Model Drawing Word Problems in Grade 3

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

Solution: Exercises 1 to 3
1 Addition Word Problem
Exercise 1
Sarah collected 25 seashells on Monday and 18 more on Tuesday. How many seashells does she have altogether?
Definition:

Model Drawing: A visual problem-solving strategy that uses rectangular bars to represent quantities and relationships in mathematical problems.

Model Drawing Method:
  1. Read the problem carefully
  2. Identify what is being added
  3. Draw bars to represent each quantity
  4. Combine the bars to find the total
  5. Solve the problem
Monday
25 seashells
Tuesday
18 seashells
Total
43 seashells
Step 1: Draw bars representing each day's collection

Monday's bar: 25 units long, Tuesday's bar: 18 units long

Step 2: Place the bars end-to-end

This visually represents the addition of both quantities

Step 3: Calculate the total

25 + 18 = 43 seashells

Sarah has 43 seashells altogether
Final answer:

Sarah has 43 seashells altogether.

Applied rules:

• Visual Representation: Bars represent quantities

• Addition: Combining quantities to find total

• Proportional Length: Bar lengths reflect actual quantities

2 Subtraction Word Problem
Exercise 2
Tom had 42 marbles. He gave 16 marbles to his friend. How many marbles does he have left?
Definition:

Subtraction Model: A bar model that shows how a total quantity is reduced by removing a part.

Start
42 marbles
Given Away
16 marbles
Left
26 marbles
Step 1: Draw the starting bar

One bar representing 42 marbles total

Step 2: Mark the portion given away

Shade or segment 16 units from the bar

Step 3: Calculate the remaining

42 - 16 = 26 marbles left

Tom has 26 marbles left
Final answer:

Tom has 26 marbles left.

Applied rules:

• Part-Whole Relationship: Total = Part + Part

• Subtraction: To find remaining amount

• Verification: 26 + 16 = 42 ✓

3 Comparison Word Problem
Exercise 3
Anna has 35 stickers. Ben has 23 stickers. How many more stickers does Anna have than Ben?
Definition:

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

Anna
35 stickers
Ben
23 stickers
Difference
12 stickers
Step 1: Draw separate bars for each person

Anna's bar: 35 units, Ben's bar: 23 units

Step 2: Align the bars to compare

Place bars side by side to see the difference

Step 3: Calculate the difference

35 - 23 = 12 stickers

Anna has 12 more stickers than Ben
Final answer:

Anna has 12 more stickers than Ben.

Applied rules:

• Comparison: Difference between quantities

• Subtraction: To find how much more

• Visualization: Bars show the difference clearly

Solution: Exercises 4 to 5
4 Multiplication Word Problem
Exercise 4
Each bag contains 8 cookies. If there are 5 bags, how many cookies are there in total?
Definition:

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

Groups
5 bags
Items per Group
8 cookies
Total
40 cookies
Step 1: Draw 5 equal bars (bags)

Each bar represents one bag with 8 cookies

Step 2: Show the same quantity in each bar

Each bag contains 8 cookies

Step 3: Calculate the total

5 bags × 8 cookies = 40 cookies

There are 40 cookies in total
Final answer:

There are 40 cookies in total.

Applied rules:

• Equal Groups: Same number in each group

• Multiplication: Number of groups × Items per group

• Verification: 8+8+8+8+8 = 40 ✓

5 Division Word Problem
Exercise 5
36 candies are shared equally among 4 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
36 candies
Number of Parts
4 children
Each Part
9 candies
Step 1: Draw one bar representing total

One bar representing 36 candies

Step 2: Divide the bar into equal parts

Divide into 4 equal sections (one for each child)

Step 3: Calculate each part

36 ÷ 4 = 9 candies per child

Each child gets 9 candies
Final answer:

Each child gets 9 candies.

Applied rules:

• Equal Sharing: Total divided into equal parts

• Division: Total ÷ Number of parts = Each part

• Verification: 9 × 4 = 36 ✓

Solution: Exercises 6 to 10
6 Two-Step Word Problem
Exercise 6
A store has 60 pencils. They sell 24 pencils in the morning and 15 in the afternoon. How many pencils are left?
Definition:

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

Start
60 pencils
Sold
39 pencils
Left
21 pencils
Step 1: Draw bar for initial amount

One bar representing 60 pencils

Step 2: Subtract morning sales

60 - 24 = 36 pencils remaining

Step 3: Subtract afternoon sales

36 - 15 = 21 pencils remaining

21 pencils are left
Final answer:

There are 21 pencils left.

Applied rules:

• Sequential Operations: Perform operations in order

• Tracking Changes: Keep track of running total

• Verification: 24 + 15 + 21 = 60 ✓

7 Comparison with Remainder
Exercise 7
Peter has 43 marbles. He wants to put them in bags with 7 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
43 marbles
Per Bag
7 marbles
Full Bags
6 bags
Step 1: Draw bar representing total marbles

One bar representing 43 marbles

Step 2: Divide into groups of 7

43 ÷ 7 = 6 remainder 1

Step 3: Interpret the result

6 full bags can be made with 1 marble left over

6 full bags
Final answer:

Peter can make 6 full bags.

Applied rules:

• Division with Remainder: Quotient tells how many full groups

• Interpretation: Understand practical meaning of remainder

• Verification: 6 × 7 + 1 = 43 ✓

8 Fraction Word Problem
Exercise 8
A pizza is cut into 10 equal slices. If 7 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
10 slices
Eaten
7 slices
Left
3/10 of pizza
Step 1: Draw bar divided into 10 equal parts

Represent the whole pizza as 10 equal slices

Step 2: Shade 7 parts to show eaten slices

7 out of 10 slices are eaten

Step 3: Count remaining parts

10 - 7 = 3 slices remain, which is 3/10 of the pizza

3/10 of the pizza is left
Final answer:

3/10 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 Word Problem
Exercise 9
A farmer has 56 eggs. He puts 8 eggs in each carton. He sells 4 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
56 eggs
Per Carton
8 eggs
Cartons Sold
4 cartons
Eggs Left
24 eggs
Step 1: Find how many cartons he can make

56 ÷ 8 = 7 cartons

Step 2: Find how many cartons are left

7 - 4 = 3 cartons remaining

Step 3: Calculate remaining eggs

3 × 8 = 24 eggs remaining

24 eggs left
Final answer:

The farmer has 24 eggs left.

Applied rules:

• Multiple Operations: Division, subtraction, multiplication

• Sequential Thinking: Solve step by step

• Verification: 4 × 8 + 24 = 56 ✓

10 Multi-Group Word Problem
Exercise 10
In a school, there are 4 classes. Class A has 22 students, Class B has 19 students, Class C has 25 students, and Class D has 18 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.

Class A
22 students
Class B
19 students
Class C
25 students
Class D
18 students
Total
84 students
Step 1: Draw separate bars for each class

Four bars representing Classes A, B, C, and D

Step 2: Add the classes together

22 + 19 + 25 + 18 = 84 students

Step 3: Verify the calculation

Count all students in all classes: 22 + 19 + 25 + 18 = 84

84 students total
Final answer:

There are 84 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 Word Problems

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 Word Problems

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.