Week 2 of 10

Operation Quest

Students meet the four operations as characters with special powers and learn to choose the right one for a story problem - joining, taking away, making equal groups, or sharing.

Estimated time: 45-60 minutes
Grade range: Grades 2-5
Skill focus: Addition, Subtraction, Multiplication thinking, Division thinking, Choosing operations
Theme: Four heroes on a quest: Add, Subtract, Multiply, and Divide

The story

A bridge is out on the road to Math Mountain, and four heroes step up. Add can join two groups into one. Subtract can find what's missing. Multiply can build many equal groups in a flash. Divide can share a treasure fairly. But each hero only works on the right kind of problem - pick the wrong hero and the bridge stays broken. Your quest: send the right hero for each challenge.

What you'll learn

Match a story problem to the right operation by asking what is happening: joining, separating, making equal groups, or sharing equally.
Explain multiplication as repeated equal groups (4 x 3 means four groups of three) and division as splitting into equal groups.
Solve a two-step word problem and explain which operation was used at each step.

Key ideas

Addition joins amounts; subtraction finds a difference or takes away.
Multiplication is a fast way to add equal groups.
Division splits a total into equal groups or finds how many are in each group.

Words to know

Operation: A math action: adding, subtracting, multiplying, or dividing.
Sum: The answer to an addition problem.
Difference: The answer to a subtraction problem.
Product: The answer to a multiplication problem.
Quotient: The answer to a division problem.
Equal groups: Groups that all have the same number of things, the heart of multiplying and dividing.

The lesson

The secret to word problems is not the numbers - it's figuring out what is happening in the story. Are two groups coming together? That's addition. Is something being taken away, or are you comparing to find a difference? That's subtraction.

Multiplication is the hero for equal groups. '4 baskets with 3 apples each' is 4 x 3 = 12. Instead of adding 3 + 3 + 3 + 3, you multiply. The clue is the phrase 'each' or 'every' - it signals equal groups.

Division is the sharing and splitting hero. If 12 apples are shared equally among 4 friends, each friend gets 12 / 4 = 3. Division answers two kinds of questions: 'how many in each group?' and 'how many groups can I make?'

Some quests take two steps. 'You have 20 dollars, buy a book for 8, then split the rest with a friend.' Step one is subtraction (20 - 8 = 12). Step two is division (12 / 2 = 6). Naming the operation at each step keeps you from getting lost.

Worked examples

A class has 6 tables with 4 students at each table. How many students?

6 x 4 = 24 students

The words 'at each table' signal equal groups, so this is multiplication: six groups of four is twenty-four.

There are 15 cookies to share equally among 5 kids. How many each?

15 / 5 = 3 cookies each

Sharing equally is division. Split 15 into 5 equal groups; each group has 3.

A game costs $18. You have $25. How much is left after buying it?

$25 - $18 = $7

Spending money takes an amount away, so this is subtraction. The difference between 25 and 18 is 7.

Try it: interactive practice

This is the week's practice game. Work through it right here - try each step yourself, then check your thinking.

Activity

Pick the Right Hero

Sorting problems by operation builds the habit of asking 'what is happening here?' before reaching for numbers - the most important skill in word problems.

Problem 1 of 8

A shelf has 4 rows of books with 6 books in each row. How many books in all?

Hands-on challenge

Dice Operation Duel

What you need

Two dice
Index cards for operation symbols
Pencil and paper

Steps

1
Roll two dice to get two numbers.
2
Draw an operation card (+, -, x, or /) from a face-down pile.
3
Solve the problem your roll and card create; if the card is division and it doesn't divide evenly, re-roll one die.
4
Score a point for each correct answer and play to 10.

You've got it when: You can carry out all four operations with small numbers and say a quick word-problem story that matches each roll.

Checkpoint

Quick checks before you move on. Try each one first, then reveal the answer.

1
Which operation solves '5 bags with 7 apples each'? What is the answer?
Show answer
Multiplication. 5 x 7 = 35 apples.
2
Write 4 + 4 + 4 as a multiplication.
Show answer
3 x 4 = 12 (three groups of four).
3
24 pencils split into boxes of 6. How many boxes?
Show answer
Division: 24 / 6 = 4 boxes.

Think about it

How can you tell whether a story problem needs multiplication or addition? What word or clue helps you decide?

Challenge problem

A baker makes 4 trays of muffins with 6 muffins on each tray. She sells 9 muffins. How many muffins are left?

Show hint

This is a two-step quest. First find the total number of muffins, then take away the ones she sold.

Show answer

15 muffins. Step 1: 4 x 6 = 24 muffins made. Step 2: 24 - 9 = 15 muffins left.

Extension · go further

Write your own two-step word problem where the first step is multiplication and the second is subtraction. Give it to someone and check that they name both operations.

Finished the lesson, activity, and challenge? Mark this week complete to track your progress through the 10-week course.