, what it is for, and how to calculate it;
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 does knowing four of the numbers in this set, and also the mean in this set, help us to find the missing number? 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 multiple missing numbers);
Use one activity per week over a half term to encourage regular revisiting of the content (finding the mean average) and strategies (working backwards/trial and improvement/algebra);
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 the areas of mathematics that often get neglected in our jam-packed curriculum? Then look no further than this ‘Start the Day’ activity pack involving compass directions and code-cracking.
In this pack there is one free sample activity from our full pack - Playing Safe: ‘Start the Day’ Puzzle, which has 10 similar activities (each with teacher answers) in both PDF form and PowerPoint for easy sharing with your children on an interactive whiteboard.
The activity is designed to encourage children to work systematically to find the correct route through the safe code to reach the key at the centre. Each button tells them how many spaces to move (1, 2, 3, 4, 5 or 6) and in which direction (North, East, South or West).
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 compass directions;
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, there is only one button which links to the key. Can we find it? There is only one button that links to that button (the one we just used to get to the key). Can we find it? 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 rows or columns, or through adding diagonal movements in the instructions - NE, SE, SW, NW);
Use two activities per week over a half term to encourage regular revisiting of the content (directions) and strategies (working backwards);
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 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 free 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:
Sir, 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 recall addition and subtraction facts, or worse, cannot recall them at all? Look no further than this Daily Fluency with Calculations booklet.
This resource has been developed through a proven research-based approach. The sequence of sessions follows a specific sequence which helps children to build upon common techniques of calculation. For example, the first week is as follows:
Day 1: Adding 9
Day 2: Subtracting 9
Day 3: Adding 11
Day 4: Subtracting 11
Day 5: A mixture of adding 9, 10 and 11.
Each week follows a similar structure, with columns of questions conveniently colour coded to help children recognise how much of the session they manage to complete.
Note: This is a free sample set to give you an insight into how the entire fluency pack works. The full Daily Fluency with Calculations booklet can be found here.
For best results:
Use the PDF file to create an A5 booklet;
Teach the main strategy for each session using a whole class approach;
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 complete their own tracking charts at the end of each week, and bar chart on the back cover. This gives them a good feedback about how well they are performing, and also gives them ownership over the process.
The power of this daily approach is truly remarkable, and will have your children recalling their number facts in no time.
Most of our schools reprint this booklet and complete it a second and third time in order to maintain their rapid recall. This can be an important part of creating long term memory of the facts.
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 with addition and subtraction? Then look no further than this ‘Start the Day’ activity pack.
This is the free sample of the Sum Steps: ‘Start the Day’ reasoning addition problems 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 encourage children to work systematically to find the correct totals of each step in the pyramid. Children will be able to find some spaces as a direct result of some of the known numbers, with only one number in the bottom row remaining unknown.
Children might choose to use a trial and improvement method for finding this unknown number, reasoning out their others answers based on their choices. Otherwise, children might use algebra to replace this unknown number with x. The answer pages provide both the full answer, and the stages involved in using algebra to enable teacher follow up during plenary or mini-plenary discussions.
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. 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 fewer pyramid steps);
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/algebra);
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.
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 encourage children to work systematically to find the correct totals of each step in the pyramid. Children will be able to find some spaces as a direct result of some of the known numbers, with only one number in the bottom row remaining unknown.
Children might choose to use a trial and improvement method for finding this unknown number, reasoning out their others answers based on their choices. Otherwise, children might use algebra to replace this unknown number with x. The answer pages provide both the full answer, and the stages involved in using algebra to enable teacher follow up during plenary or mini-plenary discussions.
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. 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 fewer pyramid steps);
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/algebra);
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 full pack of reasoning starter activities. You can find the free version of this resource by visiting our shop.
In this pack, you will find:
5 packs of activities which each contain:
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 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 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 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 your children need practice solving problems and puzzles? Do you need activities that specifically practise reasoning about the mean average to help your children master the content? 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 mean averages by giving them three styles of practise problems:
Calculating the mean from a set of numbers;
Using the known mean and the known numbers in a set, to find one missing number from the same set;
Using observed patterns in each mean, to predict a the unknown mean, and then calculate the missing number from this mean and the known numbers.
Children might choose to use a trial and improvement method for finding this unknown number, reasoning out their others answers based on their choices. Otherwise, children might use algebra to replace this unknown number with x. The answer pages the answer, to enable teacher follow up during plenary or mini-plenary discussions.
Note: It is possible that the children will find different answers for part 3 above. This does not make them wrong, and teachers should be prepared to challenge children to justify why they made the choices they did.
Tips on how to deliver these activities:
These activities are best delivered after the children have learnt about the mean average, what it is for, and how to calculate it;
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 does knowing four of the numbers in this set, and also the mean in this set, help us to find the missing number? 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 multiple missing numbers);
Use one activity per week over a half term to encourage regular revisiting of the content (finding the mean average) and strategies (working backwards/trial and improvement/algebra);
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 multiplication? 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. This pack could also be used for challenging more able children (who already know their times tables) during whole class practice/fluency sessions.
The activity is designed to help children master multiplication, including (but not limited to):
Recognising square numbers as products;
Recognising the properties of the factors and multiples of different numbers;
Reasoning about numbers multiplied by 1 and 0, and how this helps in the big picture of a problem;
Recognising patterns between the number of tens and ones in a product, and the factors of these products;
Considering the problem solving strategies of trial and improvement, working systematically, and logical reasoning.
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 the rules (0-9 digits and how they are used in 1 and 2-digit number representations);
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 times tables have only two 1-digit products? (5, 6, 7, 8, 9). How many square numbers have only a 1-digit answer? (1, 2, 3). How many square numbers have ones in the product that are the same as the multiple being used? (1, 5, 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 (multiplication) and strategies (working backwards/trial and improvement);
Have children create their own versions and send them to us to challenge our followers - Twitter: @UKExceED

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.

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 - Quarters booklet, complete with 25 pages, plus answers.
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 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.