Using Diagrams
Learn
Drawing a diagram or picture can help you understand and solve word problems. Diagrams make it easier to see what's happening in the problem and plan your solution.
Types of Diagrams
- Bar Models: Use bars to show parts and wholes, great for comparison problems.
- Number Lines: Show addition and subtraction by jumping along a line.
- Pictures/Drawings: Draw simple shapes to represent objects in the problem.
- Tables/Charts: Organize information in rows and columns.
- Arrays: Show multiplication as rows and columns of objects.
Examples
Example: Bar Model
Problem: Sam has 45 marbles. Jake has 18 fewer marbles than Sam. How many marbles do they have together?
Diagram:
Sam: |---------------45---------------|
Jake: |-------?-------| (18 fewer)
Solution:
Step 1: Jake's marbles = 45 - 18 = 27
Step 2: Total = 45 + 27 = 72 marbles
Example: Table
Problem: A fruit stand sells apples for $2 each. How much do 1, 2, 3, 4, and 5 apples cost?
| Apples | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Cost ($) | 2 | 4 | 6 | 8 | 10 |
Pattern: Multiply number of apples by $2.
Practice Quiz
For each problem, think about what diagram might help. Then solve the problem.
1. Mia has 32 stickers. Her friend has 15 more stickers than Mia. How many stickers do they have in total?
Hint: Draw a bar model comparing their stickers.
Show Answer
79 stickers
Bar Model: Mia = 32, Friend = 32 + 15 = 47
Total: 32 + 47 = 79 stickers
2. A garden has 4 rows of tomato plants with 6 plants in each row. How many tomato plants are there?
Hint: Draw an array (4 rows of 6).
Show Answer
24 tomato plants
Array: 4 rows x 6 plants = 24 plants
3. A ribbon is 50 inches long. Amy cuts off 18 inches, then cuts off 12 more inches. How long is the ribbon now?
Hint: Use a number line or bar model.
Show Answer
20 inches
50 - 18 = 32 inches
32 - 12 = 20 inches
4. Three friends share 36 crackers equally. Then each person eats 4 crackers. How many crackers does each person have left?
Show Answer
8 crackers each
36 / 3 = 12 crackers each
12 - 4 = 8 crackers left per person
5. A bookshelf has 5 shelves. Each shelf holds 14 books. How many books can the bookshelf hold in all?
Show Answer
70 books
5 x 14 = 70 books
6. Julia scored 28 points in a game. Kevin scored twice as many points as Julia. How many points did Kevin score?
Hint: Draw bars - Kevin's bar should be twice as long as Julia's.
Show Answer
56 points
Kevin = 2 x 28 = 56 points
7. A parking lot has 8 rows of cars. Each row has 9 cars. 15 cars leave. How many cars are left?
Show Answer
57 cars
Total: 8 x 9 = 72 cars
After leaving: 72 - 15 = 57 cars
8. The table shows prices at a cafe:
Muffin: $3, Juice: $2, Cookie: $1
If you buy 2 muffins and 1 juice, how much do you spend?
Show Answer
$8
2 muffins: 2 x $3 = $6
1 juice: $2
Total: $6 + $2 = $8
9. A rectangle has a length of 12 cm and a width of 8 cm. What is its perimeter (distance around)?
Hint: Draw and label the rectangle.
Show Answer
40 cm
Perimeter = 12 + 8 + 12 + 8 = 40 cm
Or: 2 x (12 + 8) = 2 x 20 = 40 cm
10. Ben walked 3 blocks north, then 5 blocks east, then 3 blocks south. How many total blocks did he walk? How far is he from where he started?
Hint: Draw his path on a grid.
Show Answer
Total: 11 blocks walked
Distance from start: 5 blocks east
3 + 5 + 3 = 11 total blocks
He went 3 north and 3 south (back to same line), but 5 blocks east, so he's 5 blocks from his starting point.
Check Your Understanding
Did drawing a diagram help you understand the problems better? Practice using different types of diagrams to find which works best for you.
Next Steps
- Practice drawing bar models for comparison problems
- Use tables to organize information in multi-step problems
- Move on to Lesson 5: Review and Mistakes