Add and subtract whole numbers: word problems
key notes :
1.Understanding the Problem
- Read Carefully: Teach students to read the word problem carefully and more than once to ensure they understand what is being asked.
- Identify Keywords: Look for keywords that indicate whether to add or subtract.
- Addition Keywords: Sum, total, in all, combined, together, plus, increase.
- Subtraction Keywords: Difference, how many more, less, decrease, remain, subtract, minus.
2. Identify the Operation
- Determine the Operation: Decide whether the problem requires addition or subtraction based on the keywords and context.
- Example: “If you have 150 apples and you give away 45, how many do you have left?” – This requires subtraction.
3. Breaking Down athe Problem
- Underline Key Information: Highlight or underline the numbers and important details in the problem.
- Write Down the Equation: Translate the word problem into a mathematical equation.
- Example: “Maria has 120 stickers. She buys 35 more. How many stickers does she have now?”
- Equation: 120+35=155
- Example: “Maria has 120 stickers. She buys 35 more. How many stickers does she have now?”
4. Solving the Problem
- Perform the Calculation: Add or subtract the numbers as required by the problem.
- Double-Check: Encourage students to check their work to ensure the calculation is correct.
5. Answer the Question
- Complete the Answer: After solving the equation, ensure students answer the question in the context of the problem.
- Example: “Maria has 155 stickers now.”
6. Practice with Examples
- Addition Word Problem: “There are 238 students in the school. If 125 more students join, how many students are there in total?”
- Solution: 238+125=363 students.
- Subtraction Word Problem: “John had 500 baseball cards. He gave 147 to his friend. How many cards does he have left?”
- Solution: 500−147=353 cards.
7. Problem-Solving Strategies
- Estimation: Before solving, estimate the answer to see if your final answer is reasonable.
- Draw a Picture: Sometimes drawing a picture or using a number line helps visualize the problem.
- Work Backward: If the problem is complex, start with the final information and work backward to figure out what is needed.
8. Multi-Step Word Problems
- Multiple Operations: Some word problems require both addition and subtraction (or multiple additions/subtractions).
- Example: “Sarah bought 3 packs of pencils with 12 pencils each. She gave 15 pencils to her friend. How many pencils does she have now?”
- Solution: First, find the total pencils: 3×12=36.
- Then subtract: 36−15=21 pencils.
- Example: “Sarah bought 3 packs of pencils with 12 pencils each. She gave 15 pencils to her friend. How many pencils does she have now?”
Learn with an example
🗼 Newberg Paper Company just sent 21,273 cases of paper to a customer. Of those cases, 8,957 cases have lined paper. The rest have unlined paper.
How many cases have unlined paper?
_______ cases
- Subtract the number of cases of lined paper from the total number of cases.
- Subtract:
- Subtract the ones. You need to carry over first. Subtract 13 − 7.
- Subtract the tens. Subtract 6 − 5.
- Subtract the hundreds. You need to carry over first. Subtract 12 − 9.
- Subtract the thousands. You need to carry over first. Subtract 10 − 8.
- Subtract the ten thousands.
- The difference is 12,316. 12,316 of the cases are unlined paper.
🗼 A carnival makes most of its money from the bumper cars and the horse race game. Last year, it pulled in ₹87,420 from the bumper cars and ₹38,139 from the horse race game. In all,
how much did those two games make?
₹______
- Add the amounts of money.
- Add:
- 87,420 + 38,139 =
- Add the ones. Add 0 + 9.
- Add the tens. Add 2 + 3.
- Add the hundreds. Add 4 + 1.
- Add the thousands. Add 7 + 8. Remember to carry over.
- Add the ten thousands. Add 1 + 8 + 3.
- The sum is 125,559. The carnival made ₹125,559 from those two games.
🗼 Since he was hired, a chef has served a total of 63,259 guests. Of those guests, 12,673 were adults.
How many children has the chef served?
______ children
- Subtract the number of adults served from the total number of guests.
- Subtract:
- 63,259 – 12,673 =
- Subtract the ones.
- Subtract the tens. You need to carry over first. Subtract 15 − 7.
- Subtract the hundreds. You need to carry over first. Subtract 11 − 6.
- Subtract the thousands. Subtract 2 − 2.
- Subtract the ten thousands.
- The difference is 50,586. The chef has served 50,586 children.
Let’s practice!