Learning objectives
- Recognise, explain, and apply “πίνακας”.
- Recognise, explain, and apply “διάγραμμα”.
- Recognise, explain, and apply “τύπος”.
- Recognise, explain, and apply “έλεγχος λογικότητας”.
Greek Primary Grade 5 / Mathematics / Στατιστική και επίλυση
Προβλήματα πολλαπλών αναπαραστάσεων: structured theory, worked examples, answered practice, and a mastery checklist for Greek Primary Grade 5.
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.
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.
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.
3 equal groups contain 6 objects each. How many objects are there, and how can the answer be checked?
18
Explain “πίνακας” 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.
Προβλήματα πολλαπλών αναπαραστάσεων
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Calculate 3 + 3 and show two representations connected with “πίνακας”.
Use a number line, place value, or objects.
3 + 3 = 6. Valid representations include number-line jumps and grouped objects.
5 equal groups contain 6 objects each. Find the total and write an addition and multiplication statement.
Add 6 a total of 5 times.
6 + 6 + 6 + 6 + 6 = 5 · 6 = 30.
Continue 9, 11, 13, ... for three more terms and explain the rule.
Check how much each term increases.
15, 17, 19; +2.
A rectangle has sides 5 cm and 4 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 5 + 4 + 5 + 4 = 18 cm.
Out of 48 objects, 8 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
8/48 = 1/6.
The measurements are 4, 3, 4, and 3. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 4, least 3, range 1.
Anna has 35 cards, gives away 7, then shares the rest into 4 equal groups. How many are in each group?
Subtract first, then divide.
35 - 7 = 28; (28) : 4 = 7.
A learner says 3 + 2 = 6. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
3 + 2 = 5; 5 - 2 = 3.
Προβλήματα πολλαπλών αναπαραστάσεων
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Calculate 6 + 4 and show two representations connected with “πίνακας”.
Use a number line, place value, or objects.
6 + 4 = 10. Valid representations include number-line jumps and grouped objects.
Homework 2: 6 equal groups contain 9 objects each. Find the total and write an addition and multiplication statement.
Add 9 a total of 6 times.
9 + 9 + 9 + 9 + 9 + 9 = 6 · 9 = 54.
Homework 3: Continue 5, 8, 11, ... for three more terms and explain the rule.
Check how much each term increases.
14, 17, 20; +3.
Homework 4: A rectangle has sides 8 cm and 5 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 8 + 5 + 8 + 5 = 26 cm.
Homework 5: Out of 8 objects, 4 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
4/8 = 1/2.
Homework 6: The measurements are 7, 4, 7, and 4. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 7, least 4, range 3.
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 4 + 4 and show two representations connected with “πίνακας”.
2 marks4 + 4 = 8. Valid representations include number-line jumps and grouped objects.
2. 6 equal groups contain 7 objects each. Find the total and write an addition and multiplication statement.
3 marks7 + 7 + 7 + 7 + 7 + 7 = 6 · 7 = 42.
3. Continue 3, 6, 9, ... for three more terms and explain the rule.
3 marks12, 15, 18; +3.
4. A rectangle has sides 6 cm and 5 cm. Find its perimeter and explain why four sides are counted.
4 marksPerimeter = 6 + 5 + 6 + 5 = 22 cm.
5. Out of 18 objects, 9 are shaded. What fraction is shaded and how does it simplify?
4 marks9/18 = 1/2.
6. The measurements are 5, 4, 5, and 4. Find the greatest, least, and range.
4 marksGreatest 5, least 4, range 1.
7. Anna has 48 cards, gives away 8, then shares the rest into 5 equal groups. How many are in each group?
5 marks48 - 8 = 40; (40) : 5 = 8.
8. A learner says 4 + 3 = 8. Find the error, correct it, and check the correction.
5 marks4 + 3 = 7; 7 - 3 = 4.
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.