Teachers are always asking how to generate more mathematical conversations in their classrooms. What do you notice is a great place to start!
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A favorite book on my bookshelf is Connecting Arithmetic to Algebra, and Chapter 1 is about generalizing in arithmetic. Now, while this book is specifically about arithmetic, we can apply the principles to all areas of math. And a great question to ask to begin wonderful mathematical conversations is What do you notice about…?
- Boys and girls, we’ve been reading clocks to the hour. I have pictures of several different clocks showing an “on the hour” time. What do you notice about them?
Possible responses: The minute hands are all pointing directly to the 12. The hour hand is always pointing right at the hour number.
- Let’s look at these clocks showing half hour times. What do you notice about them?
Possible responses: The minute hand is always pointing right at the 6. The hour hand is halfway between the two hour numbers.
- Interesting observations! And when the minute hand is pointing to the 6, we know we say 30. There are 60 minutes in an hour, right? What do you notice about the numbers 30 and 60?
Possible responses: 30 and 60 are like 3 and 6, and 3 is half of 6. So 30 might be half of 60.
- Wow! Great mathematical thinking! And what if I draw a line right through the clock from the 12 to the 6? What do you notice?
Possible responses: It cuts the clock in half. Both sides are the same. It’s like each side is one half!
Pretty cool, huh? And do you see how noticing these generalizations helps the students understand the concept better?
For more on telling time to the hour and half hour, check out this post.