There is nothing like chocolate to motivate some hard work thinking. Fair sharing a giant block of chocolate was a deliciously rich mathematical task - in more ways than one.
Mrs Sprague has bought a giant block of chocolate. The block of chocolate needs to be fairly shared amongst the class. Work out how many pieces of chocolate each student in Room 3 will get.
Our purpose is to solve mathematical problems
We will know we have successed when
Show everything you did to solve the problem.
Explain your thinking using numbers, pictures, and or words.
Show as many solutions as you can.
To find out how many pieces of chocolate were in the block we counted in twos and got 56. Then we saw the block was a timetable and it was 7 x 8 = 56 . On our photocopied block of chocolate we wrote the name of each person in the class on the pieces of chocolate to prove we got two pieces each.
I figured out how many students there were in Room 3 today by counting the photos on the “I am at school board”. If everyone is here we have 28 students.
I halved the block of chocolate and got two groups of 28. We had 24 students in the class today to share with so I took away one row of chocolate which was 8 squares and then I had two groups of 24 so each person in the class got 2 pieces of chocolate.
Lennon and Benjamin - the most speedy problem solvers
We work out that 56 ➗ 24 = 2 with 8 pieces left over because we knew 24 + 24 = 48 and 56 - 48 = 8.
We tried to give Mrs Sprague the last 8 pieces but she said no left overs and that we had to share them with the class so we had better think about cutting up the last 8 pieces and using our fractions. So we had to share 8 pieces between 24.
Benjamin knew that 24 ➗ 8 = 3 so we worked out each person would get 2 pieces and ⅓ of a piece of chocolate.
Then Mrs Sprague said we had to prove it and show Laura our thinking. So we cut up our photocopied block of chocolate into 24 groups to prove it to her.
We had to come up with as many solutions as possible. So after we used our brains we used a calculator. The calculator said 56 ➗ 24 = 2.31. 0.3 is part of a whole like a fraction. ⅓ = 0.3.
I tried to share the 8 left over pieces in quarters first but quarters were too many. Then I worked out it was thirds that we needed to share the leftovers into. I drew 8 pieces of chocolate and then shared 24 between the pieces and found it was three - so thirds.
I figured out that 24 + 24 = 48. I know this because 20 + 20 = 40 and 4 + 4 = 8 so 40 + 8 = 48.
Mrs Sprague has shared this rich task with the rest of the Ohaaki Team to have a go at. She is also investigating another problem solving activity that involves sharing chocolate from nrich.maths.org.
There are some amazing mathematical problem solvers coming through our school. Look out for these students in future Mathmatters Competitions in 2024 and 2025.
Mathematics - Number and algebra
Key Words: mathematics, problem solving, rich task, chocolate