Photo by Jake And Lindsay

It’s easy to fall in love with trying to use the latest technology in the classroom. But, I think it’s better to begin with a specific need, and then find the best tool that meets that need.

In other words, rather than saying “what can I do with these iPads,” it’s better to ask “what will help my students to ______.”

### Multiplying By Decimals

In this example, I want students to develop curiosity about multiplying by decimals.

At this point, they don’t know how to do the calculation. I don’t want them to get bogged down in the steps. Instead, I want them to see the big picture and ask interesting questions.

The perfect tool for this is a *plain old calculator.* It will handle the calculations for them, so their minds are freed up to see the numbers.

Plus: no need to check out iPads, worry about wifi, or avoid district internet filters.

### One To Many

No need to give a calculator to every student. In this exploration, we want kids *sharing* their tools. This sets up discussion and conflict. I’d recommend one calculator per group of three students.

### Set Up A Pattern

Give groups a set of problems which will create an interesting pattern. Set the stage for discovery!

Remember, students *do not* know how to multiply with decimals by hand yet. They’re just using their calculators.

- 8 × 3 = ___
- 8 × 2 = ___
- 8 × 1 = ___
- 8 × 0.5 = ___
- 8 × 0.25 = ___

Ask students to look for patterns. Your groups may notice things like:

- multiplying by smaller numbers makes a smaller product
- multiplying by a decimal gives a product less than the original number
- sometimes multiplying by a decimal results in a decimal, and sometimes it doesn’t

### The Roaming Helper

Your job during this time isn’t to instruct. Instead, you’ll roam around, troubleshooting, encouraging, and even confusing!

- Troubleshoot: Help kids solve their issues with the calculators or group members.
- Encourage: Congratulate them on spotting even the simplest patterns. Celebrate their mathematical discoveries. Most kids never get to
*figure it out*in math. - Confuse: Do they think they see a pattern? Add some complexity by recommending new numbers. Push them past simple understandings.

### Further Exploration

When you make a discovery on your own, there’s a natural pull to keep going. Your students might want to explore further!

Let them try many different decimals. Multiply by: 0.1, 0.01, 0.001. Try: 0.9, 0.99 0.999. What patterns do they see?

If you’re lucky, groups might even ask about *dividing* by decimals. Or what if we multiply *a decimal* by a decimal? Even a simple calculator can handle these operations, so let them go for it (feel free to demonstrate calculator use as needed).

Let your students experiment and explore. They’re getting a *feel* for the numbers before getting their hands dirty with the algorithm.

### The Big Chat

Save time at the end for a whole group discussion about their discoveries. Let them do the talking and explaining. Say things like:

- Did anyone else see that?
- Jane, did your group find anything different (you know they did because you checked in on them)?
- What do you think would happen if… (especially great if a group tried this already)?
- Anyone
*disagree*with this pattern? Do we need to add something? - Can we summarize these findings in five words?

### What Else?

I’ve used calculators to play with exponents, percents, and adding negatives, but I’m sure you can come up with even more uses for the plain-old calculator. Let me know what you come up with!

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