Greek Gymnasium Grade 1 / Mathematics / Μέρος Α: Αριθμητική - Άλγεβρα
Εξισώσεις και προβλήματα: structured theory, worked examples, answered practice, and a mastery checklist for Greek Gymnasium Grade 1.
单元
练习前按清晰顺序掌握本章核心概念。
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
逐步查看方法，并理解每一步为何成立。
2 equal groups contain 11 objects each. How many objects are there, and how can the answer be checked?
22
Explain “Η έννοια της μεταβλητής” 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.
Εξισώσεις και προβλήματα
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 8 + 2 and show two representations connected with “Η έννοια της μεταβλητής”.
Use a number line, place value, or objects.
8 + 2 = 10. Valid representations include number-line jumps and grouped objects.
4 equal groups contain 4 objects each. Find the total and write an addition and multiplication statement.
Add 4 a total of 4 times.
4 + 4 + 4 + 4 = 4 · 4 = 16.
Continue 7, 13, 19, ... for three more terms and explain the rule.
Check how much each term increases.
25, 31, 37; +6.
A rectangle has sides 3 cm and 3 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 3 + 3 + 3 + 3 = 12 cm.
Out of 30 objects, 6 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
6/30 = 1/5.
The measurements are 9, 2, 9, and 2. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 9, least 2, range 7.
Anna has 20 cards, gives away 5, then shares the rest into 3 equal groups. How many are in each group?
Subtract first, then divide.
20 - 5 = 15; (15) : 3 = 5.
A learner says 8 + 6 = 15. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
8 + 6 = 14; 14 - 6 = 8.
Εξισώσεις και προβλήματα
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 4 + 3 and show two representations connected with “Η έννοια της μεταβλητής”.
Use a number line, place value, or objects.
4 + 3 = 7. Valid representations include number-line jumps and grouped objects.
Homework 2: 5 equal groups contain 7 objects each. Find the total and write an addition and multiplication statement.
Add 7 a total of 5 times.
7 + 7 + 7 + 7 + 7 = 5 · 7 = 35.
Homework 3: Continue 3, 5, 7, ... for three more terms and explain the rule.
Check how much each term increases.
9, 11, 13; +2.
Homework 4: A rectangle has sides 6 cm and 4 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 6 + 4 + 6 + 4 = 20 cm.
Homework 5: Out of 54 objects, 9 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
9/54 = 1/6.
Homework 6: The measurements are 5, 3, 5, and 3. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 5, least 3, range 2.
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 9 + 3 and show two representations connected with “Η έννοια της μεταβλητής”.
2 分9 + 3 = 12. Valid representations include number-line jumps and grouped objects.
2. 5 equal groups contain 5 objects each. Find the total and write an addition and multiplication statement.
3 分5 + 5 + 5 + 5 + 5 = 5 · 5 = 25.
3. Continue 8, 10, 12, ... for three more terms and explain the rule.
3 分14, 16, 18; +2.
4. A rectangle has sides 4 cm and 4 cm. Find its perimeter and explain why four sides are counted.
4 分Perimeter = 4 + 4 + 4 + 4 = 16 cm.
5. Out of 42 objects, 7 are shaded. What fraction is shaded and how does it simplify?
4 分7/42 = 1/6.
6. The measurements are 3, 3, 3, and 3. Find the greatest, least, and range.
4 分Greatest 3, least 3, range 0.
7. Anna has 30 cards, gives away 6, then shares the rest into 4 equal groups. How many are in each group?
5 分30 - 6 = 24; (24) : 4 = 6.
8. A learner says 9 + 2 = 12. Find the error, correct it, and check the correction.
5 分9 + 2 = 11; 11 - 2 = 9.
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 1: 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。
