### The Number Framework Strategy Stages

 Stage 0 - Emergent - They are learning to rote count.Stage 1 - One-to-one counting - They can count up to ten objects.Stage 2 - Counting from One on Materials - They can add and subtract using their fingers or objects (up to ten).When they add 4 + 3 they will start counting from one. Children can count numbers from 0 – 20 (backwards and forwards).Stage 3 - Counting from One by using Images - They can see objects in their mind rather than using real objects. When they add 4 + 3 they will still start counting from one. Children can count numbers from 0 – 20 (backwards and forwards).Stage 4 - Counting On (Advanced Counting) - When adding 4 +3 they will count on from four (4, 5, 6, 7). Children can work with numbers from 0 – 100. At this stage children may use materials or may image and in some cases might “just know it”. Children use skip-counting as an early means of multiplying. E.g. 5 x 2 as 2, 4, 6, 8, 10Stage 5- Early Additive (part-whole) - They can separate numbers into useful units to solve addition and subtraction, e.g. 9 + 7 is the same as 10 + 6 (tidy tens). Children can work with numbers from 0 – 1000. Recognise and begin to use symbols for common fractions. e.g. 1/2, 1/3, 1/4, 1/5,1/10Stage 6 - Advanced Additive (part-whole) - Separate numbers into useful units in a variety of ways to solve addition and subtraction, and are beginning to solve multiplication and division problems. Children can work with numbers from 0 – 1 000 000.Stage 7 - Advanced Multiplicative (part-whole) - They can choose from a range of strategies to solve problems involving multiplication and division, including problems with fractions. Students can work with decimal numbers to three places. e.g. 6.234. They are able to make use of more complicated strategies where one or more of the numbers may need to be broken up, manipulated then recombined.Stage 8 - Advanced Proportional (part-whole) - They can make use of a variety of complex strategies to solve problems involving fractions, proportions, and ratios. Students are able to find relationships between quantities of two different measures. e.g. You can make 21 glasses of lemonade using 28 lemons. How many glasses can you make using 8 lemons?