Word Problems — Speed/Distance/Age, Discount & Interest - Memory Anchors
Memory techniques transform abstract mathematical concepts into unforgettable images and stories. These creative memory aids turn formulas into vivid stories, complex problems into familiar analogies, and boring numbers into exciting adventures. Your brain naturally remembers stories, emotions, and visual images better than abstract concepts—so let's make every formula and problem-solving step stick in your mind forever!
Memory anchors
Speed = Distance ÷ Time formula
Memory aid
Super Dog Travels - SDT triangle where Speed is at the top, Distance and Time at the bottom. Cover what you want to find!
Why it works
Visual triangles create spatial memory, and the silly 'Super Dog Travels' phrase makes it emotionally memorable
Example usage
When asked 'A jeepney travels 150km in 3 hours, find its speed' - think Super Dog Travels, cover S in triangle, get D÷T = 150÷3 = 50 kph
Recall trigger
Picture a superhero dog flying through the air when you see speed problems
Simple Interest formula I = PRT
Memory aid
A pirate named Captain PRT buried treasure. To find his Interest (I), he needed his Principal (P) gold coins, the Rate (R) of growth per year, and Time (T) buried underground. I = P × R × T
Why it works
Pirates and treasure create strong emotional connections, making the abstract formula concrete and memorable
Example usage
For 'Find interest on P10,000 at 5% for 2 years' - Captain PRT: I = 10,000 × 0.05 × 2 = P1,000
Recall trigger
Think of a pirate counting treasure when you see interest problems
Discount formula: Discount = List Price - Selling Price
Memory aid
Imagine a price tag with two numbers: the BIG original price and the SMALLER sale price. The discount is the chunk that got 'eaten away' between them - like a pac-man chomping the difference!
Why it works
Visual imagery of Pac-Man eating the price difference creates a strong mental picture that's hard to forget
Example usage
T-shirt listed at P500, sold at P400. Pac-man ate P500 - P400 = P100 discount
Recall trigger
Picture Pac-Man eating money when you see discount problems
Age problems - setting up present, past, and future ages
Memory aid
Age problems are like time machines! Create a table with three columns: Past (subtract years), Present (now), Future (add years). Each person is a time traveler with their own journey.
Why it works
Time travel is exciting and familiar from movies, making abstract age relationships concrete and visual
Example usage
Maria is 3 times older than Juan. In 5 years, she'll be twice as old. Set up: Present (M=3J), Future (M+5=2(J+5))
Recall trigger
Think 'Back to the Future' when solving age problems
Compound Interest vs Simple Interest difference
Memory aid
Simple Interest is like a lazy employee - earns the same amount each year. Compound Interest is like an ambitious entrepreneur - earns money on the money it already earned, growing exponentially like a snowball rolling downhill!
Why it works
Contrasting personalities (lazy vs ambitious) and familiar images (snowball) make the concepts distinct and memorable
Example usage
P1,000 at 10%: Simple stays flat (100+100+100), Compound grows (100+110+121)
Recall trigger
Picture a lazy person vs a snowball when comparing interest types
Converting km/hr to m/s
Memory aid
King Henry's Magic: Multiply by 5, Divide by 18. Or remember 'Keep Happy, Make Sure' - K(m)/H(r) to M(eters)/S(econds) = × 5/18
Why it works
Rhyming phrases and royal imagery create memorable patterns for the conversion factor
Example usage
Convert 72 km/hr: 72 × 5/18 = 20 m/s (King Henry's Magic!)
Recall trigger
Think of King Henry when converting speed units
Average Speed formula
Memory aid
Meet Average Joe - he never rushes or slows down. To find his constant speed on any trip, he adds ALL the distances he traveled and divides by ALL the time it took. Average Speed = Total Distance ÷ Total Time
Why it works
Personifying average speed as 'Average Joe' makes the concept relatable and the formula logical
Example usage
Trip 1: 60km in 1hr, Trip 2: 90km in 2hrs. Average Joe: (60+90)÷(1+2) = 50 kph
Recall trigger
Think of a steady, consistent person named Average Joe
Discount Percentage formula
Memory aid
Imagine a pizza cut into 100 slices (100%). The discount percentage is how many slices you DON'T have to pay for. Discount % = (Original Price - Sale Price) ÷ Original Price × 100
Why it works
Pizza slices make percentages visual and concrete - everyone understands pizza portions!
Example usage
Shoes: P2000 → P1600. Missing pizza slices: (2000-1600)÷2000 × 100 = 20%
Recall trigger
Picture pizza slices when calculating discount percentages
Future Value in Compound Interest F = P(1+r)^t
Memory aid
Future Fairy grants wishes! She takes your Present money (P), adds the rate (r) to make it grow, then waves her magic wand (1+r) and multiplies it by itself for each year (^t). F = P(1+r)^t
Why it works
Fairy magic explains the mysterious power of exponential growth in a memorable way
Example usage
P10,000 at 5% for 3 years: Future Fairy says F = 10,000(1.05)³ = P11,576.25
Recall trigger
Think of a magical fairy when calculating compound interest
Time conversion in interest problems
Memory aid
Months to years, never fear! Divide by twelve, the answer's here! Days to years, don't you cry! Divide by three-sixty-five!
Why it works
Rhymes create rhythm and melody that stick in memory better than plain facts
Example usage
9 months = 9÷12 = 0.75 years, 180 days = 180÷365 = 0.49 years
Recall trigger
Sing the rhyme when you need to convert time units
Setting up age problem equations
Memory aid
Walk through your house: Front door = Present ages (let x be younger person), Living room = Past relationships (subtract years), Kitchen = Future relationships (add years), Bedroom = Write equations and solve
Why it works
Method of loci uses familiar spatial memory to organize complex problem-solving steps
Example usage
Father 4x older than son. In 20 years, only 2x older. House tour: Door(F=4S), Kitchen(F+20=2(S+20)), solve!
Recall trigger
Mentally walk through your house when solving age problems
Types of discount (Trade, Quantity, Promotional)
Memory aid
TQP - 'Top Quality Products' = Trade (business to business), Quantity (bulk buying), Promotional (marketing/clearance)
Why it works
The phrase 'Top Quality Products' is positive and business-related, making it easy to remember all three types
Example usage
Question asks about discount types - recall TQP: Trade (distributor to retailer), Quantity (bulk discounts), Promotional (sales/clearance)
Recall trigger
Think 'Top Quality Products' when asked about discount types
Distance problems with multiple speeds
Memory aid
Picture a race track with different lanes - each lane has different speeds but the same distance. Make a table like a scoreboard: Distance | Speed | Time for each 'lane' of the journey
Why it works
Race tracks are visually familiar, and scoreboards naturally organize information in tables
Example usage
Car travels 200km at 50kph, returns same route at 100kph. Scoreboard: Lane 1 (200|50|4), Lane 2 (200|100|2)
Recall trigger
Visualize a race track scoreboard when dealing with complex distance problems
Principal calculation P = I÷(RT)
Memory aid
Principal is like the seed that grows into the Interest fruit. To find the original seed size, you take the fruit (Interest) and divide by how much it grew (Rate × Time). Bigger growth factors mean smaller original seed needed!
Why it works
Seeds growing into fruit is a natural, intuitive process that explains inverse relationships clearly
Example usage
Interest earned P2,400 at 8% for 3 years. Seed size: P = 2,400÷(0.08×3) = P10,000
Recall trigger
Think of seeds growing into fruit when finding principal
Maturity Value calculation M = P + I
Memory aid
Picture a piggy bank growing fat! The Maturity Value is the final fat piggy (M) = Original skinny piggy (P) + All the extra weight it gained (I). Simple addition!
Why it works
Piggy banks are associated with savings, and the visual of growth makes addition logical
Example usage
Invested P50,000, earned P7,500 interest. Fat piggy: M = 50,000 + 7,500 = P57,500
Recall trigger
Picture a piggy bank getting fat when calculating maturity value
Rate calculation R = I÷(PT)
Memory aid
Rate Detective investigates: 'How fast did this money grow?' He takes the Interest evidence (I) and divides by the Principal suspect (P) and Time witness (T) to find the growth Rate. R = I÷(P×T)
Why it works
Detective stories create narrative structure, making abstract division meaningful and memorable
Example usage
P20,000 earned P3,000 in 2 years. Detective work: R = 3,000÷(20,000×2) = 0.075 = 7.5%
Recall trigger
Channel your inner detective when finding interest rates
Selling Price calculation after discount
Memory aid
Think '100 minus discount, then multiply': SP = List Price × (100% - Discount%). Break it into chunks: Step 1: 100 - discount%, Step 2: Convert to decimal, Step 3: Multiply by list price
Why it works
Chunking breaks complex calculations into manageable steps, reducing cognitive load
Example usage
P800 shirt, 25% off. Chunks: 100-25=75%, 75%=0.75, SP = 800×0.75 = P600
Recall trigger
Count '100 minus, then multiply' on your fingers
Age relationship patterns
Memory aid
Draw age problems like a family tree that travels through time! Present ages at the trunk, past ages on the left branches (subtract), future ages on right branches (add). Relationships stay proportional as the tree grows!
Why it works
Family trees are familiar visual structures, and the time-travel aspect makes age changes logical
Example usage
Mom 3x older than daughter now, will be 2x older in 10 years. Tree shows: Now(3x|x), Future(3x+10|x+10), equation: 3x+10=2(x+10)
Recall trigger
Sketch a time-traveling family tree for age problems
Word problem identification strategy
Memory aid
SWIFT strategy: S-Scan for keywords (speed, discount, age, interest), W-What is being asked?, I-Information given, F-Formula needed, T-Time to calculate! Like a SWIFT response team!
Why it works
SWIFT suggests speed and efficiency, and the military/emergency response analogy makes problem-solving feel organized and confident
Example usage
Problem mentions 'annual rate' and 'how much earned' - SWIFT scan identifies interest problem, formula I=PRT needed
Recall trigger
Deploy SWIFT team tactics when facing any word problem
Common word problem mistake prevention
Memory aid
Picture a red STOP sign with common traps: Units not matching (km/hr vs m/s), Time not converted (months to years), Forgetting to add principal to interest, Using wrong formula. The STOP sign prevents crashes!
Why it works
STOP signs are universal warning symbols, creating strong associations with danger/mistakes to avoid
Example usage
About to submit interest calculation - STOP sign reminds to check: Did I convert 6 months to 0.5 years? Did I add principal to get maturity value?
Recall trigger
Visualize a red STOP sign before submitting answers
Revision game
I'm a triangle that helps you travel, with Speed on top and Distance-Time below. What am I?
Answer
SDT Triangle
Memory link
Super Dog Travels memory anchor (A1)
I'm a pirate who counts treasure using P times R times T. Who am I?
Answer
Captain PRT (Simple Interest)
Memory link
Pirate treasure story (A2)
I eat the difference between two prices - the big one and the smaller sale price. What am I?
Answer
Pac-Man Discount
Memory link
Pac-Man eating price difference (A3)
I'm like a time machine with three columns: subtract for past, now for present, add for future. What am I?
Answer
Age Problem Table
Memory link
Time machine analogy (A4)
I'm lazy and earn the same each year, unlike my ambitious snowball friend. What am I?
Answer
Simple Interest
Memory link
Lazy employee vs snowball analogy (A5)
I grant wishes by taking Present money, adding rate, then raising to the power of time. Who am I?
Answer
Future Fairy (Compound Interest)
Memory link
Future Fairy magic story (A9)
I'm a SWIFT team that Scans, asks What, lists Information, finds Formula, then calculates Time. What am I?
Answer
SWIFT Problem-Solving Strategy
Memory link
SWIFT strategy acronym (A19)
I'm a red sign that prevents crashes by warning about units, conversions, and formula mistakes. What am I?
Answer
STOP Sign Error Prevention
Memory link
Red STOP sign visualization (A20)
Formula mnemonics
Speed = Distance ÷ Time
Mnemonic
Super Dog Travels - SDT triangle, cover what you want to find
When to use
Any problem asking for speed, distance, or time in motion
What each part means
Speed (how fast), Distance (how far), Time (how long)
Simple Interest: I = PRT
Mnemonic
I Prefer Reading Tonight - Interest equals Principal × Rate × Time
When to use
When interest is calculated only on the original principal amount
What each part means
I (interest earned/paid), P (principal/original amount), R (rate as decimal), T (time in years)
Compound Interest: F = P(1+r)^t
Mnemonic
Future Perfect - Present grows by (1 plus rate) powered by time
When to use
When interest earns interest (compounds)
What each part means
F (future value), P (present value), r (rate as decimal), t (time periods)
Discount = List Price - Selling Price
Mnemonic
Don't Lose Sales Profits - Discount equals List minus Selling Price
When to use
When finding the peso amount of discount given
What each part means
Discount (amount saved), List Price (original price), Selling Price (final price paid)
Average Speed = Total Distance ÷ Total Time
Mnemonic
All Students Take Tests - Average Speed equals Total Distance over Total Time
When to use
When finding constant speed for trips with different speeds
What each part means
Average Speed (constant speed equivalent), Total Distance (sum of all distances), Total Time (sum of all times)
Quick recall chains
Steps to Solve Speed Problems
Recall test
What are the 5 steps to solve any speed problem?
Memory chain
I Will Surely Calculate Correctly - like a racing driver checking everything before the race
Items to remember
- Identify what's missing
- Write the formula
- Substitute known values
- Calculate the answer
- Check units
Age Problem Setup Sequence
Recall test
What 5 steps help organize age problems?
Memory chain
Detective Creates Tables, Writes Reports, Solves Cases - like a detective investigating through time
Items to remember
- Define variables
- Create time table
- Write present relationship
- Write future/past relationship
- Solve equations
Interest Problem Types
Recall test
Name the 6 key elements in interest problems
Memory chain
Smart Children Practice Reading Time Management - all the components of interest problems
Items to remember
- Simple Interest
- Compound Interest
- Principal
- Rate
- Time
- Maturity Value
Discount Problem Elements
Recall test
What are the 4 main elements in discount problems?
Memory chain
Lazy Dogs Don't Sell - the four key prices/rates in discount problems
Items to remember
- List Price
- Discount Amount
- Discount Rate
- Selling Price
Unit Conversion Factors
Recall test
What are the 5 most important conversion factors for word problems?
Memory chain
King Henry's Magic Numbers: 1000, 60, 12, and the magic fractions 5/18 and 18/5
Items to remember
- 1 km = 1000 m
- 1 hour = 60 minutes
- 1 year = 12 months
- km/hr to m/s: ×5/18
- m/s to km/hr: ×18/5
Diagrams
Word Problems Master Mind Map
Complete concept map showing all major topics and their relationships in word problems
Word Problem Solving Strategy Flowchart
Step-by-step decision tree for approaching any word problem systematically
Age Problem Time Analysis
Shows the time flow and relationship dependencies in age word problems
Common Word Problem Types Distribution
Shows the relative frequency of different word problem types in Philippine entrance exams