Solving Systems by Substitution Resources

I asked the #mtbos if anyone had resources for solving systems by substitution that is not a worksheet. I have some nicely scaffolded worksheets to introduce substitution and elimination in this unit so I don't want to worksheet them to death for practice. And maybe they won't need any more practice but every year is different.

I had a lot of great responses so I thought it was worth sharing here.

Desmos Line Zapper
-Submitted by @Leeanne Branham and @kathyhen_

Speed Dating:
Each pair solves and becomes an "expert" on a system that's printed on a slip of paper. Then one half of the class rotates by 1 seat, and the new pairs exchange problems and solve/check each other's work.
-Submitted by @KentHaines

You could do an Add ‘em up where they find the intersection point but only add up one of the values. I found one online, but I’m not sure who it came from
-Submitted by @KellyRLove21 and link from @strom_win

Multiple Representations
-Submitted by @msalgebrateachr

solvemoji.com
is a fun website of emoji puzzles, the medium difficulty level is perfect for practicing substitution method. Students get really into it, and you can have them create their own, and try and solve them.
-Submitted by @TollesSteiner

Scavenger Hunt
-Submitted by @adinam225

I make cut out pizzas, topping, and pizza order forms. Students have to work in a group to solve the system and figure how many if each topping goes on the pizza and deliver it. They get fake tip money for their fast and correct service.
-Submitted by @TopperMathClass

Algebra Tiles Visual Practice
-Submitted by @GenevaMath

There’s also a clue game out there that someone made a while back where students had to solve a system in a scenario to find the murderer, the weapon, and where the crime was committed. I’m not sure who created it though, but I used to use it when I taught algebra 1.
-Submitted by @KellyRLove21

The Great Collide (Desmos)
-Submitted by @AsymptoticLiz

Scavenger Hunt
-Submitted by Brandy Norwine

Scavenger Hunt
-Submitted by @PeterRobynson

Thanks for sharing everyone!

The Function Notation Trident

Three years ago I blogged about using the function notation slider and every year I tweet about it for #teach180. One year someone suggested I make the slider have a third prong for the answers too. At first, I was appalled that someone didn't love the slider as is and then randomly this year I decided it was a great idea and I should do it. Now. lol

And it was a great idea! I love how it turned out and it's my favorite use of the Boomerang.

Here's the file:

Odds and Ends

I've used this activity for the past few years, using foam circles from Dollar Tree that I labeled with sharpies and stuck up all over the room.



My ceilings are too high to reach and I felt like that always threw them off. This year I got the bright idea to cut up tissue boxes and use blank yard sale stickers.

I gave them the worksheet with a picture on it too and asked them to make sure the stickers were in the right place. Sadly they were nowhere near sticky enough and repeatedly fell off. Now I feel like I need some laminated circles and hot glue them to the box. Any better suggestions?

This was the last activity before their quiz. After like 6 DAYS of point, lines, and planes, the grades were still bad. I think the highest was an 86% and the majority of the class was between 50%-75%. Why is this so hard? It's like the more time I spend, the worse it gets. I hate that it's the first lesson of the year because it drags on forever, they get a bad grade, and then they decide that geometry is too hard and they're going to fail.

Moving right along....

I used this 'number line' to introduce absolute value equations.

Questions I asked:

1. What is something weird or unusual about this diagram?
2. What is something familiar about it?
3. What kind of math thing could it represent?
4. If the pink magnet was a number, what would it be?
5. What is three magnets away from the pink magnet?
6. Why are there two possible answers?
7. What is two magnets away from the star?
8. What could the magnets represent?
9. Can you have a negative distance?
10. What is the definition of absolute value?

This was done in about 2 minutes and then we jumped right into INB notes.

And here's a fun video of us playing Grudge Ball but I call it The X Game because there are no balls and there are X's.

Any time they run to the board, it's a win. =)

Solving Equations

Both of my 9th grade Algebra I classes had 8th grade algebra so the majority of my course is review.

I started the year with solving equations by using Katrina Newell's equation flip book. (I loved that this included infinite and no solutions as well as fractions and multi-step equations with variables on both sides!)

I used my new document camera to show them how to put it together and we used my mini staplers for the first time ever- it went pretty smoothly.

Next we followed up with an equation card sort.



This is the first time they've ever done a card sort (to my knowledge) so here's how I introduced it.

"Get out all of the pieces that have numbers on them."

"Can you tell which piece is the original problem? Since you all have different problems, what is a hint you could give to pick the original problem?" (It's the longest one.)

"Now can you put the piece with numbers on them in the order they are being solved?

"Now look at the pieces with words. The word Given should go next to the original problem. Now can you put the words in order of what's happening in the problem?"

Then I went around giving feedback and checking answers. Each group also had one extra step that didn't belong.

One bag had two subtraction property pieces and it did not sit well with them that you could do that twice in a row until I pointed to each step of the problem and ask how they get there from the line above.

Each group rotated until they had done all sorts.

Then we used dice to play this partner dice rolling activity from All Things Algebra.

Plan With Me...Infinite and No Solutions

So I'm planning this lesson for the upcoming week and I have 3 slides that I feel like are a good start. I'm just about to tweet them out and ask what I can add to them when I decide to check the MTBoS search engine first. I land on this great blog post about using Desmos to check answers after combining like terms by graphing.

And instantly my lesson just got better. I get to use Desmos for the first time with my freshman and we are just beginning!

Here's a general outline and my thought process.

I will ask students to share out some answers and I will write them on the board. I will have one chrome book per group of three students and ask them to each take turns typing in an expression from the board (I'm thinking 6 so each student types in 2 and purposely include wrong ones).  But what if I don't get very many answers?

I will ask them what they notice as they type in each equation.

We will discuss the connection between the expression and the line.

Next:

I will ask students to prove me right or wrong. I'm thinking I'll have to explain that they either need to solve for x or plug in random values and see what happens. Some kind of work will happen which will lead us to graphing it in Desmos and seeing if it is the same line or not.

Third:

Some kind of work happening, either with Algebra or Desmos leading up to the fact that they graph two parallel lines which have no intersecting solution and how they simplify to the same slope with different y-intercepts.

Is that it? Now we just practice?

What are some good questions I can ask? What needs to go in their notes?

#MTBoS30: Diamond Math Puzzles aka X-factor

I found this at a conference somewhere and it is the only way I've ever introduced factoring x^2 + bx + c.

It was called diamond math but I think it makes more sense to call it x-factor, mostly because it is a type of factoring.



I give this to students at the start of class and tell them I have a puzzle for them to figure out. I tell them the first two are done as examples for them and I want them to figure out the rest.

That's it.

Then....we wait. There are always a few who figure it pretty quickly. I make them work 3-4 in a row to prove to me they know what's going on. I don't let students help each other or tell the answers.

Then there are a few who immediately start complaining...these are usually the students who get good grades but are not used to actually thinking.

After a few minutes/complaints I tell them to figure out a pattern with the numbers that can be repeated for every x.

This seems to help some. I let this drag out. I act very unhelpful. We wait some more. I try to hold out until every person has figured it out. If I can tell some people are getting verrrrry frustrated, I go to them one-on-one and try to prompt them with questions only.

From there, I give them a quadratic expression like x^2 + 6x + 8. I tell them that the c always goes on top and the b always goes on bottom and that we are always looking for the left and right numbers. I show them how to write the answer (x + 4)(x + 2) and then we practice.

A lot. A lot a lot.

Tip: Give students expressions with variables other than x to make sure they realize that the answer is written with the variable from the problem, not always an x.

See this post for my INB pages on x-factoring.

#MTBoS30 System of Equations: Elimination

I'm prepared to kill three birds with one stone:

1. I'm shooting for a goal of 110 posts this calendar year to break my all time best record of 109 posts so 30 posts in 30 days will really help my count.
2. I'm continuing an unintentional series about systems of equations from 2011 (how many solutions, graphing and substitution)
3. Answering @k8nowak's January call to share the unsexy, borderline boring basics.

My normal way of teaching is to do INB pages together as a class as notes and then some kind of worksheet/structure/activity to practice. Since January I've been working really hard at not giving worksheets. But this, for some reason, is just one of my golden worksheets that somehow works like a charm.

It starts with really simple vertical addition problems that lead into elimination where one variable automatically cancels out. It just keeps building from there up until you have to multiply both equations and change the sign. 

I give this out first before we ever do any notes. We do 1-5 together and then it's like you have unleashed the krakken and you can't get them to stop. Some of the problems have answer banks so they are not shown in the powerpoint. But honestly, I barely use the powerpoint anyway because they can't be bothered to look up from their papers to watch me.

It's love.

And I don't really even know why but this is probably the sixth year in a row that I've used it. After we finish this, I give them examples to put in their INBs (stolen from here) but it's more like an afterthought after all the time they've spent working these problems. (BTW this took about three full 47 minute class periods.)

It also seems to motivate them to rework problems when they mess up without me having to push for it. My guess is they like that it is answered with a nice and tidy ordered pair and they feel a sense of accomplishmeny when they finish.

But I'm just guessing.

It's definitely unsexy....and yet so satisfying!

Build-a-Function

Earlier this year I introduced function transformations through absolute value functions. I always feel like this is such an obvious lesson but I didn't get that same feeling from my students. They could see it when they looked at graphs and equations but not just by looking at an equation.

I originally called this dry erase build-a-function because I was going to have students just write equations on their desk. Then I decided to actually make them pieces to literally build-a-function with their hands.

I think having pieces to choose from helped them make connections quicker because it didn't seem to materialize out of thin air. It narrowed their options.

The first half of the Powerpoint described a function and students created the equation. This focused on only absolute value functions. 

For example, the slide says:

Flipped

Left 4

Down 5

And the students build this:

The second half of the powerpoint gives them equations and they have to identify the type (linear, quadratic, absolute value, exponential) and the transformations.

For example, the slide says:

y = -|x+4| - 5

And the students build this:

Another plus about this activity is that you don't need a fancy powerpoint. Just write it on the board or say it out loud and students go to work.

Low prep FTW.

Here are the pieces:



I printed each groups on different colors of paper and laminated.

Here is the powerpoint:



Good luck!

Algebra I Unit 4: Systems Interactive Notebook

Unit 4: Systems

Page 35-36  LHP borrowed from Mrs. Hester and the right side is mine. The outside shows what the lines look like and the inside shows what the equations look like.

Page 37-38 I love this because it forces students to read directions and learn more about the calculator. They sketch the graph and write the solution as an ordered pair.

Page 39-40 I printed these in color for the students as well and we tried to match our work to the printed pages to get in the habit of the correct steps.

Page 41-42 came from here and I liked how it showed the two different methods with the steps out to the side.

Page 43-44 LHP I might have stole these from somewhere but I think I ended up changing them to my own so if they are yours, I apologize. These were great for sorting and matching because students couldn't just use the numbers in the problem since those same numbers were used in other problems. I think this is a great scaffold to actually writing the equations themselves. We wrote underneath the flaps for obvious reasons on the RHP.

Page 45-46 LHP is mine and the RHP page is a borrowed idea from @samjshah. Students used different colored markers to mark on a continuum which would be the best method and then explain why underneath.

4

Page 47-48 I thought I stole this from Sarah Carter but maybe I just modified her one-variable inequality idea. Either way, she gets the credit, I used the superman S as a reminder to write an S over the solution set and pick an ordered pair that is a solution. RHP I had them decide on solid or dotted before we did any solving to keep them from ignoring that part.

And here are the files:

Linking Cube Towers

This activity was completely stolen from Mary Bourassa's blog post so I will let you go there to read about it and download the file.

The premise is that students will use one color of blocks as their starting value for the tower and a bunch of different color blocks to use as their rate of change. They write a table, graph, and form an equation.

That part went pretty well, once students realized that I was not going to read the directions for them or tell them what to do. {Apparently I waited too late in the year to start teaching freshman about the beauty of reading and following directions.}

Then towards the end when students had to make predictions abut when towers would be the same height or at what step a tower has a certain amount of cubes, it kind of fell apart. I had to give a lot of instruction there when I had hoped that they could work through it without me.

And some who worked it out, didn't make connections to the algebra or the equations. It also seemed that they made no connections to slope, y-intercept, or the meaning of the graph being linear. The activity went okay but they didn't make any of the connections I was shooting for.

I put similar questions on their assessment and ended up not counting them as a grade since only 2 out of 14 students answered correctly.

I noticed at the end of this activity that I was thinking about presenting this activity to my juniors and seniors, just to see that they could do it and make the connections I wanted. I think I was putting blame on the students for not getting what I wanted out of the activity instead of taking responsibility for not scaffolding the activity well enough. I wanted to 'prove' to myself that I was still a good teacher, even if 'these' students didn't learn the way I wanted them to.

Now that it's over, I want to think of ways to make it better as well as more activities where students have to read and follow directions in order to learn something new without me. I've done this many times in the past, but not with 'these' students. Which is why I felt confident that my older students could do it. Instead of blaming students, I put the blame on my lack of quality activities.

Function Notation Slider

I pinned a great idea for function notation and then found out it's from someone I actually know {I love when that happens}. Download the files and read Kathryn's original post here.

I'm basically posting about this for my blog readers who are not part of the MTBoS because I love it so much. The blue part is on card stock and the green part is just copy paper. A student told me I should have used card stock for that too.Next year!

We taped the green piece down on the empty squares with dotted lines. When I asked students what they thought those empty boxes were for one of them said "For us to make up our own numbers!" which is a great idea. The blue box slides while the green part stays attached. I almost made them glue it down before I realized then it wouldn't slide at all. Oops!

I also really liked the definition of a function that I found online: "f(x)" means "plug in a value for x into a function f". I also like to emphasize that f(x) is a label, a way to name an equation, and that we never do math with it.

Short and sweet!

Function Taboo

I was looking for a way to introduce a bunch of vocab at the beginning of my functions unit and I wanted something fun. I remembered some Taboo cards I had saved but of course, they didn't work for me. So I made my own.



I also don't know why I thought this was going to be a good idea. I guess because my Algebra I students had Algebra I as 8th graders so I thought they would at least be a little familiar with the words.

It started out excruciatingly painful. A few students in a row barely found one card they knew to even begin describing. Then students were using words not related to math at all to describe the math vocab word. It picked up over time but then students started just repeating what previous students had said before so the teams started to guess faster and faster.

I hope you have better luck with them than I did.

I will say that the next day I felt like students knew all the words and maybe some of the definitions. =)

Good luck.

Algebra 1 Unit 3: Equations and Inequalities

Unit 3: Equations and Inequalities

Pg 25-26 I'm still using Engage NY curriculum at this point but I made this sorting activity on my own to go in the INB. There is a problem to solve and then the solution set in three different forms: number line, in words, in set notation.

Pg 27-28 These two inequality foldables are modified from Sarah Hagan. I added no solution and all real numbers to the left side foldable.

Page 29-30 I've never taught ZPP as a stand alone lesson but it went over really well. I used Washi tape below to separate the problems, it's not actually a highlighter.

Page 31-32 Another lesson I've never thought about teaching is variables in the denominator but it naturally followed the zero product property. I used this powerpoint to make a huge deal out of NEVER DIVIDING BY ZERO. I even made little pictures for them to tape in their notebook but I forgot to tape mine in! I even made posters.

Page 33-34 Literal equations aren't that fun to teach and I don't really have any comments to make.

Here are the files: