Greek Primary Grade 6 / Mathematics / Αριθμοί και αλγεβρική σκέψη

Μεταβλητές και απλές εξισώσεις

Μεταβλητές και απλές εξισώσεις: structured theory, worked examples, answered practice, and a mastery checklist for Greek Primary Grade 6.

学习目标

Recognise, explain, and apply “άγνωστος”.
Recognise, explain, and apply “ισότητα”.
Recognise, explain, and apply “αντίστροφες πράξεις”.
Recognise, explain, and apply “έλεγχος λύσης”.

核心概念与检查

I can expand and factor with a check.
I solve equations using equivalent steps.
Every solution or explanation for “Μεταβλητές και απλές εξισώσεις” 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。

Variables and equivalence

A variable represents a number or quantity. Every algebraic transformation must preserve the equivalence of the original expression or equation.

One valid step at a time

Write each transformation on a new line and apply the same valid operation to both sides. This keeps the solution easy to audit.

Substitute and verify

A final value is not a complete solution until it is substituted into the original relation. Verification catches sign and expansion errors.

άγνωστος

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.

ισότητα

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.

αντίστροφες πράξεις

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.

έλεγχος λύσης

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 10 objects each. How many objects are there, and how can the answer be checked?

1Write repeated addition: 10 + 10 + 10 + 10 + 10.
2Connect it to 5 × 10.
3Check with division: 50 ÷ 5 = 10.

Thinking and explanation example

Explain “άγνωστος” 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.

Μεταβλητές και απλές εξισώσεις

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 7 + 5 and show two representations connected with “άγνωστος”.

提示

Use a number line, place value, or objects.

答案指南

7 + 5 = 12. Valid representations include number-line jumps and grouped objects.

基础熟练4 分钟

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

提示

Add 3 a total of 2 times.

答案指南

3 + 3 = 2 · 3 = 6.

应用4 分钟

Continue 6, 10, 14, ... for three more terms and explain the rule.

提示

Check how much each term increases.

答案指南

18, 22, 26; +4.

应用5 分钟

A rectangle has sides 9 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 = 9 + 6 + 9 + 6 = 30 cm.

推理5 分钟

Out of 15 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

5/15 = 1/3.

推理6 分钟

The measurements are 8, 5, 8, and 5. Find the greatest, least, and range.

提示

Range = greatest value minus least value.

答案指南

Greatest 8, least 5, range 3.

考试题型7 分钟

Anna has 8 cards, gives away 4, then shares the rest into 1 equal groups. How many are in each group?

提示

Subtract first, then divide.

答案指南

8 - 4 = 4; (4) : 1 = 4.

考试题型8 分钟

A learner says 7 + 4 = 12. Find the error, correct it, and check the correction.

提示

Check with a number line or inverse subtraction.

答案指南

7 + 4 = 11; 11 - 4 = 7.

常见错误

Changing a sign without applying it to every term.
Combining terms that are not like terms.
Dividing by an expression that may be zero without stating a restriction.

掌握度检查

I can expand and factor with a check.
I solve equations using equivalent steps.
I verify the solution in the original relation.

Μεταβλητές και απλές εξισώσεις

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 3 + 6 and show two representations connected with “άγνωστος”.

提示

Use a number line, place value, or objects.

答案指南

3 + 6 = 9. Valid representations include number-line jumps and grouped objects.

基础6 分钟

Homework 2: 3 equal groups contain 6 objects each. Find the total and write an addition and multiplication statement.

提示

Add 6 a total of 3 times.

答案指南

6 + 6 + 6 = 3 · 6 = 18.

进阶7 分钟

Homework 3: Continue 9, 14, 19, ... for three more terms and explain the rule.

提示

Check how much each term increases.

答案指南

24, 29, 34; +5.

进阶8 分钟

Homework 4: A rectangle has sides 5 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 = 5 + 2 + 5 + 2 = 14 cm.

挑战10 分钟

Homework 5: Out of 32 objects, 8 are shaded. What fraction is shaded and how does it simplify?

提示

Put shaded objects over the total.

答案指南

8/32 = 1/4.

挑战12 分钟

Homework 6: The measurements are 4, 6, 4, and 6. Find the greatest, least, and range.

提示

Range = greatest value minus least value.

答案指南

Greatest 6, least 4, 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 8 + 6 and show two representations connected with “άγνωστος”.

2 分

答案指南

8 + 6 = 14. Valid representations include number-line jumps and grouped objects.

2. 3 equal groups contain 4 objects each. Find the total and write an addition and multiplication statement.

3 分

答案指南

4 + 4 + 4 = 3 · 4 = 12.

3. Continue 7, 12, 17, ... for three more terms and explain the rule.

3 分

答案指南

22, 27, 32; +5.

4. A rectangle has sides 3 cm and 2 cm. Find its perimeter and explain why four sides are counted.

4 分

答案指南

Perimeter = 3 + 2 + 3 + 2 = 10 cm.

5. Out of 24 objects, 6 are shaded. What fraction is shaded and how does it simplify?

4 分

答案指南

6/24 = 1/4.

6. The measurements are 9, 6, 9, and 6. Find the greatest, least, and range.

4 分

答案指南

Greatest 9, least 6, range 3.

7. Anna has 15 cards, gives away 5, then shares the rest into 2 equal groups. How many are in each group?

5 分

答案指南

15 - 5 = 10; (10) : 2 = 5.

8. A learner says 8 + 5 = 14. Find the error, correct it, and check the correction.

5 分

答案指南

8 + 5 = 13; 13 - 5 = 8.

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 6: 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。

άγνωστος

ισότητα

αντίστροφες πράξεις

έλεγχος λύσης

重点关注

通常容易出错或需要更多复习的部分。

I can expand and factor with a check.

I solve equations using equivalent steps.

I verify the solution in the original relation.

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。