The aim of the activity is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships. This structure of problem is more difficult than the usual “I had 2 bones and then ate 2 more, how many did I eat altogether?”
What has Digit Dog been doing? Can you tell me in your own words? What is Calculating Cat wondering?
How many bones could Digit Dog have had in the beginning? How many could he not have had? Explain your thinking.
Take suggestions for numbers of bones.
Is there just one answer?
Use one number as an example.
If Digit Dog started with 3 bones, how many bones did he eat?
Explain how you can find out. You might want to use bones, drawings, Numicon shapes, cubes to help.
Can you write a number sentence? 3 – ? = 2
Try some other numbers of bones. Record your answers. Can you put your answers in order? What do you notice?
Use this speaking frame to explain your work:
Digit Dog started with ______ bones, he ate _____ bones, now he has 2 bones left.
He had a different number of bones left?
Make up your own problem like this about Calculating Cat and some fish.
The five proficiences
Learners will use:
- strategic competence to make sense of the problem, work out what is known and what needs to be found out and to decide on a way of solving it.
- logical reasoning to explain their thinking and work systematically to find possible numbers.
- conceptual understanding of, and fluency with, number bonds to recognise that they need numbers with a difference of 2 or to see this pattern as they try out numbers, to see that 1 or 2 are not possible numbers to start with and to be efficient and accurate with the basic calculations.
- communication using symbols and correct mathematical vocabulary to show and explain their thinking .
Learners will need to be competent in all five proficiencies to make up their own problems.