B. Number · Operations: Adding, Subtracting and Equal GroupsSubtracting Two-Digit Numbers within 100
B2.4 B2.1About 35 minutes
Learning goals- I can subtract two-digit numbers up to 100.
- I can trade 1 ten for 10 ones when I need more ones.
- I can subtract by jumping back or by counting up on a number line.
- I can check my subtraction by adding.
Words to know
subtract
To take away, or to find the difference between two numbers.
trade (regroup)
To break 1 ten into 10 ones so you have enough ones to take away.
difference
The answer to a subtraction. It tells how much more or less one number is than another.
count up
Start at the smaller number and jump up to the bigger number. The jumps add up to the difference.
check
Make sure an answer is right. For subtraction, add the answer and the number you took away.
Let's start with a story
A bakery made 52 maple cookies for the winter carnival. By noon, 27 cookies were sold. How many cookies are left?
We need 52 − 27. Let's learn three ways to subtract bigger numbers.
Way 1: Base-ten blocks
52 is 5 tens and 2 ones. We need to take away 27, which is 2 tens and 7 ones.
Uh oh! We only have 2 ones. We can't take away 7 ones from 2 ones.
Trade! Break 1 ten into 10 ones. Now 52 is 4 tens and 12 ones. It is still 52, just shown a different way.
Now take away:
- Ones: 12 − 7 = 5.
- Tens: 4 tens − 2 tens = 2 tens (20).
- 20 + 5 = 25.
So 52 − 27 = 25. There are 25 cookies left.
Check by adding
Add the answer and the number you took away. You should get the number you started with.
25 + 27 = 52. It checks out! (20 + 20 = 40, 5 + 7 = 12, 40 + 12 = 52.)
Worked exampleExample 1: No trade needed
- Ones: 8 − 5 = 3. We have enough ones, so no trade.
- Tens: 6 tens − 3 tens = 3 tens = 30.
- 30 + 3 = 33.
68 − 35 = 33. Check: 33 + 35 = 68.
Way 2: Jump back on a number line
Start at the big number and jump back. Take away tens first, then ones. Jump back to a ten when it helps.
52 − 27: Start at 52. Jump back 20 to 32. Now take away 7: jump back 2 to 30, then 5 more to 25.
Way 3: Count up (think addition)
Subtraction can also mean finding the difference between two numbers. Start at the smaller number and count up to the bigger one.
52 − 27: Start at 27. Jump 3 to 30. Jump 20 to 50. Jump 2 to 52. Add up the jumps: 3 + 20 + 2 = 25.
Worked exampleExample 2: Count up when numbers are close
- The numbers are close together, so count up.
- Start at 76. Jump 4 to 80. Jump 1 to 81.
- 4 + 1 = 5.
Worked exampleExample 3: Jump back from 100
Mr. Singh has 100 sheets of paper. The class uses 45. How many are left?
- Write it: 100 − 45 = □.
- Jump back 40: 100 → 60.
- Jump back 5: 60 → 55.
- Check: 55 + 45 = 100. (50 + 40 = 90, 5 + 5 = 10, 90 + 10 = 100.)
Worked exampleExample 4: Comparing
Emma read 63 pages this week. Owen read 48 pages. How many more pages did Emma read?
- "How many more" means find the difference. Subtract: 63 − 48.
- Count up from 48: jump 2 to 50, jump 10 to 60, jump 3 to 63.
- 2 + 10 + 3 = 15.
Emma read 15 more pages. Check: 48 + 15 = 63.
A comparing bar. Emma's bar is 63. Owen's bar is 48. The difference is the dashed part: 15.Which way should I use?
- Ones are big enough? Take away tens and ones.
- Not enough ones? Trade a ten, or jump back to a ten.
- Numbers close together, or a "how many more" question? Count up.
All the ways give the same answer. Use the one that makes sense to you!
Just for funWhat did the ten say when it was traded for 10 ones?
"I feel like I'm falling to pieces. Ten of them, to be exact!"
Hands-on activitySnack shop subtraction
You need: bundles of 10 straws or sticks (from the adding lesson), 10 loose sticks, and paper.
- Make 72 with 7 bundles and 2 loose sticks.
- A grown-up says: "A customer buys 35."
- Look at the ones. Do you have 5 loose sticks? No! Open one bundle (take off the elastic) so you have 12 loose sticks.
- Take away 5 loose sticks and 3 bundles. Count what is left: 3 bundles and 7 sticks = 37.
- Check by adding: 37 + 35 = 72.
- Play 5 rounds. Then try the same questions by counting up on a number line you draw.
Your turn
34. Ones: 7 − 3 = 4. Tens: 5 − 2 = 3 tens. 34. Check: 34 + 23 = 57.
26. Trade: 44 = 3 tens and 14 ones. 14 − 8 = 6. 3 tens − 1 ten = 2 tens. 26.
60. 9 tens − 3 tens = 6 tens.
54. 80 − 20 = 60. 60 − 6 = 54.
6There were 95 people at the hockey game. 40 left after the second period. How many stayed?
55 people. 95 − 40 = 55. Check: 55 + 40 = 95.
7Kim says 63 − 29 = 34. Check by adding. Is she right?
34 + 29 = 63. 30 + 20 = 50, 4 + 9 = 13, 50 + 13 = 63. Yes, she is right.
More practice: warm-up
25. 9 − 4 = 5, 3 − 1 = 2 tens.
More practice: on your own
162 − 37 = ? Show your strategy.
25. Count up from 37: +3 to 40, +20 to 60, +2 to 62. 3 + 20 + 2 = 25. (Or jump back: 62 − 30 = 32, 32 − 2 = 30, 30 − 5 = 25.)
36. 85 − 50 = 35, but we took away 1 too many, so add 1 back: 36. Check: 36 + 49 = 85.
28. Count up from 72: +8 to 80, +20 to 100. 8 + 20 = 28.
4A class trip to the science centre has 54 students. 18 are in Grade 1 and the rest are in Grade 2. How many Grade 2 students are there?
36 students. 54 − 18: 54 − 10 = 44, 44 − 4 = 40, 40 − 4 = 36. Check: 36 + 18 = 54.
5Leo got 43 − 17 = 34. What did he do wrong?
He took 3 away from 7 (7 − 3 = 4) instead of 7 from 3. He needed to trade: 43 = 3 tens and 13 ones. 13 − 7 = 6, 3 − 1 = 2 tens. 43 − 17 = 26.
Challenge
1Find the missing number: □ − 35 = 47
82. The missing number is the whole. Add the parts: 47 + 35 = 82. (40 + 30 = 70, 7 + 5 = 12, 70 + 12 = 82.)
2A toboggan hill is climbed by 91 kids in one afternoon. 46 of them climb it before 2 o'clock. How many climb it after 2 o'clock? Explain how you know your answer is reasonable.
45 kids. Count up from 46: +4 to 50, +41 to 91. 4 + 41 = 45. Estimate: 90 − 50 = 40, and 45 is close. Check: 45 + 46 = 91.
3Use the digits 3, 5, 7 and 1 once each to make two two-digit numbers with the biggest difference you can.
75 − 13 = 62. Make the biggest number (75) and the smallest number (13). Check: 62 + 13 = 75.
Quiz
2. For 53 − 18, why do we trade?
4. Which addition checks that 90 − 37 = 53?
6. Ava has 81 beads. Mia has 79 beads. How many more beads does Ava have?
Big idea: B2.4 includes subtraction situations with numbers to 100, solved with objects (blocks, bundles), diagrams (number lines, bar models) and equations. B2.1 asks children to check their calculations by using the relationship between addition and subtraction. The stacked "borrowing" algorithm is not expected in Grade 2.
Common mistakes:
- Subtracting the smaller digit from the bigger one in each place (43 − 17 = 34). This is the most common error. Build the number with bundles so your child sees they must open a bundle.
- Counting up but forgetting to add all the jumps. Write each jump above the number line and add them at the end.
- Checking by adding the wrong numbers. Check 52 − 27 = 25 with 25 + 27, not 52 + 27.
How to help: Use real situations: "We need 40 sandbags and have 26. How many more?" Let your child pick a strategy and explain it. Ask "Is your answer reasonable?" and estimate together.