B. Number · Adding and Subtracting

Solving Story Problems up to 50

B2.4 B2.1 B2.3About 35 minutes

Learning goals

I can show a story problem with objects, a drawing, or a bar model.
I can write an equation (number sentence) for a story.
I can solve problems where the start, the change, or the end is missing.
I can add and subtract with numbers up to 50 using tens and ones.
I can check if my answer makes sense.

Words to know

equation
A number sentence with an equal sign, like 20 + 5 = 25.

unknown
The number we don't know yet. We can show it with a box: □ or a question mark.

tens and ones
Ways to break up a number. 34 is 3 tens and 4 ones.

bar model
A drawing of bars that shows the parts and the whole of a story.

Be a math detective!

Story problems are like puzzles. A good detective follows steps. Here are ours:

Step	What to do
1. Read	Read the story (or listen) two times. What is happening?
2. Show	Show it with objects, a drawing, a number line or a bar model.
3. Write	Write an equation. Use □ for the number you don't know.
4. Solve	Use a strategy you know.
5. Check	Does the answer make sense? Check it another way.

The 5 detective steps

Numbers up to 50: tens and ones

Bigger numbers are made of tens and ones. 23 is 2 tens and 3 ones. Bundles of 10 make bigger numbers easy to add.

23 is 2 tens (two tall rods of 10) and 3 ones (3 small squares).

Worked example

Example 1: Adding tens and ones

On Canada Day, Zoe hands out 23 small flags. Her cousin hands out 14 flags. How many flags did they hand out altogether?

Read: Two groups are put together. We add.
Write: 23 + 14 = □
Show and solve: 23 is 2 tens and 3 ones. 14 is 1 ten and 4 ones.
Add the tens: 2 tens + 1 ten = 3 tens (30).
Add the ones: 3 + 4 = 7 ones.
3 tens and 7 ones is 37.
Check: 37 − 14 should give 23. 3 tens − 1 ten = 2 tens, and 7 − 4 = 3 ones. 23! Yes.

They handed out 37 flags. 23 + 14 = 37.

23 + 14 = 37. That's 3 tens and 7 ones.

Worked example

Example 2: Counting on by tens

25 + 20 = □

20 is 2 tens. Start at 25 and count on by tens.
25 ... 35, 45.

25 + 20 = 45

25 + 20: start at 25, jump 10 to 35, jump 10 more to 45.

Worked example

Example 3: Taking away

There are 38 apples in a basket at the orchard. Families pick 15 of them. How many apples are left?

Read: Apples are taken away. We subtract.
Write: 38 − 15 = □
Solve: Take away the tens: 3 tens − 1 ten = 2 tens.
Take away the ones: 8 − 5 = 3 ones.
2 tens and 3 ones is 23.
Check: 23 + 15 = 38. Yes!

23 apples are left. 38 − 15 = 23.

Worked example

Example 4: Going past a ten

Jack has 28 hockey cards. He gets 5 more for his birthday. How many does he have now?

Write: 28 + 5 = □
Make the next ten: 28 needs 2 to get to 30. Break 5 into 2 and 3.
28 + 2 = 30. Then 30 + 3 = 33.
Check by estimating: 28 is close to 30, and 30 + 5 = 35. 33 is close to that. It makes sense!

Jack has 33 hockey cards. 28 + 5 = 33.

28 + 5: jump 2 to 30, then 3 more to 33.

When the change is missing

Sometimes we know the start and the end, but not what happened in the middle.

Worked example

Example 5: Missing change

Priya had 12 beads. Her auntie gave her some more beads. Now she has 20 beads for her beadwork. How many beads did her auntie give her?

Read: She started with 12 and ended with 20. Some beads were added, but we don't know how many.
Write: 12 + □ = 20
Show: Draw a bar model. The whole is 20. One part is 12. The other part is unknown.
Solve: Count up from 12 to 20: 12 + 8 = 20 (because 2 + 8 = 10, so 12 + 8 = 20).
Check: 20 − 12 = 8. Yes!

Her auntie gave her 8 beads. 12 + 8 = 20.

Bar model for 12 + □ = 20. The missing part is 8.

Worked example

Example 6: Comparing

Lucas is 45 months old. His sister is 30 months old. How many months older is Lucas?

Read: We are comparing two amounts. How many more? We subtract.
Write: 45 − 30 = □ (or 30 + □ = 45)
Solve: Count up from 30 by tens and ones: 30 → 40 is 10, 40 → 45 is 5. 10 + 5 = 15.
Check: 30 + 15 = 45. Yes!

Lucas is 15 months older.

More than one equation

A story can have more than one correct equation. For Priya's beads, both 12 + □ = 20 and 20 − 12 = □ are correct. They are in the same fact family!

Just for fun

A silly story problem: 25 penguins get on a bus. 20 more penguins get on. How many penguins are on the bus?

45 penguins! (How they paid for the bus is a whole other problem.)

Hands-on activity

Story problem store

You need: small toys or snacks, sticky notes for price tags, and real or play coins.

Make a store with 5 items. Give each a price from 1¢ to 25¢ (use dimes, nickels and counters for 1¢).
A grown-up gives you a problem, like "You buy a 12¢ eraser and a 15¢ pencil. How much do you spend?" (Answer: 27¢.)
Show it with coins or a drawing, then write the equation.
Make up your own problem for the grown-up!

Math talk: "How did you show the problem? Is there another way?"

Your turn

There are 20 kids at the rink. 6 more kids come. How many kids are at the rink now?

31 + 12 = ?

There were 47 maple leaves on a tree. 20 fell off. How many are still on the tree?

Emma had 9 crayons. She found some more. Now she has 15. How many did she find? Write an equation.

A pack has 36 stickers. Ben uses 14. How many are left?

19 + 4 = ?

There are 25 red beads and 40 blue beads. How many more blue beads than red beads?

Write a story problem for 16 + 10 = 26.

More practice: warm-up

30 + 10 = ?

How many tens and how many ones are in 34?

20 + 7 = ?

There are 15 kids on a bus. 2 more kids get on. How many kids are on the bus now?

45 − 10 = ?

More practice: on your own

A Grade 1 class brought 22 cans for the food bank on Monday and 15 cans on Tuesday. How many cans altogether?

A farm stand has 48 ears of corn. People buy 26. How many ears of corn are left?

Owen had 14 pinecones. He found some more. Now he has 20. How many did he find? Write an equation.

27 + 6 = ?

Noah has 35 hockey cards. Mia has 20 hockey cards. How many more cards does Noah have?

Challenge

Find the mistake. Kate solved 43 − 21 and got 64. What did she do wrong?

Sam has 20 stickers. He gets 15 more. Then he gives 10 to his sister. How many stickers does Sam have now?

There are 30 kids in the gym. Some go outside. Now 18 kids are in the gym. How many went outside? Write two different equations.

Check your understanding

Quiz

Sara has 21 marbles. She gets 15 more. Which equation matches?

What is 34 + 13?

There are 40 geese. 10 fly away. How many are left?

Tom had 7 cars. He got more. Now he has 11. How many did he get?

A class read 26 books in September and 23 books in October. About how many is that?

Ella has 32 beads. She uses 11. How many beads are left?

Ravi had 15 rocks. He found some more. Now he has 19. Which equation matches?

For parents and teachers

Big idea: B2.4 asks children to use objects, diagrams and equations to solve addition and subtraction situations with numbers up to 50. There are several types of story problems: joining, taking away, part-part-whole, comparing, and problems where the start or change is unknown. Missing-change problems (like 12 + □ = 20) are the trickiest, so give them extra practice.

Common mistakes:

Adding every number in a story because they see two numbers. Ask: "What is happening in the story? Is it getting bigger or smaller?"
Mixing tens and ones (for 23 + 14, adding 2 + 4). Use bundles of 10 straws or popsicle sticks with elastic bands, and keep tens and ones in separate piles.
Answering a missing-change problem with the total. For "had 12, now has 20, how many did she get?", a child may say 32. Draw the bar model to show 20 is the whole.
Not checking. Encourage "Does it make sense?" and checking with the opposite operation.

How to help: Use real situations: counting cans in the pantry, coins in a piggy bank, pages read in a book. Let your child choose how to show the problem. A drawing is just as good as objects.