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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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