Have you even seen this yet?! Click on the image to go straight to the PDF of this amazing multiplication table by David Millar of thegriddle.net. It is free to educators to print and use in the classroom. Even better if you go to the educator section, there is a black and white version that is both with and without numbers.
My mind is churning with the possibilities for using this in the classroom! I think it is the best multiplication table I’ve certainly ever seen. Talk about helping students conceptually understand multiplication, connect it to arrays as well as the concept of area.
I am not sure if you’ve ever had that “moment”. The moment where you are at a frustration level with why things aren’t working. I used to look for extra worksheets to give more time for tricky math concepts to “stick” with students. I looked online for further practice activities, I asked colleagues for their extra resources for more practice, I looked for games. I felt like I’d tried everything. That’s when I read some research that making math real world, connecting it to student’s lives was REALLY good practice. So a few years ago I started to create real world problem solving projects to help this problem.
That was how the Book Order Proposal project started (for my gifted and talented students I’ve used The Housing Market Analysis). I knew that I needed to continually reinforce the concept of rounding/estimation, comparing numbers, and mental math addition strategies. I gave my students the chance to do just that by offering to buy books for our classroom library. I decided to coincide this project with my parent Scholastic Book Club order. Here is how it worked:
- I made it my problem of the day for 4 consecutive days, giving 20 minutes each day for the project. The first three were days for them to work (with a mini lesson or two if needed), and the fourth day was the peer review day.
- All students were given a budget of $50 (bonus points offset this cost-I was able to get all of our books free this last round) to look through three Scholastic flyers.
- The students had to put together a proposal, thinking about their classmate’s reading interests, as well as thinking of what we currently have in our classroom library.
What happened was kind of interesting. The majority of the students got within $2 of the $50 budget. A few of the students tried to hand in proposals that were $1, $30 or $25. When we talked as a class on the second day, I asked my students if it was okay if someone didn’t get close to $50. The resounding answer was “NO!”. When asked why, they explained that it would be a waste of money if they didn’t spend it all, especially since they would become THEIR books for their classroom. I handed back those few papers and asked them to start again. (Now that is what we call peer accountability!)
At the end of the project we laid the papers out and did a gallery walk. Students voted on their top 3 favorite proposals. The proposal with the most votes actually got ordered! It was such a fantastic way to end the project.
My favorite part though, the very best part of the entire project, was the gallery walk and natural reflection. Students could see how others choose to put the proposals together. Some were neat and organized, others were missing information, some of them had a hard time with their handwriting, and other student’s numbers didn’t quite add up. It led to great discussion, and the students wrote goals on their proposals for the next time we have to present information to our peers.
It has been clear to me that making math real world, and connecting it to their own lives is a powerful thing!
I will never forget my first reaction when I read through the Standards for Mathematical Practice.
I think it took me another 5 reads to even scratch the surface of what they meant. The rest of the common core seemed like a piece of cake in comparison!
I really tried hard to understand them, but truth be told, I wasn’t sure how they fit in to my classroom. How were elementary students supposed to understand this stuff when I barely could?
As we began to implement the common core, I noticed my students struggling with the deeper problem solving concepts. I was so frustrated. I tried everything…I looked for strategies online to see if there was some kind of magic answer, I asked colleagues what they had tried and began to pull my hair out.
That was when it dawned on me…why don’t I try to incorporate the Standards for Mathematical Practice? So I dug deep and did some research. One of my favorite things I found is from our friend Marilyn Burns (if you don’t know who this is, get to know her!). Her site is amazing, and the video series is really great.
All of the research allowed me to create a guide to introducing the standards for my students. I started with putting them into kid friendly I can statements. I added some sample problems and allowed the students to see each other’s work habits.
Voila! It was like a revolution was born. One of my students had the idea that we should post the standards on the wall, and get a point every time we had a question or gave a compliment with the language of the standard in our comment. Done! We had points like you wouldn’t believe by the end of the school year. (Incidentally the points counted toward absolutely nothing, they were just points for the sake of getting points!)
Intentionally putting the language of these math practices in our every day commentary did the trick. Students gained confidence, it was fun and best of all problem solving was no longer a stress in our classroom.
If I were to count how many times I use my Smart Phone to look something up every day, it would be at least a dozen…maybe more! I use it to find out random facts, convert numbers, convert languages, remind myself of an interesting article I read 3 months ago…I could go on and on.
Anchor charts are truly “Google” for our students. I’ve seen it time and time again. The students are sitting at their desk, drawing out something for their latest project. When they can’t remember what an equilateral triangle is they simply look on the wall where the lesson they just learned about (but haven’t memorized yet) is hanging nicely there. Whenever I have massive amounts of students coming up to me to ask me what something is, it never fails, I’ve forgotten to hang the anchor chart.
So hang those anchor charts! Give them the tools they need so that they can use and remember these important concepts.
One of my favorite practices that has really caught fire in education is the formative assessment. I love it because I know that the “check” I am doing will help me figure out what to teach next, who knows the information and who needs help. I’ve taken formative assessment a little further by allowing their handwriting, work and calculations to become our classroom anchor charts.
In this example, I introduced the students to different types of angles to prepare them for the Mini Golf Course Project. It is one thing to be able to identify them, but a completely different skill is needed to draw them! As a morning message the following day, I asked them to draw me three types of angles: acute, right, and obtuse. It was interesting to see who was most confident, they posted their note up immediately. Others were cautious and wanted to make sure they had it right first. Then, there were those few who were completely baffled. On the spot I was able to guide their thinking, it took only 5 minutes as the rest of the students were getting ready for the day. It was a neat way to slip in a quick intervention. As another review during morning meeting, we looked at how the figures were similar and different.
The best part was, these beautiful angles they drew became an anchor chart for the project! They were able to reference it during the entire project. Their pride in seeing such a simple thing on the wall was simply priceless.
This is a photo of our current math series and its Problem of the Day. This problem was solved in 10 minutes by my students. This is not rigorous enough, not complex enough, not inspiring at all, and just not good enough for my third graders.
Instead, I’ve been using Open Ended Math Problems for the last eight years about once per week. These problems require basic math, but complex thinking. They are multi-step, require more than one class period to complete, and are real world.
Here is an example, called The Museum Trip:
Some ways I’ve used them:
* as a “what to do when you are done” option
* as partner activities
* whole class discussions to talk about problem solving strategies
* small group gifted and talented students have tackled them
* parent volunteers have come in and used them with groups of students who are struggling with problem solving
Open ended math challenges present so many opportunities for dialogue and engagement in the elementary classroom. If we expect students to respond to the common core and the impending assessment that comes along with it, we must practice this type of thinking.
I am just getting started in my TpT store, and wanted to offer a give-a-way in addition to the back to school sale at my store. To enter just follow my blog by entering your email and I will add you into the drawing. (If you already follow me, you are automatically entered!)
Find my products at my TpT store (click the photo to see my store)!
You could win:
Open Ended Math Challenge (7 problems + rubric)
Housing Market Analysis Math Project (2 week unit)
Mini Golf Course Hole Math Project (2 week unit)
Float Challenge Math Project
Elementary Architect Area Math Project (2 week unit)
Party Planning Awesomeness Math Project (1-2 week unit)
* You can “save” your win for future products as well!
You know students are learning when there is an abundance of glue, scissors, pencils, markers and writing about math at the table.
Sometimes it is okay to abandon the quiet, sometimes they learn more from each other.
Let it be a hot mess!