N1–N3Place value, ordering and order of operations

• B1 for 18

Worked solution: \(6 \div 2 = 3\) is worked out first, then \(20 - 3 + 1 = 18\).

• C1 for explaining that Sam worked out 20 − 6 before dividing, when the division must be done first

Worked solution: Sam's 8 comes from \((20 - 6) \div 2 + 1 = 7 + 1\). Division comes before subtraction, so \(6 \div 2\) should be worked out first.

• M1 for converting at least three of the fractions and decimals to the same form (e.g. \(-\frac{1}{4} = -0.25\) and \(\frac{3}{8} = 0.375\))
• A1 for \(-0.27\), \(-\frac{1}{4}\), \(0.37\), \(\frac{3}{8}\), \(0.6\) (the numbers may be written in their original form)

Worked solution: As decimals: \(-0.27\) = −0.27, \(0.6\) = 0.6, \(-\frac{1}{4}\) = −0.25, \(\frac{3}{8}\) = 0.375, \(0.37\) = 0.37.
In order: \(-0.27\),  \(-\frac{1}{4}\),  \(0.37\),  \(\frac{3}{8}\),  \(0.6\).

• M1 for writing at least three of the numbers correctly as decimals (or fractions)
• A1 for all five correct: \(\frac{5}{12}\) = 0.4166…, \(0.4^{2}\) = 0.16, \(4.1 \times 10^{-1}\) = 0.41, \(42\%\) = 0.42, \(3^{-2}\) = 0.1111…
• A1 for \(3^{-2}\), \(0.4^{2}\), \(4.1 \times 10^{-1}\), \(\frac{5}{12}\), \(42\%\) (in their original form)

Worked solution: Convert each number to a decimal: \(\frac{5}{12}\) = 0.4166…, \(0.4^{2}\) = 0.16, \(4.1 \times 10^{-1}\) = 0.41, \(42\%\) = 0.42, \(3^{-2}\) = 0.1111….
In order: \(3^{-2}\),  \(0.4^{2}\),  \(4.1 \times 10^{-1}\),  \(\frac{5}{12}\),  \(42\%\).