The UPSC Strategy in Action

Emma has 24 stickers. She gives 8 stickers to her brother and then buys 12 more. How many stickers does Emma have now?

UNDERSTAND: What do we know?: Emma starts with 24 stickers, gives away 8, then gets 12 more = Start: 24, Give: 8, Get: 12

UNDERSTAND: What are we finding?: How many stickers Emma has at the end = Find the final amount

PLAN: What operations do we need?: Give away = subtract, Get more = add = $24 - 8 + 12$

SOLVE: Do the math in order: $24 - 8 = 16$, then $16 + 12 = 28$ = $28$ stickers

CHECK: Does it make sense?: She gave some away (less) then got more (more). 28 > 24. Yes! = Answer is reasonable

Answer: Emma has $28$ stickers.

Finding Hidden Information

A pizza has 8 slices. Marcus ate 3 slices and his sister ate twice as many as Marcus. How many slices are left?

UNDERSTAND: List what we know: Total: 8 slices. Marcus: 3 slices. Sister: twice as many as Marcus = Key info identified

UNDERSTAND: Find hidden info: "Twice as many as Marcus" means $2 \times 3 = 6$ slices = Sister ate 6 slices

PLAN: Choose the operations: Total slices eaten, then subtract from 8 = $8 - (3 + 6)$

SOLVE: Calculate: $3 + 6 = 9$ slices eaten. But wait! $9 > 8$! = Problem has an issue!

CHECK: Re-read the problem: If they ate 9 slices but only 8 exist, the answer is 0 (or they need more pizza!) = $0$ slices left

Answer: There are $0$ slices left (they actually needed more pizza!).

Multi-Step Problem

A farmer has 45 apples. He puts them into bags of 5 apples each. He sells 4 bags and gives 2 bags to his neighbor. How many apples does he have left?

UNDERSTAND: Identify all the information: 45 apples, 5 per bag, sells 4 bags, gives 2 bags = Four pieces of info

PLAN: Break into smaller steps: Step A: Find total bags. Step B: Find bags given away. Step C: Find apples left = 3-part plan

SOLVE Step A: How many bags total?: $45 \div 5 = 9$ bags = 9 bags total

SOLVE Step B: How many bags left?: $9 - 4 - 2 = 3$ bags remaining = 3 bags left

SOLVE Step C: How many apples?: $3 \times 5 = 15$ apples = 15 apples

CHECK: Verify with different method: Bags gone: $4 + 2 = 6$. Apples gone: $6 \times 5 = 30$. Left: $45 - 30 = 15$ = Confirmed!

Answer: The farmer has $15$ apples left.

Mistake: Starting to calculate before fully reading the problem

Why: Students see numbers and immediately start adding or multiplying, missing important details or the actual question.

Correct: Always complete the UNDERSTAND step first. Read the entire problem, identify what you know and what you need to find.

Mistake: Ignoring key words that indicate operations

Why: Words like 'altogether,' 'remaining,' 'each,' and 'shared equally' tell you what operation to use.

Correct: Highlight or underline key words. 'Total' often means add, 'left' often means subtract, 'each' often means multiply or divide.

Mistake: Forgetting to check if the answer makes sense

Why: A calculation error might give an impossible answer (like negative apples or more than you started with).

Correct: Always ask: Does this answer make sense for the story? Is it reasonable?

Mistake: Answering a different question than what was asked

Why: The problem might ask for the remaining amount, but students calculate the total.

Correct: Circle or highlight the question. Before writing your final answer, re-read what the problem asks for.

Shopping and Budgeting

Every shopping trip involves word problems: Do I have enough money? How much change will I get?

You have 20 dollars. A book costs 12 dollars and a pen costs 3 dollars. How much money will you have left after buying both?

Sharing Fairly

Dividing things equally among friends or family is a common word problem.

You have 24 cookies to share equally among 6 friends. How many cookies does each friend get?

Time and Scheduling

Planning your day often requires solving word problems about time.

You need to be at school by 8:00 AM. It takes 15 minutes to get ready and 20 minutes to walk. What time should you wake up?

Q: What if I don't understand the problem even after reading it twice?

A: Try drawing a picture or diagram. Act out the problem with objects. Rewrite it in your own words. Sometimes breaking it into smaller pieces helps!

Q: How do I know which operation to use?

A: Look for key words: 'altogether' or 'total' often mean add; 'left' or 'remaining' often mean subtract; 'each' or 'per' often mean multiply or divide; 'shared equally' usually means divide.

Q: What if there's extra information I don't need?

A: Some problems include extra details to make them more realistic. Focus on what the question asks, and only use the information needed to answer that specific question.

Q: Is it okay to solve problems in my head?

A: For simple problems, yes! But writing down your work helps you catch mistakes, especially for multi-step problems. It also lets you check your work easily.