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# What the teacher knows about Pupil A's attainment in number and algebra

Pupil A independently uses simple formulae, such as $p=2l+2w$ for the perimeter of a rectangle. In the practical context of area and perimeter she recognised the different meanings of 2a and ${a}^{2}$, explaining ‘2a is that part of the perimeter and it's 2a plus 2a altogether so that means four lots of a. And a2 is for the area and it's a times a’. Pupil A is beginning to construct expressions and formulae in symbolic form to represent practical situations. Following up her work on visible and invisible faces when joining cubes, she recognised that the total of visible and invisible faces was the number of cubes multiplied by six. In group discussion she suggested recording this as $V+H=6C$, using V for the number of visible faces, H for the number of hidden faces and C for the number of cubes. She checked the formula by substituting values from her table of results. With the support of probing questions she explained, ‘each cube has six faces and when the cubes are fixed together all of the faces must be visible or hidden so it's got to be six times the number of cubes you've used’.

Pupil A understands that repeated addition can be represented as multiplication and when matching equivalent expressions she matched $a+a+a+a$ to 4a. In arithmetic, she understands that $12×35=10×35+2×35$ and uses this understanding to multiply $6\left(a+4\right)$ for example. She also simplifies algebraic expressions by collecting like terms.

Pupil A plots graphs of linear functions in all four quadrants. She substitutes negative as well as positive numbers into expressions when constructing tables of values. She plots points and draws graphs as well as using ICT to create them.

Pupil A understands place value and uses this to order decimals with up to three decimal places. She rounds decimals to one decimal place. She understands the effect of multiplying and dividing by 10, 100 and 1000 and uses this to multiply 1250 by 25 for example. She uses her understanding of place value to change units and compare measurements in metres, centimetres and millimetres.

She knows the percentages that are equivalent to the fractions she uses most often, such as, $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{3}$ and $\frac{1}{10}$. She converts other fractions such as fifths or twentieths into tenths and hundredths to change them to percentages. She converts percentages to fractions and reduces them to them to their simplest form.

Pupil A calculates simple percentages of a number mentally, for example to find the value of a 10% discount on an item originally costing £22.50. In a similar way she calculates 10% of an amount and halves the result to find 5%. In her written methods she uses mental calculation of 50%, 25%, 10% and 1% as interim steps when calculating other percentages such as 65% of the 170 pupils in the year group. She makes good use of her knowledge of multiplication facts in both multiplication and division problems.

She knows and uses the correct order of operations when calculating. Her written methods of addition and multiplication are efficient and correct and are supported by mental strategies when using the four operations. Pupil A checks her work by considering whether her answer is reasonable in the context and by referring to the size of the numbers.