Math in Kindergarten: Making Math Meaningful Visual Prompts for Math Inspiration at RainbowsWithinReach

Conceptual understanding: what is it, and how do we teach it? An ideal picture of conceptual understanding in math class: Students exploring the patterns they see. Students making sense and reason…

Literature is a fun, relatable way for kids to learn math concepts. When presented in words and pictures, abstract concepts are more concrete.

Read about how I incorporated a variety of ways to teach math in my first grade classroom to help make math meaningful!

My grade 10 academic math class is filled with great kids. For the last week or so we have been exploring quadratics in vertex and factored form, with the help of Desmos. My students are pretty solid at going between equations and their graphs. On Friday, about half of my class was away on a history field trip. We finished some questions from the previous day but I didn't want to start anything new - I wanted to do something fun! At TMC13, Sam Shah organized a Rational Headbanz game for the pre-calc group and I thought I could modify it for quadratics. With the help of my colleague, Michelle, we made 30 headbanz. We used coloured card stock, cut into rectangles with 2 slits cut along the sides to accommodate ribbon. I wrote the equations and this is how they turned out: The kids were pretty excited to play. I like to have written instructions on top of what I say, so here is what they saw: They each got a whiteboard to record their work. It was interesting to see them thinking about what to ask. Many started with "Am I in vertex form?" or "Am I in factored form?" but the poor student who had had a hard time getting good answers. They had to think about what questions to ask. The nice thing is that those who were struggling heard the questions others were asking them and were able to move forward. The trickiest part was with the value of h in They would ask "Is my h value positive?" but then either interpret the answer incorrectly or not be sure whether the person they had asked truly understood what a positive h value meant. They all figured out their equations and had fun doing so. And they want to play again next week when the whole class is there. I'll be happy to oblige. Thanks, Sam, for the inspiration : )

I teamed up with Alex Overwijk this year to offer a morning session at Twitter Math Camp on something we are both passionate about: activity-based teaching. We had a fantastic group, 30 strong, who jumped right in with us. Day 1: After quick introductions we started right away with an activity. We showed this picture: and asked them what questions came to mind. Al brought the original picture from National Geographic so everyone could look at it up close. Look really closely - that speck at the bottom is a person! Next, they formed groups and came up with their group's top three questions with justification for choosing them. After that the groups snowballed around the room - they chose the top question from each other group's top three and wrote why they chose it, then put it under the desk so as not to influence other groups (I was supposed to take envelopes - that's what we do in class - but forgot to pack them). Then each group got back to where they had started and read what the others had chosen as the best question and why. Each group then chose and wrote what they deemed was their best question on the blackboards surrounding the classroom, along with all the reasons for having chosen that one. Here is what some of that looked like: We then moved into a discussion of what makes a good question. Co-creating this criteria in the classroom helps students learn how to ask better questions. Here is the list we created: Not every question has to hit all of these criteria, but it is something to strive toward. Next, we talked about criteria for a good activity. Each criterion was written on the board and then everyone had 5 votes for the ones they valued most. Here is the list, in order, based on those votes: As [optional] homework, we asked them to read Al's blog post on 26 Squares, found here. Day 2: We started by talked about 26 Squares which, over the course of about 3 weeks, allows students to see linear relations, quadratic relations, Pythagorean theorem (sum of squares), similar triangles and right angle trig. You can read more detail via the link to Al's blog above. Perhaps this is a good time to mention that I blogged every day in my grade 10 applied (MFM2P) course last semester so if you want more of a day-to-day breakdown, start here. We did another group activity called Serial Position Curve. Al and I had come up with a list of 20 words which he read. No paper/pens or devices allowed - everyone had to remember as many as they could. Then they had time to write down as many as they could. Such focused students here! We then counted how many had written each one and I put that into Desmos to show number of words vs. position of the word in the list: Here are the words, in case you were curious: hat, fork, golf, nose, horse, glass, belt, canoe, watch, book, shirt, phone, tent, ball, truck, foot, pencil, gum, ring, skate. The relationship looks somewhat quadratic and can be used to ask questions about the features of a quadratic in context. My students get pretty good at telling me what the vertex means, not in terms of "it's the lowest point", but "the fewest people remember the word in position 12". We came up with a number of good questions to draw out the math. We also talked about what this means in terms of memory and how this can be used in real life. We also did a 2nd run with a new set of words, only this time at the end Al "burned" everyone's short term memory. Here is my data and graph and this is what Dylan Kane did with it: I think we spent some time just talking about spiralling (I wrote this after TMC14 as an overview) and answering questions to finish off day 2. Day 3: We started day 3 with me saying that although I have jumped off the edge of the cliff with my grade 10 applied classes, I still teach with units in other courses. I have been incorporating activities in my classes for, well, forever, but have made a much more concerted effort in the past few years to add meaningful activities where they make sense in each of my classes. I find this more difficult the higher the grade, but continue to look. I often find that matching activities work to help consolidate learning. I'm pretty sure I showed a few examples of other activities - this blog post likely highlights most of them. Initially Al and I thought we would have everyone in the group create an activity of their own, but we changed the plan. I had started a Google spreadsheet to collect activities as I thought this would be more helpful in the long run. The intent was that this way we would all share with each other and everyone would have a starting point if they wanted to add activities to their class(es) this year. Well, the one-and-only John Stevens ran with this and turned it into the MTBoS Activity Bank which is searchable and all kinds of awesome. We populated it with 68 activities during that morning session and everyone can submit their own using the link at the top of the Activity Bank page. This is such a great example of "together we are better"! A huge thank you to the participants in our morning session for making it so great. Apologies from me for not contributing as much as I would have liked. I know we will all stay connected throughout the year and support each other in our journey to make our classrooms better for all our students. Post Script: Since TMC15 I have decided to go against the flow and will be spiralling my grade 10 academic class this fall. I'm very grateful to have the full support of my principal. My plan is to blog every day to help me reflect and perhaps provide something useful to others along the way.

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One of the best ways to integrate word problems and real world applications into math lessons is through problem solving activities and math stations.

Specializing in engaging activities for middle school math and science. Providing resources and support for busy teachers.

Whether your children love or hate math, it’s a necessary subject. Many children don’t understand its necessity, though, and continually ask the question, “When will I ever use this in real life?” We can help our children understand the answer to that question when we make math meaningful by connecting it to real life.

So, I’m homeschooling my second first grader (Did that make sense? My second son has reached first grade) and we’re on our FOURTH math curriculum. Actually, our curriculum-hopping spanned second grade as well. Kind of embarrassing considering that I was an education major and all! Along the way, I’ve come to a couple of conclusions: […]

Read about how I incorporated a variety of ways to teach math in my first grade classroom to help make math meaningful!

Four days ago I wrote this blog post about using Which One Doesn't Belong? as an activity for my calculus classes. I have had a lot of positive feedback about it and along the way Pam Wilson tweeted this: and that also got a good response. So I decided to take this on. It's a good thing that I'm on March break as this has taken a few (!) more hours than I normally have "free" during the week. Announcing the Which One Doesn't Belong? website at http://wodb.ca/ I really hope that many of you will contribute to the site (some of my children already have!) as that is the only way it will grow. I plan on having my students create their own and will add them - please do the same with your students. You can also follow @WODB?Math on Twitter. 2015-03-20 - Update In order to help you use and create WODB?, here are some links. To help you create: WODB? Template (SMART Notebook) Graph software that I use (produces very clean graphs) To help you use (especially if your students have trouble with right & left): WODB? ABCD Template (SMART Notebook) WODB? ABCD Template - white background (.jpg) WODB? ABCD Template - blue background (.jpg) Please let me know if there is anything else that would be helpful. Also - I am happy to format submissions if you just send in content.

For many people, Mathematics has been an extremely challenging subject. However, these useful Math hacks will guide you! Ready to solve some equations?

Looking for a fun and hands on way to teach multiplication and division? How about LEGO! There are so many easy ideas here for LEGO multiplication and division to help your kids succeed.

At the beginning of my math teaching career, I was not an effective teacher. At the time, I thought I was. I was a good orator and mixed in funny [...]

Store Flyer Math Activities! Every week I get flyers in the mail- so why not turn them into meaningful math activities in the classroom? Read more now!

Color by Number Subtraction Facts - No Prep with Answer Keys is a student favorite. Practicing math facts with these 17 student pages motivates students. Teachers love the NO PREP printable pages with answer keys for developing basic subtraction fact fluency. "Color by Subtraction Facts" - 17 stude...

I stopped using timed tests to assess math fluency. Check out what I'm doing to foster meaningful fluency and help my students develop number sense!

Easy ways to increase student participation in mathematical discourse in the upper elementary math classroom, grade 3, 4, 5 common core aligned math group work

Math Properties Anchor Chart! Teach students about the commutative, associative, distributive and identity properties this this anchor chart!

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At the moment I’m involved in a project with the Sydney Metro (Transport for NSW), currently the largest infrastructure project in Australia. When complete, the Sydney Metro project is going to cha…

I decided to skip today's warm-up as I had made a Kahoot for my class. I'm fairly certain that I can't share it unless you have a Kahoot account so I will tell you that my username is "maryatwest" and

Math and manipulatives go together like peas and carrots. Math stations are the perfect vehicle for collaborative learning. Learn more here.

Store Flyer Math Activities! Every week I get flyers in the mail- so why not turn them into meaningful math activities in the classroom? Read more now!

Top Picks for AMAZING Math Supplies from Moms and Teachers that will have your kids begging for MORE math time!

Understanding ratios, rates, and proportions is essential for middle school students, not only for their math curriculum but also for applying these concepts in real-world scenarios. Here are strategies for middle school math teachers to make these topics engaging and relevant to their students.

Looking for a fun and hands on way to teach multiplication and division? How about LEGO! There are so many easy ideas here for LEGO multiplication and division to help your kids succeed.

The good news is that no matter your child's performance thus far, these tips for how to improve math skills will help them succeed.