Greek Lyceum Grade 1 / Mathematics / Curriculum
Γεωμετρία: structured theory, worked examples, answered practice, and a mastery checklist for Greek Lyceum Grade 1.
CHAPTER PLAN
Follow the steps in order or jump directly to the part you need.
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Estimated active study time
140 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 rectangle is 10 cm long and 6 cm wide. Find its perimeter and, where covered, its area.
Perimeter 32 cm, area 60 cm².
Explain “Αξιώματα και απόδειξη” in your own words and use a picture, objects, a table, or a simple measurement to support it.
A complete explanation connects the correct idea, a clear representation, and a sensible check.
Γεωμετρία
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Calculate 7 + 6 and show two representations connected with “Αξιώματα και απόδειξη”.
Use a number line, place value, or objects.
7 + 6 = 13. Valid representations include number-line jumps and grouped objects.
3 equal groups contain 3 objects each. Find the total and write an addition and multiplication statement.
Add 3 a total of 3 times.
3 + 3 + 3 = 3 · 3 = 9.
Continue 6, 11, 16, ... for three more terms and explain the rule.
Check how much each term increases.
21, 26, 31; +5.
A rectangle has sides 9 cm and 2 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 9 + 2 + 9 + 2 = 22 cm.
Out of 20 objects, 5 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
5/20 = 1/4.
The measurements are 8, 6, 8, and 6. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 8, least 6, range 2.
Anna has 12 cards, gives away 4, then shares the rest into 2 equal groups. How many are in each group?
Subtract first, then divide.
12 - 4 = 8; (8) : 2 = 4.
A learner says 7 + 5 = 13. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
7 + 5 = 12; 12 - 5 = 7.
Γεωμετρία
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Calculate 3 + 2 and show two representations connected with “Αξιώματα και απόδειξη”.
Use a number line, place value, or objects.
3 + 2 = 5. Valid representations include number-line jumps and grouped objects.
Homework 2: 4 equal groups contain 6 objects each. Find the total and write an addition and multiplication statement.
Add 6 a total of 4 times.
6 + 6 + 6 + 6 = 4 · 6 = 24.
Homework 3: Continue 9, 15, 21, ... for three more terms and explain the rule.
Check how much each term increases.
27, 33, 39; +6.
Homework 4: A rectangle has sides 5 cm and 3 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 5 + 3 + 5 + 3 = 16 cm.
Homework 5: Out of 40 objects, 8 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
8/40 = 1/5.
Homework 6: The measurements are 4, 2, 4, and 2. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 4, least 2, range 2.
35 minutes / 30 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. Calculate 8 + 2 and show two representations connected with “Αξιώματα και απόδειξη”.
2 marks8 + 2 = 10. Valid representations include number-line jumps and grouped objects.
2. 4 equal groups contain 4 objects each. Find the total and write an addition and multiplication statement.
3 marks4 + 4 + 4 + 4 = 4 · 4 = 16.
3. Continue 7, 13, 19, ... for three more terms and explain the rule.
3 marks25, 31, 37; +6.
4. A rectangle has sides 3 cm and 3 cm. Find its perimeter and explain why four sides are counted.
4 marksPerimeter = 3 + 3 + 3 + 3 = 12 cm.
5. Out of 30 objects, 6 are shaded. What fraction is shaded and how does it simplify?
4 marks6/30 = 1/5.
6. The measurements are 9, 2, 9, and 2. Find the greatest, least, and range.
4 marksGreatest 9, least 2, range 7.
7. Anna has 20 cards, gives away 5, then shares the rest into 3 equal groups. How many are in each group?
5 marks20 - 5 = 15; (15) : 3 = 5.
8. A learner says 8 + 6 = 15. Find the error, correct it, and check the correction.
5 marks8 + 6 = 14; 14 - 6 = 8.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
The key is algebraic accuracy: operations, domains, equations/inequalities, functions, and proofs.
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.
