Stage 7 - coming soon
This new section of the website is designed for Key Stage 3 students. It aims to ensure that all students in Year 7 develop a robust 'number sense' by learning to select the most efficient strategy for a specific calculation, rather than applying a single method to every problem they encounter. While the column method is often essential for larger, more complex calculations, it is often less efficient for simpler numbers. The Stage 7 programme enables KS3 staff to reset students’ understanding, ensuring their mathematical practice is firmly grounded in strategic thinking.
Block 1 ●
Methods for addition and subtraction that bridge the next logical unit [1]
This block focuses on developing fluency in four core methods for addition and three for subtraction.
The methods for addition are making the next ten, partitioning both addends, the relationships method and compensation. The methods for subtraction are making the previous ten, partitioning the minuend and the relationships method.
The methods are learnt using place value variants for single digit numbers.
Block 2 ●
Methods for multiplication and division [1]
Block 2 explores a range of methods for multiplication and division.
For multiplication these are partitioning the first factor, using factors of the second factor, relationships and compensation.
For division the methods are partitioning the dividend, dividing by using factors of the divisor, relationships and compensation.
To enable students’ understanding to be focused on the processes of the various methods, each set of slides involves multiplying or dividing using facts from a single multiplication facts table.
Block 2 includes revision of multiplicative facts.
Block 3 ●
Methods for addition and subtraction that bridge the next logical unit [2]
Block 3 returns to strategies for addition and subtraction. In Block 1, the next logical unit was always the next power of ten. For example, 80 + 60 = 80 + 20 + 40.
In Block 3, the next logical unit will not necessarily be a power of ten. For example, 28 + 26 = 28 + 2 + 24. Or 2.5 – 0.8 = 2.5 – 0.5 – 0.3.
The block contains activities to consolidate finding the next logical unit.
Block 4 ●
Methods for multiplication and division [2]
In Block 4, students consolidate their understanding of the various strategies for multiplication and division. They now use the strategies to multiply and divide by 2-digit numbers. Towards the end of the block the strategies are applied to situations involving the multiplication of decimals.
Block 4 includes revision of multiplicative facts.
Block 5 ●
Methods for addition and subtraction that bridge the next logical unit [3]
Students now apply their knowledge of the strategies to the addition and subtraction of fractions. Key skills needed are revisited, including finding equivalent fractions and conversion from mixed numbers to improper fractions (and vice versa).
Block 6 ●
Percentages and decimals
For these topics, the slides use the instructional approach of intelligent practice.
Intelligent practice in mathematics uses carefully sequenced questions to promote conceptual understanding rather than relying on rote repetition or application of overly complex procedural methods. It aims to help learners to think, make connections and identify patterns.
There will be further updates during the 2026/27 academic year.