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
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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.
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?
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!