Represent before calculating
Write the number in a useful form, check sign and place value, and only then choose the operation. A clear representation reduces mechanical errors.
Greek Gymnasium Grade 2 / Mathematics / Μέρος Α: Άλγεβρα
Πραγματικοί αριθμοί: structured theory, worked examples, answered practice, and a mastery checklist for Greek Gymnasium Grade 2.
Unit
The essential chapter ideas in a clear sequence before practice.
Write the number in a useful form, check sign and place value, and only then choose the operation. A clear representation reduces mechanical errors.
Fractions, decimals, percentages, ratios, and powers can describe the same quantity. Changing form is a solving tool, not a separate trick.
Estimate before and after the exact calculation. The sign, order of magnitude, and unit must agree with the problem context.
Mathematics
Follow the method step by step and check why every step is valid.
Calculate and simplify 3/21 + 7/21.
Mathematics
The goal is to connect equations, word problems, and graphs without mechanical memorisation.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
10/21
Before calculating, explain the key idea from “Τετραγωνική ρίζα θετικού αριθμού” and which conditions must be checked.
The answer should show not only which rule is used for “Τετραγωνική ρίζα θετικού αριθμού”, but also why it is valid here.
Πραγματικοί αριθμοί
Try independently, use the hint if needed, then open the answer guide.
1. Explain the idea and give one correct foundation example for “Τετραγωνική ρίζα θετικού αριθμού”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Τετραγωνική ρίζα θετικού αριθμού”, shows equivalent steps, and includes a final check.
2. Solve an application and show every intermediate step for “Άρρητοι αριθμοί”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Άρρητοι αριθμοί”, shows equivalent steps, and includes a final check.
3. Compare a correct and an incorrect approach and justify the difference for “Πραγματικοί αριθμοί”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Πραγματικοί αριθμοί”, shows equivalent steps, and includes a final check.
4. Create a short exam-style question and check your answer for “Προσεγγίσεις”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Προσεγγίσεις”, shows equivalent steps, and includes a final check.
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.