Math BreakoutEdu

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Today is the last day before my school’s Spring Break. Generally, my classes end up finishing up a particular unit before a large break. This time is different. Both my fourth and fifth grade classes are in the middle of a unit.   I’m also finding that both classes are due for some review. Foundational pieces involving place value and order of operations are tripping up some of the students. While looking around for resources, I came across a BreakoutEdu that corresponds with March Madness. I need to give a huge shoutout to Rita for creating this game. I’ve used Breakout in my class before, but am still in the rookie stage. I printed out the files and started to compile them last week. I figured out which locks where needed and started to compile a few different ideas on how it would work.

What’s great is that my school’s media specialist, the fantastic @mrsread, has a teacher BreakoutEdu box that’s available for checkout. I was able to checkout the box and fiddle with the locks earlier this week. I was able to get most of the locks figured out and reset to the codes needed for the activity.  I say most and not all because the multi-lock is still giving me issues. After checking on the forums it seems like this tends to happen more frequently than I originally thought.

After becoming a bit more confident in how to use the set in my own classroom, I decided to use the Breakout with a fourth grade math class this past Thursday. Since I couldn’t use the multi-lock, I decided to use a combination lock that I had at home. I put together a small Google form that coordinated with that particular lock. The next day I spent my planning period organizing the materials. I decided to go with manila envelopes to store the papers and deviously hid them around the classroom. I introduced the game with the slide show in the file at the bottom of this post.

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From the March Madness Breakout PowerPoint

The kids were excited as they already completed a Breakout a few months ago. I told the students that four manila folders were in the room and they had to find them to locate the clues to open the box. I then started the timer and they were off.

Observations

The class of 21 split themselves fairly evenly and started working on the tasks. It just so happened the Google form was completed quickly and one of the locks was open in less than five minutes. That wasn’t my intention.  I was hoping it would be a bit more challenging.   The other tasks, especially the order of operations, took more than 20 minutes to complete. I noticed that around 4-5 students would be working on the sheet while others congregated and tried to find more clues. Some of the kids were making simple errors with the order of operations. The bracket challenge was also tricky, as some students didn’t understand how a bracket worked. Students would complete the bracket and not understand that the larger number would move on to the next section. I could tell that students were getting frustrated as time ticked away.   I didn’t interject although I wanted to help. Eventually, students had to use a hint card, but they prevailed. We had a great conversation afterwards using the Breakout reflection cards. This was also great for me to hear, as students gave feedback about which particular tasks were the most difficult and how they contributed to their team.

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The Breakout worked so well that I decided to use it with my fifth graders the next day. I changed up the Google form piece and made it more aligned to what we’ve been learning over the past few months. I even added a question where students had to translate a problem from German to English. I may or may not have had a ton of fun helping create questions for the game.

Overall, the game went just as well with the fifth grade group, although they had more trouble with the locks. They were a bit confused with the combination lock. Once they figured out at that skill the class opened up the final locks with about 15 minutes or so to spare. The class didn’t have time to review the reflection cards. I’m hoping we can take those out after spring break is over.

Rita’s files for this Breakout can be accessed here. Feel free to use the Google forms (1) (2) that can be copied and used as well.

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Understanding Number Relationships

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Grouping Strategies

Today I was able to dig a bit deeper into Kathy Richardson’s book. The first chapter was related to counting and critical phases that are needed as students develop numeracy skills.  The second chapter focuses on number relationships. In order for students to compare numbers they need to be able to distinguish between larger and smaller. Once at this stage students can recognize that numbers are found within numbers.  For example, eight is found within 10. When comparing numbers students generally start to identify differences between the original number and one.

Richardson states that being able to change a number by counting on or adding to a group is a Critical Learning Phase.  Counting on or adding to a group of numbers is a strategy students use when comparing numbers. I believe primary students might use this strategy to find out how many blocks are in both stacks below.

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Assume that each block is the same size.  Now, how do you think primary students would count these two different stacks?  The strategy that they may use to solve this can tell  more about their understanding.  Are they counting each block individually or using the first stack to count on to find the second stack? While comparing numbers younger students often count each block individually.  The model below shows a different strategy.

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In this case the student has taken the five and built upon it to find four more.  The five and four are nine.  This student didn’t count each stack individually.

I find this interesting as it may apply to other areas of mathematics.  After reading this I started to think of how increasing the complexity could apply to fraction concepts.  Specifically, I thought of how theses blocks and fractions are similar:

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If the green stack is one whole what is the second stack’s value?  How would your students solve this?  In the example students may identify that each block is 1/5.  When looking at the parts on the right they might start off at 5/5 and add to that particular block line. Fractions can lead to confusion with a non-linear scale being present.  This is especially the case if students are always seeing 1:1 ratio when counting objects.

I thought a number line might be a better representations for a fraction problem. Richardson notes that number lines are only symbolic relationships.  She also states that when students use number lines they’re most likely not thinking of quantities, but more so using the line to find the solution. They’re using it as a tool to count on to find a solution.  Number lines are used frequently at the early elementary levels so this is something I’m going to keep in mind for the new school year.

Connecting Math Games and Computation

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I feel like the curriculum stars are in alignment. Many of my classes are exploring computation in some capacity. This rarely happens because of the scope and sequence of the curriculum at the elementary level. Computation is an interesting concept to explore in the classroom. I find students come to class with a variety of computation knowledge, although some of the background relates to procedures or tricks used to compute numbers. Other students have a conceptual understanding of the computation, but might be lacking in the procedural department. Either way, I find that students need more practice to become fluent with computing numbers. They also need to be able to distinguish and apply rules to problems e.g. signed numbers, fractions and order of operations.

Developing computational fluency can be found in a variety of forms, but as of late I’m finding games to be the most beneficial. Computation timed tests drive me nuts. I couldn’t stand that as a student and feel a bit embarrassed when they are assigneds. An alternative to this can be found using math games. Games provide low-risk opportunities for students to engage in math conversation and practice computation skills. This past week I was able to use one of these games with students in second and fourth grade.

The game involves using dice and strategy and computation skills.  Students were given a game board and recording sheet. I pair the students using Michael‘s grouping spreadsheet and the students grab the sheet, dice and find a cozy place in the room. Students then roll the dice and fill in each line slot and match it with an answer on the game board. The game is over when all the slots have been filled. Click on the pictures to download a file of the game.

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2nd Grade – Adding / Subtracting Multi-Digit Numbers

I first used the above game with second grade and then decided to use the same format with a fourth grade class.

4th Grade – Adding / Subtracting Signed Numbers

Both games seem to serve their purpose.  Students are practicing their computation skills while using a variety of strategies to compute numbers. Students are also engaging in math conversations around computation and using vocabulary associated with computation.  In addition to the game sheet, some students decided to grab a whiteboard and complete their computation there before transferring it to the game sheet.  Hopefully these skills will develop into a deeper sense of computational fluency and cement as students progress through school.

 

 

 

 

Operations and Mazes

In a few weeks my fifth grade students will start their pre-algebra unit. Before delving into the unit students often need a reminder on how to use the order of operations with fractions and decimals. Half of today’s class was dedicated to reinforcing number sense and computation skills. At some point students will need to be able to use these skills along with maneuvering variables on both sides of an equation. I find that some students struggle with pre-algebra if they don’t have sound number sense skills.   So today I ended up using an Illuminations operations activity.

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Click for file

I passed out the above sheet to each student then reviewed the directions. Students were paired and asked to find a spot in the room to work. Students were asked to hide their calculators and estimate one path that will lead to the largest number. Each group came up with their own path.

Trial and Error

Students were then asked to use a calculator to find the path that ends with the largest number. It was interesting to listen in on the student conversations. Here are a few of the statements that I picked up:

 

“If you divide the number it will decrease”

“Not really, if you divide less than one the number will increase”

“If you divide by a really small number than our number will skyrocket”

“But we can’t multiply by a number less than one”

“But we can multiply by a large number”

“Let’s just work with the multiplication and division paths, those will make the number jump”

“Let’s work sideways instead of making a path straight down.  Gives us more opportunities to increase”

While listening to the students I decided to not intervene. It was insightful to hear how the different strategies were planned and executed. There were some student arguments and stonewalling.  Eventually students had to defend their reasoning as groups needed to find a solution. Near the end of class students presented their final paths and the class calculated the total. Students soon started to realize that their answer would differ depending on if they followed the order of operations. This changed many of the answers as some groups completed each operation individually. In the end students all decided on one pathway to find the largest number. Students then informally reflected on this activity through a class conversation.

Solutions

Before sending the students on to their next class I mentioned to them the Pick-a-Path game website. The interactive component has more options and might be a decent supplemental activity.  I’m hoping to see that a few students took the initiative to check out the site tonight. It might even be part of a classroom discussion tomorrow.

Math and Puzzles

Math Puzzles

I’ve experimented with using more math puzzles in the classroom this school year.  I continue to find that games and puzzles have the potential to engage students in meaningful ways. Similar to games, puzzles can encourage collaboration and perseverance skills that will help students long-term.

About a month ago I came across a free puzzle maker called Tarsia.  Tarsia is a program for PC users that allows the creation of different types of digital puzzles that you can print out. There’s a large database of math puzzles that are compatible with Tarsia here. A colleague and I have used them during our math station activities.  Students work in collaborative groups of 2-3 to complete the puzzles.  Last week I heard students having math conversations about whether a specific piece fits or not.  Hearing students confirm their reasoning for putting a piece in a particular place can be useful in seeing if a student is understanding a particular concept.  I feel like the puzzles have been especially beneficial in reinforcing many math concepts.  They are reusable for station work and could be used in conjunction with a student math journal piece.

Station Work

Keep in mind that I only use these types of puzzles for stations about once per week. Moderation is key with these types of puzzles.  I also found that cutting and bagging the puzzles in advance saves time.   In addition to the puzzles, I’m using math card games, technology tools, and self-directed learning activities for math groups that don’t directly meet with the teacher during guided math.  I’m looking forward to seeing how the puzzles continue to impact student engagement and learning in the classroom.

Moving Towards Algebra

Write Equations and Inequalities Game
 Equations and Inequalities Game

I’ve been fortunate to have an opportunity to participate in #MTBoS over the past few weeks.  It’s been a worthwhile experience to collaborate with math teachers around the world.  I’ve been able to share/use many of the resources found through this community.  This post is associated with #MTBoS mission eight.

My upper elementary students are now starting to dabble into a few algebra concepts and will be getting a formal introduction in the next few months.  There’s algebraic concepts sprinkled through my district’s curriculum, but solving equations and inequalities isn’t formally introduced till March.  That being said, I’m always on the lookout for additional algebra resources that help gradually emphasize the topic throughout the year.  Otherwise, the unit kind of brings a sticker shock to the students that haven’t encountered writing or solving equations before.

I’ve used visual patterns and Hands on Equations in the past to prepare students for the algebra unit.  Both have been beneficial in wetting the appetite for algebra.  While searching for a few other resources I came across the msmathwiki.  If you haven’t had a chance yet, check it out and maybe contribute some of your math teaching ideas.  I was eventually directed towards @cheesemonkeysf ‘s post about the Words into Math game.  I believe the idea was created by Maria and found in her post here. Two pdfs are included for this game, one informally termed beginning and one advanced.

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1-3 AB

Both of the documents can be used to match equations and inequalities.  They’re many ways to use this activity in the classroom.  I decided to print one side on orange paper and the other on yellow.  Students cut out each rectangle.  The easiest way for my students to do this was to overlap the yellow and orange sheets and cut them at once.  Both pages line up so it wasn’t that big of an issue.  Students turned all the rectangles so the blank side faced them.

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Students then took turns and were allowed to turn over one orange and yellow card.  All cards that were turned over stayed that way.  This is similar to a memory matching game except the cards all stay turned over.  Students then took turns to see if they could match any of the visible cards.  Each match resulted in one point.

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As the games progressed students started to become more comfortable with using equations and inequalities.  The game was over after all the game pieces were matched.  Students then bagged up the game pieces for future use.  I shared the ideas with a colleague at another school but haven’t yet heard how it went.

Organization

As the class becomes more familiar with algebra, it’s my hope that students are better able to connect past concepts to algebra topics later in the school year. This was an #eduwin for my class as we continue to explore algebra.

Factoring in Classroom Math Games

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Today was unofficially factor day in my fourth grade math classroom.  The lesson focused on factors, prime/composite numbers and prime factorization. For some students, the lesson reinforced preconceived notions, while others were introduced to a fairly new concept.  The goal of the lesson was for students to develop a deeper understanding of factors and the role that they play in mathematics.  I decided to use a variety of math games to review the concept, as well as to extend the concept of factors. One of my favorite methods to review and enrich the learning experience is to use math games in the classroom.  Math games often encourage students to take risks and use strategies in an attempt to win.  In the process they often have to work together to ask questions and clarify their mathematical understanding.

Today began with a brief mini lesson on factors.  I then split up the class into stations.  Each station was designed to reinforce and provide enrichment opportunities.  Students worked in partners at every station.  In some stations they worked together, while in others they were competitors.  Here are the stations:

Factor Captor
Factor Captor

Factor Captor – This is a staple game in my classroom. There are three different levels and students progress to the next level when they feel ready. To play this game students need to be able to identify prime and composite numbers. Here’s a short video of the game in process.  A template with sheets can be found here.

Divisibility Dash
Divisibility Dash

Divisibility Dash – This iPad app is designed (at least for me) for students to work in groups to identify various factors.  I found this app for free about a year ago and took advantage.  Many McGraw Hill apps are free during special times of the year.  Students record their scores/factors on a separate sheet of paper.

Sliding Factors
Sliding Factors

Sliding Factors is a computer game that encourages students to find factors of composite numbers.  There’s a two player function, which definitely comes in handy.  While browsing the #mathchat tag I saw @Richard_wade post a link to this game.

  • I should also mention that one section of the classroom was designed to be an “exit card” station.  Students completed a quick three question formative assessment and I discussed the answers with them.  This is another opportunity to give direct feedback that may help the student clear up misconceptions and help them make mathematical connections.

When used correctly, math games can truly benefit students.  When the students are in stations I like to sneak by the groups and listen in on the math talk that’s happening.  The math talk often gives students an opportunity to defend their mathematical thinking.  Students often correct each other, but are generally respectful in the process.  Tomorrow the class will be writing up a quick reflection of the station/factor experience in their math journal.

How do you use math games in the classroom?