6th Grade Unit 5: Percents

We start our unit on percentages by talking about converting between fractions, decimals, and percents.

I start with this Which One Doesn’t Belong? to get students thinking about percents and for me to see where my students are at in their understanding of this.  Then I ask them to brainstorm everything they know about percentages.

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I created matching cards for converting between decimals and percents years ago.  I intentionally picked numbers with lots of 2s and 4s in them so students can’t just say, “These are the only two cards with a 5 and a 6, so they have to match”.  You can download the file here.

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I spend several days letting students practice converting between fractions, decimals, and percents with different puzzles I’ve found over the years.  If I remember where I’ve found them, I’ll link to them here.

This is one puzzle I like for fractions and percents.

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From Chris Smith‘s newsletter via Jo Morgan’s blog.

Here is an Open Middle problem too.

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And yet another good Open Middle problem on percents.

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Then we get into applications of percents:  finding tip, tax, and discount.  I think this was the first year that I didn’t have a student do a discount problem with an answer greater than the original cost of the item.

One of my students favorite things to do during this part of our unit is for me to pull up a store’s website, find an item, and then calculate tax, discount, or tip.  (Side note:  Little Caesar’s website was super nice for adding things students wanted to the cart and finding the price.)

We used this loop activity for practice.

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6th Grade Unit 3: Fractions (Part 4 – Multiplying and Dividing)

This is the fourth post in our unit on fractions in 6th grade (Part 1, Part 2, Part 3).


This is the first year that I’ve used a rectangle model to introduce multiplying fractions.  I’ll be honest, until seeing the image below (particularly the 2nd and 3rd picture in the top row), I never fully understood this method.  I had only ever seen the first and last images in the top row before, didn’t spend much time thinking about it, and it never clicked for me.  Seeing the middle two images really helped my understanding.

 

I started by first giving students one of the fractions and asked them, “What is half of 3/4?”  We did several of these before I had students try a few on their own.

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After doing several of these types of problems many students started noticing a pattern, which was exactly what I was hoping for!  Then we started doing multiplication without the models and talked about how the models are nice because we can visually see what’s going on, but depending on what the numerators and denominators are, other methods may be more efficient.


For dividing fractions, I came across Fawn Nguyen’s blog post on using the rectangle method a couple years ago.  Read her post here.

This year I really stressed that students need to write out the questions, “How many groups of _____ are in _____?” before starting the problems.  I really liked how this student color coded the fractions in the problem as well.

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Then I also used another idea from Fawn found in this blog post.  I used her “divide by 1” method -method 3 below.

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As we go through this, I really stress with students how the fraction bar is another way of showing division, so we can use a fraction bar to write the division in our original problem.  Then we talk about how we want to undo the fact that we have fractions inside of fractions, so we want to multiply the bottom fraction by its reciprocal.  If we do that, we need to multiply the top of the “big” fraction by the same thing.  We talk about how we’re really multiplying by 1 and are using the identity property.  (I love seeing students write in the “1” as part of their work!)  It is sort of a lengthy process, and it’s weird for students to have fractions inside of fractions, but after a couple days most students are able to explain what they are doing and why throughout the process.

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Here is a link to download some of the practice problems students do throughout this portion of the unit.

6th Grade Unit 3: Fractions (Part 3 -Fraction Stations Set 2)

I blogged here about the setup for fraction stations and here about the first set of fraction stations.  Below are links to many of the resources I use for the second set of fraction stations.  I’ll give the same caveat I did in my post on the first set -not all of the activities here are great.  I know that, but it’s a start.  My goal is to now gradually start improving each station.

The first set of fraction stations is solely review concepts.  The first year I did it, I liked how it was going so much and I felt that the concepts I was going to be teaching next would work well in another round of stations, so I created a second set of mostly new concepts to my students.

Here is the checklist I used.

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1.  Number Line
Videos:
Activities:

2.  Equivalent Fractions
Videos:
Activities:

3.  Decimal to Fraction
Videos:
Activities:
  • IXL
  • QR Cards
    • I *think* I created these, but I can’t remember.  If anyone finds them online, please let me know so I can give credit.
  • Dice
    • Roll dice to create a decimal.  Convert to fraction.
  • Quizlet
  • Desmos
  • Card Sort
    • I pulled out the percents.

4.  Fraction to Decimal
Videos:
Activities:

5.  Order Fractions
Videos:
Activities:
  • IXL
  • Order in the Court (The directions are on page 33 of this handout, similar to one I received at a conferences years ago.)

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6.  Estimating Fractions
Videos:
Activities:

Once a student has completed all of the stations, they are able to work on the puzzle/enrichment station.  Here is a list of many of the things available to students.  I’ve found that students like if I don’t put everything out right away and add a couple new things everyday.

6th Grade Unit 3: Fractions (Part 2 -Fraction Stations Set 1)

Last year I tried Michelle’s review stations for the first time, and loved it!  You can read about some of the logistics and set up of it here.

For the most part, the set up of everything was the same this year as last year, and I wanted to share what activities I had at each station.

I fully admit that not everything at every station is fantastic.  Not even close, but I tried something different and something pretty far outside of my comfort zone.   Now that I’ve done this for two years, I can see things I want to change, and one of my summer goals is to go through each station and really pick it apart and make improvements as needed.

Here is the checklist I give students to keep track of their progress.

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1.  Mixed Numbers and Improper Fractions
Videos:
Activities:

2.  Simplify Fractions
Videos:
Activities:

3.  Comparing Fractions
Videos:
Activities:
  • IXL
  • Fraction War
    • Like the normal war game, but students flip over two cards to create a fraction.  The student whose fraction is greater gets all 4 cards.
  • Comparing Fraction Puzzle
  • Worksheet (It doesn’t look like the one I use is free anymore.)

4.  Adding Fractions & Mixed Numbers
Videos:
Activities:
  • IXL
  • QR Cards (not free)
  • Tarsia Puzzle (I cannot find the file for this, but it is likely from this site.)
  • Bump Game
  • Dominoes/Dice
    • Students create fractions using dominoes or dice, add them, and check answers using Desmos.

5.  Subtracting Fractions & Mixed Numbers
Videos:
Activities:
  • IXL
  • QR Cards (not free)
  • Bump Game
  • Dominoes/Dice
    • Students create fractions using dominoes or dice, subtract them, and check answers using Desmos.
  • QR Cards
    • These are for regrouping.  I haven’t used this with students yet, but created them after doing the stations when I saw students needed more practice with these types of problems.

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Once students complete all of the stations, I have a 6th station for them to work at with puzzles, challenge problems, and other activities.  Here is a list of many of the things available to students.  I’ve found that students like if I don’t put everything out right away and add a couple new things everyday.

A “One Problem Lesson Plan” that didn’t Go as Planned

I’ve been trying to incorporate more “one problem lesson plans” into my classroom this year.  My first few attempts were pretty successful.  My most recent one didn’t go quite as I had hoped.

I gave students this problem from 1 to 9 Puzzle.

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I was disappointed at how many students had forgotten how to multiply fractions already, but at the same time I was happy to see them use their resources to figure it out before asking me how to.

I really didn’t expect this to be as much of a struggle as it was for students.  I don’t know if it was the fractions or what, but was like we were back to the first time I had given students a problem like this.  They didn’t know where to start, so many just sat there.  Ugh!

Shortly after students got in groups, I could tell this was going differently than the other times we did problems like this.  There were times throughout the class period that I thought about giving up, having students stop, and move on to the next lesson, but I decided to use this as an opportunity for myself to learn how to move students forward in situations like this.  I don’t know that this was the best approach to this, but here’s what I did.

  1.  About five minutes into student work time on this problem when many students were “stuck on the escalator”, we talked about how students could get off the escalator.  They gave me a couple ideas of how to do this in the context of this problem.  (Scroll through this post from Sara Van Der Werf to read about the escalator and beagle video she shows her students.  I highly recommend using them in your classroom!)
  2. A little while later when I noticed students getting “stuck on the escalator” again, I brought the class together and asked students to share anything they had figured out so far.  A few students shared fractions they had put in cells a and b.
  3. A while later, I gave students one number in the puzzle – I think it was 7.  I told them I wasn’t sure if this was the only solution to the puzzle, there may be more, but for one of the solutions, this is where the 7 goes.  For whatever reason, this really got students going and excited to work again.
  4. With about 5-10 minutes left in class and as the students energy started to work on the problem started to decrease again, I let students vote on what number they wanted me to give them next.  I think they voted for me to tell them where the 1 went.

By the end of class I think 2 groups out of about 10 had figured out the solution.

The homework for students that night was to spend 10 minutes working on the problem.

When we came back the next day, the majority of my students told me they spent 10 minutes on the problem, and in that time I think one or two students came up with a solution.  We did go over the answer the next day.  My students worked on the problem for an entire class period and most spent additional time on it at home, and around 5 students had a solution, yet I gave the entire class the solution.  Was this there right thing to do?  Probably not.  Should I have had students work on it again that night?  I don’t know.  When a problem like this is more of a struggle for students than I anticipated, I don’t know the right balance between giving them enough time to wrestle with the problem and burning them out/frustrating them too much with one task.

BUT I do know that because I, as the teacher, persisted through the lesson rather than giving up and moving on, I gave myself experience in this situation that I can use in future lessons that don’t go as planned and because of that, I don’t consider the lesson a complete fail.


And in case you’re interested, here is a solution to the problem.

One Problem Lesson Plans

I’ve heard of people who spend an entire class period on one problem.  One problem!  With middle schoolers!  Most days, getting middle schoolers to focus on anything for 40 minutes, let alone a math problem, is an insurmountable task.  (Side note:  I’ve been working on a grad paper recently aka trying to make myself sound formal by using big words like insurmountable that you would likely never hear come out of my mouth if I were to ever have a conversation with you in person.)

I couldn’t wrap my head around finding a problem that would engage middle schoolers for 40+ minutes.   I didn’t have a clue what that type of problem would look like.  I didn’t know where to begin with a lesson like that.

I worried that my students wouldn’t “learn” as much by spending so much time on one problem compared to multiple problems on a worksheet or some other form of practice.

Enter this problem:

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I learned I was wrong.  So very wrong.


Several weeks ago, I gave my students the Open Middle problem above.

Oh. my. goodness.

I was not prepared for the awesomeness that took place that day.  I still smile thinking about it.  I anticipated the problem taking 5-10 minutes, maybe.  Some students worked on it for the entire 40 minutes!

The concept of the problem was simple.  Students knew how to write equivalent ratios.  They understood they needed the digits 1-9 and knew they could only use each digit once.  But the answer?  That wasn’t quite as easy to find.  They were hooked.

And so was I.  I wanted to find other problems to re-create that atmosphere in my classroom.  I completely underestimated the rich conversation that could take place from what I considered a simple task.

By the end of that class period, I knew I needed to do more of this in my class, but what sealed the deal for me was listening as students tried to figure out how to continue working together on the task as a group after class.  They asked me if they could do a group chat with each other that night so they could keep working on it.  Then I overheard, “If I figured it out, I’ll email you! And if you figure it out, email me!”

They were excited over solving a problem in a way that I hadn’t seen from them before.


This week I used the problem below in the same class.

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From Chris Smith‘s newsletter via Jo Morgan’s blog.

I was actually nervous for this lesson after how well the lesson with the Open Middle problem went.  I tried not to hope for the same results I got the first time but was worried it would flop.  It didn’t, and again, I was amazed at the conversation that resulted from this one task.


This week I used the problem below from 1to9 Puzzle with my other two sections of 6th graders.  I thought it would take about 5 minutes.

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I quickly realized it would likely take longer than I anticipated and saw the opportunity for those students to experience what my other class had.  While it didn’t relate to the content we were covering like the other two problems, I decided to deviate from the lesson plan and give students more time on this.  It was well worth it.


In the few times I’ve done problems like this, a couple things stand out to me.

  1. I am amazed at how many students don’t know how to guess, check, and adjust their answers on problems like these.   Some students could not wrap their head around the idea of just picking numbers as a starting point and going from there.  It was an eye opener for me, and I realized I need to continue to incorporate more situations where students need to do this.
  2. My doubts about whether students would “learn” as much from doing one problem like this rather than another practice activity were erased.  The conversations amongst students while doing problems of this nature still amaze me.
  3. One of my absolute favorite parts of doing these are watching students’ reactions when they finally find a solution.  They are SO proud of themselves.  This past summer I had the privilege of spending a lot of time learning from Sara Van Der Werf.  One of the things I heard from her over and over again was how one of her goals in her classroom is to get kids addicted to the cycle of being puzzled and becoming unpuzzled.  I was able to physically see this in my students more while doing these types of problems than possibly anything else I’ve done so far this year.

Do I have the “one problem lesson plan” down pat?  Absolutely not.  Is it even close to great?  No.  So far it’s really been pretty unintentional.  I’ve pretty much just been lucky and stumbled upon problems that have turned into great lessons.  I need to get better at bringing everyone back together to close the lesson after doing a task like this.  I’ve added finding more tasks like these to my summer to-do list.


UPDATES:  I’ll add more of “one problem lesson plans” below as I try them in my classroom.

This problem found here was another winner with students.  After students found a solution, they continued to work to find other solutions with me telling them to.  Sigh.  I needed that little reminder that week that we were in fact making progress.

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