Learning objectives
- Recognise, explain, and apply “άγνωστος”.
- Recognise, explain, and apply “ισότητα”.
- Recognise, explain, and apply “αντίστροφες πράξεις”.
- Recognise, explain, and apply “έλεγχος λύσης”.
Greek Primary Grade 6 / Mathematics / Αριθμοί και αλγεβρική σκέψη
Μεταβλητές και απλές εξισώσεις: structured theory, worked examples, answered practice, and a mastery checklist for Greek Primary Grade 6.
Unit
The essential chapter ideas in a clear sequence before practice.
Mathematics
Start with theory and core examples, then move to worked exercises and short test-style practice.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
A variable represents a number or quantity. Every algebraic transformation must preserve the equivalence of the original expression or equation.
Write each transformation on a new line and apply the same valid operation to both sides. This keeps the solution easy to audit.
A final value is not a complete solution until it is substituted into the original relation. Verification catches sign and expansion errors.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. 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.
5 equal groups contain 10 objects each. How many objects are there, and how can the answer be checked?
50
Explain “άγνωστος” 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.
Μεταβλητές και απλές εξισώσεις
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Calculate 7 + 5 and show two representations connected with “άγνωστος”.
Use a number line, place value, or objects.
7 + 5 = 12. Valid representations include number-line jumps and grouped objects.
2 equal groups contain 3 objects each. Find the total and write an addition and multiplication statement.
Add 3 a total of 2 times.
3 + 3 = 2 · 3 = 6.
Continue 6, 10, 14, ... for three more terms and explain the rule.
Check how much each term increases.
18, 22, 26; +4.
A rectangle has sides 9 cm and 6 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 9 + 6 + 9 + 6 = 30 cm.
Out of 15 objects, 5 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
5/15 = 1/3.
The measurements are 8, 5, 8, and 5. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 8, least 5, range 3.
Anna has 8 cards, gives away 4, then shares the rest into 1 equal groups. How many are in each group?
Subtract first, then divide.
8 - 4 = 4; (4) : 1 = 4.
A learner says 7 + 4 = 12. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
7 + 4 = 11; 11 - 4 = 7.
Μεταβλητές και απλές εξισώσεις
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Calculate 3 + 6 and show two representations connected with “άγνωστος”.
Use a number line, place value, or objects.
3 + 6 = 9. Valid representations include number-line jumps and grouped objects.
Homework 2: 3 equal groups contain 6 objects each. Find the total and write an addition and multiplication statement.
Add 6 a total of 3 times.
6 + 6 + 6 = 3 · 6 = 18.
Homework 3: Continue 9, 14, 19, ... for three more terms and explain the rule.
Check how much each term increases.
24, 29, 34; +5.
Homework 4: A rectangle has sides 5 cm and 2 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 5 + 2 + 5 + 2 = 14 cm.
Homework 5: Out of 32 objects, 8 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
8/32 = 1/4.
Homework 6: The measurements are 4, 6, 4, and 6. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 6, least 4, 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 + 6 and show two representations connected with “άγνωστος”.
2 marks8 + 6 = 14. Valid representations include number-line jumps and grouped objects.
2. 3 equal groups contain 4 objects each. Find the total and write an addition and multiplication statement.
3 marks4 + 4 + 4 = 3 · 4 = 12.
3. Continue 7, 12, 17, ... for three more terms and explain the rule.
3 marks22, 27, 32; +5.
4. A rectangle has sides 3 cm and 2 cm. Find its perimeter and explain why four sides are counted.
4 marksPerimeter = 3 + 2 + 3 + 2 = 10 cm.
5. Out of 24 objects, 6 are shaded. What fraction is shaded and how does it simplify?
4 marks6/24 = 1/4.
6. The measurements are 9, 6, 9, and 6. Find the greatest, least, and range.
4 marksGreatest 9, least 6, range 3.
7. Anna has 15 cards, gives away 5, then shares the rest into 2 equal groups. How many are in each group?
5 marks15 - 5 = 10; (10) : 2 = 5.
8. A learner says 8 + 5 = 14. Find the error, correct it, and check the correction.
5 marks8 + 5 = 13; 13 - 5 = 8.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
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.