Drawing Class Model - Visual Problem Solving Guide

Learn how to use drawing models to solve math problems with visual examples, practice exercises, and interactive guides for 3rd grade math.

Drawing Model Examples
1 Addition Model
Problem: 8 + 5
Using a bar model to represent addition
Bar Model for Addition
8
5
8 + 5 = 13
Combine two parts to make a whole
1
Draw first part
2
Draw second part
3
Combine parts
4
Find total
Step 1: Represent first number

Draw a bar segment representing 8 units

Step 2: Represent second number

Draw a bar segment representing 5 units

Step 3: Combine segments

Put both segments together to see the total

8 + 5 = 13
2 Subtraction Model
Problem: 12 - 7
Using a bar model to represent subtraction
Bar Model for Subtraction
12
7
12 - 7 = 5
Take away part from the whole
Step 1: Draw the whole

Represent the total amount (12)

Step 2: Show what's taken away

Mark the part being subtracted (7)

Step 3: Find remaining part

Count what's left after subtraction

12 - 7 = 5
3 Comparison Model
Problem: Sarah has 15 apples, Tom has 9 apples. How many more does Sarah have?
Using a comparison model to find the difference
Comparison Model
Sarah
15
Tom
9
15 - 9 = 6
Sarah has 6 more apples than Tom
Step 1: Draw both quantities

Represent Sarah's and Tom's amounts separately

Step 2: Align for comparison

Line up the bars to see the difference

Step 3: Find the difference

Measure how much taller Sarah's bar is

15 - 9 = 6 (Sarah has 6 more)
Types of Drawing Models
Visual + Concrete = Understanding
Model Benefits
Bar Models: Rectangular bars to represent quantities
Area Models: Rectangles to show multiplication and division
Pie Models: Circles to represent parts of a whole
Tip 1: Start with simple models before complex ones
Tip 2: Use consistent scaling in your models
Tip 3: Label each part clearly
Tip 4: Use different colors for different parts
Model Characteristics:

• Visual: Makes abstract concepts concrete

• Proportional: Sizes reflect actual quantities

• Organized: Shows relationships clearly

• Flexible: Adapts to different problem types

Model Benefits:

Understanding: Visual representation clarifies problems

Planning: Shows what operations to use

Verification: Helps check if answers make sense

Model Applications & Practice
Problem → Model → Solution
Model Process
Problem-Solving Steps
1
Read problem
2
Identify parts
3
Draw model
4
Solve
Problem Types Modeled

Addition: Combining parts to make a whole

Subtraction: Taking away part from whole

Multiplication: Repeated addition of equal groups

Division: Sharing equally or grouping

Comparison: Finding differences between amounts

Addition: Bars joined together
Subtraction: Part of bar removed
Multiplication: Equal sized bars repeated
Best Practices:

• Read the problem carefully before drawing

• Identify what you know and what you need to find

• Choose the appropriate model type

• Make sure your drawing reflects the numbers accurately

Complete Summary & Study Guide
Key Definitions:

Drawing Model: A visual representation of a math problem using shapes, bars, or diagrams

Bar Model: A rectangular representation showing relationships between quantities

Visual Representation: Using pictures or diagrams to show mathematical concepts

Concrete Visualization: Making abstract concepts visible and tangible

Problem-Solving Strategy: A methodical approach to solving mathematical problems

Model Creation Process:
  1. Read and Understand: Carefully read the problem
  2. Identify Parts: Find known and unknown quantities
  3. Choose Model Type: Select appropriate visual representation
  4. Draw Model: Create accurate visual representation
  5. Solve: Use the model to find the solution
  6. Verify: Check if answer makes sense with the model
Visualization: Makes abstract concepts concrete
Relationships: Shows how quantities relate to each other
Organization: Structures information clearly
Tip 1: Practice with simple problems first
Tip 2: Use graph paper for accurate drawings
Tip 3: Label all parts of your model
Tip 4: Use models to check your work
Simple Example

Problem: 5 + 3 = ?

Model: Draw 5 squares + 3 squares = 8 squares

Solution: 5 + 3 = 8

Advanced Example

Problem: I have 20 candies, eat 8, how many left?

Model: Draw 20 circles, cross out 8, count remaining

Solution: 20 - 8 = 12

Essential Rules for Success:

• Always draw models that match the problem's scale

• Use consistent units in your drawings

• Make sure your model shows the relationship clearly

• Practice different types of models for different problems

• Use models to verify your answers

• Don't rush - take time to draw accurately

Questions & Answers

Question: How do drawing models help students understand math better?

Answer: Drawing models provide several benefits:

  • Visual representation: Abstract concepts become concrete and visible
  • Relationship clarification: Shows how different parts of a problem relate to each other
  • Problem-solving structure: Provides a systematic approach to solving problems
  • Memory aid: Visual memory helps retain mathematical concepts
  • Confidence building: Students can see their thinking process

Models serve as a bridge between concrete manipulation and abstract thinking.

Question: Do I really need to draw pictures for math? Can't I just solve it in my head?

Answer: Drawing models are helpful for several reasons:

  • Complex problems: Help organize information when problems get harder
  • Mistake prevention: Make it easier to spot errors in your thinking
  • Verification: Provide a way to check if your answer makes sense
  • Learning tool: Help your brain understand the math better
  • Communication: Show your teacher how you solved the problem

As you get more experienced, you might visualize the models in your head!

Question: My child struggles with drawing models. How can I help?

Answer: Support your child with these strategies:

  • Start simple: Begin with basic objects like circles or squares
  • Use manipulatives: Physical objects first, then draw representations
  • Practice regularly: Short, frequent practice sessions
  • Be patient: Allow time for visual thinking to develop
  • Connect to real life: Use actual objects to model problems

Remember, drawing models are a skill that improves with practice!