Michael Fenton has graciously accepted every request I sent his way regarding the current version of the Estimation 180 handout. [UPDATE: Handout without examples] It's been fun bouncing ideas back and forth along with his generosity to customize the handout as necessary. He was part of a teacher workshop recently and shared with me the feedback he received about Estimation 180. I feel it's only fair to briefly discuss how one can use the handout with their students to continue building number sense. Although the handout appears pretty straightforward with two examples at the top, I'd still like to give it a little personality and depth here. I'll go column by column, left to right on the handout.
In Estimation 180's first year, I was just trying to keep up with creating these estimation challenges in time for use in my own classroom. There really wasn't a scope and sequence involved. That said, now that there are over 160 estimation challenges available, teachers and students can use them at anytime throughout the school year and without completing them in sequential order. Therefore, use the Day # column simply to number your daily challenges according to the site. Tell your students or write it up on the board that you're doing the challenge from Day 135 even though you might be on the fifth day of school.
In my opinion, this column is more important than the Day # column. Don't go crazy here. Keep it short and sweet, but as specific as possible. For example, there's a lot of scattered height estimates on the site. Don't write down "How tall?" for Day 110. Instead write "Bus height" because when you get to Day 111, I'd write in "Parking structure height". I believe the teacher has the ultimate say here, but it can be fun to poll your students for a short description in which you all can agree. Give students some ownership, right?
If unit measurement is involved, try and sneak it in here:
Take Day 125 for instance. I'd suggest entering "Net Wt. (oz.) of lg Hershey's bar." Keep in mind that Day 126 asks the same question, but I'd suggest you encourage your class to use pounds if they don't think of it.
*By the way, sometimes unit measurement(s) are already included in the question. Use discretion.
Think of an estimate that is too low.
Don't accept one (1), that's just rubbish. Unless one (1) is actually applicable to the context of the challenge. Stretch your students. Think of it more as an answer that's too low, but reasonably close. After all, this is a site of estimation challenges, not gimmes.
Refer to my notes in Too Low. Just don't accept 1 billion unless it's actually applicable. Discuss with students the importance of the Too Low and Too High sections: we are trying to eliminate wrong answers while creating a range of possible answers.
This is the place for students to fill in their answer. If the answer requires a unit of measurement, we better see one. Not every estimation challenge is "How many..." marshmallows? or christmas lights? or cheese balls?
Even if a unit of measurement has already been established (see the Description notes), I'd still encourage your students to accompany their numerical estimate with a unit of measurement.
The My Reasoning section is the most recent addition to the handout and I'm extremely thrilled about it. This is a student's chance to shine! Encourage their reasoning to be short and sweet. When a student writes something down, they'll be more inclined to share it or remember it. Accept bullet points or phrases due to the limited space. We don't need students to write paragraphs. However, we're looking for students to identify any context clues they used, personal experiences, and/or prior knowledge. Hold students accountable for their reasoning behind the estimate of the day.
Don't let student reasoning go untapped! If you're doing a sequence of themed estimation challenges, don't accept, "I just guessed" after the first day in the sequence. For example, if you're doing the flight distance themed estimate challenges starting on Day 136, you will establish the distance across the USA on the first day. Sure, go ahead and guess on Day 136, but make sure you hold students accountable for their reasoning every day thereafter.
Have students share their reasoning before and after revealing the answer. Utilize Think-Pair-Share. This will help create some fun conversations before revealing the answer. After revealing the answer, get those who were extremely close (or correct) to share their reasoning. I bet you'll have some great mathematical discussions. I'm also curious to hear from those that are way off and how their reasoning could possibly be improved.
I'd say the My Reasoning section was born for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others. Keep some of these thoughts in mind regarding Mathematical Practice 3:
Explain and defend your estimate
- Construct a detailed explanation referencing context clues, prior knowledge, or previous experiences.
- Invest some confidence in it.
- Ask "Was anyone convinced by this explanation? Why? Why not?" or
- "Are you guys going to let [student name] off the hook with that explanation?"
- Find out what that reasoning is!
- DON'T let student reasoning go untapped!
Jot down the revealed answer. I'd also encourage students to write down the unit of measurement used in the answer. The answer might use a different unit of measurement than what you and your class agreed upon. Take the necessary time to discuss the most relative unit of measurement. I might be subjectively wrong on some of the answers posted. As for more thoughts on unit of measurement, refer to the My Estimate notes above. Continue having mathematical discussion after revealing the answer. Refer to my notes regarding the use of Mathematical Practice 3 in the My Reasoning section.
Find the difference between My Estimate and Answer. Have students circle either the "+" or the "-" if they didn't get it exactly correct.
+ Your estimate was greater than (above) the actual answer.
- Your estimate was less than (below) the actual answer.
Error as a %
This column is designed for you to do percent error with your students. Divide the Error by the Answer. Maybe have a little competition in your classroom: who has the best average at the end of 10 days? The winner gets a tub of cheese balls!
I hope this handout helps assist your students with the estimation challenges on the site by keeping them organized. In return, I hope the organization allows for some wonderful student reasoning and mathematical discussions so students are experiencing Mathematical Practice 3 and building number sense one day at a time. Drop a line of gratitude to Michael Fenton if you get the chance or offer me any constructive feedback in the comments.
I'll be presenting about these estimation challenges and mathematical tasks where estimation is part of the problem-solving process at CMC South in November. Look for upcoming thoughts and ideas regarding this presentation, here and on my other blog, Divisible by 3.