January 30, 2016 by Beyond Traditional Math

Build It = Deep Conceptual Understanding of Multiplication

Being a math interventionist is one of the hardest jobs I’ve ever had. It’s like a constant cycle of diagnose…teach…teach…teach…light bulb on…light bulb off…diagnose…teach…teach…teach…

I’ve been working with a group of fourth graders that were just struggling BIG TIME with multiplication. They weren’t able to see how a fact like 3×7 could help them solve 6×7 by just doubling. The numbers were too abstract, and they had nothing to connect it to.

Of course as I dug deeper I found that they simply had zero understanding of what 3×7 really means. So as usual, I tried to find a way to connect it to real life, my favorite thing ever. I was trying to think of a way to help them remember the difference between rows and columns. And then it occurred to me as I was waiting in line at the theater, no one wants to wait in line to sit in the first COLUMN for a popular movie. We all want the best seats in the house, so we wait to sit in the first ROW.

Enter the Movie Theater Multiplication Project. I went home over the weekend, turned off all distractions and poured days and days into authoring this project. I needed to really think for myself what 3×7 represented. I was not taught this way and I know that it doesn’t come easily to me. I also had to think of a way that would be meaningful and that would STICK, since that seems to be the biggest challenge facing students in intervention. The last thing that I really needed to think about was the Concrete-Representational-Abstract instructional approach. Kids LOVE to build. The second they walk into my math lab, their hands are all over my cubes, blocks, counters, etc. Starting with building means that they can usually connect a pictorial representation to it, and then connect that to numbers.

So I made a movie theater or two or three as I wrote the project. I made theaters that were 3 rows of 4 seats, making 12 seats total (3 x 4=12). I made tickets placing them in the correct row and seat number. And finally I made some mega theater designs so they could learn to use known facts to solve harder facts. There is a fourth stage to the project also that involves some open ended challenges to calculate profits and revenue. Say hello to my little friends:

Multiplication-conceptual-understanding

Seemed like it might actually work!

So I brought the idea to school. I got out some tools and some little tiny bears and THAT got their attention. Tiny bears! Seriously, that is all it took?!

The first three days of the project were brutal. They were making columns instead of rows, they were making rows of 20 instead of 20 seats total. With probing questions they started to see what was happening. And THEN, light bulbs turned on…and for several days now the light bulbs have stayed on! Is it sticking?! I hope so, and we’ll find out when they get to the mega theaters and can break down more difficult multiplication. Wish me luck!

If you want to try this out, in the preview you will find three parts of the four stages of the project that are free. You could totally continue the project by giving them your own specifications!

April 21, 2014March 29, 2017 by Beyond Traditional Math

Earth Day Water Pollution Activity: A Cross Curricular Inquiry Study

Today was one of those magical days at school. It was the kind of day that makes me LOVE my job, where all the pieces go together very nicely and the worldview expands for the students in the classroom. Today was one of those “teach like a pirate” days, where we took risks and immersed ourselves fully into an important issue.

We began our Earth Week (not just Earth Day) by learning about the Great Pacific Garbage Patch, something that is largely unknown to the general population. We read about the issue with a two page informational text today, while responding in writing with our new understandings.

Then we watched this video:

After lots of important discussion, I asked them a question, “How would you clean it up?”

That led to an awesome water pollution experiment, which ended up both engaging and frustrating the students. The groups had to try to clean up the water using the least amount of money possible. They had to write out their plan as a group together, figure out the cost and bring their proposal to my supply table to collect the materials they needed to clean the water. They had to be detailed and precise, use math in a very real way, and had to work under time pressure. Here is a peak into what it looked like:

Buckets were prepared with water and biodegradable items like coffee grounds, shredded paper, food that the kitchen hadn’t served but had to throw away, and soil.

Reused or recyclable items were for sale for students to use to clean up the water. (I wash out the cups and forks to reuse each year for this experiment! We reuse ziplock bags collected throughout the week. We recycle other plastics and aluminum foil.)

The students cleaned the water after “purchasing” materials.

Many methods were used to clean the water.

We compared water samples at the end, to see who was most successful. We also compared budgets, to see who was able to keep costs down.

We’ll continue this work for the rest of the week:

We’ll be writing a letter to explain what we learned today about the Great Pacific Garbage Patch and the difficulties of cleaning up water.
I plan to immerse them in lots of good Earth Day literature like: The Great Kapok Tree by Lynne Cherry, Oil Spill by Melvin Berger, The Lorax by Dr. Seuss, The Wump World by Bill Peet.
We’ll be learning about alternative energy to make wind powered cars later in the week, and we’ll even try to harness the sun by measuring and making solar ovens.
We’ve also got some tough math problems in the works as part of the Great Pacific Garbage Patch unit to help us think about conserving!

I love Earth Day…Earth Week, and more importantly introducing important issues to our young learners, encouraging critical thinking in meaningful ways. I’d love to hear what you do in your classroom! The more ideas we have to share, the more we can teach our children to be environmental stewards.

Learn more with these resources and dig deep into the issues:

March 30, 2014March 31, 2014 by Beyond Traditional Math

3 Hands On Earth Day Activities that Integrate Math

Here are three really amazing Earth Day activities for your elementary classroom that all include math. I’ve done them all and they’ve been memorable, educational, and fun! The best part is they always lead to deep moral and ethical conversations.

1. Hold a Trash Free Lunch Picnic: This is a two day project. The first day, you ask the students to keep track of how many pieces of trash they have as they eat lunch. For the second day, you send home a note asking parents to pack a trash free lunch, (as trash free as possible) to see if you can cut down on the amount of trash. On the day of the trash free lunch, you ask the students to count how many pieces.

Here is an example of a student’s trash free lunch.

We kept track on a tally chart and realized the impact we can have if we change one simple thing, how we pack our lunches! Then, the students draw a bar graph or a pie chart to show the results of the tally chart.

Record the data of a trashy lunch vs. a trash free lunch!

2. Build a Solar Oven and Bake S’Mores: Show a tutorial for how to make a solar oven a few days before Earth Day. Here is one that could be made from a pizza box!

Tell the students to bring their own supplies from home (cardboard boxes, plastic wrap, aluminum foil, tape) and give them time to make them when they first get to school. It took our class about 2 hours. The math involved is awesome, measurement, measurement and more measurement! I brought the graham crackers, chocolate, and marshmallows and they melted like crazy in the sun. It was super fun! Here are a few photos.

Students bring in their own materials, but you may want to have some extras on hand.

This student even put a skewer in the middle of the oven, too bad they decided not to use it in the end.

Some students learned the hard way that you need to CLOSE the solar oven!

3. Study an Important Environmental Issue and Act on it: Perhaps the best Earth Day activity we’ve done is something that felt meaningful, like we could make change happen! We studied the Great Pacific Garbage Patch by watching videos, reading about it, doing some math problems surrounding conservation, and by writing persuasive letters. We ended the project by doing a water pollution science experiment.

Here is a video about the Great Pacific Garbage Patch if you haven’t heard about it (Depending on the age of your students, you may be able to show it to your class.):

Here are some photos of us trying to “clean” water, so students could find out how truly difficult it was. As they work, each tool they borrow from me costs them money. They have to keep track of the cost of their clean up.

Earth Day Activity Water Pollution Experiment

Students are trying to clean out a polluted basin of water using different tools (all of which cost different amounts of money). They keep track of their successes and the cost of cleaning out their basin of water.

A student is trying to remove vegetable oil from their basin of polluted water. NOT easy!

The bottom line, is there are so many things that students can do to learn about alternative energy, and to study current environmental issues. Instead of encouraging them to recycle with a coloring sheet or a worksheet, engaging them in these issues will help them feel an authentic push to do it!

I love Earth Day and the awareness it brings to young people! What kinds of things do you do with your class on Earth Day? Share below in the comments. 🙂

January 30, 2014 by Beyond Traditional Math

Push Past the Tears: Peers Teach Perseverance

Today was the final stage of our Elementary Architects Project. Students were about to turn in their design plans for approval (and classroom money), and were feeling the pressure as the clock was winding down. With 5 minutes to go, one student (“Corey”- I certainly don’t want to cyber embarrass anyone with their real name) came to me, tears welling up and blurted, “I don’t want to turn this in, I don’t want to be paid, and I just want to throw it in the garbage!”

I was a little taken aback, because Corey’s blueprint of his dream bedroom was beautiful! It had all the right things, and was designed with all kinds of creativity. Miraculously it was to scale (many third graders struggle with this a bit!) and it was a totally perfect birds eye view.

So I sat him down at my table where four other students were sitting. Corey was fighting back tears as we went through the specifications sheet. As we named each specification the other four students at the table gave him encouragement, pointing to each item on his blueprint as I read it off. When we got to the part where it said to calculate the area of the space, that was when he really broke down in tears.

Now I know I should never underestimate the power of anchor charts, because at that moment, one of the other boys at the table looked at him and said, “Look up on the Smartboard!” We had worked through calculating area in three ways just a few days prior, so I’ve kept this slide up every time we worked on the project.

Then, he proceeded to help Corey figure out which way would be the best way to calculate the area of the space. The student who was helping used a calm voice, and his method was methodical. Once Corey had the help, the tears went away and he handed me his final page with a very proud smile.

I learned today that a kind classroom community will support all learners. Students can stay calm in the face of obstacles if those around them are calm and supportive! I think sometimes I feel like I have to be the one to help them, but their peers can be just as helpful if not more so. As I reflected on my day today, I want to think more about how to foster that type of community so that everyone can learn to persevere together.

January 25, 2014 by Beyond Traditional Math

Elementary Architects: Free Math Project – January 25-27th

I am going to preface this post with a note about me. I am not at all a person who self promotes or constantly mentions things I’ve created in blog posts to sell them to everyone. I don’t use cutesy clip art or decorative borders. My cover pages for the things I create are always pretty straightforward with real photos of students doing real math. The units I write are meant to take students to a deep level of understanding, with research based practices.

In addition, I want this blog to be all about teaching tips, reflections on the best ways for our brains to learn math…not a non-stop promotion of myself. The whole idea of putting items up for sale took me a full year to actually agree to do, and only because the staff members in my building kept on pressing and encouraging me to share to the world what I had created for all of them. My hopes and dreams are to raise enough money that I can design an online math fact fluency program that is all in my head and just waiting to happen.

With all that being said, I did join an event called a Facebook free-for-all. I joined because there are people out there that are just like me, they want their ideas spread because our primary focus is not about making money. We know that the more we share, the more we’ll learn about becoming better for our students. I have been going through the “map” and am amazed at all of the things that other teachers have created and are giving away for free. It’s truly remarkable.

If you go to my Facebook Page and click on the tab right under my cover photo that looks like this:

It will take you to my free resource, Elementary Architects. The reason I linked this to my facebook page, is because there is a map that you can use to find other people who are participating in this same event (you’ll see on the picture it says “click here to find more”. If you don’t have facebook, hate facebook or really hate the whole idea, you can still get Elementary Architects for free in my TPT store. It’ll be free until January 27th!

In Elementary Architects, students design a space, calculate the area of that space and then figure out the cost of flooring. It is sort of cool because it differentiates naturally, and it requires LOTS of precision. I pay my students with classroom dollars if they get everything perfect on the specification sheet which is very motivating to them.

Here they are at work!

What I like best about this project, is the structured days leading up to the actual work that they do. They learn little bits at a time, and I can even introduce the distributive property as a third way to calculate area. I hope you find it useful, and would appreciate any feedback you can give to help me get better!

January 1, 2014January 1, 2014 by Beyond Traditional Math

Math In Real Life: I Am The Worst Party Planner

So I am the worst, and I mean the WORST at estimating party needs. In the past I have ordered pizza for my classroom and ended up with 6 extra pizzas. Part of the problem is that I’m not very good at estimation (including how much less pizza an average third grader will eat compared to myself), but also I rarely practice this skill.

This year for our holiday party, it COMPLETELY slipped my mind to ask parents to volunteer to bring snacks, napkins, drinks, etc…somehow the day of the party was only 2 days away and I was in a bind. As we all know, no one has tons of cash to throw around for holiday parties anyway.

So I was determined to NOT screw this one up. I was going to go in to the grocery store with a calculator, the number of students in my class, and a tight budget. I felt good about this trip, I knew that it would be easier because I was calculating 1 candy cane per student, a handful of pretzels per student and 1 capri sun per student. I even found some napkins…on sale!

So get this! After the party I ended up with 2 leftover candy canes, 4 extra capri suns and a stack of napkins.

Why I have been historically terrible at this is sort of a mystery to me. It’s not like it is complex math, rather it involves using simple math in a complex way. This was not how I was taught math growing up, so I have to actually practice this to get better at it! It is why I created the Party Planning Awesomeness Project for my students. It is the reason that I create all of the things I do, because I feel that students really do need to be able to practice these skills.

Check it out! We actually did this prior to our last math test, with a class goal. If we got 94% as a whole class average, we’d earn the party that the students voted for. And…they did it! I now have another party to shop for, but this time the student did all the math!

Thanks to these ladies: 4mulaFun, Fourth Grade Studio, Teaching to Inspire in 5th, AND MissMathDork for the opportunity to link up! Apparently this is a monthly thing that they do, being new to blogging for only a few months, I had no clue how awesome this is.

January 1, 2014 by Beyond Traditional Math

Even and Odd: The Importance of Conceptual Understanding

I can’t tell you how many times I learn through the eyes of my five year old. She asks amazing questions, especially when it comes to numbers. While we were doing some daily math play today, I thought about introducing her to the concept of even and odd numbers. I was taught even and odd by being told to memorize the numbers: 2,4,6,8. As a tiny child I don’t think I truly understood why a number was even vs. odd.

So we built the numbers 1-10 (in hindsight I wish I had included zero) with unifix cubes. Then I told her to put them in pairs. We put the pairs together, and lined everything up. During this process she was uncomfortable whenever one was left over, and wanted to pair it up with one from another number set! This is how it looked once we had it all situated.

Then I asked her what she noticed.

“There is ‘ones’ all by itself!”

We pointed out which numbers had an “odd one out” as I put it. That was when I introduced the words odd and even. I think it is essential to introduce the vocabulary to kids after they have explored the concept, so that they have a way to name what it is they are seeing.

She then noticed that every other number was odd. So we looked at and extended the pattern: odd, even, odd, even….until we got to the 10. I then asked her what she thought 11 would be, odd or even? She shouted out “odd!” without even thinking about it.

I still have a few third graders that are struggling with this concept (can you even believe that?). I am going to try to see if this could help them understand this very basic concept.

December 30, 2013January 1, 2014 by Beyond Traditional Math

Fit: A Free Multiplication Strategy Game Using Arrays

Tis’ the time of year to learn multiplication! I’ve created a new game (TOTALLY free for you to grab) for my students. My third graders have gone absolutely *bonkers* over it. We had been studying arrays as a way to represent multiplication, when it hit me that legos are a beautiful and motivating way to explore arrays! Truth be told the idea came to me at about 3:00 A.M. (isn’t that when our best ideas come to us?) to try to make this a game.

In this game the student multiplies the array of each piece they lay down. (Example: a 2 x 4 piece is written on the recording sheet as 2 x 4 = 8.) They can only lay down a piece by connecting corners, which makes it challenging to fit as many pieces as they can. In the end there is a good amount of mental math addition of multiple numbers that is required to determine the winner. There is a challenge mode included where the students multiply the two blocks together (and in some cases three blocks where the corners touch). This is more appropriate for the practice of facts, as well as for multiplying two or more numbers together.

This resource includes:

1. Introduction, and game set up tips
2. Recording sheet
3. Regulation mode instructions
4. Challenge mode instructions

Right now we have a tournament going on, in which the winner chooses a $25 lego set as a prize. They are so motivated that they are staying in at recess to play practice games.

Check it out!

Thanks to Nancy for the link up!

Thanks to Charity Preston for the link up!

December 29, 2013December 30, 2013 by Beyond Traditional Math

Assume Nothing! Why Some Strategies Might Not Work (At First)

Remember when analog clocks were the only kinds of clocks around? I grew up with them, digital clocks didn’t really creep into my life until I was in middle school. I learned to tell time at a very early age because of the lack of cell phones and computers with their digital displays. So, I always assume (which I NEVER should) that my third graders know how to tell the time.

I was reminded once again last week that assumptions are a foolish thing! We were in the middle of learning about multiplication. My goal is to expose my students to as many strategies as I can think of to learn multiplication, especially when the strategy relates to real life. I was so excited to share this strategy:

I shared it with my students, eager to see their familiar “oh, I get it” or “I can connect with that” faces. I got absolutely NONE of that. They just kind of gazed at me with blank eyes.

So I said, “You know, if the minute hand is on the 7, then you know 5 x 7 is 35…?”

Again, nothing.

I couldn’t believe it. I asked (very gently), “Do you all know how to tell the time?” (We haven’t done a time unit yet this year, so I haven’t checked their understanding regarding analog clocks.) Instead of a resounding “yes”, I got many downcast eyes. I took an anonymous poll by asking them to close their eyes and raise their hands if they know how to tell the time on the clock on the wall. I was surprised to see only 2 hands go up out of 26. Ouch.

We really cannot assume anything of our students. Now that I’ve unearthed this little gem, we’ve got two things to work on at once! We came up with the solution of labeling our classroom clock with the numbers to help us get more familiar with each tick mark. When we get back from break, I am going to brainstorm with my students how we can use the clock in our classroom more often. The more we use it, the more useful this particular multiplication strategy will become!

December 3, 2013December 30, 2013 by Beyond Traditional Math

Let THEM Make Those Math Connections!

One of my favorite parts about teaching math (and multiplication specifically) is all of the amazing patterns and connections from one thing to the next. When I first started teaching I would to preach these patterns to my students. They thought they were cool, but that was about all. One day a student in my class saw a pattern I hadn’t seen before, and I realized that it has WAY more meaning if they discover the connections themselves. Now, when THEY discover the patterns/connections it feels even more amazing, not to mention the fact that it sticks in their minds.

My students finally connected with a multiplication concept today. We are at the beginning stages of teaching multiplication, so the whole thing is a little mind blowing to them. They learned to multiply with repeated addition, equal groups, arrays, and with using a number line. I noticed that they didn’t seem to understand how they were all related.

So I sat them down with a blank piece of paper with the words: “Multiplication: It’s all related!” I asked them to see if they could find how each thing I put on the chart was related. I didn’t speak as I put up each one, one at a time.

The moment came when I got to the third one…arrays…and placed each square up (in rows of 5). I heard a few “oh’s!” and hands flew up in the air. Then they started to predict what my number line was going to do (I drew it out first before the hops-again not even saying a word!). Seeing them predict meant that many of them were catching on to how they are all connected. At the end I asked them what they thought the multiplication fact was, and the answer was shouted to me by 26 children.

“5 times 3!”

Beyond Traditional Math

Fostering conceptual understanding with real world connections.

Tag / project based learning