Word Problems — Number, Age, Work, Motion, Mixture, Investment - Memory anchors
Memory techniques transform abstract word problems into vivid, memorable experiences. Instead of struggling to remember which formula to use or how to set up equations, these anchors create instant mental bridges to solutions. Each anchor here connects complex algebraic concepts to familiar Filipino experiences, making them impossible to forget.
Memory anchors
The 3 R's and ESP Strategy for Word Problems
Memory aid
Remember 'REP ESP' - like a famous rapper with psychic powers! READ (the problem), REPRESENT (with variables), RELATE (variables to each other), then ESP: EQUATE, SOLVE, PROVE.
Why it works
The rapper ESP image is memorable and the acronym groups the 6 steps into two catchy chunks, making the sequence unforgettable.
Example usage
When facing any word problem, visualize the rapper ESP and go through each letter: R-E-P then E-S-P
Recall trigger
Think of a rapper on stage solving math problems with supernatural powers
Translation Keywords for Mathematical Operations
Memory aid
Picture a SAMS (Samsung) phone with 4 apps: PLUS app (sum, more than, increased by), MINUS app (less than, decreased by, difference), TIMES app (product, of, twice), DIVIDE app (quotient, per). The phone's EQUALS button says 'is, was, will be'.
Why it works
The familiar smartphone interface creates a mental filing system for operation keywords, and SAMS helps remember the 4 operations (Subtraction, Addition, Multiplication, Division).
Example usage
When you see 'the product of 4 and x', open the TIMES app and write 4x
Recall trigger
Visualize opening apps on a Samsung phone
Switching Rule for 'Less Than' and 'Subtracted From'
Memory aid
Maria has 4 apples. Juan says 'I want 4 less than what Maria has' (Maria's amount minus 4). But if Juan says '4 subtracted from Maria's apples', he's taking 4 away from Maria's pile. In both cases, we SWITCH and put Maria's amount first: x - 4.
Why it works
The story shows why the switching happens naturally in Filipino context, and Maria/Juan are common Filipino names making it relatable.
Example usage
For '4 less than twice a number', think Juan wants 4 less than Maria's 2x apples: 2x - 4
Recall trigger
Think of Maria and Juan sharing apples, and who comes first in the math
Consecutive Integer Patterns
Memory aid
Picture stepping stones across a river: Regular integers step by 1 (x, x+1, x+2), but odd/even stones are spaced wider, stepping by 2 (x, x+2, x+4). The river represents the number line.
Why it works
The stepping stone metaphor makes the +1 vs +2 pattern visually clear and memorable through physical movement.
Example usage
For 3 consecutive even integers, place stepping stones 2 apart: x, x+2, x+4
Recall trigger
Visualize crossing a river on stepping stones
Two-Digit Number Representation
Memory aid
A two-digit number is like a jeepney route: The tens digit is the MAIN route number (multiplied by 10), and the ones digit is the SPECIFIC stop number (multiplied by 1). Route 56 means 5 main routes × 10 + 6 specific stops × 1.
Why it works
Jeepneys are uniquely Filipino and the route system mirrors place value perfectly, making 10x + y intuitive.
Example usage
If tens digit is x and ones digit is y, the number is like Route 10x + y
Recall trigger
Think of reading jeepney route numbers
Age Problem Time Relationships
Memory aid
Walk through your house timeline: Living room = Present ages, Kitchen = Past ages (subtract years), Bedroom = Future ages (add years). Everyone ages at the same rate as you walk through rooms.
Why it works
The spatial memory of house rooms creates a natural timeline, and the consistent aging concept becomes physically intuitive.
Example usage
If present ages are in the living room, move to kitchen (subtract 2) for '2 years ago'
Recall trigger
Walk through your house from living room to bedroom
Work Rate Formula: 1/n + 1/m = 1/h
Memory aid
Think of two water faucets filling a swimming pool: Faucet A fills 1/n pools per hour, Faucet B fills 1/m pools per hour. Together they fill 1/h pools per hour. It's like combining water flow rates!
Why it works
Water flowing from faucets is a concrete, visual representation of abstract work rates that students can easily visualize.
Example usage
If Ana finishes a job in 4 hours and Ben in 6 hours, think: 1/4 + 1/6 = 1/h faucets
Recall trigger
Picture two faucets filling a pool together
Distance = Velocity × Time (D = VT)
Memory aid
Distance, Velocity, Time - remember this rhyme: 'Darna Visits Tondo, flying Very fast through Time!' D = V × T, where Darna's distance equals her velocity times time flying.
Why it works
Darna is an iconic Filipino superhero, making the formula culturally memorable, and the rhyme structure aids recall.
Example usage
When solving motion problems, think 'Darna Visits Tondo' and write D = V × T
Recall trigger
Picture Darna flying to Tondo
Motion Problem Setup Strategy
Memory aid
Two tricycle drivers, Mang Jose and Mang Pedro, start from opposite ends of EDSA. They're racing toward each other - their distances ADD UP to total EDSA length. But if one is chasing the other in the same direction, their distances must be EQUAL when the faster one catches up.
Why it works
Filipino tricycle drivers on EDSA is relatable, and the opposite vs same direction scenarios create clear visual distinctions.
Example usage
Meeting problems: distances add up. Chasing problems: distances are equal when caught
Recall trigger
Think of tricycle drivers on EDSA racing
Solution Percentage Concept
Memory aid
A solution is like halo-halo: The solute (salt/sugar) is like the ube, beans, and sweets - the FLAVOR parts. The solvent (water) is like the shaved ice - the BASE that holds everything. A 20% saline solution is like halo-halo that's 20% flavor ingredients and 80% ice.
Why it works
Halo-halo is distinctly Filipino and the mixture concept perfectly parallels chemical solutions, making percentages intuitive.
Example usage
For 30% solution problems, imagine halo-halo that's 30% flavoring, 70% ice
Recall trigger
Picture making halo-halo with different ingredient ratios
Interest Formula: I = PRT
Memory aid
I PaRTy! - 'I love to PaRTy with my money!' Interest = Principal × Rate × Time. Picture yourself partying because your money earned interest!
Why it works
PaRTy is phonetically identical to PRT, and the celebration connects emotionally to earning money, making it memorable.
Example usage
For investment problems, shout 'I PaRTy!' and write I = P × R × T
Recall trigger
Think of partying because your investment earned money
Mixture Problem Table Setup
Memory aid
Picture a sari-sari store inventory table: 3 columns like store shelves - % Solution (concentration label), Volume (how many bottles), Pure Solute (actual content). Each row is a different product, plus a TOTAL row at bottom like store summary.
Why it works
Sari-sari stores are everywhere in the Philippines, and inventory management mirrors mixture problem organization perfectly.
Example usage
Draw your mixture table like organizing store inventory: % | Volume | Pure Content
Recall trigger
Visualize organizing products on sari-sari store shelves
Investment Problem Scenarios
Memory aid
Tita Rosa splits her ₱50,000 pasalip between two banks: BPI at 6% and BDO at 8%. She's smart - the HIGH interest investment (BDO) earns MORE than the LOW interest (BPI). The problem tells you the RELATIONSHIP between earnings to find how much went where.
Why it works
Filipino family context (Tita Rosa, pasalip culture) and familiar banks make investment scenarios relatable and memorable.
Example usage
Set up two investment amounts that add to total, with different rates earning different amounts
Recall trigger
Think of Tita Rosa managing her pasalip money
Work Problem Time Logic
Memory aid
Think of cooking rice: If you can cook 1 pot in 30 minutes ALONE, you cook 1/30 of a pot per minute. If your partner cooks 1 pot in 20 minutes ALONE, they cook 1/20 per minute. TOGETHER, you cook 1/30 + 1/20 pots per minute.
Why it works
Rice cooking is universal in Filipino households, and the per-minute breakdown makes fractional rates intuitive.
Example usage
Convert 'hours to complete' into 'fraction completed per hour', then add fractions
Recall trigger
Picture cooking rice with someone else
Age Problem Variable Assignment
Memory aid
PAST-PRESENT-FUTURE: Always assign your variable to the PRESENT age (easiest to understand), then subtract for PAST, add for FUTURE. Think PPF like 'Please Pay First' - always start with Present!
Why it works
The acronym PPF mirrors a common Filipino business phrase, and starting with present ages is the most logical approach.
Example usage
Let x = present age, then (x-3) = 3 years ago, (x+5) = 5 years from now
Recall trigger
Think 'Please Pay First' - start with Present age
Number Problem Translation Order
Memory aid
When translating sentences, follow LORI: Look for the variable noun first, Order operations from left to right, Remember to switch for 'less than' and 'subtracted from', Identify the equals word (is, was, will be).
Why it works
LORI is a common Filipino name, making the 4-step process personal and memorable through name association.
Example usage
For 'twice a number decreased by 5 equals 13', LORI helps: Look (number=x), Order (2x-5), Remember (no switching needed), Identify (equals) → 2x-5=13
Recall trigger
Think of your friend LORI helping you translate
Digit Problem Reversal Logic
Memory aid
Reversing digits is like flipping a playing card: If the original number is 10x + y (like King of Hearts = 10×King + Hearts), then the reversed number is 10y + x (like Hearts of King = 10×Hearts + King). Same cards, different order!
Why it works
Playing cards are familiar and the suit-number reversal perfectly mirrors digit reversal in an entertaining way.
Example usage
Original: 10x + y, Reversed: 10y + x, like flipping card components
Recall trigger
Picture flipping a playing card to reverse its parts
Compound Interest vs Simple Interest
Memory aid
Simple interest is like lending to a friend - they pay the same amount each period, never growing. Compound interest is like viral TikTok videos - it grows on TOP of previous growth! Your money earns money, then that earned money ALSO earns money.
Why it works
The TikTok viral analogy perfectly captures exponential growth that teenagers understand, contrasting with simple linear friend-lending.
Example usage
Simple: same interest each period. Compound: interest earns interest, like viral growth
Recall trigger
Think: friend loan vs viral TikTok growth
Motion Problem Time Units
Memory aid
Picture a jeepney speedometer with THREE clocks: Big clock shows HOURS (kph matches this), medium clock shows MINUTES (convert by ÷60), small clock shows SECONDS (convert by ÷3600). Always match your speed units to time units!
Why it works
Jeepney dashboard is familiar to Filipino students, and three different clocks create visual unit hierarchy.
Example usage
If speed is kph (per hour), time must be in hours. If speed is m/s, time must be seconds
Recall trigger
Look at jeepney dashboard with three clocks
Word Problem Verification Strategy
Memory aid
After solving, CHECK using SANA: Substitute your answer, Are the units correct? Numbers make sense? Answer fits the question? SANA means 'hopefully' - hopefully your answer is right!
Why it works
SANA is a common Filipino word expressing hope, making the checking process feel natural and culturally relevant.
Example usage
Found x=5? SANA check: Substitute 5, Are units right? 5 makes sense? Answers the question?
Recall trigger
Say 'SANA correct!' and verify using each letter
Revision game
This Filipino superhero's flight formula helps solve motion problems
Answer
Darna (D = V × T)
Memory link
Anchor A8 - Darna Visits Tondo formula
What do you shout when your investment earns money?
Answer
I PaRTy! (I = P × R × T)
Memory link
Anchor A11 - Interest formula celebration
This dessert teaches us about solution mixtures
Answer
Halo-halo
Memory link
Anchor A10 - Halo-halo solution analogy
What does Tita Rosa split between two banks?
Answer
Her pasalip money (investment splitting)
Memory link
Anchor A13 - Investment scenario story
Like viral TikTok videos, this type of interest grows on growth
Answer
Compound interest
Memory link
Anchor A18 - Viral growth analogy
What vehicle route system helps understand two-digit numbers?
Answer
Jeepney routes (10x + y)
Memory link
Anchor A5 - Jeepney route analogy
Which house rooms represent past, present, and future ages?
Answer
Kitchen (past), Living room (present), Bedroom (future)
Memory link
Anchor A6 - House timeline method
What do you say hopefully after solving to check your answer?
Answer
SANA (Substitute, Are units right, Numbers make sense, Answer fits)
Memory link
Anchor A20 - SANA verification
Formula mnemonics
D = V × T
Mnemonic
Darna Visits Tondo - Distance = Velocity × Time
When to use
All motion problems involving distance, speed, and time relationships
What each part means
D is distance traveled, V is velocity/speed, T is time duration
Work Rate: 1/n + 1/m = 1/h
Mnemonic
One over N plus one over M equals one over H - like filling pools with multiple faucets
When to use
When two or more people/machines work together on the same job
What each part means
n = time person 1 works alone, m = time person 2 works alone, h = time working together
I = P × R × T
Mnemonic
I PaRTy! - Interest = Principal × Rate × Time
When to use
Simple interest investment and loan problems
What each part means
I = interest earned, P = principal amount invested, R = interest rate, T = time period
Two-digit number: 10x + y
Mnemonic
Jeepney route: 10 times the main route plus the specific stop
When to use
Digit problems involving two-digit number relationships
What each part means
x = tens digit, y = ones digit, 10x gives tens place value, y gives ones place value
Consecutive integers: x, x+1, x+2, ...
Mnemonic
Stepping stones across river - each stone is 1 step apart
When to use
Problems with consecutive whole numbers
What each part means
x = first integer, each next integer adds 1 more
Consecutive odd/even: x, x+2, x+4, ...
Mnemonic
Wide stepping stones - each stone is 2 steps apart for odd or even
When to use
Problems with consecutive odd numbers or consecutive even numbers
What each part means
x = first odd/even number, each next number adds 2
Mixture: (% × Volume) gives Pure Solute amount
Mnemonic
Halo-halo recipe: percentage of flavoring times total volume gives actual flavor amount
When to use
All mixture and solution problems
What each part means
% = concentration as decimal, Volume = total solution amount, Pure Solute = actual substance amount
Quick recall chains
Word Problem Solving Steps
Recall test
What are the 6 steps to solve any word problem?
Memory chain
REP ESP - Rapper ESP with psychic powers: READ the problem, REPRESENT with variables, RELATE variables, then ESP (EQUATE-SOLVE-PROVE) with supernatural math powers
Items to remember
- READ
- REPRESENT
- RELATE
- EQUATE
- SOLVE
- PROVE
Types of Word Problems
Recall test
What are the 6 main types of word problems covered?
Memory chain
NAW-MiMi: Number problems, Age problems, Work problems, then Motion-Mixture-Investment (MiMi sounds like 'Me-Me' - all about me managing different problem types)
Items to remember
- Number
- Age
- Work
- Motion
- Mixture
- Investment
Motion Problem Scenarios
Recall test
What are the three main motion problem scenarios and their distance relationships?
Memory chain
SOR: Same=equal, Opposite=add, Round=total. Think of SORry for getting motion problems wrong before learning this!
Items to remember
- Same direction - distances equal when caught
- Opposite directions - distances add to total
- Round trip - use total distance
Investment Problem Setup
Recall test
What are the 4 key components of investment problems?
Memory chain
PDIS: Principal Divides Into Splits, Different Interest rates, Interest relationship Statement, Solve for splits. Think 'Please Don't Ignore Solutions'
Items to remember
- Principal splits into two parts
- Different rates for each part
- Interest relationship given
- Solve for how much at each rate
Age Problem Time Frames
Recall test
How do you handle different time frames in age problems?
Memory chain
Walk through house: Present in living room, Past in kitchen (subtract), Future in bedroom (add), Same aging rate as you walk through
Items to remember
- Present ages (assign variables)
- Past ages (subtract years)
- Future ages (add years)
- Same aging rate for everyone
Diagrams
Word Problems Master Map
Overview of all word problem types and their key concepts, showing the interconnected nature of different problem categories
Word Problem Solving Decision Tree
Step-by-step decision tree for identifying problem types and applying the correct solution method
Translation Keywords System
Visual representation of the SAMS phone system for remembering mathematical operation keywords
UPCAT Word Problem Distribution
Distribution of word problem types typically found in UPCAT exams, helping students prioritize study time
Problem Solving Timeline
Sequential timeline showing the 6-step REP ESP process for solving any word problem systematically