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.
单元
练习前按清晰顺序掌握本章核心概念。
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.
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
逐步查看方法，并理解每一步为何成立。
6 equal groups contain 9 objects each. How many objects are there, and how can the answer be checked?
54
Explain “Τετραγωνική ρίζα θετικού αριθμού” 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.
Πραγματικοί αριθμοί
八道分层练习，从基础熟练到考试应用。请先独立完成，再查看提示或答案。
Calculate 6 + 6 and show two representations connected with “Τετραγωνική ρίζα θετικού αριθμού”.
Use a number line, place value, or objects.
6 + 6 = 12. Valid representations include number-line jumps and grouped objects.
3 equal groups contain 9 objects each. Find the total and write an addition and multiplication statement.
Add 9 a total of 3 times.
9 + 9 + 9 = 3 · 9 = 27.
Continue 5, 10, 15, ... for three more terms and explain the rule.
Check how much each term increases.
20, 25, 30; +5.
A rectangle has sides 8 cm and 2 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 8 + 2 + 8 + 2 = 20 cm.
Out of 16 objects, 4 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
4/16 = 1/4.
The measurements are 7, 6, 7, and 6. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 7, least 6, range 1.
Anna has 9 cards, gives away 3, then shares the rest into 2 equal groups. How many are in each group?
Subtract first, then divide.
9 - 3 = 6; (6) : 2 = 3.
A learner says 6 + 5 = 12. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
6 + 5 = 11; 11 - 5 = 6.
Πραγματικοί αριθμοί
六道不同作业，从基础到挑战，包含预计用时、提示和答案指南。
Homework 1: Calculate 9 + 2 and show two representations connected with “Τετραγωνική ρίζα θετικού αριθμού”.
Use a number line, place value, or objects.
9 + 2 = 11. Valid representations include number-line jumps and grouped objects.
Homework 2: 4 equal groups contain 5 objects each. Find the total and write an addition and multiplication statement.
Add 5 a total of 4 times.
5 + 5 + 5 + 5 = 4 · 5 = 20.
Homework 3: Continue 8, 14, 20, ... for three more terms and explain the rule.
Check how much each term increases.
26, 32, 38; +6.
Homework 4: A rectangle has sides 4 cm and 3 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 4 + 3 + 4 + 3 = 14 cm.
Homework 5: Out of 35 objects, 7 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
7/35 = 1/5.
Homework 6: The measurements are 3, 2, 3, and 2. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 3, least 2, range 1.
35 分钟 / 30 分
带计时器、完整分值和参考答案的章节自测。
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Calculate 7 + 2 and show two representations connected with “Τετραγωνική ρίζα θετικού αριθμού”.
2 分7 + 2 = 9. Valid representations include number-line jumps and grouped objects.
2. 4 equal groups contain 3 objects each. Find the total and write an addition and multiplication statement.
3 分3 + 3 + 3 + 3 = 4 · 3 = 12.
3. Continue 6, 12, 18, ... for three more terms and explain the rule.
3 分24, 30, 36; +6.
4. A rectangle has sides 9 cm and 3 cm. Find its perimeter and explain why four sides are counted.
4 分Perimeter = 9 + 3 + 9 + 3 = 24 cm.
5. Out of 25 objects, 5 are shaded. What fraction is shaded and how does it simplify?
4 分5/25 = 1/5.
6. The measurements are 8, 2, 8, and 2. Find the greatest, least, and range.
4 分Greatest 8, least 2, range 6.
7. Anna has 16 cards, gives away 4, then shares the rest into 3 equal groups. How many are in each group?
5 分16 - 4 = 12; (12) : 3 = 4.
8. A learner says 7 + 6 = 14. Find the error, correct it, and check the correction.
5 分7 + 6 = 13; 13 - 6 = 7.
单元
课程参考来源；教学顺序请始终与学校和老师确认。
Mathematics
Greek Gymnasium Grade 2: 数学与物理的结构化路线，包含章节、练习和下一步。
结构跟随教材，用来帮助组织学习。
通常容易出错或需要更多复习的部分。
从教材、daily material、PDFs、videos 和 worked examples 开始。
进入 full tests 前先做 targeted practice，让覆盖情况更清楚。
如何衡量本章进度，以及何时加入综合 mock。
完成本章后该做什么，以及它如何连接到下一单元。
说明：每学年的正式考试范围请始终以学校、老师和当前官方来源为准。
