8th Grade Unit 4: Applications of Lines

We start our unit on applications of lines by discussing independent and dependent variables.  I have a note to myself to remember to use the following language next year because it worked well this year.  Nothing earth shattering, I know.

  • “(independent variable) causes change to (dependent variable)”
  • “(dependent variable) depends on (independent variable)”

I use a lot of Sarah’s resources found here for my notes, and I’m pretty sure that’s where I got the problems for this Desmos activity.

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The next day we do Sarah’s Ghosts in the Graveyard activity with independent and dependent variables.  Every time I use that activity I think to myself, “Why don’t I do this more often?  It’s great!”

After students have a pretty solid understanding of defining the dependent and independent variable, writing linear equations from word problems goes a lot better.


Then we get into parallel and perpendicular lines.  I blogged briefly about what I did last year here.

I start with parallel lines and use this Desmos activity.  One of the downfalls of starting with that activity is that when students are asked to solve problems where they need to write the equation of a line parallel to a given line through a specific point, they want to use Desmos to guess and check.  This is a good strategy, but I also want them to know another method.  I start the next day with a couple problems like these.

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After spending another day or so on parallel lines, we finally get into perpendicular lines.  I start with this Desmos activity.

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We spend another day or so practicing with perpendicular lines.  I’ve used this activity before and like how it brings back different forms of lines.

We also talk a little bit about parallel and perpendicular lines and quadrilaterals using this Desmos activity.

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Then we get into scatter plots.  I start with this Notice/Wonder

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We do Desmos Polygraph next.  Last year I had a student ask if there were two “loners”, and I will forever think of outliers as loners.

After students do that activity, I put the graphs up on the board and ask students to put them in groups.  They end up describing the different correlations to me.

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This Which One Doesn’t Belong? is great around this time in the unit.

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I took a couple tasks from this page and turned them into Desmos activities.  (I know she tweeted out links to the activities at one point, but I couldn’t find them.

Here’s one on correlation.

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And another on lines of best fit.

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Here is the link to download some of the worksheets I use in this unit.
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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 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 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.

8th Grade Unit 3: Functions (Part 3 – Point Slope Form & Standard Form)

Here’s part 1 and part 2 of unit 3.


I used this warm-up the first day after our test on slope-intercept form to get students thinking about equations and graphs again.

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Then I do notice/wonder with this.

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I heard things like:

  • There are two x’s and two y’s.
  • There are little 1’s by one of the x’s and one of the y’s.
  • There are parenthesis.
  • There’s an m (slope).
  • There’s no y-intercept
  • Is it another form of a linear equation?

It leads nicely into discussing point-slope form and students realize that it isn’t as scary as it may look at first because they recognize the similarities between slope-intercept form.

When going over point-slope form, I make a point to emphasize to students why it’s named point-slope form -we can see the coordinates of a point and the slope from the equation.  I remind them that this is similar to slope-intercept form where we saw the slope and the y-intercept.

Then we go over a few examples of writing equations in point-slope form before doing an activity similar to what Sarah shared here.  I didn’t have big foam die like Sarah used, but I do have double dice, which students always think are fun.  Students rolled the dice to create two ordered pairs and wrote an equation in point-slope form of the line between those two points.  Then they checked their answers using Desmos.  Having students check with Desmos was key to helping them see what they were doing when writing the equation of the line.

I also modified this Desmos marbleslides activity to rearrange the equation so that they looked like what my students were used to seeing.  My modified version can be found here.


Then after some more practice using point-slope form, students are introduced to standard form.

I use notice/wonder again to get students thinking about this.

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Again, students came up with the following things:

  • There’s 2’s in all of them.
  • The two is always by the x.
  • One of the equations is in slope-intercept form.
  • One of the equations is in point-slope form.
  • In the purple one, the x and y are on the same side.

We also talk about how, unlike slope-intercept form and point-slope form, we don’t see the slope, the y-intercept, or a point.


Of the three parts to this unit, this one is takes up the fewest number of class periods.  Writing up this post made me realize that I could probably use a few more activities on these concepts.  If you have any ideas for me, please share!

8th Grade Unit 2: Inequalities (Part 2 -Compound Inequalities and Absolute Value Inequalities)

You can read about the first part of our unit on inequalities here.  In the next part of the unit we do some word problems, compound inequalities, and absolute value inequalities.


Word Problems

I know the word problems I give students aren’t very “real world” and that this is an area I need to work on -finding/creating better word problems for students and doing a better job of teaching them as well as incorporating them into class.  I don’t have anything fancy I do for these other than a couple examples together as a class and then partner practice.

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Compound Inequalities

I use Notice/Wonder to start our conversation on compound inequalities.  Then we do this Desmos activity.  I also like this Polygraph activity for compound inequalities.

This year I also realized I could make a connection between “compound inequalities” and “compound words” and “compound sentences” that students are familiar with already from their English classes.  Why did it take me so long to do this?

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The following day I use this Which One Doesn’t Belong? for a warm-up and then we go back to the image from the notice/wonder the day before.  I put numbers on the graphs and students write inequalities for each.

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I used one of Sarah Carter’s awesome questions stacks for practice on solving these types of inequalities.  You can download the file she shared here.

One of my classes got to Point Collector.  This was my first time using this activity with students.  It’s SO fun!

One of my students came up with this for the last challenge.  He didn’t quite follow the directions exactly, but I love that he wanted to get the maximum number of points.  I overheard him telling another student about it later on during the class period when they were working on something else.  His friend goes, “Oh, so you cheated the system?” 😉

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Absolute Value Inequalities

I tried a couple different ways of introducing absolute value inequalities this year.  In a couple classes I started with Notice/Wonder.  Then in another class I started with an absolute value equation such as 3|x – 1| + 4 = 19 and had students solve that.  Then I changed it to an inequality and asked students what they thought would be the same/different about solving the problem.  Both ways of introducing the topic were good for different reasons.  I think for next year I may try to find a good combination of both.

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We did some vertical non-permanent surface practice with solving absolute value inequalities at the whiteboards around my room.

I also used this Open Middle type problem I made.  You can download the file here.

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Here is the link to download the test review.

8th Grade Unit 1: Solving Equations (Part 1)

The first unit we do in 8th grade is on equations.  I start by reviewing order of operations, evaluating expressions, and simplifying expressions.  Then we get into solving more basic equations.  Here is a semi-brief overview of the first part of this unit.


Order of Operations

We start off with order of operations.  I use the following Notice/Wonder to lead into our discussion/review of order of operations.

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We also review absolute value as well as square roots as part of our order of operations practice.  These are great problems for vertical nonpermanent surfaces (#VNPS)

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This Desmos activity from Cathy Yenca is also a great review of squares and square roots.

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After a couple days of absolute value problems and square root problems, students work on a worksheet similar to the one below.  You can download it here.  I’ve thought about changing up this worksheet since it doesn’t include square roots or absolute value, but it is a good challenge for students, since students are only allowed to use the numbers 0 through 9 once, and I like that about it.

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Students also see their first Find the Flub warm-up in this unit.

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Evaluate Expressions

Then we spend a little bit of time on evaluating expressions.  I use the worksheet below as practice for students.  I blogged about this type of worksheet here.  You can find the link to download it in that post.

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Simplifying Expressions

Both years I’ve taught this, I forget that students aren’t as comfortable simplifying expressions as I expect them to be.  I start by having students simplify expressions that don’t involve the distributive property, and then I add that in a day or so later.  I found a Desmos activity in the Desmos Bank that I modified and uses on one of the first days on this topic.  Here is the link to the activity I modified.

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Then we do a couple days of simplifying expressions with the distributive property.  Again, I use a “One Incorrect” Worksheet.  You can download it in this post.

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The Notice/Wonder I used below was GREAT to discussion some common mistakes I was seeing students make when simplifying expressions.  For example, I had students who would say that 5x² was 25x.  We had a really good discussion about the differences in the expressions below and how that changed things.

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Solving Equations

Then we get start solving equations.  A few years ago, I had a group of students that struggled to plot points on a number line, so when we got to solving equations, I saw that as an opportunity for them to get more practice with that by having them graph the solution to the equation.  They also struggled with order of operations/evaluating expressions, so again,  I decided to have them practice this by checking their answers to the equations.  I’ve never looked back, and now I have students graph and check their answers to nearly every problem they do for me.

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If you’re interested in the worksheet I use, you can download it here.  Below are a couple of warm-ups we use when we’re talking about solving equations.

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