Expand your math toolkit! Discover powerful strategies like drawing pictures, making tables, finding patterns, and working backwards. Become a problem-solving expert! 🧰🎯
Try different problem-solving strategies and discover which works best for each situation!
Choose the best strategy for each problem type!
🖱️ Drag options below to the correct boxes (computer) or click to move (mobile)
Solve a problem using visual representation!
Extend a number pattern using strategy!
Identify when a strategy works best!
Click all correct options
Master multiple problem-solving approaches and know when to use each one
Drawing transforms words into visuals. When you can see the problem, the solution becomes clearer!
When to Use
Great for geometry, distance, arrangement, or comparison problems. Visual models clarify relationships!
Types of Diagrams
Bar models, tape diagrams, number lines, area models, tree diagrams—choose what fits!
Example Problem
Tom has 3 times as many marbles as Sue. Together they have 24. How many does each have? Draw bars!
Benefits
Makes abstract concrete, reveals hidden information, helps organize thinking visually!
Don't worry about artistic skill. Simple rectangles, lines, and circles work perfectly!
Skipping diagrams because 'I can see it in my head.' Drawing catches errors mental images miss!
Architects, engineers, designers—all use diagrams to solve complex problems!
Solve 5 word problems twice: once with calculations only, once with diagrams. Compare ease!
Tables organize messy information into neat rows and columns. They're perfect when comparing multiple options!
When to Use
Perfect for organizing data, comparing options, tracking patterns, or testing multiple cases!
Table Structure
Columns for categories, rows for different cases. Label clearly! Add totals if needed!
Example Problem
Tickets cost $8 for adults, $5 for kids. How much for different group combinations? Make a table!
Spotting Patterns
Tables reveal patterns you might miss. Look down columns and across rows!
Add a 'notes' column for observations. Writing thoughts helps you notice patterns!
Making tables too complicated. Keep it simple with clear labels and clean organization!
Business decisions, budget comparisons, scientific experiments—tables organize complex choices!
Create tables for family decisions: 'Which streaming service is cheapest for our usage?'
Patterns let you predict without calculating every case. Finding the rule unlocks efficiency!
When to Use
Excellent for sequences, repeating situations, predictions, or when things seem to follow a rule!
Types of Patterns
Arithmetic (+same amount), geometric (×same amount), visual (shapes), functional (formulas)!
Example Problem
Fence posts are 2m apart. How many posts for 20m? Pattern: posts = (distance ÷ spacing) + 1 = 11!
Testing Patterns
Always test your pattern on a few cases before using it. Does it work consistently?
Write out at least 3-4 terms before deciding on the pattern. One or two can be misleading!
Assuming a pattern continues without testing. Always verify with multiple examples!
Stock market analysis, weather prediction, growth projections—patterns everywhere!
Find patterns in nature (flower petals), architecture (tile designs), music (rhythms)!
Guess and check isn't random—it's strategic trial and error. Each guess teaches you something!
When to Use
Great when you have constraints, limited options, or need to find unknowns that fit conditions!
Smart Guessing
Start with reasonable guesses. Use results to adjust: too high? Guess lower! Too low? Guess higher!
Example Problem
Two numbers multiply to 48 and add to 14. What are they? Try: 6×8=48, 6+8=14. Success!
Keeping Track
Record guesses in a table. Track what works, what doesn't, and why. Learn from each attempt!
Make educated guesses based on the numbers in the problem. Narrow the range quickly!
Giving up after one wrong guess. It's called guess and CHECK—keep refining!
Password cracking (ethically!), optimization problems, finding best fits in engineering!
Play guess-my-number games with constraints: 'It's between 1-100, divisible by 3, and odd.'
Working backwards is like rewinding a movie to find where it started. Reverse the steps!
When to Use
Perfect when you know the end result and need to find the beginning or intermediate steps!
Reverse Operations
Undo each step: if problem added, you subtract; if multiplied, you divide. Go backwards!
Example Problem
Think of a number. Triple it. Add 12. You get 39. Original? Work back: 39-12=27, 27÷3=9!
Verification
After working backwards, go forwards to check. Does it lead to the given result?
Draw arrows showing each step and its inverse. Visual flowcharts make backwards work clear!
Forgetting to reverse the operation correctly. Addition ↔ subtraction, × ↔ ÷!
Debugging code, retracing mistakes, finding origins in historical research!
Create 'mystery number' challenges for classmates using working backwards strategy!
Expert problem solvers have a toolbox of strategies and know which tool fits each job!
Ask Questions
What type of problem? What information do I have? What's being asked? Questions guide strategy choice!
Try Multiple Strategies
Sometimes combining strategies works best: draw a picture AND make a table!
Flexibility
If one strategy isn't working after a few minutes, try another. Be willing to switch!
Build Experience
The more problems you solve, the faster you'll recognize which strategy fits. Practice builds intuition!
Keep a strategy log. Note which strategy you used for each problem type. Patterns will emerge!
Always using your favorite strategy even when it doesn't fit. Match the tool to the task!
Life requires strategic thinking: choose job-search methods, parenting approaches, health strategies!
Solve one problem using three different strategies. Compare which was fastest and clearest!