Solved Exercises on Drawing Problem Solving in Grade 1

Master drawing problem solving: visual representations, diagrams, models, counting strategies, spatial reasoning through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Drawing to Count Objects
Exercise 1
Sarah has 7 apples and her brother gives her 5 more. Draw the apples to find out how many she has now.
Definition:

Drawing strategy: Creating visual representations to solve math problems

Drawing problem solving method:
  1. Read the problem carefully
  2. Draw the initial situation
  3. Draw the changes that happen
  4. Count the total
  5. Write the answer
Initial
7 apples
Added
5 apples
Total
12 apples
🍎
🍎
🍎
🍎
🍎
🍎
🍎
+
🍎
🍎
🍎
🍎
🍎
Step 1: Draw Sarah's apples

Sarah starts with 7 apples: 🍎🍎🍎🍎🍎🍎🍎

Step 2: Draw the added apples

Her brother gives her 5 more: 🍎🍎🍎🍎🍎

Step 3: Count all apples

Total: 🍎🍎🍎🍎🍎🍎🍎 + 🍎🍎🍎🍎🍎 = 12 apples

Step 4: Write the answer

Sarah has 12 apples now

7 + 5 = 12
Final answer:

Sarah has 12 apples

Applied rules:

• Visual representation: Draw pictures to represent the problem

• One-to-one correspondence: Each apple drawn represents one real apple

• Counting: Count all items to find the total

2 Drawing to Subtract
Exercise 2
Tom had 10 cookies. He ate 3 cookies. Draw the cookies to find out how many are left.
Definition:

Subtraction drawing: Drawing to represent taking away or removing objects

Start
10 cookies
Taken
3 cookies
Remaining
7 cookies
🍪
🍪
🍪
🍪
🍪
🍪
🍪
🍪
🍪
🍪
-
🍪
🍪
🍪
=
🍪
🍪
🍪
🍪
🍪
🍪
🍪
Step 1: Draw all cookies

Tom starts with 10 cookies: 🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪

Step 2: Cross out eaten cookies

Cross out 3 cookies: 🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪

Step 3: Count remaining

Count the uncrossed cookies: 7 are left

Step 4: Write the answer

Tom has 7 cookies left

10 - 3 = 7
Final answer:

Tom has 7 cookies left

Applied rules:

• Visual subtraction: Cross out items that are taken away

• Remaining count: Count items that are not crossed out

• Subtraction concept: Taking away reduces the total

3 Drawing Patterns
Exercise 3
The pattern is red ball, blue ball, green ball. Draw the next 3 balls in the pattern.
Definition:

Pattern drawing: Identifying and continuing visual sequences

Pattern
Red, Blue, Green
Next
Red, Blue, Green
Result
Red, Blue, Green
🔴
🔵
🟢
🔴
🔵
🟢
🔴
🔵
🟢
Step 1: Identify the pattern

The pattern repeats: Red ball, Blue ball, Green ball

Step 2: Continue the sequence

After the given pattern, continue with Red, Blue, Green

Step 3: Draw the next 3 balls

Draw Red ball (🔴), Blue ball (🔵), Green ball (🟢)

Step 4: Verify the pattern

Check that the sequence continues correctly

Next 3 balls: 🔴🔵🟢
Final answer:

The next 3 balls are: Red, Blue, Green

Applied rules:

• Pattern recognition: Identify the repeating sequence

• Continuation: Follow the same order to continue

• Repetition: The pattern repeats in the same order

Rules and methods, laws,...
Draw + Count = Answer
Drawing Strategy
Rule 1
Read Carefully
Understand the problem
Rule 2
Draw Visually
Create visual model
Rule 3
Count Accurately
Get exact answer
Key definitions:

Drawing strategy: Using visual representations to solve math problems

Visual model: A picture or diagram that represents the problem

Pattern: A repeated sequence of shapes, colors, or objects

Complete methodology:
  1. Read: Understand what the problem is asking
  2. Plan: Decide what to draw to represent the problem
  3. Draw: Create visual representations
  4. Count/Solve: Use the drawing to find the answer
  5. Check: Verify that the answer makes sense
Tip 1: Use simple shapes or symbols to represent objects.
Tip 2: Draw neat and organized pictures.
Tip 3: Count carefully to avoid mistakes.
Tip 4: Practice with different types of problems.
Common errors: Drawing too many or too few items, miscounting, not following the pattern.
Key concepts: Visualization, counting, pattern recognition, problem solving.
Formulas to know by heart:

• Draw what the problem says

• Count what you drew

• Look for patterns that repeat

• Check your answer makes sense

Solution: Exercises 4 to 5
4 Drawing Shapes to Compare
Exercise 4
Draw 6 triangles and 4 squares. Which shape has more? How many more?
Definition:

Comparing with drawings: Using visual models to compare quantities

Triangles
6
Squares
4
Difference
2
🔺
🔺
🔺
🔺
🔺
🔺
vs
⬜
⬜
⬜
⬜
Step 1: Draw 6 triangles

Draw 6 triangle shapes: 🔺🔺🔺🔺🔺🔺

Step 2: Draw 4 squares

Draw 4 square shapes: ⬜⬜⬜⬜

Step 3: Compare quantities

Count: 6 triangles vs 4 squares

Step 4: Find the difference

6 - 4 = 2 more triangles than squares

Step 5: Write the answer

Triangles have more, 2 more than squares

Triangles: 6, Squares: 4, Difference: 2
Final answer:

Triangles have more. There are 2 more triangles than squares.

Applied rules:

• Visual comparison: Draw both sets to compare directly

• Counting: Count each set separately

• Difference: Subtract smaller from larger to find how many more

5 Drawing to Solve Word Problems
Exercise 5
There are 8 birds on a tree. 3 fly away. Then 2 more come back. How many birds are on the tree now? Draw to solve.
Definition:

Multi-step drawing: Using drawings to solve problems with multiple actions

Start
8 birds
Fly Away
-3 birds
Come Back
+2 birds
End
7 birds
🐦
🐦
🐦
🐦
🐦
🐦
🐦
🐦
→
🐦
🐦
🐦
🐦
🐦
→
🐦
🐦
🐦
🐦
🐦
🐦
Step 1: Draw initial birds

Start with 8 birds on the tree: 🐦🐦🐦🐦🐦🐦🐦🐦

Step 2: Show birds flying away

Remove 3 birds: 🐦🐦🐦🐦🐦 (5 birds left)

Step 3: Show birds coming back

Add 2 birds: 🐦🐦🐦🐦🐦 + 🐦🐦 = 🐦🐦🐦🐦🐦🐦🐦 (7 birds)

Step 4: Count final birds

There are 7 birds on the tree now

Step 5: Write the answer

7 birds are on the tree now

8 - 3 + 2 = 7
Final answer:

There are 7 birds on the tree now.

Applied rules:

• Sequential drawing: Show each action step by step

• Multi-step problem: Handle one change at a time

• Tracking: Keep track of the current state after each change

Drawing Problem Solving Guide: Laws, Methods, Definitions, Expressions
Draw + Count = Answer
Drawing Strategy
Key definitions:

Drawing strategy: Using visual representations to solve math problems

Visual model: A picture or diagram that represents the problem

Pattern: A repeated sequence of shapes, colors, or objects

Complete methodology:
  1. Read: Understand what the problem is asking
  2. Plan: Decide what to draw to represent the problem
  3. Draw: Create visual representations
  4. Count/Solve: Use the drawing to find the answer
  5. Check: Verify that the answer makes sense
Tip 1: Use simple shapes or symbols to represent objects.

Tip 2: Draw neat and organized pictures.

Tip 3: Count carefully to avoid mistakes.

Tip 4: Practice with different types of problems.

Common errors: Drawing too many or too few items, miscounting, not following the pattern.

Key concepts: Visualization, counting, pattern recognition, problem solving.

Formulas to know by heart:

• Draw what the problem says

• Count what you drew

• Look for patterns that repeat

• Check your answer makes sense

Questions & Answers

Question: Why do I need to draw when I can just count in my head?

Answer: Great question! Drawing helps in many ways:

  • Visualization: You can see the problem clearly
  • Organization: It keeps everything neat and tidy
  • Accuracy: You won't lose track of what you're counting
  • Understanding: It helps you understand what's happening

Think of it like having a picture of the problem so you don't forget anything important!

Example: If you draw 7 + 5, you can see exactly 12 items, not guess.

Question: My child draws very messy pictures. Should I worry about neatness?

Answer: Neatness is helpful but not the most important thing. Focus on:

  • Clarity: Can your child tell what each drawing represents?
  • Organization: Are items grouped logically?
  • Accuracy: Does the drawing match the problem?

Encourage organization and clear labeling, but don't stress about perfect artwork.

Tip: Simple shapes like circles, squares, or dots work perfectly for representing objects.

Question: How can I help students who resist using drawing strategies?

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Answer: Here are strategies to encourage drawing:

  1. Make it fun: Use colorful markers, stickers, or stamps
  2. Start simple: Begin with basic shapes, not detailed drawings
  3. Show benefits: Demonstrate how drawing makes problems easier
  4. Model: Show how you use drawing to solve problems

Emphasize that drawing is a tool, like a calculator, to help solve problems.

Provide drawing templates or grids to help organize their work.

Drawing Problem Solving: Complete Learning Summary

Key Definitions

Drawing Strategy: Using visual representations to solve math problems

Visual Model: A picture or diagram that represents the problem

Pattern: A repeated sequence of shapes, colors, or objects

One-to-One Correspondence: Each drawing represents exactly one real object

Sequential Drawing: Showing each step of a multi-step problem

Core Rules & Laws

Visual Representation Rule: Draw what the problem describes

Counting Rule: Count what you drew to find the answer

Pattern Rule: Identify the repeating sequence

Comparison Rule: Draw both sets to compare quantities

Sequential Rule: Show each action step by step

Step-by-Step Method

Step 1: Read the problem carefully

Step 2: Plan what to draw

Step 3: Create visual representations

Step 4: Use the drawing to solve

Step 5: Check that the answer makes sense

Examples & Applications

Addition: Draw 7 apples + 5 apples = 12 apples

Subtraction: Draw 10 cookies - 3 eaten = 7 left

Patterns: Red, Blue, Green → Red, Blue, Green

Comparison: Draw 6 triangles vs 4 squares

Multi-step: 8 birds - 3 fly + 2 return = 7 birds

Tips & Common Pitfalls

Tip 1: Use simple shapes or symbols for clarity

Tip 2: Organize drawings in rows or groups

Tip 3: Label drawings when needed

Pitfall: Drawing too many or too few items

Pitfall: Not following the pattern correctly

Key Takeaways

Memorize: Draw what the problem says

Remember: Count what you drew

Practice: Work with different problem types

Verify: Check that your answer makes sense

Master: Drawing is a powerful problem-solving tool