Drawing to Solve
Learn
Sometimes math problems are easier to solve when you draw a picture! Drawing helps you SEE the problem and understand what is happening. Let's learn how to use pictures to solve word problems.
What is Drawing to Solve?
Drawing to solve means making a simple picture to help you understand a math problem. You can draw circles, lines, boxes, or stick figures to show what the problem is about.
Steps to Draw a Problem
- Read the problem carefully. What is happening?
- Decide what to draw. What objects are in the problem?
- Draw simple shapes. Circles, squares, or stick figures work great!
- Label your drawing. Write numbers to show how many.
- Use your picture to solve. Count, add, or subtract.
What Can You Draw?
- Circles: Draw circles for objects like apples, cookies, or balls
- Stick figures: Draw stick people for problems about children or people
- Boxes: Draw boxes for groups or sets of things
- Lines: Draw tally marks to count things quickly
- Shapes: Draw the shapes mentioned in geometry problems
Test-Taking Tip
On the SAT and ACT, many math problems can be solved by drawing! Even a quick sketch can help you see the answer. Don't be afraid to draw in the margins of your test.
Examples
Let's practice drawing to solve word problems.
Example 1: Adding with a Picture
Problem: Tom has 3 apples. His mom gives him 2 more apples. How many apples does Tom have now?
Draw it:
Tom's apples: O O O (3 circles)
Mom gives him: O O (2 more circles)
Count all circles: O O O O O = 5
Answer: Tom has 5 apples.
Example 2: Subtracting with a Picture
Problem: Sara has 7 balloons. 3 balloons fly away. How many balloons does Sara have left?
Draw it:
Start: O O O O O O O (7 balloons)
Cross out 3: X X X O O O O
Count what's left: 4
Answer: Sara has 4 balloons left.
Example 3: Groups Problem
Problem: There are 3 boxes. Each box has 4 toys. How many toys are there in all?
Draw it:
Box 1: [O O O O] - 4 toys
Box 2: [O O O O] - 4 toys
Box 3: [O O O O] - 4 toys
Count all: 4 + 4 + 4 = 12
Answer: There are 12 toys in all.
Example 4: Comparing Problem
Problem: Jake has 5 stickers. Emma has 8 stickers. How many more stickers does Emma have?
Draw it:
Jake: O O O O O
Emma: O O O O O O O O
Compare: Line them up. Emma has 3 more.
Answer: Emma has 3 more stickers than Jake.
Example 5: Sharing Problem
Problem: Mom has 10 cookies. She wants to share them equally between 2 children. How many cookies does each child get?
Draw it:
Child 1: O O O O O (give one at a time to each child)
Child 2: O O O O O
Count each pile: 5 each
Answer: Each child gets 5 cookies.
Practice
Draw a picture to help you solve each problem.
1. Ben has 4 toy cars. He gets 3 more for his birthday. How many toy cars does Ben have now?
Show Answer
Draw: O O O O + O O O = 7 cars
Answer: Ben has 7 toy cars.
2. There are 9 birds on a tree. 4 birds fly away. How many birds are left on the tree?
Show Answer
Draw: O O O O O O O O O - cross out 4 = 5 left
Answer: There are 5 birds left.
3. A farmer has 2 baskets. Each basket has 5 eggs. How many eggs does the farmer have?
Show Answer
Draw: [O O O O O] + [O O O O O] = 10 eggs
Answer: The farmer has 10 eggs.
4. Lisa has 6 crayons. Her friend has 3 crayons. How many more crayons does Lisa have?
Show Answer
Draw: Lisa: O O O O O O vs Friend: O O O = 3 more
Answer: Lisa has 3 more crayons.
5. There are 8 flowers. Half of them are red. How many red flowers are there?
Show Answer
Draw: O O O O | O O O O - split in half = 4 on each side
Answer: There are 4 red flowers.
6. Mike has 5 pencils. Sam has 5 pencils too. How many pencils do they have together?
Show Answer
Draw: | | | | | + | | | | | = 10 pencils
Answer: They have 10 pencils together.
7. There are 12 grapes. Mom puts them on 3 plates equally. How many grapes are on each plate?
Show Answer
Draw: Plate 1: O O O O | Plate 2: O O O O | Plate 3: O O O O = 4 each
Answer: There are 4 grapes on each plate.
8. A dog has 4 legs. How many legs do 2 dogs have?
Show Answer
Draw: Dog 1: | | | | + Dog 2: | | | | = 8 legs
Answer: Two dogs have 8 legs.
9. Anna has 11 candies. She eats 6 of them. How many candies are left?
Show Answer
Draw: O O O O O O O O O O O - cross out 6 = 5 left
Answer: Anna has 5 candies left.
10. There are 3 tables. Each table has 2 chairs. How many chairs are there in all?
Show Answer
Draw: Table 1: [ ] [ ] | Table 2: [ ] [ ] | Table 3: [ ] [ ] = 6 chairs
Answer: There are 6 chairs in all.
Check Your Understanding
Question 1: Why does drawing help you solve word problems?
Show Answer
Drawing helps you SEE what is happening in the problem. It turns words into pictures, making it easier to understand and count.
Question 2: What can you use to draw objects in a problem?
Show Answer
You can use circles, squares, dots, stick figures, tally marks, or any simple shapes. The drawing doesn't have to be fancy - just clear enough to count!
Question 3: If a problem says "take away" or "fly away" or "eat," what operation should you use?
Show Answer
Subtraction! These words mean something is being removed. In your drawing, you cross out or remove some objects.
Question 4: How do you solve a "sharing equally" problem with a picture?
Show Answer
Draw all the objects, then divide them into equal groups. Give one object to each group, going around and around, until all objects are shared. Count how many are in each group.
Next Steps
- Practice drawing: Every time you see a word problem, try drawing it first before solving.
- Keep it simple: Your drawings don't need to be beautiful - just helpful!
- Keep learning: In the next lesson, you will learn about Reading Diagrams that are already made for you.