Mixed Set
Learn
Congratulations! You've made it to the final lesson in this unit. Now it's time to put everything together.
What You've Learned
- Drawing to Solve: Creating your own pictures to understand problems
- Reading Diagrams: Getting information from pictures and graphs
- Question Types: Counting, comparison, part-part-whole, and picture graphs
- Timed Practice: Working quickly and accurately
- Review Mistakes: Learning from errors to get better
Mixed Set Challenge
Real tests mix up different types of problems. You don't know what's coming next! This mixed set will help you practice switching between different strategies.
Strategy for Mixed Sets
- Read the whole problem first
- Look at any diagrams or pictures
- Identify the question type
- Solve using the right strategy
- Check that your answer makes sense
Examples
Let's work through two examples together, identifying the type and strategy.
Example A
Problem: The picture shows snacks in a lunchbox.
+---------------------------+
| [apple] [apple] |
| [cracker][cracker][cracker]|
| [cheese] |
+---------------------------+
How many snacks are in the lunchbox?
Step 1 - Identify: This is a counting problem.
Step 2 - Solve: Count each item: 2 apples + 3 crackers + 1 cheese = 6 snacks
Step 3 - Check: Count again to verify. Yes, 6 total snacks.
Answer: 6 snacks
Example B
Problem: The pet store has 18 fish. They sell 7 fish. Then 3 more fish are born. How many fish are in the store now?
Step 1 - Identify: This is a two-step problem (part-part-whole).
Step 2 - Solve:
- Start: 18 fish
- After selling: 18 - 7 = 11 fish
- After births: 11 + 3 = 14 fish
Step 3 - Check: Does 14 make sense? Started with 18, lost 7 (that's less), gained 3 (a little more). Yes, 14 is reasonable.
Answer: 14 fish
Practice
Mixed Set: 12 Problems
These problems are mixed up! Use everything you've learned.
Problem 1
Look at the picture graph of weather this month:
Sunny: [sun][sun][sun][sun][sun][sun][sun][sun]
Cloudy: [cloud][cloud][cloud][cloud][cloud]
Rainy: [rain][rain][rain][rain]
Snowy: [snow][snow]
a) How many sunny days were there? _______
b) How many more sunny days than rainy days? _______
c) How many days total are shown? _______
Problem 2
Maya has 16 beads. She uses 9 beads to make a necklace. How many beads are left?
Answer: _______
Problem 3
Count all the shapes in this picture:
O O O []
[] O [] O
O [] O O
a) How many circles? _______
b) How many squares? _______
c) How many shapes in all? _______
Problem 4
Room A has 12 students. Room B has 15 students. Room C has 11 students.
a) Which room has the most students? _______
b) How many more students in Room B than Room C? _______
c) How many students in all three rooms? _______
Problem 5
The toy box has 25 toys. Tom takes out 8 toys to play with. Then he puts 3 toys back. How many toys are in the box now?
Answer: _______
Problem 6
Look at the bar model:
+------------------+
| Total: ? |
+--------+---------+
| 13 | 9 |
+--------+---------+
What is the total? _______
Problem 7
The store has these items:
Apples: [a][a][a][a][a][a]
Oranges: [o][o][o][o][o][o][o][o]
Bananas: [b][b][b][b]
The store gets 5 more bananas. Now how many bananas are there? _______
Problem 8
Jake has 14 stickers. Emma has some stickers. Together they have 23 stickers. How many stickers does Emma have?
Answer: _______
Problem 9
Count the dots in this pattern:
.
. .
. . .
. . . .
. . . . .
How many dots in all? _______
Problem 10
The library has 30 books on the shelf. Students borrow 12 books. Then 5 books are returned. How many books are on the shelf now?
Answer: _______
Problem 11
Look at the picture graph of ice cream flavors sold:
Chocolate: [cone][cone][cone][cone][cone][cone][cone]
Vanilla: [cone][cone][cone][cone][cone]
Strawberry: [cone][cone][cone]
Mint: [cone][cone][cone][cone][cone][cone]
a) Which flavor sold the most? _______
b) Which two flavors sold the same amount? _______ and _______
c) How many fewer strawberry than chocolate? _______
Problem 12
Sara collected 8 shells on Monday, 6 shells on Tuesday, and 9 shells on Wednesday.
a) How many shells did she collect in all? _______
b) On which day did she collect the most? _______
c) How many more shells on Wednesday than Tuesday? _______
Check Your Understanding
Answer Key
Problem 1:
- a) 8 sunny days
- b) 4 more sunny than rainy (8 - 4 = 4)
- c) 19 days total (8 + 5 + 4 + 2 = 19)
Problem 2: 7 beads left (16 - 9 = 7)
Problem 3:
- a) 8 circles
- b) 4 squares
- c) 12 shapes in all
Problem 4:
- a) Room B has the most (15 students)
- b) 4 more students (15 - 11 = 4)
- c) 38 students total (12 + 15 + 11 = 38)
Problem 5: 20 toys (25 - 8 + 3 = 20)
Problem 6: Total is 22 (13 + 9 = 22)
Problem 7: 9 bananas (4 + 5 = 9)
Problem 8: Emma has 9 stickers (23 - 14 = 9)
Problem 9: 15 dots (1 + 2 + 3 + 4 + 5 = 15)
Problem 10: 23 books (30 - 12 + 5 = 23)
Problem 11:
- a) Chocolate (7 cones)
- b) Vanilla (5) and Mint sold 6, no two are the same. Actually: None sold same - V=5, S=3, M=6. Trick question!
- c) 4 fewer strawberry (7 - 3 = 4)
Problem 12:
- a) 23 shells (8 + 6 + 9 = 23)
- b) Wednesday (9 shells)
- c) 3 more shells (9 - 6 = 3)
Final Score
Count your correct answers (each part counts as 1 point).
Total possible: 20 points
Your score: _______ / 20
Score Guide
- 18-20: Excellent! You've mastered this unit!
- 14-17: Great work! Review any problem types you missed.
- 10-13: Good progress! Practice more before moving on.
- Below 10: Review the earlier lessons and try again.
Next Steps
- Celebrate completing this unit!
- Review any problem types that were tricky
- Move on to the next SAT/ACT Skills unit
- Come back and practice this mixed set again in a few weeks
Unit Complete!
You have finished all 6 lessons in the Word Problems with Diagrams unit. You've learned to:
- Draw pictures to solve problems
- Read and understand diagrams
- Identify different question types
- Work under time pressure
- Learn from your mistakes
- Solve mixed problem sets
These skills will help you on the SAT, ACT, and any math test!