A Routine for Between 2 Numbers

I hadn’t realized the last few entries of between2numbers.com were left blank. They are done now. Thought I’d share a more revised warmup routine of how I’ve used the contents.

I’ll use entry #1 as an example.

I project the two images only and set the timer for 30 seconds for quiet notice-and-wonder. No writing necessary during this time.

I then say, “Before I show you the speed of each of these, I’d like you to discuss with a neighbor what the numbers might be, let’s think miles per hour.” I ask them to write down their estimates [in a journal]. Set the timer for another minute.

I call randomly on two students to tell the class what their guesses are for the snail. Call on two more students for their guesses for the jet. I record these on the board.

Now I reveal the snail’s rate and ask, “Who has the closest guess to this?” Record their answers. This is a good opportunity for students to check their decimal comparison.

Now I reveal the jet’s rate and ask for the same.

I entertain any other related information at this point. I might ask them if they knew what the average speed of a passenger airplane was. Then, I reveal the question.

Okay, this step is important. It saves time writing and fussing over actual quantities, and I find that it helps students focus on the mathematical operation rather than feel anxious about the numbers. I say, “We’re going to let the snail’s rate be A, the jet’s rate be B, and the distance 2,800 miles be C…”

“... Discuss with your neighbor what calculation(s) you would do to find out how much time it takes each object to travel across the US. Just use the letters now. For example, if you wanted to add the two rates, you’d just write A + B.” Set the timer for one minute.

Randomly call on one group to share. Record on the board what they share and ask, “Who has a different solution?” Write down what they say. Continue asking until I have recorded all the different solutions. (Normally, there are usually just 2 or 3 different ones.)

I now take out a calculator and get an answer for each of the solutions shared. I go back to the owners of each solution and ask, “What unit should your answer have?” (If the units were not mentioned earlier.) We discuss the reasonableness of the correct answer.

I’m proud of this site because the routine affords several of these:

1. interesting facts

2. estimating

3. talking and listening

4. proportional reasoning

5. unit rates

6. dimensional analysis

Here is the key. Please share this resource widely, and if you use it, please let me know how it goes.