Place Value Models and Proportional Sharing — Lesson Plan, Mathematics, Grade 3
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Lesson plan
| Section |
Numbers and Mathematical Problem Solving
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| Lesson title |
Place Value Models and Proportional Sharing
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| Class |
3
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| Lesson objectives according to program |
3.5.2.1 строить графические модели многозначных чисел, использовать таблицу разрядов и классов
3.5.1.4 анализировать и решать задачи на зависимость между величинами/на пропорциональное деление
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| Lesson objectives |
Students know how to represent multi-digit numbers with graphical models and record them in a place-value and class table.
Students know how to identify relationships between quantities and solve proportional-sharing problems.
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| Values |
Accuracy and responsibility are developed as students represent numbers and check their calculations.
Cooperation and fairness are encouraged when students solve proportional-sharing problems and explain how quantities are shared.
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Lesson progress
| Lesson stage/time | Teacher's action | Student's action | Evaluation | Resources |
|---|---|---|---|---|
| Welcome and Review 5 minutes |
Organisational moment:
Welcome students, check that they have notebooks and pencils, and display a multi-digit number for a quick review.
Ask students to name the number and identify the value of one selected digit.
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Students prepare their notebooks and materials. Students name the displayed number and state the value of the selected digit. | Correctly name the displayed number — 1 point. Correctly identify the selected digit's value — 1 point. Stage maximum — 2 points. | board, number cards, notebooks |
| Model Place Value 10 minutes |
New material explanation:
Demonstrate how to build a graphical model of a multi-digit number using place-value units.
Record the number in a place-value and class table, explaining the value of each digit and how the classes are grouped.
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Students observe the model, copy the place-value and class table, and describe how each digit represents a value. | Build the graphical model with correct place-value units — 2 points. Record all digits in the correct places and classes — 2 points. Explain the value of one digit — 1 point. Stage maximum — 5 points. | place-value blocks, place-value and class table, board |
| Analyze Quantity Problems 8 minutes |
Questions to the class:
If 4 notebooks cost 800 tenge, what relationship connects the number of notebooks and the total cost, assuming each notebook costs the same?
How can you find the cost of 1 notebook and then the cost of 7 notebooks?
Answers:
The quantities are directly proportional: as the number of notebooks increases, the total cost increases at the same rate.
Divide 800 by 4 to find the unit cost of 200 tenge, then multiply 200 by 7 to find 1,400 tenge.
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Students answer the questions: the quantities are directly proportional; one notebook costs 200 tenge, and 7 notebooks cost 1,400 tenge. Students explain the division and multiplication used. | Identify the direct relationship between quantities — 1 point. Find the unit cost correctly — 1 point. Find the cost of 7 notebooks correctly — 1 point. Stage maximum — 3 points. | board, problem cards, notebooks |
| Place Value Crossword 7 minutes |
Instructions:
Give pairs a crossword with clues about digit, place, class, and multi-digit number representations.
Ask pairs to solve the clues and use the completed entries to check their understanding of place-value vocabulary.
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Students work in pairs to solve the crossword, discuss the clues, and check that the completed terms match the definitions. | Solve four crossword clues correctly — 1 point each. Stage maximum — 4 points. | |
| Proportional Sharing 8 minutes |
Problem statement:
Give students an assignment: 36 apples are shared equally among 4 groups. Find how many apples each group receives. Then share 36 apples among 6 groups and compare the results.
Ask students to show the calculations and explain how the number of groups affects the amount each group receives.
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Students complete the assignment independently: 36 ÷ 4 = 9 apples per group and 36 ÷ 6 = 6 apples per group. Students compare the results and explain that with more groups, each group receives fewer apples when the total stays fixed. | Calculate the share for 4 groups correctly — 1 point. Calculate the share for 6 groups correctly — 1 point. Explain the relationship between the number of groups and each share — 1 point. Stage maximum — 3 points. | |
| Quick Knowledge Check 4 minutes |
Summing up:
Conduct a short Kahoot-style quiz with questions on digit values, place-value tables, quantity relationships, and proportional sharing.
Review the correct answers and address one common error without repeating the quiz activity.
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Students answer the quiz questions individually and review the correct answers. | Answer four quiz questions correctly — 1 point each. Stage maximum — 4 points. | |
| Reflection 3 minutes |
Runs the "Where did this lesson land?" reflection. Students drop a point on a 2D grid — clarity vs interest. The class scatter reveals the quadrant problem.
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Students complete the "Where did this lesson land?" reflection and assess their understanding of the topic. | State one accurate idea from the lesson — 1 point. Name one relevant problem-solving step — 1 point. Stage maximum — 2 points. |
Health and safety compliance
| Health and safety compliance | Keep place-value blocks and pencils on the desk and use them carefully; do not throw or put small materials in the mouth. During the quiz, use devices responsibly and keep cables clear of walkways. |
Material details
- Material type
- Lesson Plan
- Subject
- Mathematics
- Grade
- Grade 3
- Language
- English
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