Math Core

Some stories need more than one step to solve. First you find a middle number, then you use it to find the answer. Now that you know your facts, you can mix multiplication and division with adding and subtracting.

Plan with two questions

Read this story:

Maya has 3 bags of apples. Each bag has 6 apples. She eats 4 apples. How many apples are left?

The question is "how many are left?" But you can't answer it yet. You don't know how many apples Maya started with. So ask two smaller questions.

Step 1: How many apples at the start? 3 bags of 6: $3 \times 6 = 18$ .

Step 2: How many are left? She eats 4: $18 - 4 = 14$ .

Maya has 14 apples left.

Solving a two-step problem

Read the question. What do you need to find?
Find the hidden question: what must you know first?
Solve step 1, then use that answer in step 2.
Check: does your answer make sense?

Use a letter for the unknown

You can write an equation with a letter standing for the number you don't know. For Maya's apples, let $a$ be the apples left:

3 \times 6 - 4 = a

Multiply first, then subtract: $18 - 4 = 14$ , so $a = 14$ .

Does it make sense?

After you solve, estimate to check. Round the numbers to ones that are easy to work with. If your answer is close to the estimate, it's reasonable. For Maya: 18 is about 20, and $20 - 4 = 16$ . Our answer, 14, is close to 16, so it makes sense.

Worked example: Multiply, then add

A bookshelf has 4 shelves with 8 books on each. Kim puts 5 more books on top. How many books are there now?

Step 1: $4 \times 8 = 32$ books on the shelves.

Step 2: $32 + 5 = 37$ books.

There are 37 books.

Worked example: Add, then divide

Leo has 17 stickers. His friend gives him 11 more. He shares all of them equally among 4 pages. How many stickers go on each page?

Step 1: $17 + 11 = 28$ stickers in all.

Step 2: $28 \div 4 = 7$ , because $4 \times 7 = 28$ .

Each page gets 7 stickers.

Worked example: Money and a check

Tickets cost $6 each. A family buys 5 tickets. They pay with a $50 bill. How much change do they get?

Let $c$ be the change: $50 - 5 \times 6 = c$ .

Step 1: $5 \times 6 = 30$ , so the tickets cost $30.

Step 2: $50 - 30 = 20$ , so $c = 20$ .

They get $20 in change.

Check: $30 for tickets plus $20 change is $50. It makes sense.

Common mistake

Don't stop after step 1! In Maya's story, 18 is the number of apples she started with, not the number left. Read the question again before you write your answer.

Tip

Look for key ideas. "Each" and "equal groups" often mean multiply or divide. "More" and "in all" often mean add. "Left" and "fewer" often mean subtract. But always think about what the story is really doing.

Practice

Practice 1

There are 5 vans. Each van carries 4 kids. Then 3 more kids walk up. How many kids are there in all?

Type a number.

Practice 2

A baker makes 4 trays of muffins. Each tray has 9 muffins. She sells 10 muffins. How many muffins are left?

Type a number.

Practice 3

Jada has 20 beads. Her sister gives her 22 more. Jada puts all the beads into 7 equal piles. How many beads are in each pile?

Type a number.

Practice 4

Pens cost $3 each. Omar buys 8 pens and pays with a $30 bill. Which equation finds his change, $c$ ?

Practice 5

A class has 3 boxes of 9 markers and one box of 8 markers. How many markers does the class have?

Type a number.

Practice 6

Sam and Ava each pick 16 flowers. They put all of their flowers into vases, with 8 flowers in each vase. How many vases do they fill?

Type a number.

Practice 7

A coach buys 6 bags of balls. Each bag has 7 balls. She gives 12 balls to another team. How many balls does she have left? Use an estimate to check that your answer makes sense.

Type a number.