Maths News

The importance of rich tasks in maths classrooms. 

Over the last 5 years the EPS maths program has incorporated ‘Rich Tasks’ to transform the subject from a collection of memorised procedures and facts into a living, connected whole that develops our students' understanding, reasoning and problem solving (Downton, Knight, Clark, Lewis. 2011). In 2023 we have continued to develop our use of targeted detailed rich tasks to assess students' understanding as well as make our everyday learning more engaging. 

But first, what is a rich task?

Rich tasks allow the learner to 'get inside' the mathematics. The resulting learning process is far more interesting, engaging and powerful; it is also far more likely to lead to a lasting understanding. There is less emphasis on there being one correct answer and tasks are designed for students of all abilities to demonstrate their knowledge and understanding with a variety of entry and exit points.

For example, in a Grade 3 or 4 classroom there is a focus on multiplication and division. The way many of us were taught would have been through memorising or ‘rote learning’ times tables from 1 - 12. To do this we may have sung songs, looked for patterns and been presented with many multiplication number sentences eg. 3 x 7 =_. These types of tasks often don’t encourage students to develop strategies to solve unknown multiplication problems; either the students know the answer or they don’t.

However, a rich task we could give to Grade 3 or 4 students is:

On our recent excursion to the farm we saw some chickens and some dogs. I can’t remember how many there were of each. I do remember that altogether I counted 25 heads and 78 legs. How many of each animal could there have been?

Student A: A developing understanding of multiplication and division.

• Student A might draw 25 animal bodies and start drawing 2 or 4 legs onto each. They would then add up the total amount of legs checking and modifying their answer as they neared the total of 78 legs. This student's experience of repeatedly adding 2 and 4 will help them progress towards using more efficient multiplicative thinking in the future. 

Student B: Building from known facts and using doubles to problem solve.

• Student B might start with a known multiplication fact and build towards 78 legs. For example they could know that if there were 10 dogs there would be 40 legs. They would have a strong understanding of doubles and know that if there were 20 dogs there would be 80 legs. This is too many legs so they may try adding 5 more dogs which would mean there would be 15 dogs with a total of 60 legs. They would then know they needed 18 more legs which they would know is 9 chickens as they have a strong understanding of doubles. This student's experience of building from known facts will support them to build on from a more efficient fact in the future.

Student C: Flexible use of multiplication and division to methodically solve problems.

• Student C might know immediately that 20 dogs is 80 legs in total. They could then see that if there are 19 dogs there would be 76 legs so there would only need 1 chicken to make 78. The student may then notice that there needs to be multiple chickens and will find their first solution of 18 dogs and 3 chickens. This student could then follow this pattern to methodically find every possible combination of dogs and chickens. This student's experience of finding every possible solution will support them to spot patterns and create generalisations or even a formula when solving problems in the future.

Why Rich Tasks are important for students and teachers

Through the example of a Grade 3 or 4 classroom, we've seen how rich tasks promote different strategies for problem-solving, from developing a foundational understanding to building upon known facts and ultimately employing flexible methods to tackle complex problems. These diverse approaches empower our students to think critically and develop problem-solving skills that extend far beyond the classroom.

Rich tasks are not just valuable for students but also for teachers. They enable our educators to guide students as they become more daring problem solvers. By delving into students' thinking processes, teachers gain insight into their current mathematical understanding and the logical steps they follow. This valuable information goes beyond right or wrong answers, allowing teachers to tailor their support and instruction to each student's unique needs and progress. 

For more information on how we teach maths, why we teach it this way and how you can support at home look out for an invite to a maths information session in the first half of Term 4.

Regards,

Will Saunders

Learning Specialist of Mathematics