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KS2 SATs Paper 3 (Reasoning)
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Place value and number
Identify digit value in large numbers
\[ \text{Which digit in ten thousands?} \]
Identify the value of a specific digit in numbers up to 10 million.
Write a number in words
\[ 85{,}034 \rightarrow \text{?} \]
Write a given number in words.
Round large integers
\[ 3{,}576{,}219 \rightarrow \text{nearest million} \]
Round whole numbers to a specified degree of accuracy.
Compare numbers to a threshold
\[ \text{How many} < 1{,}050{,}000\text{?} \]
Count how many numbers from a list satisfy a given condition.
Calculate across zero
\[ \text{16 less than 7} = -9 \]
Find a number relative to another when crossing zero.
Partition large numbers
\[ 1{,}023{,}045 = 1{,}000{,}000 + \square + … \]
Find a missing part in the partition of a large number.
Sequences
Continue a linear sequence
\[ 82, 96, \square, 124, 138 \]
Find a missing term in a linear sequence with constant difference.
Continue a sequence with fractions
\[ 1, 1\frac{1}{4}, 1\frac{1}{2}, 1\frac{3}{4}, \square \]
Find the next term in a sequence that includes fractions.
Fractions and equivalence
Convert fraction to decimal
\[ \frac{3}{4} = 0.75 \]
Convert a common fraction to its decimal equivalent.
Create fractions from digit cards
\[ 25\% = \frac{1}{4} \]
Use digit cards to make a fraction equivalent to a percentage.
Write fraction from shaded grid
\[ \text{Shaded} = \frac{2}{5} \]
Write a fraction representing the shaded part of a grid.
Decimal-fraction equivalences
\[ \frac{3}{20} = 0.15 \]
Complete a conversion between fraction and decimal.
Comparing and ordering
Order fractions
\[ \frac{1}{5} < \frac{3}{4} < \frac{4}{5} < \frac{7}{8} \]
Order a set of fractions from smallest to largest.
Compare fractions and decimals
\[ \frac{3}{5} \text{ vs } 0.55 \]
Compare a fraction and a decimal to identify which is larger.
Compare products of fractions
\[ \frac{1}{2} \times \frac{4}{5} \text{ vs } \frac{1}{3} \times \frac{9}{10} \]
Calculate and compare two products of fractions.
Four operations
Missing number in subtraction
\[ 8{,}450 – \square = 3{,}725 \]
Find the missing number in a subtraction equation.
Missing digits in column subtraction
\[ \square 57 – 3\square 5 = 68\square \]
Complete a column subtraction by finding missing digits.
Long division with remainder
\[ 768 \div 12 = 64 \text{ r } 0 \]
Complete a long division calculation showing remainders.
Use known facts (inverse)
\[ \text{If } 5542 \div 17 = 326… \]
Use a given calculation to find a related answer.
Distributive law recognition
\[ 54 \times 6 + 54 \times 3 = 54 \times \square \]
Recognise and apply the distributive law.
Missing number in division
\[ 75 \div \square = 7.5 \]
Find the divisor when given dividend and decimal quotient.
Word problems
Money problem with change
\[ £5 – £1.45 – £2.40 = \text{?} \]
Calculate change from a multi-item purchase.
Equal sharing with division
\[ 72 \div 6 = \text{?} \text{ each} \]
Divide an amount equally between a group.
Multi-step with fractions
\[ \frac{1}{4} \text{ given away} \rightarrow \text{left?} \]
Solve a multi-step problem involving fractions of amounts.
Using formulae with substitution
\[ \text{Cost} = £15 + £25 \times h \]
Substitute values into a given formula to calculate a result.
Ratio scaling
\[ 2:3 \text{ ratio, 8 of first} \rightarrow \text{?} \]
Use a ratio to find missing quantities.
Proportional reasoning
\[ 3 \text{ cost } 45\text{p} \rightarrow 7 \text{ cost?} \]
Use proportional reasoning to find unit costs or amounts.
Algebra
Identify correct expression
\[ \text{multiply by 3, add 5} \rightarrow 3n+5 \]
Select the algebraic expression matching a word description.
Substitute and evaluate
\[ n=5: 3n + 7 = 22 \]
Substitute a value into an expression and calculate.
Work backwards from formula
\[ y = 3x + 5, \text{ if } y=20… \]
Find an input value given the output of a formula.
Follow a number rule
\[ \text{Input} \rightarrow [\times 3] \rightarrow [+4] \rightarrow \text{?} \]
Apply a function machine or number rule.
Geometry
Count angles in shape
\[ \text{Acute angles in pentagon?} \]
Count the number of acute (or obtuse) angles in a shape.
Find missing angle in triangle
\[ 70° + 40° + ? = 180° \]
Calculate the missing angle using angle sum property.
Properties of 3D shapes
\[ \text{Cube: 6F, 12E, 8V} \]
State properties of 3D shapes (faces, edges, vertices).
Coordinates after translation
\[ (2,3) + 5R + 2U = (7,5) \]
Find the coordinates of a point after translation.
Coordinates using shape properties
\[ \text{Rectangle: find 4th corner} \]
Use shape properties and coordinates to find unknowns.
Total edge length of cuboid
\[ 4 \times (h + l + w) = \text{?} \]
Calculate the total edge length of a cuboid.
Statistics
Read value from table
\[ \text{Difference: } 70 – 35 = 35 \]
Read values from a table and perform a calculation.
Interpret negative values
\[ -3°C \text{ to } 4°C = 7°C \text{ warmer} \]
Find the difference between positive and negative values.
Pie chart angle from percentage
\[ 25\% \rightarrow 90° \]
Calculate the angle for a pie chart sector from a percentage.
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