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

Solving Story Problems to 100

B2.4 B2.1 B2.3 A1About 40 minutes

Learning goals

I can figure out if a story problem needs adding or subtracting.
I can draw a bar model or a number line to show a story.
I can write an equation with a box for the missing number.
I can solve a two-step problem and check that my answer makes sense.
I can keep trying when a problem feels hard.

Words to know

story problem
A math question told as a short story. It is also called a word problem.

bar model
A drawing with long boxes (bars) that shows the parts and the whole in a story.

unknown
The number we are trying to find. We show it with a box □ or a question mark.

two-step problem
A problem where you need to do two calculations to find the answer.

reasonable
Makes sense. A reasonable answer is close to your estimate.

Let's start with a story

The Grade 2 class is going to a sugar bush in March to see how maple syrup is made. There are 24 students in Room 5 and 27 students in Room 6. One bus holds 48 students. Will one bus be enough?

To answer, you need to understand the story, choose a strategy and check your answer. In this lesson you will become a story problem detective.

Metal sap buckets hanging on maple tree trunks in a snowy sugar bush, with a steaming sugar shack behind. — At a sugar bush in early spring, buckets collect sap from maple trees. The sap is boiled in the sugar shack to make maple syrup. AI-generated image

The four detective steps

Understand: Read the story (or have it read to you). What do you know? What do you need to find?
Plan: Is the story about putting together, taking away, or comparing? Draw a picture, a bar model or a number line.
Solve: Write an equation and work it out.
Look back: Does the answer make sense? Check by estimating or with the opposite operation.

Worked example

Example 1: Will one bus be enough?

Room 5 has 24 students and Room 6 has 27 students. One bus holds 48 students. Will one bus be enough?

Understand: We know 24 and 27. We need the total, then compare it to 48.
Plan: The groups go together, so we add. 24 + 27 = □.
Solve: 20 + 20 = 40. 4 + 7 = 11. 40 + 11 = 51.
Look back: 51 is more than 48. Estimate: 20 + 30 = 50, which is more than 48 too.

No. There are 51 students, which is 3 more than the bus holds. They need another bus (or a car).

Bar models show the parts and the whole

A bar model helps you see what is missing. The long top bar is the whole. The bars under it are the parts.

If you know both parts, add to find the whole.
If you know the whole and one part, subtract (or count up) to find the other part.

Example 1 as a bar model: parts 24 and 27. The whole is missing, so add.

Worked example

Example 2: Missing part

Maya has 65 beads. 38 are blue and the rest are red. How many red beads does she have?

Understand: The whole is 65. One part is 38. We need the other part.
Plan: Draw a bar: 65 on top, 38 and □ underneath. Equation: 38 + □ = 65, or 65 − 38 = □.
Solve: Count up from 38: +2 to 40, +20 to 60, +5 to 65. 2 + 20 + 5 = 27.
Look back: 38 + 27 = 65. (30 + 20 = 50, 8 + 7 = 15, 50 + 15 = 65.) It checks!

Maya has 27 red beads.

The whole is 65. One part is 38. The missing part is 27.

Worked example

Example 3: Missing start

Some geese were in a field. 25 more geese landed. Now there are 70 geese. How many geese were in the field at the start?

Understand: We don't know the start. We know 25 more came and the total is now 70.
Plan: □ + 25 = 70. The total is the whole, so subtract: 70 − 25 = □.
Solve: 70 − 20 = 50. 50 − 5 = 45.
Look back: 45 + 25 = 70. Yes!

There were 45 geese at the start.

Worked example

Example 4: Comparing

A family's cat weighs 6 kg. Their dog weighs 31 kg. How much heavier is the dog?

Understand: "How much heavier" means compare. Find the difference.
Plan: 31 − 6 = □.
Solve: Jump back 1 to 30, then 5 more to 25.
Look back: 25 + 6 = 31. Yes!

The dog is 25 kg heavier.

Worked example

Example 5: Two steps

Owen has $40 in his piggy bank. He earns $15 for raking leaves. Then he spends $22 on a book. How much money does he have now?

Step 1: He earns money, so add: 40 + 15 = 55.
Step 2: He spends money, so subtract: 55 − 22 = 33.
Look back: Estimate: 40 + 15 is about 55, minus about 20 is about 35. 33 is close.

Owen has $33.

Example 5: start at 40, jump +15 to 55, then jump back 22 to 33.

Kind of story	Clue	Example equation
Join (put together)	more come, in all, altogether	24 + 27 = □
Separate (take away)	go away, eat, spend, left	52 − 27 = □
Part-part-whole	some are ___, the rest are ___	38 + □ = 65
Compare	how many more, how much heavier, how many fewer	31 − 6 = □
Missing start	some were there, then ...	□ + 25 = 70

Kinds of story problems

When a problem feels hard

Everybody gets stuck sometimes, even grown-up mathematicians! When you feel stuck or frustrated:

Take a slow, deep breath.
Read the story again, slowly.
Act it out with toys, or draw it.
Try a smaller number first, like 5 instead of 45, to see what to do.
Say to yourself: "I can't do it yet. I'll try another way."

Mistakes help your brain grow. Checking your work and fixing it is what good math thinkers do.

Just for fun

Sugar bush fact: it takes about 40 litres of maple sap to make just 1 litre of maple syrup. That's one story problem the maple trees work very hard on!

Hands-on activity

Make up story problems

You need: paper, a pencil, and things to act with (toy cars, stuffed animals, coins or dried pasta).

Choose a theme: a hockey game, a bake sale, a snowy day, the library.
You make up a story problem with numbers up to 100, like "There are 46 cars in the parking lot. 19 drive away. How many are left?"
A grown-up solves it and draws a bar model. You check their answer!
Now switch. The grown-up makes up a story for you.
Try to make one of each kind: join, take away, compare, and a two-step story.

Math talk: "How did you know if it was adding or subtracting?"

Your turn

There are 36 children on the soccer field and 29 on the playground. How many children are outside in all?

A box holds 50 crayons. 17 are broken. How many are not broken?

Nia has 42 hockey cards. Leo has 58. How many more cards does Leo have?

Some kids were skating at the rink. 14 more kids came. Now there are 40 kids. How many were there at the start? Write an equation with a box.

A shelf has 75 books. 30 are about animals, and the rest are storybooks. How many storybooks are there?

Draw a bar model for: "Ali picked 23 apples. Sam picked 19 apples. How many did they pick altogether?" Then solve.

More practice: warm-up

There are 20 red cars and 30 blue cars. How many cars in all?

A farmer had 60 eggs. She sold 20. How many eggs are left?

Is this adding or subtracting? "45 people were on the train. 12 got off."

Mom drove 35 km. Dad drove 10 km. How many more kilometres did Mom drive?

A class has 12 girls and 13 boys. How many students?

More practice: on your own

The class wants to collect 100 cans for the food bank. They have 64. How many more cans do they need?

A baker made 48 bagels in the morning and 39 in the afternoon. How many bagels did he make? Is your answer reasonable?

Zoe had some stickers. She gave 15 to her brother. Now she has 28. How many did she have at the start?

A pumpkin weighs 9 kg. A watermelon weighs 4 kg. How much heavier is the pumpkin?

There are 33 people on a bus. At the first stop, 12 get off. At the next stop, 20 get on. How many are on the bus now?

Challenge

Jin has 27 marbles. Kate has 15 more than Jin. How many marbles do they have altogether?

Write a story problem that matches 80 − □ = 35. Then solve it.

A class needs 90 paper snowflakes for the winter concert. Kids make 34 on Monday and 38 on Tuesday. How many more do they still need to make?

Check your understanding

Quiz

There are 45 kids at the park. 18 kids go home. Which equation matches?

Tia has 26 shells. She finds 37 more. How many shells does she have now?

A rope is 72 cm long. Another rope is 50 cm long. How much longer is the first rope?

Some birds were at a feeder. 9 more came. Now there are 30. Which equation shows the story?

Ben has $50. He spends $18. Then he gets $10 from his grandma. How much does he have now?

Mia says 39 + 42 = 61. Which estimate shows she made a mistake?

For parents and teachers

Big idea: B2.4 asks children to represent and solve addition and subtraction situations to 100 with objects, diagrams and equations. Children should meet many kinds of stories: joining, separating, part-part-whole and comparing, with the unknown in different places (□ + 25 = 70, not only 45 + 25 = □). The four detective steps and the "keep trying" tips come from strand A: the mathematical processes (problem solving, reasoning, representing) and social-emotional skills (managing frustration, perseverance).

Common mistakes:

Grabbing the numbers and adding. Ask your child to retell the story and act it out before solving.
Missing-start problems ("some were there, 25 more came, now 70"). Children often add 70 + 25. A bar model shows that 70 is the whole.
Compare problems. "How many more" does not mean add. Line up two bars and look at the extra part.
Stopping after one step in a two-step problem. Ask "Did you answer the question the story asks?"

How to help: Read problems aloud as many times as needed; reading should not block the math. Encourage drawings. When your child gets frustrated, model calm self-talk: "Let's try a smaller number first."