Hello Math Teachers,
Which One Doesn't Belong is a collection of shapes, numbers, and other math representations that I present as morning work or warm-up before math. Curation is done on the web by Mary Bourassa and is inspired by the Christopher Danielson book of shapes, but I mostly have Sesame Street stuck in my head as I share one of these with students. Nothing too complex, but it does present a good challenge at first for those students who are sure that there must be a correct answer. Students then have great discussion (argument!) how each shape has a quality that is different than the others. In the subsequent examples, the students know that their claims are important, but must be backed up with evidence and reasons why (good practice for math and science practice standards to argue from evidence). The collection includes examples with money, numbers, clocks, games, and some seasonal pictures that are just fun: Check out the full collection here: http://wodb.ca/index.html I use Google Slides to share them with my class, you can access the slideshow here They even inspire student created examples. Here is one from Mariska in Team 508: Throughout our curriculum there are activities that utilize rounding and estimation to help show that the answer is reasonable. This seems to be the scaffolding for that infamous last question on every the unit test: The Extended Response.
Examples from 5th grade: -Explain how you know your answer is reasonable (Unit 1) -Explain how you found your answers (Unit 2) -Explain how you know (Unit 3) -Explain (Unit 4) -What do you do with the remainder (Unit 5...I like this one!) I'm guessing that 5th grade assessments are not the only ones that include these questions. The problem with this structure is that the estimation is still disconnected from the real world. At Graham Fletcher's NCTM session in Chicago he demonstrated that a room full of math teachers were not very good at estimating. With a number line from 0 to 1 trillion and a dot on the far right, he asked all in the room to stand up. He shared that the dot was going to move backwards down the number line and we should sit down when the dot reaches 1 billion. Most in the room sat down at the halfway mark and the rest sat down long before the correct spot. *Take a moment to draw that number line and mark where 1 billion is. His message was that we need to be doing number sense and estimation activities daily. Ones that connect to the real world and beyond that final question on the unit test. The best resource for estimation is from Andrew Stadel. His site is called Estimation 180 and is a collection of pictures and videos that students can relate to (bacon, halloween candy!) The activities build upon one another, day after day, so that students use previous reference points to guide their estimations. Once they are using benchmarks, they are no longer guessing. A strategy to use while facilitating is to ask students for their range, including a "too low" and a "too high." Ask them to use benchmarks from previous activities or real world experiences to explain their claims. One note from Graham is to not accept unreasonable answers like 0 or "a million." Guide students to stake a claim based on evidence so that their estimations have value. The day after returning from NCTM, I was waiting at the Harding's deli and the women next to me was eyeing the parmesan chicken. She was asking the weight of one chicken piece. She was worried that one piece would be 1 pound and cost close to $8. I could not have made up her quote, "I'm just not that good at estimating." So I pulled out my phone and asked her if I could take a couple pictures, because I had just noticed an estimation activity! Graham Fletcher was the presenter at NCTM that I was most looking forward to...and I was not alone. Sharon and I arrived 30 minutes early and we were lucky to find two seats together, the doors were closed shortly after we got settled. The subject of the session was 3 Act Math Lessons and I learned a lot about the structure and delivery of this type of lesson by being a participant. It is a joy to be a student in the room of a stellar teacher. There was much more to learn from Graham beyond the 3 Act strategy, including thoughts on estimation, developing number sense, and whole group engagement.
I will be able to share many notes from this session, but I decided to start with one of the videos from Graham that first caught my eye. After watching the Progression Videos in his Making Sense Series, I knew that he was someone who I wanted to continue to learn with. The videos demonstrate the progression of topics from their introduction to upper elementary. The topics include counting, adding/subtracting, multiplication, division, and fractions. They have been helpful to me, a teacher that has spent all of my time at 5th grade, to see the building of foundations for each student. I have noticed how helpful watching Olivia's progression (through all subjects) has informed my teaching, but these videos allow me to check out the math progression in "fast forward." Check them out on Graham's page here: Making Sense Series Hello math teachers, Welcome back and Happy New Year! I wanted to share some golden nuggets from the NCTM math conference I attended in December. All the sessions I attended were worthwhile. They included many new activities and strategies to deepen student thinking. I don't want to dump too much at once, so I thought I would share a little at a time. Here goes... A session by Tracy Zager (@traceyzager) challenged us to slow down our approach and allow time for students to develop math questions themselves. This doesn't mean to completely #ditchthattextbook, but try sharing the context of a word problem with the question removed. Ask students what they notice about the scenario and then what they wonder. There is a good chance that one of the things they wonder about is the question that is already in the textbook, but there is more student ownership since they are now answering their own question instead of yours. A recent example from 5th grade: One lap around the track is 1/4 mile. Amy ran 13 laps. How far did she run? We just removed the question "How far did she run?" However, enough of our class is going to be curious to ask that question themselves. I already wrote much more than I thought I would at the start, but if you are still with me, Annie Fetter from the Math Forum shares this much better than I do. Click on the link below for the short video (only 5 - fantastic - minutes). |
Matt HawkinsGull Lake Middle School Archives
March 2018
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