Stage 7
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 procedural 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 ●
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; compensation.
The methods for subtraction are: making the previous ten; partitioning the minuend; the relationships method.
In this block, the calculations are restricted to numbers with a zero in the ones place (eg multiples of 10).
Block 1 also includes revision of core additive facts through a range of problem solving activities.
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; compensation.
For division the methods are: partitioning the dividend; dividing by using factors of the divisor; relationships; compensation.
To keep students' attention focused on the process of each new strategy, each set of slides isolates calculations to facts from a single multiplication table.
Block 2 also includes systematic revision of multiplicative facts.
Block 3 ●
Methods for addition and subtraction that bridge the next logical unit [2]
Block 3 returns to addition and subtraction strategies, introducing calculations where the starting numbers have non-zero ones digits.
In Block 1, the calculations always had a zero in the ones place (like 80 + 60).
In Block 3, the starting numbers have non-zero ones digits (for example, 28 + 26).
Addition: 28 + 26 = 28 + 2 plus 24 (bridging to 30)
Subtraction: 34 - 7 = 34 - 4 - 3 (bridging back to 30)
This block builds the mental flexibility needed to seamlessly cross a tens boundary from any starting number on the number line.
The block contains activities to consolidate finding the next logical unit.
Block 3 also includes continued revision of additive facts.
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 continued 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.
Essential prerequisite skills are woven directly into the instruction, including finding equivalent fractions and converting between mixed numbers and improper fractions.
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.