8th Grade Unit 6: Exponents (Part 2 Scientific Notation)

I shared part 1 of our unit on exponents here.


I got most of my notes from Sarah’s blog.  She also has a ton of activities on her blog here.

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As I was writing this, I remembered this image that Heather shared from one of Sara’s presentations.  I think this would be a GREAT way to introduce scientific notation next year.  I’ve got to remember to do that!

The last couple years, I’ve used tables similar to those below to help students notice patterns.

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After we talk about converting between standard form and scientific notation, I’ve used this Desmos activity.  I also like this Desmos activity.

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Then we get into multiplying and dividing numbers in scientific notation.

I made this Desmos activity for practice.

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The biggest thing my students struggle with at this point in the unit is when they multiply or divide and get a number that isn’t in scientific notation.  Something like 64 x 10^6.  They know the exponent will change by one, but many students get mixed up on whether it gets bigger or smaller.  I always, “Don’t try to memorize a “shortcut”.  Think about what 64 x 10^6 is.  Write it out in standard form, and then convert it to scientific notation.  Then you don’t have to try to memorize anything.”  The students that listen and follow my advice, usually have no issues with this, but it’s the students who want to take a “shortcut” that end up not getting these problems correct.  Please tell me I’m not the only one who has this issue!


I’ve got a couple Which One Doesn’t Belong? warm-ups for scientific notation.  I know I pulled the second one from Twitter.  I can’t remember who shared it.  If it’s yours, please let me know so I can give you credit for it.

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I’ve used this scavenger hunt as well.  I like that it gets students up and moving around.

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I created this worksheet for students to practice.  (I think I created it.  I may have modified it from somewhere.  Again, if you recognize it, please let me know so I can give credit to who originally created it.) . You can download it here.  I’ve created a few other worksheets of this format and like that it’s self checking for students.

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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.

6th Grade Unit 3: Fractions (Part 1 -Greatest Common Factor & Least Common Multiple

I start our unit on fractions by going over Greatest Common Factor and Least Common Multiple.  It seems that no matter how many times we go over what factors of a number are and what multiples of a number are and break apart what it means to find the “greatest common factor” and “least common multiple”, some students still get these mixed up.  I try to be super intentional about not saying “GCF” or “LCM” with students very often because I know there is likely at least one student who doesn’t know what those letters stand for -I try to use the vocabulary as much as possible with students instead of acronyms.  I want them to know what GCF and LCM mean because they will likely see that other places, but if I say “GCF” I always pair it with “Greatest Common Factor”.

We start with greatest common factor and first review what factors are, and then discuss what it means to find the greatest common factor of two numbers.  Once students get a quick review of this, they usually remember doing this in 5th grade.  I found this year that the methods my students used as 5th graders to find the greatest common factor were the “rainbow method” and T-charts.

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We do a few examples where students use one of those two methods before I put up an example with larger numbers like 192 and 320.  Students usually give me the reaction I’m looking for by groaning, and I ask why they’re groaning.  They tell me the numbers are big and there’s a lot of factors to list.  I then ask if they’d like a more efficient method of finding the greatest common factor and introduce students to what I call the “ladder method” to find the greatest common factor.  I think I first heard about it from Sarah here.  The high school teachers in my building use this method with polynomials, so I want to introduce it to students.

For practice, I have students write a number on a slip of paper that has many factors.  Then students pair up and find the greatest common factor of their numbers.  I have them check their answers with Desmos.  (Did you know that Desmos can find the greatest common factor of numbers?  It will also find the least common multiple.)  Then once they’ve checked their answers, they find a new partner.

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Then we get into finding the least common multiple of numbers.  Again, we review multiples, and how they are different from factors.

 

 

(We review the above nearly every day in this unit, so you would think I’ve got how I want to display it on the board for students down pat.  This is what I ended up liking the best, although I’m still not sold on how I showed factors.)

Then we talk about what it means to find the least common multiple of two numbers.  Students usually start to remember doing this as 5th graders.  We do a few examples of this before we talk about how we could use the ladder method to find the least common multiple.

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Next comes word problems.  I’ve modified this worksheet for practice for students.

Then I have a couple different loop activities that I use depending on when they best fit into the schedule.  The first has greatest common factor, least common multiple, and prime factorization, while the second loop activity has greatest common factor, least common multiple, and word problems.

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Each activity has 6 problems, which is nice because most groups can finish within a class period.  However, it’s not nice for keeping groups small if I want one group per problem. I ended up printing two copies of the activity on different colored paper, and this worked great.  Half of my students rotated through one color set while the other half rotated through the other color set.

You can download the files for both activities here.

6th Grade Unit 2: Intro to Algebra (Part 2 -Evaluating Expressions)

I blogged about the first part of our Intro to Algebra unit in 6th grade here.  In this part of the unit, we finally get into the algebra stuff.


Word Phrases

Before we start evaluating expressions, we talk about what variables are and what the purpose of them is.  We review word phrases.  I started this year by putting these words up on the board and having students classify them based on their operation.

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After we have done a bit of large group practice with that, I have students do a card sort/matching activity.  Once I have checked their answers, they can play memory.  Some students have also played Go Fish with the cards as well.

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I also use this Desmos card sort on another day to review this concept.

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Evaluate Expressions

Then we get into evaluating expressions.  This year I made a small tweak to how I introduce this to students.  In the past,  I would stand up in front of the class and tell students what you do when you’re asked to evaluate an expression.  I’m really trying to get away from being the teller of information in my classroom and instead be the asker of questions to get students to explain the mathematical concepts to each other.  Here’s the small change I made this year.

I put “x + 2″ on the board and asked if we could come up with a number answer for this.  I saw several heads shaking no, and when I asked why, they told me, “We don’t know what x is.”  Then I added to the board “x = 7″ and asked if we were able to come up with a number answer for this now.  They told me we could and that the answer was 9 and then explained how they got that for an answer.  I could tell that not all of my students had caught on yet or weren’t fully paying attention, so instead of me rephrasing what the student had just said, I asked, “Can someone else explain to the class how ‘Sue’ got 9 for an answer?”   Then I put something like 4x + 3 up and repeated the same process.

It was a small change, but it felt SO much better than standing up in front of the class telling them a process to follow.


The first activity I do is something I created several years ago, and I realized last year when I did this that it’s pretty similar to Sara’s Add-Em-Up activity.  I created 4 different sets of 5 cards.  Each set of cards is printed off on a different color paper so that I can tell which set students are working on.  Below is a picture of the first page of the document for this activity which has 4 copies (each column) of the first set.  I have 8-10 copies of each set.  Because all 8-10 sets are the same color, before I laminated the cards, I wrote a number on the back of each card in a set.  This way, when I find a random card on the floor I can ask, “Who has the red 3s?” and easily figure out where the card goes.

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Students are put in groups of 2-3 and in their group they work together to evaluate each of the cards.  When they are done, they add up their 5 answers and come tell me what they got.  If they are correct, I will give them the next set.  If they are incorrect, I don’t tell them which one they got wrong, and they go back to their group and work to figure out what they did wrong.  I’ve tried to level the cards so that each set gets increasingly difficult.  Set 1 has one to two operations on each card.  Set 2 has three steps to each problem.  The next set incorporates decimal operations and the final set has the variable in the problem more than once.

One of the reason I like having a different color for each of the sets is that it is easy for me to see where students are when we are doing this activity.  If I look around my room and see one group on the red set (the first set for me) and every other group is on orange or green (the 2nd and 3rd set for me), I know I need to check in with the group working on the red cards.

Below is an example of each of the four sets.

 

 

 


As I was looking through my stuff to find the file for that activity, I came across another activity I created and had forgotten about.  For this activity, I put students in groups and have them start at a problem.  They can choose to solve either problem on the card.  I encourage all students to try at least one of the more challenging problems.  Once students solve the problem, they look for the answer on another card that I have hanging around the room and then solve either problem on that card.  Eventually, they will loop through to all of the problems and end back where they started.

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I also used this Desmos card sort towards the end of the unit to review with students.

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Find the Flub warm-ups are great for evaluating expressions.

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Tables

In the past, I haven’t done much with tables in any of my classes, and I know that this is something I should do more of.  I added this Desmos activity to this unit, and overall I was pleased with how it went.  It was challenging for some of my students, which was my goal when creating it.

 

 

 

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Here is the link to download the activities from this post.

Surface Area & Volume Scavenger Hunts

How is it that even after several years of teaching 6th grade, I can still go to my old files looking for stuff to teach an upcoming unit and find pretty much nothing?  How?  How does this happen?  I know I taught it in the past, but what did I do?

This happened with a recent unit on surface area and volume, so I created two scavenger activities.  One on surface area and volume and another with word problems on the same stuff.

I’ve been using “loop” activities or “scavenger hunts” for a while.  I especially like them for the times when I need students to practice a specific type of problem.  It’s a great way to disguise a worksheet as an activity.  I love that they are self checking and get students up and moving around.

I have tried a few different ways of creating this type of activity up when making my own.  This is what I’ve found to be most efficient for me when I’m making the activity.  On the top of a sheet of paper I put the first problem.  Then I put the answer to that problem on the bottom of the next sheet.  It’s been a big help for students to make the font as big as possible so that students can see it from a ways away.  Then on the top of that sheet I put the next problem.  The final answer goes on the bottom of the first sheet.   At the end of the activity, I am able to check students’ work by checking the order of their answers.

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Students can start at any card.  They solve the problem and find that answer on another sheet.  This continues until they have done all the problems.  If they do everything correctly, they will end up back where they started.

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Because this is a self checking activity for students, I tend to be “less helpful” to students while they are working on activities like this.

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And an added bonus is that you can hang the problems just as well to the outside of the school as you can the walls of your classroom.  So when it’s beautiful outside and your class has been awesome all week, you take them outside.  🙂

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Here are the links to download the activities.


Update:  I also uploaded an area review worksheet I used to intro this unit.  I’m trying to incorporate more self-check assignments for my students so they know whether or not they are on the right track while working on them.

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I also thought I’d share the documents I used to create the images for these activities.  I recently discovered I can use Google Drawings to create prisms.  It works really well for triangular prisms and rectangular prisms.  It’s not quite as easy to create trapezoidal prisms, but it was the best I found.  Here is the link to the images I made for the surface area and volume scavenger hunt, and here is the link to the images for the word problem scavenger hunt.