Grade by Grade
B. Number · Operations: Adding, Subtracting and Equal Groups

Adding Two-Digit Numbers to 100

B2.4 B2.1About 35 minutes
Learning goals
  • I can add two-digit numbers with sums up to 100.
  • I can show adding with base-ten blocks, a number line or a drawing.
  • I can trade 10 ones for 1 ten when I have 10 or more ones.
  • I can write an equation to match an adding problem.

Words to know

base-ten blocks
Blocks for showing numbers. A long rod is 1 ten. A small cube is 1 one.
trade (regroup)
To swap 10 ones for 1 ten, because they are worth the same amount.
open number line
A number line you draw yourself with only the numbers you need, to show jumps.
equation
A number sentence with an equal sign, like 36 + 25 = 61.
total
The amount you get when you put everything together.

Let's start with a story

The Grade 2 class is collecting pop can tabs for a school project. On Monday they count 36 tabs. On Tuesday they bring in 25 more. How many tabs do they have now?

The total will be bigger than 50, so we need ways to add bigger numbers, up to 100. You already know how to add tens and ones in your head. Now we will use tools to add any two-digit numbers.

Remember: tens and ones

A two-digit number is made of tens and ones. 36 is 3 tens and 6 ones. 25 is 2 tens and 5 ones.

With base-ten blocks, a rod is 1 ten and a cube is 1 one. (No blocks at home? Use bundles of 10 straws or popsicle sticks with an elastic, and single sticks for ones.)

36+25
36 is 3 rods and 6 cubes. 25 is 2 rods and 5 cubes.

Adding with blocks

  1. Add the tens: 3 tens + 2 tens = 5 tens (50).
  2. Add the ones: 6 ones + 5 ones = 11 ones.
  3. 11 ones is too many to leave loose! 10 ones make 1 ten. Trade 10 cubes for 1 rod.
  4. Now we have 5 tens + 1 ten = 6 tens, and 1 one left.
  5. 6 tens and 1 one is 61.
61
After trading 10 ones for 1 ten: 6 rods and 1 cube. That is 61.

Why do we trade?

In our number system, each place can only hold up to 9. When you get 10 ones, they become 1 ten. It is like trading 10 loonies for one $10 bill. The amount does not change, it is just easier to count.

Worked example

Example 1: No trading needed

Solve 42 + 35.

  1. Tens: 4 tens + 3 tens = 7 tens = 70.
  2. Ones: 2 + 5 = 7.
  3. 70 + 7 = 77. We have only 7 ones, so no trade is needed.

42 + 35 = 77.

Worked example

Example 2: Trading 10 ones

Solve 48 + 27.

  1. Tens: 4 tens + 2 tens = 6 tens = 60.
  2. Ones: 8 + 7 = 15. That is 1 ten and 5 ones.
  3. Trade 10 ones for 1 ten: 60 + 10 = 70, and 5 ones are left.
  4. 70 + 5 = 75.

48 + 27 = 75. Estimate to check: 50 + 30 = 80. 75 is close.

48+27
48 + 27: 6 rods and 15 cubes. Trade 10 cubes for a rod to get 7 rods and 5 cubes: 75.

Adding on an open number line

You can also start at one number and jump. Jump by tens first, then ones. Jump to a ten when it helps.

36 + 25: Start at 36. Jump 20 (two jumps of 10) to 56. Then jump 4 to 60, and 1 more to 61.

3040506070+10+10+4+1
36 + 25: jump +10, +10, then +4 to 60 and +1 to 61.
Worked example

Example 3: Number line to 100

A family drives 57 km to the cabin in the morning and 34 km more in the afternoon. How far do they drive in all?

  1. Write the equation: 57 + 34 = □.
  2. Start at 57. Jump 30 (three jumps of 10): 67, 77, 87.
  3. Now add 4. Jump 3 to get to the ten, 90. Then 1 more to 91.
  4. Estimate to check: 60 + 30 = 90. 91 is close.

91 km. 57 + 34 = 91.

Worked example

Example 4: Make a friendly number

Solve 39 + 46.

  1. 39 is almost 40. Take 1 from 46 and give it to 39.
  2. Now it is 40 + 45. (We just moved 1, so the total is the same.)
  3. 40 + 45 = 85.

39 + 46 = 85.

TensOnesTrade?Total
30 + 20 = 506 + 5 = 11Yes, 11 = 1 ten + 161
40 + 30 = 702 + 5 = 7No77
40 + 20 = 608 + 7 = 15Yes, 15 = 1 ten + 575
50 + 30 = 807 + 4 = 11Yes, 11 = 1 ten + 191
Adding tens and ones for 36 + 25, 42 + 35, 48 + 27 and 57 + 34

Three steps every time

  1. Estimate first (closest tens).
  2. Solve with a tool or strategy you like: blocks, a number line, or tens and ones.
  3. Check: Is your answer close to your estimate? You can also add in a different order (25 + 36) and see if you get the same total.
Just for fun

Why did 10 ones cubes go to the bank together?

To trade themselves in for one shiny ten!

Hands-on activity

Straw bundle store

You need: about 100 straws, popsicle sticks or toothpicks, some elastics, paper and a pencil.

  1. Make bundles of 10 with elastics. Make 9 bundles and keep 10 loose.
  2. A grown-up writes two numbers, like 47 + 28.
  3. Build each number with bundles and loose sticks.
  4. Push the bundles together and count the tens. Push the loose sticks together and count the ones.
  5. If you have 10 or more loose sticks, wrap 10 together with an elastic. That's a trade!
  6. Count the total and write the equation: 47 + 28 = 75.

Try 5 questions. At least 3 should need a trade.

Your turn

1

23 + 45 = ?

2

37 + 26 = ?

3

58 + 30 = ?

4

45 + 45 = ?

5

64 + 18 = ? Draw the jumps on a number line.

6

A library has 52 picture books and 39 chapter books on a cart. How many books are on the cart? Write the equation.

7

Do you need to trade for 31 + 47? Why?

More practice: warm-up

1

20 + 30 = ?

2

40 + 25 = ?

3

12 + 14 = ?

4

53 + 6 = ?

5

How many ones can you trade for 1 ten?

More practice: on your own

1

29 + 35 = ? Show how you solved it.

2

46 + 46 = ?

3

73 + 19 = ?

4

A farmer picked 66 apples from one row of trees and 27 apples from another row. How many apples did she pick? Estimate first.

5

Kai added 38 + 25 and got 513. What mistake did he make? What is the right answer?

Challenge

1

27 + 38 + 15 = ? Use the math rules to add in a smart order.

2

Find two numbers that add up to 100. Both numbers must have a 5 in the ones place.

3

Fill in the missing digits: 4□ + 2□ = 70, where both missing digits are the same.

Check your understanding

Quiz

1.

What is 34 + 52?

2.

What is 47 + 36?

3.

You have 5 tens and 14 ones. What number is that?

4.

Which is the best estimate for 61 + 28?

5.

Which addition needs a trade (regrouping)?

6.

A Grade 2 class reads 45 books in October and 48 books in November. How many books is that?

For parents and teachers

Big idea: B2.4 asks children to use objects, diagrams and equations to solve addition and subtraction situations with whole numbers that add up to no more than 100. In Grade 2 children are not expected to use the stacked "carry the one" method. They should understand why 10 ones become 1 ten by using blocks, bundles, ten frames and number lines.

Common mistakes:

  • Writing tens and ones side by side (38 + 25 = 513). Go back to bundles and trade 10 loose sticks for a bundle.
  • Adding tens to ones (34 + 5 = 84). Ask: "Is 5 a ten or 5 ones?"
  • Losing count on the number line. Encourage jumping by 10 first, then ones.

How to help: Build numbers with real bundles of 10. Ask your child to estimate first, then solve, then check. Real-life sums (points in a game, kilometres on a trip, pages read) make it meaningful.