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.

NEW AND IMPROVED - NOW WITH 10 ACTIVTIES IN TWO DESIGNS
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 are 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 one activity 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 your children find counting and visualising numbers difficult? Do they need extra resources on hand to help them work independently? Look no further than this set of 5 number lines with different scales:
0 to 30 with colour-coded 10 blocks. (Y1 to Y4 version)
0 to 20 with colour-coded 5 blocks and marked quarters and halves.
-9 to 0 with intervals of 1. (Y3 to Y6 version)
0-100 with colour-coded 10 blocks.
0-1000 with colour-coded 100 blocks.
Number lines are essential tools for understanding place value, addition and subtraction strategies, informal written methods leading to more mental calculation skills, and also for understanding the intervals when using measuring devices with scales (e.g. rulers, protractors, tape measures etc).
For best results, print, trim and laminate the four number lines or individually for use as a maths bookmark. In all of my classes, I created one of these for each child. There were able to use them whenever needed, and by having all four on one sheet made them a lot more useful in everyday learning. In a mastery classroom, this is the perfect resource for supporting all children.

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

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.

A collection of 20 ‘Start the Day’ activities to support your children’s mathematics reasoning and problem solving skills whilst also developing their fluency in addition, subtraction, algebra and even compass directions.

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 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 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.

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.

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 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.
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 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 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.

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.

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 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 + 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 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.