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?”

Ask:

*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.**

What if……….

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.