Greek Primary Grade 4 / Mathematics / Κλάσματα και δεκαδικοί

Ισοδυναμία και σύγκριση κλασμάτων

Ισοδυναμία και σύγκριση κλασμάτων: structured theory, worked examples, answered practice, and a mastery checklist for Greek Primary Grade 4.

学习目标

Recognise, explain, and apply “κοινά πολλαπλάσια”.
Recognise, explain, and apply “αριθμογραμμή”.
Recognise, explain, and apply “απλοποίηση”.

核心概念与检查

I can convert safely between number forms.
I can explain why the chosen operation is appropriate.
Every solution or explanation for “Ισοδυναμία και σύγκριση κλασμάτων” 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。

Represent before calculating

Write the number in a useful form, check sign and place value, and only then choose the operation. A clear representation reduces mechanical errors.

Equivalent forms

Fractions, decimals, percentages, ratios, and powers can describe the same quantity. Changing form is a solving tool, not a separate trick.

Reasonableness check

Estimate before and after the exact calculation. The sign, order of magnitude, and unit must agree with the problem context.

κοινά πολλαπλάσια

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.

αριθμογραμμή

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.

απλοποίηση

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

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

1Write repeated addition: 7 + 7 + 7 + 7 + 7.
2Connect it to 5 × 7.
3Check with division: 35 ÷ 5 = 7.

Thinking and explanation example

Explain “κοινά πολλαπλάσια” 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.

Ισοδυναμία και σύγκριση κλασμάτων

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 + 5 and show two representations connected with “κοινά πολλαπλάσια”.

提示

Use a number line, place value, or objects.

答案指南

4 + 5 = 9. Valid representations include number-line jumps and grouped objects.

基础熟练4 分钟

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

提示

Add 7 a total of 2 times.

答案指南

7 + 7 = 2 · 7 = 14.

应用4 分钟

Continue 3, 7, 11, ... for three more terms and explain the rule.

提示

Check how much each term increases.

答案指南

15, 19, 23; +4.

应用5 分钟

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

提示

Opposite sides are equal.

答案指南

Perimeter = 6 + 6 + 6 + 6 = 24 cm.

推理5 分钟

Out of 27 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

9/27 = 1/3.

推理6 分钟

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

提示

Range = greatest value minus least value.

答案指南

Greatest 5, least 5, range 0.

考试题型7 分钟

Anna has 16 cards, gives away 8, then shares the rest into 1 equal groups. How many are in each group?

提示

Subtract first, then divide.

答案指南

16 - 8 = 8; (8) : 1 = 8.

考试题型8 分钟

A learner says 4 + 4 = 9. Find the error, correct it, and check the correction.

提示

Check with a number line or inverse subtraction.

答案指南

4 + 4 = 8; 8 - 4 = 4.

常见错误

Dropping brackets or using the wrong order of operations.
Converting a fraction or percentage without checking equivalence.
Answering without an estimate, unit, or sign check.

掌握度检查

I can convert safely between number forms.
I can explain why the chosen operation is appropriate.
I check the result with estimation or an inverse operation.

Ισοδυναμία και σύγκριση κλασμάτων

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 + 6 and show two representations connected with “κοινά πολλαπλάσια”.

提示

Use a number line, place value, or objects.

答案指南

7 + 6 = 13. Valid representations include number-line jumps and grouped objects.

基础6 分钟

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

提示

Add 3 a total of 3 times.

答案指南

3 + 3 + 3 = 3 · 3 = 9.

进阶7 分钟

Homework 3: Continue 6, 11, 16, ... for three more terms and explain the rule.

提示

Check how much each term increases.

答案指南

21, 26, 31; +5.

进阶8 分钟

Homework 4: A rectangle has sides 9 cm and 2 cm. Find its perimeter and explain why four sides are counted.

提示

Opposite sides are equal.

答案指南

Perimeter = 9 + 2 + 9 + 2 = 22 cm.

挑战10 分钟

Homework 5: Out of 20 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

5/20 = 1/4.

挑战12 分钟

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

提示

Range = greatest value minus least value.

答案指南

Greatest 8, least 6, range 2.

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 + 6 and show two representations connected with “κοινά πολλαπλάσια”.

2 分

答案指南

5 + 6 = 11. Valid representations include number-line jumps and grouped objects.

2. 3 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 = 3 · 8 = 24.

3. Continue 4, 9, 14, ... for three more terms and explain the rule.

3 分

答案指南

19, 24, 29; +5.

4. A rectangle has sides 7 cm and 2 cm. Find its perimeter and explain why four sides are counted.

4 分

答案指南

Perimeter = 7 + 2 + 7 + 2 = 18 cm.

5. Out of 12 objects, 3 are shaded. What fraction is shaded and how does it simplify?

4 分

答案指南

3/12 = 1/4.

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

4 分

答案指南

Greatest 6, least 6, range 0.

7. Anna has 27 cards, gives away 9, then shares the rest into 2 equal groups. How many are in each group?

5 分

答案指南

27 - 9 = 18; (18) : 2 = 9.

8. A learner says 5 + 5 = 11. Find the error, correct it, and check the correction.

5 分

答案指南

5 + 5 = 10; 10 - 5 = 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 4: 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。

κοινά πολλαπλάσια

αριθμογραμμή

απλοποίηση

重点关注

通常容易出错或需要更多复习的部分。

I can convert safely between number forms.

I can explain why the chosen operation is appropriate.

I check the result with estimation or an inverse operation.

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。