Model Drawing Practice in Grade 3

Master model drawing: bar models, visual representations, and problem solving strategies through these 10 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Bar Model
Exercise 1
Sarah has 12 apples. Tom has 8 apples. How many more apples does Sarah have than Tom?
Definition:

Bar Model: A visual representation that uses rectangular bars to represent quantities and relationships in mathematical problems.

Bar Model Method:
  1. Read the problem carefully
  2. Identify what is being compared
  3. Draw bars to represent the quantities
  4. Compare the bars to find the difference
  5. Solve the problem
Sarah
12 apples
Tom
8 apples
Difference
4 apples
Step 1: Draw bars representing each quantity

Sarah's bar: 12 units long, Tom's bar: 8 units long

Step 2: Align the bars to compare

Both bars start at the same point, but Sarah's bar extends further

Step 3: Find the difference

12 - 8 = 4 apples

Sarah has 4 more apples than Tom
Final answer:

Sarah has 4 more apples than Tom.

Applied rules:

• Visual Representation: Bars represent quantities

• Comparison: Difference between quantities

• Subtraction: To find how much more

2 Part-Whole Model
Exercise 2
A class has 24 students. 15 are boys. How many are girls?
Definition:

Part-Whole Model: A bar model that shows how parts combine to form a whole.

Total
24 students
Known Part
15 boys
Unknown Part
9 girls
Step 1: Draw the whole bar

One bar representing 24 students total

Step 2: Divide the bar into parts

One part for boys (15), one part for girls (? )

Step 3: Calculate the unknown part

24 - 15 = 9 girls

There are 9 girls
Final answer:

There are 9 girls in the class.

Applied rules:

• Part-Whole Relationship: Total = Part + Part

• Subtraction: To find unknown part

• Verification: 15 + 9 = 24 ✓

3 Comparison Model
Exercise 3
John has 20 stickers. Mary has 14 stickers. How many stickers do they have altogether?
Definition:

Comparison Model: A bar model that compares two or more quantities and shows their relationship.

John
20 stickers
Mary
14 stickers
Total
34 stickers
Step 1: Draw separate bars for each person

John's bar: 20 units, Mary's bar: 14 units

Step 2: Combine the bars to find total

20 + 14 = 34 stickers

Step 3: Verify the answer

John's stickers + Mary's stickers = Total stickers

They have 34 stickers altogether
Final answer:

They have 34 stickers altogether.

Applied rules:

• Combining Quantities: Addition to find total

• Visual Representation: Bars show individual amounts

• Verification: Check that parts add up to total

Solution: Exercises 4 to 5
4 Multiplication Model
Exercise 4
Each box contains 6 crayons. There are 4 boxes. How many crayons are there in total?
Definition:

Multiplication Model: A bar model that shows equal groups and helps visualize repeated addition.

Groups
4 boxes
Items per Group
6 crayons
Total
24 crayons
Step 1: Draw 4 equal bars (boxes)

Each bar represents one box with 6 crayons

Step 2: Show the same quantity in each bar

Each box contains 6 crayons

Step 3: Calculate the total

4 boxes × 6 crayons = 24 crayons

There are 24 crayons in total
Final answer:

There are 24 crayons in total.

Applied rules:

• Equal Groups: Same number in each group

• Multiplication: Number of groups × Items per group

• Verification: 6+6+6+6 = 24 ✓

5 Division Model
Exercise 5
24 candies are shared equally among 6 children. How many candies does each child get?
Definition:

Division Model: A bar model that shows how a total is divided into equal parts.

Total
24 candies
Number of Parts
6 children
Each Part
4 candies
Step 1: Draw one bar representing total

One bar representing 24 candies

Step 2: Divide the bar into equal parts

Divide into 6 equal sections (one for each child)

Step 3: Calculate each part

24 ÷ 6 = 4 candies per child

Each child gets 4 candies
Final answer:

Each child gets 4 candies.

Applied rules:

• Equal Sharing: Total divided into equal parts

• Division: Total ÷ Number of parts = Each part

• Verification: 4 × 6 = 24 ✓

Solution: Exercises 6 to 10
6 Two-Step Model
Exercise 6
A store has 50 apples. They sell 18 apples in the morning and 12 in the afternoon. How many apples are left?
Definition:

Two-Step Model: A bar model that requires multiple operations to solve.

Start
50 apples
Sold
30 apples
Left
20 apples
Step 1: Draw bar for initial amount

One bar representing 50 apples

Step 2: Subtract morning sales

50 - 18 = 32 apples remaining

Step 3: Subtract afternoon sales

32 - 12 = 20 apples remaining

20 apples are left
Final answer:

There are 20 apples left.

Applied rules:

• Sequential Operations: Perform operations in order

• Tracking Changes: Keep track of running total

• Verification: 18 + 12 + 20 = 50 ✓

7 Comparison with Remainder
Exercise 7
Peter has 35 marbles. He wants to put them in bags with 6 marbles in each bag. How many full bags can he make?
Definition:

Comparison with Remainder: A model that shows how many complete groups can be formed and what remains.

Total
35 marbles
Per Bag
6 marbles
Full Bags
5 bags
Step 1: Draw bar representing total marbles

One bar representing 35 marbles

Step 2: Divide into groups of 6

35 ÷ 6 = 5 remainder 5

Step 3: Interpret the result

5 full bags can be made with 5 marbles left over

5 full bags
Final answer:

Peter can make 5 full bags.

Applied rules:

• Division with Remainder: Quotient tells how many full groups

• Interpretation: Understand practical meaning of remainder

• 5 × 6 + 5 = 35 ✓

8 Fraction Model
Exercise 8
A pizza is cut into 8 equal slices. If 3 slices are eaten, what fraction of the pizza is left?
Definition:

Fraction Model: A bar model that shows parts of a whole using fractional representation.

Total Slices
8 slices
Eaten
3 slices
Left
5/8 of pizza
Step 1: Draw bar divided into 8 equal parts

Represent the whole pizza as 8 equal slices

Step 2: Shade 3 parts to show eaten slices

3 out of 8 slices are eaten

Step 3: Count remaining parts

8 - 3 = 5 slices remain, which is 5/8 of the pizza

5/8 of the pizza is left
Final answer:

5/8 of the pizza is left.

Applied rules:

• Fraction Concept: Part/Whole relationship

• Visual Representation: Shaded parts show fraction

• Subtraction: Remaining = Total - Taken

9 Mixed Operations Model
Exercise 9
A farmer has 48 eggs. He puts 6 eggs in each carton. He sells 5 cartons. How many eggs does he have left?
Definition:

Mixed Operations Model: A bar model that combines multiple operations to solve complex problems.

Total Eggs
48 eggs
Per Carton
6 eggs
Cartons Sold
5 cartons
Eggs Left
18 eggs
Step 1: Find how many cartons he can make

48 ÷ 6 = 8 cartons

Step 2: Find how many cartons are left

8 - 5 = 3 cartons remaining

Step 3: Calculate remaining eggs

3 × 6 = 18 eggs remaining

18 eggs left
Final answer:

The farmer has 18 eggs left.

Applied rules:

• Multiple Operations: Division, subtraction, multiplication

• Sequential Thinking: Solve step by step

• Verification: 5 × 6 + 18 = 48 ✓

10 Multi-Group Model
Exercise 10
In a class, there are 3 groups of students. Group A has 12 students, Group B has 8 students, and Group C has 10 students. How many students are there in total?
Definition:

Multi-Group Model: A bar model that shows multiple distinct groups that combine to form a total.

Group A
12 students
Group B
8 students
Group C
10 students
Total
30 students
Step 1: Draw separate bars for each group

Three bars representing Groups A, B, and C

Step 2: Add the groups together

12 + 8 + 10 = 30 students

Step 3: Verify the calculation

Count all students in all groups: 12 + 8 + 10 = 30

30 students total
Final answer:

There are 30 students in total.

Applied rules:

• Grouping: Separate distinct groups

• Addition: Combine all groups to find total

• Verification: Check that parts sum to whole

Visual Infographic: Model Drawing Practice

Types of Model Drawing

📊
Bar Model
Uses rectangular bars to represent quantities and relationships in problems.
🧩
Part-Whole Model
Shows how parts combine to form a whole quantity.
🔍
Comparison Model
Compares two or more quantities and shows their relationships.
⚡
Multiplication Model
Visualizes equal groups and repeated addition concepts.
1
Read
2
Identify
3
Draw
4
Solve
5
Check

Model Drawing Strategies

🔍
Identify key information
💡
Choose appropriate model
🎯
Draw proportional bars
🚀
Label clearly
✅
Verify solution
🔄
Practice regularly
Model Drawing = Visual Representation + Mathematical Reasoning + Problem Solving
Model Drawing Formula
Key definitions:

Model Drawing: A visual problem-solving strategy that uses bars or rectangles to represent mathematical relationships.

Bar Model: A rectangular bar that represents a quantity in a mathematical problem.

Visual Representation: Using pictures, diagrams, or models to represent mathematical concepts.

Model Drawing Methodology:
  1. Read Carefully: Understand what the problem is asking
  2. Identify Information: Note what is given and what is needed
  3. Choose Model: Select the appropriate type of bar model
  4. Draw Accurately: Create bars that represent the quantities proportionally
  5. Solve Systematically: Use the model to find the solution
  6. Verify Solution: Check that the answer makes sense
Tip 1: Always read the entire problem before drawing.
Tip 2: Make bars proportional to the quantities they represent.
Tip 3: Label bars clearly with numbers and words.
Tip 4: Practice regularly to strengthen visualization skills.
Common errors: Drawing disproportionate bars, mislabeling quantities, choosing wrong model type.
Success habits: Read carefully, draw neatly, label clearly, verify answers.
Model Drawing Principles:

• Proportionality: Bar lengths should reflect actual quantity relationships

• Clarity: Draw clearly and label all parts

• Accuracy: Represent quantities precisely

• Systematic Approach: Follow consistent steps for all problems

• Verification: Always check that the solution makes sense

Steps for Creating Model Drawings

1
Read the problem carefully and identify key information
2
Determine what type of model to use
3
Draw the model with appropriate proportions
4
Label the model with known and unknown values

Detailed Summary: Model Drawing Practice

Definitions and Key Concepts

Model Drawing: A visual problem-solving strategy that uses bars or rectangles to represent mathematical relationships and quantities.

Bar Model: A rectangular bar that represents a quantity in a mathematical problem, helping visualize relationships between numbers.

Part-Whole Model: A bar model that shows how parts combine to form a whole quantity.

Comparison Model: A bar model that compares two or more quantities and shows their relationships.

Visual Representation: Using pictures, diagrams, or models to represent mathematical concepts and problems.

Core Rules and Principles

1. Proportionality: Bar lengths should accurately reflect the quantities they represent.

2. Clarity: Draw clearly and label all parts of the model.

3. Accuracy: Represent quantities precisely and maintain consistent scale.

4. Systematic Approach: Follow consistent steps for creating all models.

5. Verification: Always check that the solution makes sense in the context of the problem.

Step-by-Step Methods and Procedures

Basic Bar Model Method:

• Read the problem carefully to understand what is being asked

• Identify the quantities involved and their relationships

• Draw rectangular bars to represent each quantity

• Make bar lengths proportional to the quantities

• Use the model to determine the solution

• Verify the answer makes sense

Part-Whole Model Method:

• Identify the total (whole) and the parts

• Draw one bar for the total

• Divide the bar into sections representing the parts

• Use addition or subtraction to find unknown values

• Check that parts add up to the whole

Examples: Simple to Advanced

Simple Example: Sarah has 5 apples, Tom has 3 apples. Draw bars to show the difference.

Answer: Draw Sarah's bar as 5 units, Tom's as 3 units, difference is 2 units

Intermediate Example: A class has 24 students total. 14 are boys. How many are girls?

Answer: Draw whole bar as 24 units, part for boys as 14 units, remaining part is 10 units (girls)

Advanced Example: A farmer has 36 eggs. He puts 6 eggs in each carton. He sells 4 cartons. How many eggs does he have left?

Answer: First divide 36 by 6 to get 6 cartons, then subtract 4 sold cartons to get 2 cartons remaining, which is 12 eggs

Tips, Tricks, and Common Pitfalls

Tips:

• Make bars proportional to actual quantities

• Use consistent units throughout the model

• Label all parts of the model clearly

• Practice with different types of problems

Common Mistakes:

• Drawing bars that don't reflect actual quantity relationships

• Forgetting to label parts of the model

• Choosing the wrong type of model for the problem

• Not verifying that the solution makes sense

Key Notes for Memorization

Memory Aids:

• "READ" = Read, Examine, Analyze, Draw

• "DRAW" = Determine, Represent, Apply, Work

• Remember that bar length represents quantity

• Part-whole: Total = Part + Part

• Comparison: Difference = Larger - Smaller

Practical Applications

Model drawing skills transfer to real-world applications like:

• Budgeting and money management

• Cooking and recipe scaling

• Shopping comparisons

• Time management

• Problem-solving in science and engineering

Essential Skills
• Visual representation
• Proportional thinking
• Problem analysis
• Mathematical reasoning
• Verification
Common Model Types
• Bar models
• Part-whole models
• Comparison models
• Multiplication models
• Division models
Problem-Solving Steps
• Read the problem
• Identify quantities
• Draw the model
• Solve the problem
• Check the answer

Questions & Answers

Question: Why is model drawing important for 3rd graders? Isn't it too early to learn this?

Answer: Actually, 3rd grade is the perfect time to introduce model drawing! At this age, children are developing their ability to think abstractly and visualize relationships. Model drawing bridges the gap between concrete manipulative work and abstract symbolic thinking.

Model drawing helps students visualize mathematical relationships, making complex problems more accessible. It's especially beneficial for students who struggle with traditional symbolic approaches, as it provides a visual pathway to understanding.

For 3rd graders, model drawing starts with simple bar models for addition and subtraction, gradually building to more complex problems.

Question: How can I help my child practice model drawing at home?

Answer: There are many fun ways to practice model drawing at home:

  • Use everyday objects like blocks or counters to create physical models first
  • Draw simple bar models for grocery shopping scenarios
  • Practice with story problems from daily life
  • Use graph paper to help maintain proportionality
  • Encourage your child to explain their drawings aloud

Start with simple comparison problems and gradually increase complexity. The key is to emphasize the visual representation and encourage your child to talk through their thinking process.

Remember, model drawing is about understanding relationships, not perfect artwork.

Question: What are some effective strategies to teach model drawing to diverse learners in my 3rd grade class?

Answer: Effective strategies for diverse learners include:

  • Start with concrete manipulatives before moving to drawn models
  • Provide templates for students who struggle with drawing
  • Use color coding to distinguish different parts of the model
  • Differentiate problems by complexity while maintaining the same modeling skill
  • Pair visual learners with kinesthetic learners for peer support

For struggling learners, provide more scaffolding and break problems into smaller steps. For advanced learners, offer extension problems that require multiple operations. Always encourage students to verbalize their thinking as they draw.

Create a supportive environment where students feel comfortable sharing their models, even if they make mistakes. Emphasize that model drawing is a tool for understanding, not a performance activity.