Grade by Grade
B. Number · Operations: Numbers to 10 000, Decimal Tenths, Multiplying and Dividing

Solving Multi-Step Problems and Checking Answers

B2.1 B2.4 B2.5 B2.6 A1About 45 minutes
Learning goals
  • I can solve problems that need more than one operation.
  • I can use a plan: understand, plan, solve, look back.
  • I can draw a bar model to show a problem.
  • I can check my answer with an estimate or the partner operation.

Words to know

multi-step problem
A problem that needs two or more operations to solve.
bar model
A drawing with bars that shows the parts and the whole in a problem.
reasonable
Makes sense. A reasonable answer is close to your estimate.

Let's start with a story

The school buys 6 packs of juice boxes. Each pack has 24 juice boxes. At the spring picnic, 128 juice boxes are given out. How many are left?

This problem has two steps. First we need the total. Then we need what's left.

A 4-step plan for problems

  1. Understand. Read the problem. What do you know? What are you trying to find? Say it in your own words.
  2. Plan. Draw a bar model or a picture. Decide which operations you need, and in what order.
  3. Solve. Do each step. Write what each number means.
  4. Look back. Is the answer reasonable? Check it with an estimate or the partner operation.
Worked example

Example 1: Multiply, then subtract

6 packs of 24 juice boxes. 128 are given out. How many are left?

  1. Understand: We know 6 packs of 24, and 128 given out. We want how many are left.
  2. Plan: First multiply to find the total. Then subtract.
  3. Solve, step 1: 6 × 24 = 120 + 24 = 144 juice boxes.
  4. Solve, step 2: 144 − 128 = 16 juice boxes.
  5. Look back: Check with addition: 16 + 128 = 144. ✓

16 juice boxes are left.

total 144242424242424128 given out?left
Top bar: 6 packs of 24 make 144. Bottom bar: 128 given out, and the unknown part is what is left.
Worked example

Example 2: Add, then subtract

Ava has $500. She buys skates for $129 and a helmet for $65. How much money is left?

  1. Understand: Ava starts with $500 and buys two things. We want what's left.
  2. Plan: Add the costs, then subtract from $500.
  3. Solve: 129 + 65 = $194. Then 500 − 194 = $306.
  4. Look back: Estimate: 500 − 130 − 70 = 300. $306 is close. ✓

Ava has $306 left.

$500 to start$129$65? = $306skateshelmetleft over
A bar model for Ava's money. Step 1: add the two costs ($129 + $65 = $194). Step 2: take that from $500 to find the unknown part, $306.
Worked example

Example 3: Multiply, then divide

Three Grade 4 classes go on a trip. Each class has 27 students. Each van holds 8 students. How many vans are needed?

  1. Solve, step 1: 3 × 27 = 60 + 21 = 81 students.
  2. Solve, step 2: 81 ÷ 8 = 10 R1 (8 × 10 = 80).
  3. Think: the 1 extra student needs a seat too, so round up.
  4. Look back: 11 vans hold 88 students. That's enough for 81, and 10 vans (80) would not be. ✓

11 vans

Ways to check

  • Estimate: Round the numbers and see if your answer is close.
  • Use the partner operation: check subtraction with addition, division with multiplication.
  • Work backwards: start at your answer and undo each step. You should land on the number you started with.

When a problem feels tricky

Hard problems are supposed to feel a bit hard at first. If you're stuck, try one of these: draw the story, try smaller numbers, or explain the problem to someone. Taking a deep breath and trying a new plan is what problem solvers do.

Just for fun

A two-step problem is like a mystery with two clues. Solve only the first clue and you'll catch the wrong number, Detective!

Hands-on activity

Make your own two-step problem

You need: a grocery flyer (paper or online, with a grown-up) or a list of prices you make up, paper and a pencil.

  1. Pick something you could buy in packs (like 4 packs of yogurt) and something else to buy.
  2. Write a two-step problem. Example: "Yogurt is $5 a pack. We buy 4 packs and a $7 loaf of bread. How much do we spend?" (Answer: 4 × 5 + 7 = $27.)
  3. Draw a bar model for your problem and solve it.
  4. Trade problems with your grown-up. Solve each other's problems, then check each other's answers with an estimate or the partner operation.

Your turn

1

Leah has 4 packs of 8 markers. 9 markers dry out. How many markers work?

2

Zoe had 1250 points in a game. She earned 375 more, then spent 500. How many points now?

3

There are 5 rows of 18 chairs and 12 extra chairs. How many chairs in all?

4

96 hockey cards are shared equally by 4 friends. Then each friend gives 5 cards to a little brother or sister. How many cards does each friend have now?

5

Tickets cost $9 for a child and $12 for an adult. How much for 6 children and 2 adults?

6

Check 4 × 63 = 252 using division.

More practice: warm-up

1

There are 3 bags of 10 apples. You eat 4 apples. How many are left?

2

20 + 20 + 20 is the same as what multiplication? What is the answer?

3

12 cookies are shared by 3 friends. Each eats 1. How many does each friend have left?

4

50 − 10 − 10 = ?

5

2 × 5 + 5 = ?

More practice: on your own

1

At a fall fair, 245 adults and 378 children came. The fair had 600 free hats. Was there a hat for everyone?

2

A coach orders 7 boxes of 12 pucks. The pucks are shared equally by 4 teams. How many pucks does each team get?

3

A book has 200 pages. Sam reads 48 pages a day for 3 days. How many pages are left?

4

Raj says 6 × 198 = 1788. Use an estimate to check.

5

Amir earns $15 for each driveway he shovels. He shovels 8 driveways, then spends $35 on a gift. How much money does he have left?

Challenge

1

A school has 4 classes of 26 students and 3 classes of 24 students. All the students make teams of 8 for a game. How many teams?

2

A library has $1000. It buys 4 sets of books for $125 each and a reading rug for $275. How much money is left?

3

I'm thinking of a number. I multiply it by 6, then add 18. I get 60. What is my number?

Check your understanding

Quiz

1.

Mom buys 3 cartons of 12 eggs and uses 7. How many eggs are left?

2.

Which operation checks 512 ÷ 8 = 64?

3.

Max has $20. He buys 3 comics for $4 each. How much is left?

4.

5 boxes of 30 pencils are shared equally by 6 classes. How many pencils does each class get?

5.

Ella buys 4 shirts for $9 each and pays with $50. What should she do first?

6.

Which is the best estimate for 7 × 302?

For parents and teachers

Big idea: The curriculum (B2.1) asks Grade 4 students to solve problems that need more than one operation, and to check calculations. Strand A (social-emotional learning skills and mathematical processes) is woven in: making a plan, persevering when a problem is hard, and explaining thinking.

Common difficulties:

  • Stopping after the first step. Ask "Did you answer the question that was asked?"
  • Using all the numbers with the same operation (adding everything). Ask your child to retell the story in their own words before computing.
  • Not checking. Make estimating and using the partner operation a routine.

How to help: Real-life problems are often multi-step: planning a party (how many packs of plates?), budgeting allowance, or figuring out a trip. Let your child work them out and explain the steps to you.