# Exceed Education's Shop

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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.

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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.

#### Number Line Reasoning Challenge (Mini-Assessment)

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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

#### Odd One Out: 'Start the Day' reasoning activity (free)

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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

#### Number Line Mats and Bookmarks

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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.

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#### Intelligent Practice: Fractions - Quarters (Free)

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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.

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#### Intelligent Practice: Fractions - Thirds (Free)

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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.

#### Tricky Totals: Problem Solving ‘Start the Day’ (Free)

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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

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#### Daily Fluency - Add & Sub (Sample Set)

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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.

#### Playing Safe 'Start the Day' Puzzle (Free)

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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

#### Odd One Out: 'Start the Day' reasoning activity

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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

#### LTHC Digits Challenge

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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.

#### Tricky Totals: Problem Solving 'Start the Day'

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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

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