Greek Primary Grade 3 / Mathematics / Αριθμοί και πράξεις

Τέσσερις πράξεις

Τέσσερις πράξεις: structured theory, worked examples, answered practice, and a mastery checklist for Greek Primary Grade 3.

学习目标

Recognise, explain, and apply “γραπτοί αλγόριθμοι”.
Recognise, explain, and apply “προπαίδεια”.
Recognise, explain, and apply “υπόλοιπο στη διαίρεση”.

核心概念与检查

I connect limit, derivative, and integral with a graph.
I apply rules with the correct conditions.
Every solution or explanation for “Τέσσερις πράξεις” should include a method, justification, and final check.

单元

核心理论

练习前按清晰顺序掌握本章核心概念。

Change and approximation

Calculus studies how a quantity changes and how small changes accumulate. Graphical interpretation should accompany the notation.

Conditions before the rule

Check domain, continuity, or differentiability where required. A correct rule cannot be applied mechanically outside its conditions.

Interpret the result

A derivative represents local rate of change and a definite integral represents net accumulation. Always reconnect the result to the original problem.

γραπτοί αλγόριθμοι

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.

προπαίδεια

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.

υπόλοιπο στη διαίρεση

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

例题讲解

逐步查看方法，并理解每一步为何成立。

Worked arithmetic example

2 equal groups contain 7 objects each. How many objects are there, and how can the answer be checked?

1Write repeated addition: 7 + 7.
2Connect it to 2 × 7.
3Check with division: 14 ÷ 2 = 7.

Thinking and explanation example

Explain “γραπτοί αλγόριθμοι” in your own words and use a picture, objects, a table, or a simple measurement to support it.

1State what is known and what is being found.
2Choose one clear representation.
3Explain what it shows and check that the answer is sensible.

A complete explanation connects the correct idea, a clear representation, and a sensible check.

Τέσσερις πράξεις

含答案练习

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。

基础熟练3 分钟

Calculate 4 + 2 and show two representations connected with “γραπτοί αλγόριθμοι”.

提示

Use a number line, place value, or objects.

答案指南

4 + 2 = 6. Valid representations include number-line jumps and grouped objects.

基础熟练4 分钟

4 equal groups contain 7 objects each. Find the total and write an addition and multiplication statement.

提示

Add 7 a total of 4 times.

答案指南

7 + 7 + 7 + 7 = 4 · 7 = 28.

应用4 分钟

Continue 3, 9, 15, ... for three more terms and explain the rule.

提示

Check how much each term increases.

答案指南

21, 27, 33; +6.

应用5 分钟

A rectangle has sides 6 cm and 3 cm. Find its perimeter and explain why four sides are counted.

提示

Opposite sides are equal.

答案指南

Perimeter = 6 + 3 + 6 + 3 = 18 cm.

推理5 分钟

Out of 45 objects, 9 are shaded. What fraction is shaded and how does it simplify?

提示

Put shaded objects over the total.

答案指南

9/45 = 1/5.

推理6 分钟

The measurements are 5, 2, 5, and 2. Find the greatest, least, and range.

提示

Range = greatest value minus least value.

答案指南

Greatest 5, least 2, range 3.

考试题型7 分钟

Anna has 32 cards, gives away 8, then shares the rest into 3 equal groups. How many are in each group?

提示

Subtract first, then divide.

答案指南

32 - 8 = 24; (24) : 3 = 8.

考试题型8 分钟

A learner says 4 + 6 = 11. Find the error, correct it, and check the correction.

提示

Check with a number line or inverse subtraction.

答案指南

4 + 6 = 10; 10 - 6 = 4.

常见错误

Applying a rule without checking domain or continuity.
Omitting the integration constant in an indefinite integral.
Giving a numerical result without graphical or physical interpretation.

掌握度检查

I connect limit, derivative, and integral with a graph.
I apply rules with the correct conditions.
I interpret the result in context.

Τέσσερις πράξεις

章节作业

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。

基础5 分钟

Homework 1: Calculate 7 + 3 and show two representations connected with “γραπτοί αλγόριθμοι”.

提示

Use a number line, place value, or objects.

答案指南

7 + 3 = 10. Valid representations include number-line jumps and grouped objects.

基础6 分钟

Homework 2: 5 equal groups contain 3 objects each. Find the total and write an addition and multiplication statement.

提示

Add 3 a total of 5 times.

答案指南

3 + 3 + 3 + 3 + 3 = 5 · 3 = 15.

进阶7 分钟

Homework 3: Continue 6, 8, 10, ... for three more terms and explain the rule.

提示

Check how much each term increases.

答案指南

12, 14, 16; +2.

进阶8 分钟

Homework 4: A rectangle has sides 9 cm and 4 cm. Find its perimeter and explain why four sides are counted.

提示

Opposite sides are equal.

答案指南

Perimeter = 9 + 4 + 9 + 4 = 26 cm.

挑战10 分钟

Homework 5: Out of 30 objects, 5 are shaded. What fraction is shaded and how does it simplify?

提示

Put shaded objects over the total.

答案指南

5/30 = 1/6.

挑战12 分钟

Homework 6: The measurements are 8, 3, 8, and 3. Find the greatest, least, and range.

提示

Range = greatest value minus least value.

答案指南

Greatest 8, least 3, range 5.

35 分钟 / 30 分

完整章节测试

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 5 + 3 and show two representations connected with “γραπτοί αλγόριθμοι”.

2 分

答案指南

5 + 3 = 8. Valid representations include number-line jumps and grouped objects.

2. 5 equal groups contain 8 objects each. Find the total and write an addition and multiplication statement.

3 分

答案指南

8 + 8 + 8 + 8 + 8 = 5 · 8 = 40.

3. Continue 4, 6, 8, ... for three more terms and explain the rule.

3 分

答案指南

10, 12, 14; +2.

4. A rectangle has sides 7 cm and 4 cm. Find its perimeter and explain why four sides are counted.

4 分

答案指南

Perimeter = 7 + 4 + 7 + 4 = 22 cm.

5. Out of 18 objects, 3 are shaded. What fraction is shaded and how does it simplify?

4 分

答案指南

3/18 = 1/6.

6. The measurements are 6, 3, 6, and 3. Find the greatest, least, and range.

4 分

答案指南

Greatest 6, least 3, range 3.

7. Anna has 45 cards, gives away 9, then shares the rest into 4 equal groups. How many are in each group?

5 分

答案指南

45 - 9 = 36; (36) : 4 = 9.

8. A learner says 5 + 2 = 8. Find the error, correct it, and check the correction.

5 分

答案指南

5 + 2 = 7; 7 - 2 = 5.

单元

官方来源与核验

课程参考来源；教学顺序请始终与学校和老师确认。

Ινστιτούτο Εκπαιδευτικής Πολιτικής (ΙΕΠ)Official curriculum programmes and announcements.Ψηφιακό Σχολείο / Διαδραστικά Σχολικά ΒιβλίαOfficial school textbooks and available digital material.

Mathematics

Greek Primary Grade 3: 数学与物理的结构化路线，包含章节、练习和下一步。

返回科目

本章覆盖内容

结构跟随教材，用来帮助组织学习。

γραπτοί αλγόριθμοι

προπαίδεια

υπόλοιπο στη διαίρεση

重点关注

通常容易出错或需要更多复习的部分。

I connect limit, derivative, and integral with a graph.

I apply rules with the correct conditions.

I interpret the result in context.

来源、日常资料与学习资源

从教材、daily material、PDFs、videos 和 worked examples 开始。

Start from the official textbook or specification referenced on the subject page.

Use the notes and examples as support, not as a replacement for the official syllabus.

Check the current syllabus version before exam preparation.

按小主题练习

进入 full tests 前先做 targeted practice，让覆盖情况更清楚。