German Gymnasium Klasse 7 / Mathematics / Curriculum
Geometrie: structured theory, worked examples, answered practice, and a mastery checklist for German Gymnasium Klasse 7.
CHAPTER PLAN
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Estimated active study time
209 minutes
Objectives, key ideas, and structured theory.
Open →Worked examples that explain every step.
Open →Graded tasks with hints and answer guidance.
Open →Assignments from core work to challenge.
Open →A timed, marked test with solution guidance.
Open →Progress is stored only in this browser and does not require AI credits.
Unit
The essential chapter ideas in a clear sequence before practice.
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Every geometric step needs a property, theorem, or definition. A result without justification is not a complete proof.
Length, area, volume, and angle use different units. Round only at the end and keep sufficient intermediate precision.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Follow the method step by step and check why every step is valid.
A right triangle has perpendicular sides 15 cm and 20 cm. Find its hypotenuse and area.
Hypotenuse 25 cm, area 150 cm².
Before calculating, explain the key idea from “Winkelarten” and which conditions must be checked.
The answer should show not only which rule is used for “Winkelarten”, but also why it is valid here.
Geometrie
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
A 5 cm by 6 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 22 cm, A = 30 cm².
A triangle has base 24 cm and height 3 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 24 · 3 = 36 cm².
Two angles in a triangle are 40° and 50°. Find the third.
Triangle angles sum to 180°.
90°.
A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
Use a²+b²=c².
10 cm.
A circle has radius 4 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 8π cm, A = 16π cm².
Scale 1:600. What real length in metres does 6 cm represent?
Multiply in cm, then convert to metres.
6 · 600 = 3600 cm = 36 m.
A cuboid is 9 cm × 3 cm × 12 cm. Find its volume.
V = lwh.
V = 324 cm³.
Points A(0,0) and B(5,5). Find AB.
AB = √(Δx²+Δy²).
AB = √50.
Geometrie
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: A 8 cm by 2 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 20 cm, A = 16 cm².
Homework 2: A triangle has base 16 cm and height 4 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 16 · 4 = 32 cm².
Homework 3: Two angles in a triangle are 70° and 60°. Find the third.
Triangle angles sum to 180°.
50°.
Homework 4: A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
Use a²+b²=c².
15 cm.
Homework 5: A circle has radius 5 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 10π cm, A = 25π cm².
Homework 6: Scale 1:900. What real length in metres does 2 cm represent?
Multiply in cm, then convert to metres.
2 · 900 = 1800 cm = 18 m.
50 minutes / 40 marks
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. A 6 cm by 2 cm rectangle: find perimeter and area.
2 marksP = 16 cm, A = 12 cm².
2. A triangle has base 36 cm and height 4 cm. Find its area.
3 marksA = 1/2 · 36 · 4 = 72 cm².
3. Two angles in a triangle are 50° and 60°. Find the third.
3 marks70°.
4. A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
4 marks15 cm.
5. A circle has radius 5 cm. Find circumference and area in terms of π.
4 marksC = 10π cm, A = 25π cm².
6. Scale 1:700. What real length in metres does 2 cm represent?
4 marks2 · 700 = 1400 cm = 14 m.
7. A cuboid is 3 cm × 4 cm × 7 cm. Find its volume.
5 marksV = 84 cm³.
8. Points A(0,0) and B(6,6). Find AB.
5 marksAB = √72.
9. Similar shapes have length scale factor 1:3. If the small area is 9 cm², find the large area.
5 marks9 · 3² = 81 cm².
10. Explain which givens and theorem are needed for a complete argument about “Volumen”.
5 marksFull response: a labelled diagram, givens, an applicable theorem with its conditions, and a logically derived conclusion.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
Keep each unit in GR/DE: concept, German term, example, exercise, recap.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.
