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Secondary school · Grade 5
Maths worksheets for grade 5
26 worksheets and 31 types of task – adjust them for free and print, with an answer sheet if you like.
From grade 5 on, types of school and German states differ more in order and pace. Typical topics are the order of operations and brackets, large numbers, fractions of shapes, decimals, factors and multiples, angles and coordinates. With the levels ★ to ★★★ every worksheet can be made easier or harder.
Which topics come when differs between the German states, schools and textbooks. The number range and the level can be set on every worksheet.
Worksheets for grade 5
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Grade 5 · MixedWeekly plan grade 5Order of operations, large numbers, column method, factors, fractions of shapes
Grade 5 · SingleOrder of operations3 + 4 · 5, without brackets, up to 100
Grade 5 · SingleBrackets & order of operationsThree steps, up to 1,000
Grade 5 · SingleFractions of shapesReading and colouring fractions of strips and circles
Grade 5 · SingleLong multiplication, three digits346 · 127 in squares
Grade 5 · SingleDividing by two-digit numbers4 368 : 24, also with remainder
Grade 5 · SinglePlace value chart up to 1 billionWriting in and reading large numbers
Grade 5 · SingleFinding factorsAll factors of a number up to 60
Grade 5 · SingleDivisibility rulesDivisible by 2, 3, 5 and 10? Tick
Grade 5 · SingleUnits of areaConverting mm², cm², dm², m², a, ha, km²
Grade 5 · SingleMeasuring anglesWith a set square, in steps of 10 up to 180°
Grade 5 · SingleTimes tables up to 20Tables 11 to 20: 13 · 7, 17 · 4 …
Grade 5 · SingleCoordinatesReading and plotting points, recognising shapes
Grade 5 · SingleVolume of cuboidsCounting cubes, working out the volume, cm³ and dm³
Grade 5 · SingleSquare numbers & powers13² = 169, 2⁵ = 32 – also backwards
Grade 5 · SingleRoman numeralsReading and writing up to 1,000
Grade 5 · SingleScaleMap ↔ real life, round scales
Grade 5 · SingleWorking with dataMean and range
Grade 5 · SingleWord problems with quantities1 m 20 cm, 2 kg 300 g: convert first, then calculate
Grade 5 · SingleTime spans past midnightUp to 24 hours, start, length or end
Grade 5 · SingleDecimals plus & minusOne decimal place, mental maths
Grade 5 · MixedPuzzle sheetMagic squares up to 1,000, sudoku 6 × 6
Grade 5 · SingleMistake detective: order of operationsFinding and explaining mistakes
Grade 5 · SingleProportion & tablesProportional tables of values, whole euros
Grade 5 · SingleEquations with a checkx + 7 = 15, 4 · x = 28 – solve and check
Grade 5 · SingleThe balanceHow heavy is one x?
Types of task for grade 5
Each type of task has its own page with an example and matching worksheets.
Calculating
- Quick calculationsGrades 1 to 6Lots of short calculations with plus, minus, times and divided by – for quick practice.
- Your own calculationsGrades 1 to 6Type in your own calculations, also with a gap – the Rechenkiste works out the answers.
- Column + −Grades 3 to 6Plus and minus written in columns in squares, with carrying – also with decimals.
- Long × and ÷Grades 3 to 5Multiplying and dividing written in columns in squares – from grade 5 also with three-digit factors and two-digit divisors.
- Order of operationsGrades 4 and 5Work out expressions with times and divide before plus and minus, and with brackets, e.g. (12 + 8) · 3.
- Calculating with decimalsGrades 5 and 6Add, subtract and multiply decimals and divide them by whole numbers.
- Square numbers & powersGrades 5 and 6Work out square numbers up to 20², powers of two, three and ten, write numbers as powers and find the exponent.
- EstimatingGrades 4 and 5First estimate with rounded numbers, then calculate exactly – or use the estimate to see which answer can be right.
- Mistake detectiveGrades 2 to 6Check other children's calculations: find typical mistakes – a forgotten carry, plus before times, a decimal comma as a separator –, say what went wrong and calculate it correctly.
- Expressions & equationsGrades 5 and 6Calculate with the variable x: find an expression for a situation, recognise equivalent expressions, find x on a balance and solve equations – with a check.
Understanding numbers
- Place value chartGrades 2 to 5Split numbers into hundreds, tens and ones – and back, from grade 5 up to a billion.
- Factors & multiplesGrades 5 and 6Find factors and multiples, use divisibility rules, split numbers into prime factors, find the HCF and LCM.
- Fractions of shapesGrades 4 to 6Read fractions of strips, circles and rectangles and colour them in – in grade 4 with pictures as a start.
- DecimalsGrades 5 and 6Change fractions into decimals and back, compare decimals, multiply and divide them by 10, 100, 1000.
- Rounding & estimatingGrades 3 to 5Round numbers and estimate answers.
- Roman numeralsGrade 5Read and write Roman numerals – with IV, IX, XL and the other symbols that are subtracted.
Measures
- Time spansGrades 3 to 5How long does something take? Work out the start, the length and the end.
- Lengths & weightsGrades 2 to 6Convert lengths, weights, capacities and, from grade 5, units of area, e.g. 1 m = 100 cm or 1 m² = 100 dm².
- ScaleGrades 5 and 6Use the scale to calculate from the map to real life and back – and work out the scale yourself.
Shape & space
- ReflectionGrades 1 to 5Reflect a shape in a mirror line on squared paper.
- Cube netsGrades 3 to 5Find out whether six squares can be folded into a cube.
- Area & perimeterGrades 3 to 5Work out the area and perimeter of shapes on squared paper.
- AnglesGrades 5 and 6Recognise types of angles, measure angles with a set square and draw them – printed true to scale.
- CoordinatesGrades 5 and 6Read and plot points on a coordinate grid, join them and name the shape.
- Volume & cuboidsGrades 5 and 6Count the cubes in a cuboid, work out the volume and convert units of volume (cm³, dm³, m³, l, ml).
Data & chance
Word problems
- Word problemsGrades 1 to 6Short stories with a question that is answered with a calculation – from grade 4 also with quantities and decimals.
- ProportionGrades 5 and 6Proportional relationships: complete tables of values, calculate via one item, compare offers by the price per item and check whether a relationship is proportional.