## A Math Trick

## Opening

# A Math Trick

Try the following.

- Think of a number.
- Add 7.
- Multiply by 4.
- Subtract 16.
- Divide by 4.
- Subtract 3.

What number did you end up with?

Try the following.

- Think of a number.
- Add 7.
- Multiply by 4.
- Subtract 16.
- Divide by 4.
- Subtract 3.

What number did you end up with?

Explore how number tricks work.

- Which of these tricks will always give you the number you started with?

Trick A * Think of a number. * Multiply by 3. * Multiply by 4. * Divide by 12.

Trick B * Think of a number * Add 4. * Multiply by 2. * Divide by 4.

Trick C * Think of a number. * Subtract 3. * Multiply by 3. * Divide by 3. * Add 3.

Trick D * Think of a number. * Multiply by 5. * Add 5. * Divide by 5. * Subtract 1.

Hint:

- Follow the steps in each trick. Be sure to start with a variety of numbers.
- Write each step as an expression, and then evaluate the expression before moving on to the next step.

Share your results with a partner. Do you agree about which of the tricks always result in the original number?

- With your partner, prepare a presentation about why you think certain tricks always work and others do not.

- Write a trick that always results in the original number, no matter what number you start with.
- Try it on another student. Ask them whether or not they ended up with the same number they started with.

Take notes about your classmates’ conclusions as to which tricks always result in the original number. Pay special attention to their explanations about why those number tricks always work.

As your classmates present, ask questions such as:

- Why do you think the trick works?
- Can you use an expression to model the math?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Something I wonder about expressions is …**