Whole number Word Problems

Virginia Standard Breakdown

5.CE.1 – What this means for 5th graders:

Students will practice solving real-world math problems using addition, subtraction, multiplication, and division. They’ll need to explain their thinking, show their work, and check if their answers make sense.

What Students Will Learn to Do:

• Estimate answers – Make a smart guess before solving (for example, “about 300” instead of “exactly 297”).

• Solve problems step by step – Use math strategies and standard methods (like the long division algorithm) to work through problems with more than one step.

• Show and explain their reasoning – Not just get the answer, but explain how they solved it and why their answer makes sense.

• Work with numbers up to certain limits:

  • Addition, subtraction, multiplication answers won’t go over 5 digits (like 12,345).

  • Multiplication problems will be no bigger than 2-digit × 3-digit numbers (like 27 × 324).

  • Division problems will have divisors no larger than 2 digits (like dividing by 15).

  • Division problems will have dividends no larger than 4 digits (like dividing 3,426 ÷ 12).

• Understand remainders – Know what to do when there’s a leftover number in division (for example, if 25 cookies are shared among 6 kids, each gets 4 cookies and 1 is left over).

When will I ever use this?

You’ll use these math skills in lots of jobs one day:

• Chef – Multiply recipes to cook for a big group.

• Builder – Add and subtract to measure wood or bricks.

• Cashier – Divide money to give the right change.

• Coach – Use multiplication to figure out team scores or stats.

• Event planner – Estimate how much food, chairs, or supplies are needed.

👉 Math helps in almost every job—you’ll use adding, subtracting, multiplying, dividing, and estimating to solve real-world problems!

Terms to know

• Estimate – A smart guess that’s close to the real answer.

• Sum – The answer to an addition problem.

• Difference – The answer to a subtraction problem.

• Product – The answer to a multiplication problem.

• Quotient – The answer to a division problem.

• Remainder – What is left over after dividing.

• Dividend – The number you want to split up in division. (Ex: 24 ÷ 6 → 24 is the dividend).

• Divisor – The number you are dividing by. (Ex: 24 ÷ 6 → 6 is the divisor).

• Algorithm – A step-by-step method to solve a problem (like long division).

• Contextual Problem – A real-life word problem, not just plain numbers.

• Multi-step Problem – A problem that takes more than one operation to solve (for example, adding then dividing).

• Justify – To explain why your answer makes sense.

• Strategy – A plan or trick you use to solve a problem (like drawing a picture or rounding first).
  
  

Adding with the standard algorithm 

1. Stack and line up the numbers by place value (ones, tens, hundreds, thousands, ten-thousands).

2. Add the ones. If the sum is 10 or more, carry the tens to the next column.

3. Add the tens (plus any carry). Carry again if needed.

4. Add the hundreds, then thousands, then ten-thousands, always adding any carry.

5. Write the final answer (use a comma after the thousands place).

Subtracting with the Standard Algorithm

1. Stack and line up the numbers by place value (ones, tens, hundreds, thousands, ten-thousands).

2. Start with the ones place. Subtract the bottom number from the top. If the top digit is smaller, borrow from the next column.

3. Move to the tens. Subtract, borrowing if needed.

4. Do the same with hundreds, thousands, and ten-thousands, always borrowing when the top digit is smaller than the bottom digit.

5. Write the answer neatly under the line.

Multiplying with the Standard algorithm 

1. Line up the numbers vertically by place value (ones under ones, tens under tens). Draw a line under them.
   
   

2. Multiply by the ones digit of the bottom number. Work right → left, write each digit below the line and carry any tens to the next column.
   
   

3. Multiply by the tens digit of the bottom number (this actually means “times 10, 20, 30…”). Write the partial product shifted one place to the left (or put a zero in the ones place), and carry as needed.
   
   

4. Add the two partial products to get the final answer.
   
   

5. Check quickly with estimation (round numbers) to see if the answer is reasonable.

Multiplying with the Lattice method

1. Draw a 3 × 2 grid (3 columns for the 3-digit number, 2 rows for the 2-digit number).

2. Put the digits of the 3-digit number (4, 0, 7) across the top (one digit per column).

3. Put the digits of the 2-digit number (3, 6) down the right side (one digit per row).

4. In each box, multiply the top digit × side digit and write the two-digit product with the tens digit in the upper triangle and the ones digit in the lower triangle. (If the product is a single digit, write a 0 for the tens place.)

5. Add the numbers along the diagonals (carry to the next diagonal on the left if needed).

6. Read the final answer from leftmost diagonal to rightmost diagonal.

Long Division (with Remainders) 

1. Look at the leftmost digits of the dividend until the number is at least as big as the divisor.
   
   

2. Ask “How many times does the divisor go into that number?” Write that digit on top (the quotient).
   
   

3. Multiply that quotient digit × divisor and subtract from the number you looked at.
   
   

4. Bring down the next digit from the dividend.
   
   

5. Repeat (how many times does divisor go into the new number?). Put 0 in the quotient if it goes in 0 times.
   
   

6. When there are no more digits to bring down, what’s left is the remainder. Check: divisor × quotient + remainder = dividend.

Key words in word problems to look for