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Mr Barton's Rich Tasks

On this page I have collected together my favourite rich tasks that I have used over the last 11 years, in an accessible, easy to use format. I also invite teachers to share their ideas for interesting probing questions and lines of inquiry for students to investigate.


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For me, a rich task is one that both engages and challenges students with a wide level of mathematical ability. They need to be “low barrier, high ceiling”, by which I mean students need to have found success/made progress with the task within the first 30 seconds, but there is still enough meat left to keep them thinking 30 minutes (or even 3 lessons) later.

I feel activities like these are crucial for students’ mathematical development. They allow them to be creative, and work together in meaningful and positive ways. When developing our Scheme of Work (you can read my series of blog posts about it), we decided to include a compulsory rich task for all students each topic unit, and many of those can be found below.

The key to a good rich task are the questions that accompany it. This is where effective differentiation happens. All students begin the task in exactly the same way, but once an initial stage has been reached, students (individual or in groups) are free to pursue different investigations, probing questions and lines of inquiry. These can be provided by the teacher, or even by the students themselves.

The strength of the rich task lies in these questions. So here is my plan: I am going to share as many of my favourite rich tasks as possible, and hopefully teachers from around the world are going to provide the questions. These can be lines of inquiry, investigations, prompts, hypotheses, extensions, simplifications, modifications, whatever you like. Crucially, you do not need to know the answer yourself. Just throw it out there! There will be space for these in the Comments section at the bottom of each TES Resource page, and I will always get the ball rolling with a few questions of my own.

Please join in. Please spread the word. Please just share even one question. And then the tasks will keep getting better, and better, and better. 

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Task 1 - Positive Differences
Brief Description: Students build simple number pyramids by taking the positive difference of pairs of numbers
Potential Skills Involved: Arithmetic, Fractions, Decimals, Writing Expressions, Proof

Task 2 - The Factors and Multiples Game
Brief Description: Students play a strategic game on a 1-100 number grid, crossing off factors and multiples
Potential Skills Involved: Arithmetic, Factors, Multiples, Primes, Proof

Task 3 - Choose 3 Numbers
Brief Description: Students try to guess each other's starting numbers by working backwards from the sums of pairs of numbers
Potential Skills Involved: Arithmetic, Writing expressions, Solving Equations

Task 4 - Will they meet?
Brief Description: Can you help Romeo and Juliet get back together in my first ever romantic maths activity?
Potential Skills Involved: Enlargement, Vectors, Similar Shapes, Rotation

Task 5 - Number Shacks
Brief Description: Can you figure out how the numbers of these shacks are formed and use this to predict answers and spot patterns?
Potential Skills Involved: Arithmetic, Writing Expressions

Task 6 - Averaging it out
Brief Description: What happens when we continually take the mean of sets of numbers?
Potential Skills Involved: Averages, ICT

Task 7 - Fraction Arrangement
Brief Description: Can you order different digits to produce the biggest and smallest possible answers for these fraction problems?
Potential Skills Involved: Operations with fractions

Task 8 - Diffy
Brief Description: The first lesson our new bunch of Year 7s experience, and one of my all time favourites
Potential Skills Involved: Arithmetic, Writing Expressions, Proof

Task 9 - Simultaneous Equations Staircase
Brief Description: Why does everyone get the same answer to these simultaneous equation problems?
Potential Skills Involved: Simultaneous Equations, Proof

Task 10 - How many angles?
Brief Description: Using a geoboard, how many angles between 10 and 180 can you make?
Potential Skills Involved: Angle Facts, Circle Theorems

Task 11 - Number Reverse
Brief Description: What happens when we reverse the digits of numbers and perform operations on them?
Potential Skills Involved: Arithmetic, Writing expressions, Proof

Task 12 - Multiplication Reduction
Brief Description: Follow the rule to reduce a number in size using multiplication. Does anything interesting happen?
Potential Skills Involved: Arithmetic, Writing Expressions

Task 13 - How many quadrilaterals?
Brief Description: Using a geoboard, how many different quadrilaterals can you make?
Potential Skills Involved: Properties of shapes, Angle facts

Task 14 - 1089
Brief Description: Why is the number 1089 so special?
Potential Skills Involved: Arithmetic, Writing expressions, Proof

Task 15 - Square Co-ordinates
Brief Description: What do the co-ordinates of the corners of squares have in common?
Potential Skills Involved: Co-ordinates, Properties of shapes, Vectors, Proof

Task 16 - Polar Bears
Brief Description: Can you figure out how to get the totals in this dice game?
Potential Skills Involved: Arithmetic

Task 17 - Pascal's Triangle
Brief Description: What maths can you discover hiding in Pascal's triangle?
Potential Skills Involved: Sequences

Task 18 - Entrapment
Brief Description: A fun strategy game using all of the transformations
Potential Skills Involved: Reflection, Rotation, Translation, Enlargement

Task 19 - Fire Hydrants
Brief Description: Where is the optimum position to place these fire hydrants to maximise their coverage?
Potential Skills Involved: Geometrical Reasoning

Task 20 - Diagonals of Rectangles
Brief Description: How many squares does the diagonal of a rectangle pass through?
Potential Skills Involved: Arithmetic, Sequences, Factors, Multiples, Primes

Task 21 - T-totals
Brief Description: How can you work out the T-number in this classic piece of maths coursework?
Potential Skills Involved: Arithmetic, Writing Expressions, Proof

Task 22 - Number Snakes
Brief Description: What is the longest number snake you can make using these simple rules?
Potential Skills Involved: Arithmetic, Properties of Numbers, Writing Expressions

Task 23 - Summing Consecutive Numbers
Brief Description: Which numbers can be made using the sums of consecutive numbers?
Potential Skills Involved: Arithmetic, Writing Expressions

Task 24 - NIM
Brief Description: The wonderful strategy game using piles of counters
Potential Skills Involved: Strategy, Factors, Multiples, Primes

Task 25 - Function Machines
Brief Description: Why do these function machines seem to give the same difference?
Potential Skills Involved: Arithmetic, Order of Operations, Writing Expressions, Expanding Brackets

Task 26 - Leap Frog
Brief Description: If you leap over this set of 3 points enough times, what do you notice?
Potential Skills Involved: Co-ordinates, Construction, Vectors

Task 27 - Solving Linear Equations
Brief Description: By arranging sets of digits, what types of solutions can you generate to these simple linear equation problems?
Potential Skills Involved: Solving linear equations

Task 28 - Decimal Arithmetic
Brief Description: By arranging sets of digits, can you make the biggest and smallest decimal totals possible?
Potential Skills Involved: Arithmetic, Decimals, Place Value

Task 29 - 24 Cubes
Brief Description: What different 3D objects can you make with 24 cubes and what do you notice about their properties?
Potential Skills Involved: Surface Area, Volume, Similarity

Task 30 - Tilted Squares
Brief Description: How many squares with area 1-20 can you create?
Potential Skills Involved: Area, Pythagoras

Frequently Asked Questions keyboard_arrow_up
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Are you saying we should be doing this every lesson?
No. Definitely not. I am acutely aware of the need for students to gain practise in key mathematical skills. But I do strongly believe that regular lessons like this are just as important for a student's mathematical development and to increase their enjoyment in the subject. They should not be seen as one-offs. Both students and teachers should value them as highly as any type of lesson.

What do I do if a child doesn't engage with a particular question or line of inquiry?
The simple answer is that I give them another one! I have to make a judgment call as to whether the student has genuinely tried and not just given up too easily. But if, for whatever reason, a probing question or line of inquiry hasn't resonated with a student, then I will set them off on something else. Indeed, the beauty of having lots of questions up your sleeve is that you are far more likely to find ones that engage your students than if you just have one line of investigation that the whole class is following.

Would you do this type of lesson for an observation?
Yes, I definitely would. 100%. Sure, such lessons are a little bit on the risky side as you don't know what is going to happen. But they are also incredibly flexible. Imagine you had meticulously planned a lesson with a 40 slide PowerPoint and 5 beautifully prepared, differentiated worksheets. And then you find that the students don't understand even the basics. Or, they understand far more than you anticipated. You might be in a bit of trouble. But with a lesson rammed full of probing questions, you can just try them out on another line of inquiry. Or, better still, get them to come up with their own.