Greek Gymnasium Grade 1 / Mathematics / Μέρος Α: Αριθμητική - Άλγεβρα
Ανάλογα και αντιστρόφως ανάλογα ποσά: structured theory, worked examples, answered practice, and a mastery checklist for Greek Gymnasium Grade 1.
Раздел
Ключевые идеи главы в понятной последовательности перед практикой.
A function maps each allowed input to one output. Formula, table, and graph are different representations of the same relationship.
Parameters change slope, position, amplitude, or rate of change. Read the key features before plotting individual points.
The domain states which inputs are allowed. In a real model, also check whether the output is physically meaningful.
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.
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
Следуйте методу шаг за шагом и проверяйте обоснование каждого шага.
4 equal groups contain 8 objects each. How many objects are there, and how can the answer be checked?
32
Explain “Λόγοι και αναλογίες” 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.
Ανάλογα και αντιστρόφως ανάλογα ποσά
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
Calculate 5 + 4 and show two representations connected with “Λόγοι και αναλογίες”.
Use a number line, place value, or objects.
5 + 4 = 9. Valid representations include number-line jumps and grouped objects.
6 equal groups contain 8 objects each. Find the total and write an addition and multiplication statement.
Add 8 a total of 6 times.
8 + 8 + 8 + 8 + 8 + 8 = 6 · 8 = 48.
Continue 4, 7, 10, ... for three more terms and explain the rule.
Check how much each term increases.
13, 16, 19; +3.
A rectangle has sides 7 cm and 5 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 7 + 5 + 7 + 5 = 24 cm.
Out of 6 objects, 3 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
3/6 = 1/2.
The measurements are 6, 4, 6, and 4. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 6, least 4, range 2.
Anna has 54 cards, gives away 9, then shares the rest into 5 equal groups. How many are in each group?
Subtract first, then divide.
54 - 9 = 45; (45) : 5 = 9.
A learner says 5 + 3 = 9. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
5 + 3 = 8; 8 - 3 = 5.
Ανάλογα και αντιστρόφως ανάλογα ποσά
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Homework 1: Calculate 8 + 5 and show two representations connected with “Λόγοι και αναλογίες”.
Use a number line, place value, or objects.
8 + 5 = 13. Valid representations include number-line jumps and grouped objects.
Homework 2: 2 equal groups contain 4 objects each. Find the total and write an addition and multiplication statement.
Add 4 a total of 2 times.
4 + 4 = 2 · 4 = 8.
Homework 3: Continue 7, 11, 15, ... for three more terms and explain the rule.
Check how much each term increases.
19, 23, 27; +4.
Homework 4: A rectangle has sides 3 cm and 6 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 3 + 6 + 3 + 6 = 18 cm.
Homework 5: Out of 18 objects, 6 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
6/18 = 1/3.
Homework 6: The measurements are 9, 5, 9, and 5. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 9, least 5, range 4.
35 минут / 30 баллов
Полный тест с таймером, баллами и образцами ответов.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Calculate 6 + 5 and show two representations connected with “Λόγοι και αναλογίες”.
2 баллов6 + 5 = 11. Valid representations include number-line jumps and grouped objects.
2. 2 equal groups contain 9 objects each. Find the total and write an addition and multiplication statement.
3 баллов9 + 9 = 2 · 9 = 18.
3. Continue 5, 9, 13, ... for three more terms and explain the rule.
3 баллов17, 21, 25; +4.
4. A rectangle has sides 8 cm and 6 cm. Find its perimeter and explain why four sides are counted.
4 балловPerimeter = 8 + 6 + 8 + 6 = 28 cm.
5. Out of 12 objects, 4 are shaded. What fraction is shaded and how does it simplify?
4 баллов4/12 = 1/3.
6. The measurements are 7, 5, 7, and 5. Find the greatest, least, and range.
4 балловGreatest 7, least 5, range 2.
7. Anna has 6 cards, gives away 3, then shares the rest into 1 equal groups. How many are in each group?
5 баллов6 - 3 = 3; (3) : 1 = 3.
8. A learner says 6 + 4 = 11. Find the error, correct it, and check the correction.
5 баллов6 + 4 = 10; 10 - 4 = 6.
Раздел
Источники программы; порядок тем уточняйте в школе и у преподавателя.
Mathematics
Greek Gymnasium Grade 1: структурированный маршрут по математике и физике с главами, практикой и следующими шагами.
Структура следует учебнику и помогает организовать изучение темы.
Темы, где чаще возникают ошибки или нужна дополнительная практика.
С чего начать: учебник, daily material, PDFs, videos и worked examples.
Целевая практика перед full tests, чтобы coverage было понятным.
Как измерять прогресс по главе и когда включать ее в общий mock.
Что делать после главы и как она связана со следующим разделом.
Примечание: официальную экзаменационную программу каждого года всегда уточняйте в школе, у преподавателя и по текущим официальным источникам.
