Whiteboard Posters

A while back, I saw a picture of these posters on Instagram from Teaching the Distance.  I really liked and them and thought of many different uses for them, so I decided to create my own.  As the year goes on, and I finalize some of the other ones I’ve been working on, I’ll add them here.


This is what I came up with.

So far this year, I’ve been using them for the area formulas.  I really like being able to “build” the formula as we talk about why it works.  I show a lot of gifs to my students during this unit so they can see where the formulas come from.  As we were using these, I had the thought that something like this would be really nice for literal equations as well.

To stick them to the whiteboard, I used whiteboard tape like this.  The magnets aren’t super strong, so in the future I may try something else, but this is what I had and it works.

My plan for this is to “build” them each day with my classes as we’re starting the unit, and then towards the middle/end of the unit, leave them up on the board until the unit is over.


I also have the ones for order of operations *almost* ready to go.  As I’m writing this post, I realized I forgot “exponents”.  Ugh.  I’ve updated the file and will print it out this week.

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Here is the link to download the files.

I’m working on ones for slope, the various forms of linear equations, the Pythagorean theorem, and arithmetic and geometric sequences.  If you can think of any others I could make, please let me know!

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Puzzles, Puzzles, and More Puzzles

One of my projects last summer was going through all of the different places I had resource stored (emails to myself, Twitter likes, Google drive documents, etc.) and compile them into one place.  I created a separate Google Doc for each of my preps and sorted the resources by unit.  It took quite a bit of time to go through all of those things, but I am reaping the benefits already.  As I start a new unit, or a new concept within a unit, I am able to check this document for resources to add to or replace things that I have done in the past.  I’m no longer spending time searching for these things in 4 different places or looking for new resources when I’ve already found things in the past.

Already in our second unit in 6th grade, I tried several new things this year that I’ve loved! We’ve been talking about exponents, prime and composite numbers, factors and multiples.  I found several puzzles that my students have been enjoying and have been SO persistent with.  I had one student at the start of the week tell me he hates puzzles.  I think probably because he’s a student who picks up on things quickly and doesn’t always like that he can’t figure out a puzzle right away.  By the end of the week he was asking for more puzzles.  🙂 Success.

It’s been fun to listen to their conversations as they’ve been working and to see them excited to share the progress they’ve been making on them.


The first task I added to this unit is the following problem from Open Middle.

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Look at the amount of work by one student!! Wow! So proud of him!


Then I used this Open Middle problem from Bryan.  I LOVED this one so much!  It was so challenging, but it really got my students thinking about exponents.

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I know there is at least one mistake in this one, but again, even despite that, look at all the great thinking that took place here!


Then we started getting into prime and composite numbers and multiples and factors.  I came across this puzzle on Twitter.  I love that it incorporates so much vocab into one puzzle.  After using this in one class, I realized that dry erase pockets would work well for this one so students could more easily change the numbers.

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Such great group work on this puzzle!


Lastly, I found this puzzle here and here.  Again, I love how it incorporates so much vocab into one puzzle, and I love the extra challenge of placing the headers versus having them already placed on the puzzle.  I did type up my own version of the puzzle.  You can download it here.  I used this on a Friday in one of my classes and they were so disappointed when it was time to clean up.  I haven’t had any students solve it yet, but several have come so close.

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Again, not everything is perfect in those, but what great thinking by my students!

 

6th Grade Unit 8: Probability

Another new unit and another Which one Doesn’t Belong? to start out.

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Then we did notice/wonder with tree diagrams.

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After doing some practice with tree diagrams, I encourage students to start looking for a pattern to figure out the total possible outcomes each time.  Most often students are able to notice the counting principle.  Sometimes students will notice the pattern before I even mention it.  They’ll ask, “Can’t you just…”  I usually nearly scream at them, “Wait! Not yet!  Don’t ruin it for those that haven’t noticed the pattern yet!”

Tree diagrams are good opportunities for students to make up the problems as they go.

One problem I like to give students is “A tree diagram has 16 possible outcomes.  What could the tree diagram be?”


Then we start talking more about probability.  After spending a day on theoretical probability we start talking about experimental probability.  I know there have to be some awesome probability activities for 6th grade, but I haven’t found them yet.  (If you’ve got some, please send them my way!)  What I’ve done the past several years is set up 5 different stations for students to work through:  coin toss, dice, deck of cards, box with different colored cubes in it, and a wheel with different colors on it.  Then students compare their experimental probabilities with the theoretical probability.

Here’s an example of one of the stations for experimental probability.

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I also use this as an opportunity to review converting between fractions, decimals, and percents.  Another way that I like to spiral concepts in this unit is to give a problem like the following:

The following numbers are written on cards and put into a box:  1, 1, 3, 4, 5, and 8.  What is the probability of randomly picking a prime number?  a factor of 20?  A multiple of 4?

To review we play mathketball.  Students LOVE this simple game.  Students make a circle around the room with their desks, and I put a trash can in the middle of the room.  Students answer a question I put up on the board, and if they get it correct, they get to crumple up their 1/4 sheet of paper and try to make a basket.

Here’s an example problem from that.

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Here’s a different class playing mathketball, but you get the idea of what it is.  I do try to pick topics for mathketball where the problems shouldn’t take students too long to solve and/or have fewer steps.  I don’t want students to feel rushed, but I also don’t want students who complete problems quickly to be waiting a long time.

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6th Grade Unit 7: Surface Area and Volume

As I’m writing posts on each unit I teach, I’m noticing a theme.  I often start a new unit with Which One Doesn’t Belong?  This unit was no different.

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Then because it had been since the beginning of the year since we had our unit on area, we reviewed with the worksheet pictured below. (Link to download is at the bottom of this post.)  I’ve thought about restructuring the order in which I teach the units, but I like that by having my unit on area at the start of the year and my unit on surface area and volume at the end, it forces students to go back and remember what they learned at the start of the year.

I actually had a parent compliment me on that worksheet at conferences.  The parent liked that it forced the kids to get the answer correct rather than just move on to the next problem right away.

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Surface Area

When we talk about surface area, I really stress that the name “surface area” makes sense based on what we’re finding -the area of the faces.  I have students count the number of faces in the figure and number their paper accordingly.  I’ve found that this really helps some students keep track of their work as they work through the process of finding the surface area.


Volume

I remember the first couple years I taught volume one of the confusions for students was all the vocab, and I wasn’t really expecting that.  Then all of a sudden the lightbulb went off for me, and I realized where the confusion was coming from.

My students were getting confused between the base of the faces of the prism and the base of the prism itself.  Same goes with the height of one of the faces of the prism and the height of the prism itself.  Up until that point when we talked about the “base” we were talking about a side length, but now the “base” was a face itself.  Also, within the same problem we were talking about multiple different heights.

Once I realized where students were getting confused, I started changing how I described what we were doing. When I talk about finding the volume of a prism, I talk about how we first need to find the area of one of the bases of the prism.  I always make sure to say “base of the prism” instead of just “base”.  We talk a lot about how the bases of the prism are two faces that are parallel to each other and are congruent.

Then, once students have found the area of the base of the prism, instead of telling them to multiply by the height, I say, “Now we need to multiply by the height of the prism -the distance between those two parallel bases of the prism.”


Last year I shared a couple of the activities I did in this unit in this blog post.  I really like loop activities because it gets students up and moving around.  It’s even better when the weather is fantastic and we can go outside! 🙂

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I use this Desmos activity prior to having students start solving word problems involving surface area and volume.

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6th Grade Unit 6: Angles and Triangles

Angle Pairs

I used this Which One Doesn’t Belong? to start our unit on angles and triangles.  I love how starting with something like this gives me insight on where students are at with this topic based on their answers and the vocabulary they are using.

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After taking some notes on different vocab words we came back to the same image at the end of the day, and I asked students to use the new vocabulary to describe the images.

I also had students do this Desmos Polygraph several times throughout the unit as they learned new vocab words.

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Sum of Angles of a Triangle

In one of my classes, I had students cut out a triangle, rip off the angles, and put those pieces together to form a line.  It didn’t go quite as I hoped with that class, so in the other classes I was the only one who cut the triangle.  I would like to figure out a way so that more students see what I want them to see as they’re cutting the triangles and putting the angles together.

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Jo Morgan shared several good Angle Chase activities in this Math Gems post.

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Interior Angles of Polygons

After talking about the sum of the angles in a triangle, I have students Notice/Wonder with polygons divided into triangles for them to figure out the sum of the interior angles of polygons.

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After they’d done some practice with that we made a table to come up with the general formula.

 

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 4: Ratios

To introduce our unit on ratios this year, I started with the following picture and asked students to notice/wonder about it and if they could figure out what was meant by the word “ratio”

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I also had this one ready to follow up with if I needed to.

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Then I used a couple of Desmos activities.  This is one that I modified from something I found from Andrew Stadel.  Then I also created this card sort.  There are multiple correct options for the card sort I created.

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Then I used an I Spy activity.  I blogged about it here.

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I like this Which One Doesn’t Belong? around this time in the unit.

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Then we get into unit cost and finding the better buy.  Some years I have students look up items online and find the unit cost of the items, but I’m finding that more and more websites already give the unit cost on them.

Students always enjoy math fails, and they work great in this unit.  Sara shares a ton of them on her blog here, here, and here!

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I used Robert Kaplinsky’s “Which Ticket Option is a Better Deal?”  I definitely want to spend more time on this one next year and really focus on question 4.

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Don Steward also has some great ratio puzzles on his blog here and here.

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As I was going through my stuff when writing this post, I also came across this video.  I always forget about it and have never actually used it in my classroom.