Greek Gymnasium Grade 1 / Mathematics / Μέρος Β: Γεωμετρία
Βασικές γεωμετρικές έννοιες: 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。
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Every geometric step needs a property, theorem, or definition. A result without justification is not a complete proof.
Length, area, volume, and angle use different units. Round only at the end and keep sufficient intermediate precision.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. 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。
A rectangle is 12 cm long and 6 cm wide. Find its perimeter and, where covered, its area.
Perimeter 36 cm, area 72 cm².
Explain “Σημείο, ευθύγραμμο τμήμα, ευθεία, ημιευθεία” 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.
Βασικές γεωμετρικές έννοιες
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 9 + 6 and show two representations connected with “Σημείο, ευθύγραμμο τμήμα, ευθεία, ημιευθεία”.
Use a number line, place value, or objects.
9 + 6 = 15. Valid representations include number-line jumps and grouped objects.
3 equal groups contain 5 objects each. Find the total and write an addition and multiplication statement.
Add 5 a total of 3 times.
5 + 5 + 5 = 3 · 5 = 15.
Continue 8, 13, 18, ... for three more terms and explain the rule.
Check how much each term increases.
23, 28, 33; +5.
A rectangle has sides 4 cm and 2 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 4 + 2 + 4 + 2 = 12 cm.
Out of 28 objects, 7 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
7/28 = 1/4.
The measurements are 3, 6, 3, and 6. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 6, least 3, range 3.
Anna has 18 cards, gives away 6, then shares the rest into 2 equal groups. How many are in each group?
Subtract first, then divide.
18 - 6 = 12; (12) : 2 = 6.
A learner says 9 + 5 = 15. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
9 + 5 = 14; 14 - 5 = 9.
Βασικές γεωμετρικές έννοιες
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 5 + 2 and show two representations connected with “Σημείο, ευθύγραμμο τμήμα, ευθεία, ημιευθεία”.
Use a number line, place value, or objects.
5 + 2 = 7. Valid representations include number-line jumps and grouped objects.
Homework 2: 4 equal groups contain 8 objects each. Find the total and write an addition and multiplication statement.
Add 8 a total of 4 times.
8 + 8 + 8 + 8 = 4 · 8 = 32.
Homework 3: Continue 4, 10, 16, ... for three more terms and explain the rule.
Check how much each term increases.
22, 28, 34; +6.
Homework 4: A rectangle has sides 7 cm and 3 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 7 + 3 + 7 + 3 = 20 cm.
Homework 5: Out of 15 objects, 3 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
3/15 = 1/5.
Homework 6: The measurements are 6, 2, 6, and 2. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 6, least 2, range 4.
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 3 + 2 and show two representations connected with “Σημείο, ευθύγραμμο τμήμα, ευθεία, ημιευθεία”.
2 分3 + 2 = 5. Valid representations include number-line jumps and grouped objects.
2. 4 equal groups contain 6 objects each. Find the total and write an addition and multiplication statement.
3 分6 + 6 + 6 + 6 = 4 · 6 = 24.
3. Continue 9, 15, 21, ... for three more terms and explain the rule.
3 分27, 33, 39; +6.
4. A rectangle has sides 5 cm and 3 cm. Find its perimeter and explain why four sides are counted.
4 分Perimeter = 5 + 3 + 5 + 3 = 16 cm.
5. Out of 40 objects, 8 are shaded. What fraction is shaded and how does it simplify?
4 分8/40 = 1/5.
6. The measurements are 4, 2, 4, and 2. Find the greatest, least, and range.
4 分Greatest 4, least 2, range 2.
7. Anna has 28 cards, gives away 7, then shares the rest into 3 equal groups. How many are in each group?
5 分28 - 7 = 21; (21) : 3 = 7.
8. A learner says 3 + 6 = 10. Find the error, correct it, and check the correction.
5 分3 + 6 = 9; 9 - 6 = 3.
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。
