What the teacher knows about Pupil C's attainment in number and algebra
Pupil C uses the order of operations in arithmetic. She has a good understanding of operations and relationships between them. She knows, for example, that addition and multiplication are commutative and that multiplication is distributive over addition and subtraction, and uses her own language to describe this. She has developed successful techniques for written calculations involving the four operations.
Pupil C understands that algebra is generalised arithmetic and that operations follow the same ordering conventions because symbols represent numbers. Pupil C manipulates algebraic expressions, multiplying an algebraic expression by a constant. She uses index notation and recognises for example that . She checks results by substituting values into each expression to decide if they are equivalent or not.
Pupil C generates sequences, for example, when investigating border tiles for rectangles of different sizes. She predicts later terms in the sequence and expresses the general rule using function machines.
Pupil C understands place value in whole numbers and decimals, evaluating 1.24 as . She multiplies and divides by 10, 100 and 1000 including in contexts such as converting millimetres to metres. She uses place value when she multiplies a decimal such as 0.4 by a single digit number mentally and to multiply larger numbers and decimals using written methods. She calculates equivalent decimals, fractions and percentages. She simplifies fractions using common factors. Pupil C orders fractions in contexts such as comparing probabilities. She calculates fractions and percentages of quantities. For example, she divides by 10 to find 10% and halves the result to find 5%. Working in this way and jotting interim results she calculates percentages such as 19% of a quantity by calculating 10%, then 20% and then calculating and subtracting 1%.
Pupil C interprets word problems set in real-life contexts. She identifies appropriate calculations to solve problems. She uses written methods to multiply and divide three-digit by two-digit numbers and extends the methods to include decimals in the context of money, mass and volume. She checks calculations using inverse operations. She estimates answers using approximations and uses her estimate to decide if her answer is of the correct magnitude. Pupil C solves problems involving ordering and calculating with negative numbers in contexts such as changes of temperature across 0 °C.