Modeling Practice Drawings 44 in Grade 3

Master modeling practice drawings 44: visual representations, problem solving strategies, and mathematical reasoning through these 10 detailed exercises.

Solution: Exercises 1 to 3
1 Addition Drawing Problem
Exercise 1
A store sold 34 notebooks on Monday and 28 on Tuesday. How many notebooks were sold in total?
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 together
  3. Draw bars to represent each quantity
  4. Combine the bars to find the total
  5. Solve the problem
Monday
34 notebooks
Tuesday
28 notebooks
Total
62 notebooks
Step 1: Draw bars representing each day's sales

Monday's bar: 34 units long, Tuesday's bar: 28 units long

Step 2: Place the bars end-to-end

This visually represents the addition of both quantities

Step 3: Calculate the total

34 + 28 = 62 notebooks

62 notebooks were sold in total
Final answer:

The store sold 62 notebooks in total.

Applied rules:

• Visual Representation: Bars represent quantities

• Addition: Combining quantities to find total

• Proportional Length: Bar lengths reflect actual quantities

2 Subtraction Drawing Problem
Exercise 2
A library had 75 books. They gave away 32 books to a school. How many books does the library have left?
Definition:

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

Start
75 books
Given Away
32 books
Left
43 books
Step 1: Draw the starting bar

One bar representing 75 books total

Step 2: Mark the portion given away

Shade or segment 32 units from the bar

Step 3: Calculate the remaining

75 - 32 = 43 books left

Library has 43 books left
Final answer:

The library has 43 books left.

Applied rules:

• Part-Whole Relationship: Total = Part + Part

• Subtraction: To find remaining amount

• Verification: 43 + 32 = 75 ✓

3 Comparison Drawing Problem
Exercise 3
Emma has 41 stickers. Jake has 27 stickers. How many more stickers does Emma have than Jake?
Definition:

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

Emma
41 stickers
Jake
27 stickers
Difference
14 stickers
Step 1: Draw separate bars for each person

Emma's bar: 41 units, Jake's bar: 27 units

Step 2: Align the bars to compare

Place bars side by side to see the difference

Step 3: Calculate the difference

41 - 27 = 14 stickers

Emma has 14 more stickers than Jake
Final answer:

Emma has 14 more stickers than Jake.

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 Drawing Problem
Exercise 4
Each box contains 5 crayons. If there are 6 boxes, how many crayons are there in total?
Definition:

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

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

Each bar represents one box with 5 crayons

Step 2: Show the same quantity in each bar

Each box contains 5 crayons

Step 3: Calculate the total

6 boxes × 5 crayons = 30 crayons

There are 30 crayons in total
Final answer:

There are 30 crayons in total.

Applied rules:

• Equal Groups: Same number in each group

• Multiplication: Number of groups × Items per group

• Verification: 5+5+5+5+5+5 = 30 ✓

5 Division Drawing Problem
Exercise 5
48 cookies are shared equally among 8 children. How many cookies does each child get?
Definition:

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

Total
48 cookies
Number of Parts
8 children
Each Part
6 cookies
Step 1: Draw one bar representing total

One bar representing 48 cookies

Step 2: Divide the bar into equal parts

Divide into 8 equal sections (one for each child)

Step 3: Calculate each part

48 ÷ 8 = 6 cookies per child

Each child gets 6 cookies
Final answer:

Each child gets 6 cookies.

Applied rules:

• Equal Sharing: Total divided into equal parts

• Division: Total ÷ Number of parts = Each part

• Verification: 6 × 8 = 48 ✓

Solution: Exercises 6 to 10
6 Two-Step Drawing Problem
Exercise 6
A farmer had 65 apples. He sold 28 in the morning and 19 in the afternoon. How many apples does he have left?
Definition:

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

Start
65 apples
Sold
47 apples
Left
18 apples
Step 1: Draw bar for initial amount

One bar representing 65 apples

Step 2: Subtract morning sales

65 - 28 = 37 apples remaining

Step 3: Subtract afternoon sales

37 - 19 = 18 apples remaining

18 apples are left
Final answer:

The farmer has 18 apples left.

Applied rules:

• Sequential Operations: Perform operations in order

• Tracking Changes: Keep track of running total

• Verification: 28 + 19 + 18 = 65 ✓

7 Fraction Drawing Problem
Exercise 7
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

8 Comparison with Multiple Groups
Exercise 8
Team A scored 72 points. Team B scored 58 points. Team C scored 65 points. Which team scored the most? How many more points did they score than the lowest scoring team?
Definition:

Multi-Group Comparison Model: A bar model that compares three or more quantities.

Team A
72 points
Team B
58 points
Team C
65 points
Difference
14 points
Step 1: Draw bars for each team

Three bars representing scores: A=72, B=58, C=65

Step 2: Compare the bars

Team A (72) > Team C (65) > Team B (58)

Step 3: Calculate the difference

72 - 58 = 14 points

Team A scored the most, 14 more than Team B
Final answer:

Team A scored the most (72 points), 14 more than Team B (58 points).

Applied rules:

• Multi-Comparison: Compare multiple quantities simultaneously

• Ordinal Ranking: Order from highest to lowest

• Difference Calculation: Subtract lowest from highest

9 Mixed Operations Drawing Problem
Exercise 9
A farmer has 72 eggs. He puts 6 eggs in each basket. He sells 5 baskets. How many eggs does he have left?
Definition:

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

Total Eggs
72 eggs
Per Basket
6 eggs
Baskets Sold
5 baskets
Eggs Left
42 eggs
Step 1: Find how many baskets he can make

72 ÷ 6 = 12 baskets

Step 2: Find how many baskets are left

12 - 5 = 7 baskets remaining

Step 3: Calculate remaining eggs

7 × 6 = 42 eggs remaining

42 eggs are left
Final answer:

The farmer has 42 eggs left.

Applied rules:

• Multiple Operations: Division, subtraction, multiplication

• Sequential Thinking: Solve step by step

• Verification: 5 × 6 + 42 = 72 ✓

10 Multi-Group Drawing Problem
Exercise 10
In a class, there are 3 groups of students. Group A has 14 students, Group B has 11 students, and Group C has 9 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
14 students
Group B
11 students
Group C
9 students
Total
34 students
Step 1: Draw separate bars for each group

Three bars representing Groups A, B, and C

Step 2: Add the groups together

14 + 11 + 9 = 34 students

Step 3: Verify the calculation

Count all students in all groups: 14 + 11 + 9 = 34

34 students total
Final answer:

There are 34 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: Modeling Practice Drawings

Types of Model Drawings

📊
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 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: Modeling Practice Drawings

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.