A girl with a clipboard outside a busy, colorful stadium

The Big Ticket Count

Maya counts tickets at the stadium all weekend. Huge crowds came both days! Can she add and subtract big numbers to report the totals?

4th Grade Math

Step 1: Add the Ones

Saturday sold 2,458 tickets. Sunday sold 3,675 tickets. To find the sum, line up the digits by place value. Start with the ones: 8 ones and 5 ones.

8 + 5 = 13 ones. That is more than 9, so we regroup: write 3 in the ones place and carry 1 ten.

Step 2: Add the Tens

1 2,458 + 3,675 ……3

Now look only at the tens column. We have 5 tens, 7 tens, and the 1 ten we carried. How many tens in all?

5 + 7 + 1 = 13 tens. Regroup again: write 3 in the tens place and carry 1 hundred. Do not forget the carried ten!

Step 3: Finish the Sum

1 1 2,458 + 3,675 ……33

Hundreds: 4 + 6 + 1 carried = 11 hundreds. Write 1 and carry 1 thousand. Thousands: 2 + 3 + 1 = 6. What is the total weekend ticket count?

2,458 + 3,675 = 6,133 tickets. Every carry counts: hundreds made 11, so 1 hundred stayed and 1 thousand moved over.

Let's Remember

The Standard Algorithm

          Step 1: Line up digits by place value.

          Step 2: Start with the ones. Work right to left.

          Step 3: Regroup when a column is more than 9.

          Step 4: Estimate to check that your answer makes sense.

Maya says: Subtraction uses the same plan! But sometimes a top digit is too small. Then we regroup the other way — we borrow.

Now Subtract!

How many more tickets did Sunday sell? We must determine the difference: 3,675 − 2,458. Look at the ones: 5 − 8. We cannot take 8 from 5!

3,675 − 2,458 ?

Borrow 1 ten: 7 tens become 6 tens, and 5 ones become 15 ones. Then 15 − 8 = 7. Finish: 6 − 5 = 1 ten, 6 − 4 = 2 hundreds, 3 − 2 = 1 thousand. The difference is 1,217.

Watch Out!

A Sneaky Mistake

          Some kids see 5 − 8 and flip it to 8 − 5 = 3.

          That gives 3,675 − 2,458 = 1,223. Wrong!

          The top number tells the true amount. Never flip the digits —
          regroup instead.

Maya says: Check with the inverse operation. Does 1,217 + 2,458 = 3,675? Yes! Addition proves the subtraction is right.

Check with a Number Line

Maya estimates to check her sum of 6,133. Between which two thousands does 6,133 land?

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

6,133 is a little more than 6,000, so it sits between 6,000 and 7,000. The estimate 2,000 + 4,000 = about 6,000 matches. The answer is reasonable!

Solve It!

4,286 + 3,957 = ?

No hints this time. Line up the place values and watch the carries!

Ones: 6 + 7 = 13, write 3 carry 1. Tens: 8 + 5 + 1 = 14, write 4 carry 1. Hundreds: 2 + 9 + 1 = 12, write 2 carry 1. Thousands: 4 + 3 + 1 = 8. Sum: 8,243.

Word Problem

The city library owns 5,342 books. This month, readers checked out 1,675 books. How many books are still on the shelves?

5,342 − 1,675 = 3,667. Ones: regroup, 12 − 5 = 7. Tens: regroup, 13 − 7 = 6. Hundreds: regroup, 12 − 6 = 6. Thousands: 4 − 1 = 3. Check: 3,667 + 1,675 = 5,342.

What Goes in the Blank?

2,850 + ? = 6,000

Hint: subtraction is the inverse of addition. Use it to find the missing number.

6,000 − 2,850 = 3,150. Check by adding: 2,850 + 3,150 = 6,000. Addition and subtraction undo each other!

Challenge!

The stadium's season goal is 100,000 tickets. Fans used 6,133 tickets this weekend. How many more tickets must they sell to reach the goal? Careful — those zeros need lots of regrouping!

100,000 − 6,133 = 93,867. Regroup across every zero: think of 100,000 as 9 ten-thousands, 9 thousands, 9 hundreds, 9 tens, and 10 ones. Then 10 − 3 = 7, 9 − 3 = 6, 9 − 1 = 8, 9 − 6 = 3, and 9 stays. Check: 93,867 + 6,133 = 100,000.

Compare and contrast: How is regrouping in addition like regrouping in subtraction? How is it different?

Think about it: In addition, extras move up to the next place. In subtraction, we borrow down from the next place. Both trade 10 of one unit for 1 of the next!

Great Work!

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correct

regroup sum difference place value estimate inverse