Place value and rounding
Ten counters make a ten, ten tens make a hundred. Once you have seen the bundling, reading millions and rounding them is no longer a mystery.
Mathematics – grade 5
The curriculum assigns these units to exactly this grade (Saxony, Gymnasium up to grade 12). The unit numbers are the curriculum’s; optional areas (“Wahlbereiche”) are labelled W1–W3 here.
Unit 1Working with natural numbers
Representing, rounding and ordering natural numbers, calculating confidently, powers, divisors, prime numbers and divisibility rules.
Expression trees: the structure of terms
An expression drawn as a tree: whatever hangs lowest is calculated first. The order of operations stops being a rule and becomes visible.
Powers, powers of ten and orders of magnitude
From a grain of sand to the Earth in steps of ten. Along the way it becomes clear why 10⁶ is a million and how to write tiny numbers.
Prime factorisation and divisibility
Break numbers down into prime factors, check divisibility rules and find primes with a sieve. This also gives you the gcd and the lcm.
Unit 2Fractions and decimals
Showing fractions on figures and the number line, simplifying and expanding, switching between fractions, decimals and percentages, and calculating with decimals.
Representing fractions
Pizza, cake or a line: share it out fairly first, then colour some pieces. That is exactly what a fraction means.
Equivalent fractions and comparing
Compare two fractions as bars or circles. When you expand a fraction, the pieces get smaller but the amount stays the same.
Unit 3Relative positions of geometric objects
Points in the coordinate system, parallel and perpendicular lines, measuring angles and angle pairs at lines, symmetry and line reflection.
Points, lines and circles: relative positions
Place and read points in a coordinate system, draw segments and lines and check whether they are parallel or perpendicular.
Estimating and measuring angles
Line up the protractor, hit the zero point, read the right scale. The estimation game then shows how well your eye already measures.
Angles at intersecting lines
Two lines cross and one of them turns. Which angles stay equal? At parallel lines they are called corresponding and alternate angles.
Reflections in a line and in a point
In a line or in a point: the shape flips over, and every construction step with the set square stays visible.
Unit 4Rectangles and cuboids
Perimeter and area of rectangles, drawing cuboids as oblique drawings and nets, surface area and volume of cuboids with their units.
Perimeter and area of rectangles
Count the squares or walk once around? An ant makes the difference between area and perimeter tangible.
Nets and surface areas of solids
Fold nets of a cube, cuboid, prism, pyramid and cylinder into a solid in 3D and calculate the surface area.
Volume of cuboids with unit cubes
First a row of cubes, then a layer, then the whole cuboid. Length times width times height follows naturally from filling it.
Converting units with a place-value chart
3.5 km is 3500 m, but 3.5 m² is 35,000 cm². The unit table shows why the decimal point jumps twice as far for areas.
Unit 5Connections: mathematics in everyday life
Solving word problems with quantities, converting units, rounding sensibly and breaking a problem into steps.
Converting units with a place-value chart
3.5 km is 3500 m, but 3.5 m² is 35,000 cm². The unit table shows why the decimal point jumps twice as far for areas.
Unit W1Dynamic geometry (optional)
Drawing and moving figures with dynamic geometry software.
No separate simulation is planned for this.
Unit W2Mathematical puzzles and games (optional)
Investigating puzzles, strategy games and games of chance.
No separate simulation is planned for this.
Unit W3Counting and calculating – then and now (optional)
Number systems of other cultures and calculating in other bases.
No separate simulation is planned for this.
The summaries describe the curriculum in our own words. The original text is authoritative. Original text (German): Lehrplan, Gymnasium, Mathematics, grade 5