I'm sure you use a variety of review activities in your elementary or middle school classroom - have you ever used Footloose activities? I've mentioned the activity in my blog posts before, but have never really explained it on this blog (I did on my old one, maybe 5(!) years ago), so unless you've used one of my Footloose activities in your classroom, you might not know how it works. It's an activity that is enjoyed by students of all ages, and can be used with just about any topic you're teaching. I use it mostly for math, because that's what I teach; but in the past, when I taught different grade levels, I used it as a review activity in other subject areas as well.
It's amazing how quiet and engaged students are when completing this activity. They are up and down, out of their seats, and you'd think they'd be very distracted...but no matter what the grade level (I've used it with 2nd, 4th, 5th, and 6th grades), students stay focused and work hard to complete the questions!
Finding the Lowest Common Denominator with the
What's the most challenging math topic to teach/most difficult for your students to ‘get'?
This was my question in a recent Instagram survey. I got a variety of responses, but the one that came up most often was fractions – remembering the ‘rules;’ students finding common denominators when they were multiplying; students (older students) not being able to find a common denominator; and so on.
So, today, I’m going to share how to use the ladder method to find the lowest (least) common denominator, and hopefully, if your students have struggled with this, it will help them (and you!). Before I explain how it works, I want to share that I've used the ladder method for several years, after many years of teaching GCF and LCM the ‘traditional’ way - the way I’d been taught! And during those years, I’d often get frustrated by the fact that students would miss the GCF because they missed factors, or they couldn’t find the LCD because the numbers got too big so they just multiplied the denominators…..or they listed out the multiples, but made a mistake in one list, and so they never found an LCM/LCD. I'm sure you know what I mean!
The ladder method took these issues away, and it also added something I didn’t initially expect – it appeared to improve number sense for many students who struggled with their multiplication facts or with the idea of finding factors and multiples. It helped them understand HOW numbers were related to each other by making the breakdown of the #s more visual (using prime factorization does this as well, but the ladder method provides a little more organization to the process, and I think that’s helpful).
Use Task Cards in a New Way, to Provide
Self-Differentiation and Promote Discussion
If you're like me (and so many other teachers), you know that task cards can be used in sooo many ways. From centers to Footloose (or Scoot) to exit tickets to entrance tickets to mini-quizzes - the list is long!
However, if you're like me in other ways, you're always looking for something new and different. This year, my "new and different" was to start using task cards to play Truth or Dare in math and language arts classes! To use them this way, some of the task/question cards need to be written as True or False questions, which can make the questions just a little trickier and lead to more in-depth thinking. I allow students to discuss the answers after the "official" answer is given, and depending on the question, students end up having great discussions!
The Dare questions are a little harder, require more calculation or perhaps more verbal explanation than the Truth cards, and so they are worth more points. (Truth cards are worth one point while Dare cards are worth 2 or 3 - I've even thrown in a 4-pointer here and there.)
What makes this game fun? Well, it's a little different - with the "dare" part in there. Students also don't always know how many points they're going to get to try, so that offers a little excitement. I like the fact that students can choose the type of question they want, so it allows for some self-determined differentiation...the choice gives the more hesitant students the chance to feel a little more confident.
After creating several paper and pencil Truth or Dare games, my wonderful friend Leah (Secondary Resources for Social Studies & English) suggested that I make a Google classroom version, and I'm so glad I did! It's so easy to use and there's little to no copying needed! (A little copying if I want students to write their work/answers on paper; no copying if I want to share the Truth or Dare game in Edit mode and have students type their answers.) Check out the 2-minute video below - it shows how the game works in Edit mode (there are one or two "slow to refresh" spots in the video, so please don't think it's not working:-)
Check out this video to learn more about the way the game is played with paper/pencil - in any subject!
I hope you can use this game idea-it can be used in any subject!
I was looking through my middle school math folders on my computer, and came across a document called "The Factor Game," and it occurred to me that in trying to think of some new things to do with my classes, I forgot to play the Factor Game this year when we started talking about factors!
I was so disappointed with myself. Of course, we can play it next week, or any other time, but I just couldn't believe that I had forgotten about it. I'm sure many people know of the Factor Game, or use a version of it, but for those who don't, here it is!
Have I mentioned that I love Jo Boaler’s books and site, Youcubed.org? Well, I do! She shares so much fantastic research and so many wonderful ideas.
So, I was reading her book Mathematical Mindsets this week, and read about the “array game” (called How Close to 100), which I’ve seen all over Pinterest and thought was very cool. I tried it with my classes last year during a little bit of down time, and they liked it. I hadn't really thought of using it this year, but last week I noticed the baggie of polyhedral dice that I've had for a looooong time and thought it would be cool to use the dodecahedron dice for the array game. With these dice, the students could use numbers up to 12, rather than 6.
To set up their game, students each outlined a 20 by 20 area on their own graph paper. They took turns rolling their dice and creating arrays to represent the multiplication problem they had rolled. It was very interesting to observe the way students arranged their arrays. Some started in the corner and worked their way out, while others started on one side and worked their way across. Some made the arrays touch, if possible, while others left a row between each one. Some just drew their first few arrays anywhere and then discovered that they didn't have a lot of room to fit additional ones. The "winner" was the student with the fewest number of boxes left (some did get to zero left). The students really had fun with this!
Of course, some finished their games earlier than others. In these cases, I asked students to create arrays that used different numbers than the numbers they rolled, but represented the same area. For example, if they rolled 12 and 5, their arrays could be 10 by 6, 15 by 4, or 20 by 3 (not 30 by 2, we discussed, because the grid is only 20 by 20). If they rolled a number that couldn't be represented by a whole-number array, they could then use an irregular shape, or a triangle - anything they could find the area of. It was interesting to see how some students got stumped when they tried to draw an irregular shape to represent a number like 81.
Most students enjoyed this twist (we continued it the next day so they all got to play this version), but a few complained that it made their heads hurt! That's ok...I know they were really thinking and growing mathematically!
The next extension for early finishers (only a few) was to use the icosahedron (20-sided) dice, and have students create area models to cover their grids and find the answer to the multiplication problems. This required a larger grid, so I had them tape 2 pieces of graph paper together and create 20 by 40 grids. Using the icosahedron dice gave a mix of 1-digit by 1-digit, 1 by 2-digit, and 2 by 2-digit problems to model and solve. Most students didn't get very far with this before we ran out of time, but I think this is a great way to them to visualize what multiplying by a two-digit number means. I'd like to revisit this one!
I'm so glad I thought about using those polyhedral dice!
Have you used polyhedral dice in your math classroom? If so, please share how!
Remove One is one of my favorite games! It's a great way to teach probability and the students love it. I've been using it nearly every year since I was introduced to it through a program called the Mathline Middle School Math Project, sponsored by PBS (back in 1997?). I was involved in the program through my graduate studies at Allentown College of Saint Francis DeSales (now DeSales University). Anyway, this year, my student teacher is teaching our probability lessons; so she is the one who taught this lesson.
This is how the lesson works:
1. Students use a piece of paper as their "game board" and number the paper from 12-2 (or 2-12) . They then place 15 chips next to the numbers. They are told that they can place one chip next to every number and then place the extras next to any number they want. Or, they can leave some numbers with no chips and put several on others. Usually, they place the chips like those in the picture to the right.
2. Once students have their chips set up, the teacher rolls 2 dice and finds the sum of the numbers that are rolled.
3. If students have a chip next to that sum, the students may remove ONE chip from their paper (thus the name of the game -Remove One).
4. Play continues, with the teacher rolling the dice and the students removing one chip each time the corresponding sum is rolled.
The "winner" is the student who removes all of the chips first.
Without much class discussion, we play the game a second time. Normally, I just ask them to make some quiet observations to themselves before placing their chips again. Students typically notice that the sums of 6, 7, and 8 are rolled the most often and that 2 and 12 are usually rolled the least often, so they arrange their chips differently.
After the second game, we have a discussion about all of the possible outcomes (sums) one can get when rolling 2 dice. We also discuss how many ways there are to roll each of those outcomes, and what the probability is of rolling each sum. We find this probability in fraction form, and then often convert them to decimals and percents.
After this discussion, we play the game for a third time, and students' "game boards" often look a bit different!
This year, since I was observing rather than teaching, I was better able to hear some of the students' quiet comments to each other... "There's a better chance of getting a seven." "I'm not going to put any on 2, because it still hasn't come up."
When I started discussing this lesson with my student teacher, I searched for the lesson online, just in case it was around, and I found it right away. Click HERE to see the full lesson plan from PBS.
Have you played this game?
What other probability games do your students enjoy?
Ratios and Proportions Activity for the Middle School
Food can make ratios and proportions more fun during a middle school math class, right? "Something Fishy" is a great hands-on activity to help students understand a real-life application of ratios and proportions. It also gives them the chance to munch on a few Goldfish :-) This is a lesson I found through the Mathline Middle School Math Project, sponsored by PBS (I mentioned this program in the "Remove One" post).
This ratios and proportions lesson presents the students with an environmental problem: "scientists have determined that the number of fish in the Chesapeake Bay has decreased. Assuming this is true, scientists must have counted the number of fish and noted the change. How did they count the fish?"
After introducing the problem, the students brainstorm ways that the scientists could count the fish. I have four math classes, and in each class, there was a student who said that scientists could tag the fish. So we discussed how tagging the fish would work, and talked about the capture-recapture method. Using a sample ratio, we talked about how we could create a proportion to figure out an estimate of the population.
For this lesson, we used:
* regular Goldfish crackers
* pretzel Goldfish crackers
* 2 paper bowls per group (any container that they can scoop from will work...we used the 2nd bowl to put the "captured" fish into)
* a spoon to scoop with
I didn't count the number of fish that I gave each group...I simply poured fish into the bowl...but they all ended up having 70-90 fish.
I demonstrated all of the following steps for the students, so they understood what to do, and then I gave them a RECORDING SHEET (found below) that also included the directions.
Student steps for the lesson:
1. Students "capture" a sample of regular goldfish from the container. This sample should be tagged by replacing them with pretzel goldfish, and the "captured" goldfish should be set aside and no longer counted in the population.
2. Students put the tagged fish back into the container and mix up the fish so that the tagged fish are evenly distributed.
Move on to the recapturing:
3. Capture a new sample and record both the total number of fish in the sample and the number of tagged fish in the sample. Return all fish to the container.
4. Recapture 6 times (or whatever you have time for...we were able to do 6 times, and we have a 40-min math period).
5. Guide the students to create and solve the proportion for their "bay."
6. Have students count their fish and then compare their estimated total with the actual number of fish. Some of my groups got fairly close...I believe the closest was an estimate of 68 and an actual count of 74. It seemed that the groups with larger sample sizes ended up with closer estimates than those with smaller sample sizes, though I didn't analyze those relationships too carefully yet!
7. Allow students to eat the goldfish (if they don't have allergies)!
To see the PBS Mathline lesson, click HERE.
What ratio and proportions lessons are your favorites?
Hi, I'm Ellie! My mission here is to support teachers as they work to provide engaging, meaningful experiences for their students. I've been in education for 25 years, teaching all subject areas at both the elementary and middle school levels, and am here to share what I've learned through those years, as well as what I continue to learn. I hope you'll find some ideas or resources here to help you out!