Long-Term Planning (Algebra I)

I personally believe that it’s a good idea to start thinking ahead to the next school year around this time of year.  I admit that I don’t normally start planning until August but this year I am getting a head start because I believe it will allow me to be much less stressed come September.

If you are looking to start planning out your year and have no idea where to start (which was me a couple of weeks ago before I just jumped in), I’ll share my process for long-term planning.  The first class I worked on was Algebra I, so I’ll share that one today.

long term planning blog pic

Step 1:  Look over everything you need to teach and break it up into units.  I try to use as few units as possible while keeping each one a manageable size.  For Algebra I, I came up with 11 different units.

Step 2:  Determine the order in which you want to teach those units.  This can be tricky because you need to make sure that students have all the prerequisite skills for each unit and you want the year to have a good flow.

Step 3:  Determine all of the different lessons that will be included in each unit and the order in which you want to teach them.  This is the most time-consuming part, in my opinion, but it will save you a lot of time throughout the year if you get the whole year figured out before school starts.

Step 4:  Determine an approximate length of time it will take you to teach each unit.  Since my Algebra I class is an advanced class for 8th graders, I am able to move fairly quickly.  Therefore, I normally plan to teach a lesson a day.  I plan on 2 days for topics that I know students will find challenging.  I add 3 days to the end of a unit since I typically spend 2 days on review and 1 day for the unit test.

Here is my long-term plan (scope & sequence/curriculum map) for Algebra I.  Feel free to download it and edit/adjust it to meet your needs.

algebra scope

The next thing I did is something I should have done long ago…I organized my Pinterest boards.  I love getting ideas on Pinterest but I previously put all the great teaching ideas I found on my “Math Teaching Ideas” board…and then forgot all about them.  So I setup a separate Pinterest board for each Algebra I unit and moved pins from my (useless) “math teaching ideas” board onto the appropriate boards.  Now when I see great Algebra ideas on pinterest or read about them on blogs, I pin them onto the board that corresponds to that unit.  I forsee this being very valuable when I am actually writing my lesson plans throughout the years – I can glance through the unit Pinterest board to remind myself of all the great ideas I want to implement.

Click the picture below if you want to check out my Algebra I Units Pinterest Boards:

pinterest

Step 5: (I won’t get around to this step until closer to the start of the year when I have my schedule…)  Translate your estimated time frames into calendar dates.  I have a blank school year calendar that is weekdays only.  I write in school holidays/half days, etc. and then write in my approximate start dates for each unit based off the estimated time frames I came up with.  I then adjust as necessary around long breaks like Christmas and Easter.

You can download my calendar FREE from my TpT store by clicking the image below:

calendar pic1

There you have it…my process for writing  long-term plans.  I have had years when I haven’t done detailed year-long plans and years when I have done them and I can say from experience that it really does pay off to do them because it helps you have a smoother, less stressful school year when you have a map to follow.

Do you have any tips or tricks for planning out a school year?  Please feel free to leave a comment sharing your ideas!

Thanks for reading,

Christina

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Discovery Lesson: Factoring Trinomials

Whenever possible I like to have students discover or figure out the lesson on their own (with some guidance from me, of course), rather than simply teaching them an algorithm.  One such topic is factoring trinomials.

I start my lesson on factoring trinomials with a = 1 by giving students 4 binomial multiplication problems and having them solve them, showing all of their work.

discover factoring pic1

I then tell them that factoring is the opposite of multiplying, so basically they are given the “answer” to a multiplication problem and they need to figure out the “problem”.  I have them look back at the previous 4 trinomial “answers” they got and to try to come up with a rule for factoring by figuring out where the b and c came from.

With a little time the students are always able to come up with the idea that the b is the sum of the 2nd terms in the binomials and c is their product.  So, when I give them a trinomial to factor they know that they will have (x +/- #)(x +/-#) and need to find 2 numbers whose product is c and sum is b to fill in the #s.

I like teaching factoring this way because the students understand that I didn’t just make up some rule.  They came up with the rule themselves by analyzing problems that they already knew how to solve.

I also teach factoring trinomials where a ≠ 1 this way.

discover factoring pic2

With these problems I have students come up with a rule to go from the trinomial answer to the “work” column.  They are usually pretty quick to notice that the first and last terms stay the same and that the middle term gets split into 2 terms.  When I ask how to know how to split up those middle terms they are able to come up with the idea that it needs to be split into 2 numbers whose sum is the original number but I usually have to push them to get them to see that the those 2 numbers also must have a product of ac.  I teach factoring by grouping earlier in the unit, so once students get to this point in the problem, they are able to just apply the factoring by grouping method to finish the problems.  (I know that there are other methods to factor trinomials where a ≠ 1, like guess & check and the “airplane” or “slip and slide” method but I personally find that factoring by grouping makes the most sense for students since they are using 2 things they already know: multiplication of binomials and the distributive property, in reverse.  I think this lends itself perfectly to helping students understand that factoring and multiplication are simply inverses).

Factoring is such an important part of algebra and is used in many different ways (solving quadratic equations, simplifying rational expressions, solving radical equations, etc.) that it is really important that students master it.  At least in my opinion, having students take some ownership of the process helps build their understanding and mastery.

[For students who understand the process of factoring but struggle to come up with the 2 numbers with the given sum and product I show them how to use a factor tree to help them find the numbers.  You can read about that here.]

Thanks for reading,

Christina

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Fun Algebra Easter Egg Hunt Activity

Just a quick post today to share a fun, quick Easter activity I’ve done in the past with Algebra/Pre-Algebra classes in case you want to try it…

Fill up an odd number of Easter eggs with pennies (put the same number of pennies in each egg).  Hide the eggs in the classroom before class begins.

When the students come in, ask for 2 volunteers.  Have those 2 students search for Easter eggs.  Since you have hidden an odd number of eggs the two students obviously will have found a different number.  Tell them that you want to be fair so you are going to even out the amount of money each student has by giving them some loose coins.

Easter Algebra Activity - math-in-the-middle.com

In the picture, you can see student A only found 1 egg and student B found 4.  So, I gave student A $0.25 and student B $0.04 to even out the total amount of money each student has.

Ask the class to figure out how much money is in each egg.  (You can give the money to the first student to get it correct as a prize if you want.)  Discuss how they figured it out and prove they are right by opening the eggs (in this case there is $0.07 in each egg).

Easter Egg Equation Activity - math-in-the-middle.com

There you have it – a fun way to have students solve equations with variables on both sides (without them even realizing that’s what they are doing!)

Enjoy!

Thanks for reading,

Christina

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Linear Equations Walk Around Activity

I’m writing about another favorite activity of mine that I use for a few different topics throughout the year – walkarounds. They require minimal prep from the teacher and are a great, effective way to practice certain skills. This post is specifically about the linear equations walk-around activity I do with my Algebra kids after they have learned Standard Form.
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Here’s how it works:
I have 6 different standard form linear equations that I copy enough times so that each student gets 1 equation. (You can download the equations at the bottom of the post). I give each student an equation and tell them to convert it to slope-intercept form and then graph it.
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After a few minutes have passed and most students are done, I tell them to form groups based on the equations they were given (all the 1’s are together, 2’s are together, etc.). In their groups they need to compare answers and come to a consensus on the correct slope-intercept equation and graph. Once they are in agreement they need to get their answer approved by me and then transfer the correct graph to a mini whiteboard. (Large graph anchor chart paper would actually be ideal, but I don’t have any so I use the whiteboards). They should NOT write the equation on the mini whiteboard, just the graph and their problem number.
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Once this is completed, I give students a recording sheet (download link is at the bottom of this post). I tell them to draw a big x through the number they graphed since they don’t have to do that one. Then the students walk around the room and have to look at the other groups’ graphs and determine the slope-intercept form of the equations that were graphed. They then need to convert those slope-intercept form equations into standard form. (The walkaround runs smoothest if you have a set order for students to walk around the room instead of letting them wander wherever. I tell them to go in order, so group 4 would start at the graph of 5, then go to 6, and then 1, 2, and end at 3). I also have found that it works best if students just write the slope-intercept form of the line while they are walking around, and then return to their seats to convert them to standard form.
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I love this activity because it gives students an opportunity to work both independently and cooperatively and gives them practice converting standard form to slope-intercept form, graphing lines, writing equations from graphs, and converting slope-intercept form to standard form.

(If you are in need of additional activities to supplement your linear equations unit, you may be interested in the linear equations relay races I have available in my TpT store.)

You can download the 6 equation cards for the walk around activity (FREE) by clicking the picture below:

linear walkaround pic1

You can download the activity recording sheet (FREE) by clicking the picture below:

linear walkaround pic2

What activities have you done for linear equations? Please share in the comments!

Thanks for reading,
Christina

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Breaking Down 2 Step Equations

Today I’m writing about a simple idea that makes 2-step equations easy for kids – a box “trick”.

2 step equations box trick

Students obviously have already learned how to solve one-step equations before being introduced to two-step equations, so I introduce 2-step equations by giving students a simple one-step equation.  The only difference is that I use an index card instead of a variable in my equation.

box trick pic1

Put an equation like the one pictured above on the board and tell students to solve it for the index card, which they should be able to do easily since it is a simple one-step subtraction equation.

Once they solve the equation for the index card, lift up the original card to reveal what is underneath it (in this case 8x).  It also works if you write 8x on the backs of the index cards and just flip them over.

box trick pic2

So, since the index card = 8x they now need to solve the equation 8x = 56, which is another simple one-step equation that they should already know how to solve.

box trick pic3

Do another example or two with the class and then discuss how to decide which part of the equation goes under the index card (whichever part comes first using the order of operations).  Have students replicate the process in their notebooks by giving them a 2-step equation.  They need to draw a box around the part that would be under the index card.  First solve the equation for the box and then solve the new equation for the variable.

box trick pic4

I have found that this method really helps students make sense of solving 2-step equations by turning them into two 1-step equations.  How do you introduce 2-step equations in your class?  Do you do something similar?  Please share in the comments!

If you are in need of resources to supplement your lessons on one and two step equations you may be interested in the following activities in my TpT strore:

one-step equations integers pic1  2 step equations bingo pic1  2 step equations partner matching pic1

Thanks for reading,

Christina

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Top 10 Things Every Middle School Math Teacher Should Have For Their Classroom

As it is almost time to start preparing classrooms for the coming school year, I thought I would share my top 10 list of things I couldn’t live without as a middle school math teacher.

Math in the Middle Blog| Top 10 Things Every Middle School Math Teacher Should Have for Their Classroom

10.  Class sets of rulers, protractors, and compasses

We don’t use these all that often but they definitely come in handy when we get to geometry, graphing, and pie charts.  I don’t ask students to supply their own because by the time we get to the units that require these tools, many of the kids have lost theirs.

 

9.  LARGE supply of pre-sharpened pencils

I either get packs of pre-sharpened pencils or regular packs of pencils that I sharpen over the summer.  Regardless of whatever system you have for pencils, students are going to show up for class without a pencil or with a pencil that needs to be sharpened at some point throughout the year.  It makes my life easier if I can just give them a pencil that’s ready to go that they can use for class instead of waiting for them to sharpen one.

 

8.  Pencil-top Erasers

Math in the Middle Blog| Smiley Eraser Tops

Kids make mistakes all the time.  It makes sense to have erasers on hand to give them when they no longer have one on their pencil.  I LOVE these ones from oriental trading – they’re cute and there are enough to last at least a year.  (The kids love the smiley faces on them, too)!

 

7.  Expanding File Folder

Math in the Middle Blog| Expanding File Folder

(This is one of those things that I never knew I needed but now that I have one I don’t know how I survived without it).  You are going to have a lot of papers to grade.  My old system was to just throw all the papers I had to grade into my bag to take home.  Now I have sections in my 13 pocket file folder from Staples for all the different papers I need to grade, and I have sections for each class where I put the graded papers to give back.   I am SOOO much more organized with it.

 

6.  Manipulatives

My favorite go-to manipulatives are two-color counters and algebra tiles.  The two-color counters are awesome for teaching integer operations and the algebra tiles are great for simplifying algebraic expressions, adding/subtracting/multiplying/factoring polynomials.  I also LOVE my 3-d figure manipulatives.  I have foam ones (that are fun to throw at the students) and ones with removable nets that are great for teaching surface area.  I also have lots of dice, coins, and spinners for my probability units.

 

5.  Looseleaf and/or Scrap Paper

You can never have too much paper!  My students are always required to show all work so I go through paper like crazy.

 

4.  Good Grading Pens

I LOOOOVE my papermate flair grading pens.  I love all the colors, they don’t bleed through papers, and they just write nice.  I get a new pack each school year and it is always my favorite summer purchase!

 

3.  Fun, Nerdy, Math Decorations

Math in the Middle| ABCs of Algebra: Math Alphabet Set for Secondary Classroom

I like my room to set the tone as a fun place to learn math.  I have math comic strips up around the room (Frank and Ernest have a bunch of good ones), cheesy math posters (such as “Life without geometry is pointless”), and my new addition that I am VERY excited about is an algebra alphabet set that I made to hang around my room.  It’s colorful, fun, and educational!

If you are interested, you can get a set of my Algebra Alphabet Cards at my TpT store.

Math in the Middle| Algebra Alphabet Set to Decorate Middle School or High School Math Classroom

Here’s a close-up of some of the cards.

2.  Graph Paper

Math in the Middle Blog| Stick-on Graph Paper If you are teaching pre-algebra or algebra your students will be graphing lines so you will need graph paper.  Depending on whether you use binders or notebooks, you may want different types of graph paper.  If your students use binders for their notes, you can just use regular 3-hole punch graph paper.  If you are using notebooks, then I highly recommend these awesome stick-on graphs that I discovered a couple of years ago!  Just stick them into your students’ notebooks and they have a nice, neat place to take notes on graphing!  (I don’t remember where I got these ones, but Amazon has a similar set for sale).

 

1.  Mini Whiteboards, Expo Markers, and “Erasers”

Math in the Middle Blog| Mini Whiteboards

Every math teacher needs a good set of mini whiteboards.  Have students work out problems on them, showing their work, and then have them hold them up to show you.  Such an easy formative assessment!  They are great for review games, too.  I definitely recommend getting a set that includes a coordinate plane side, as well, so that students can use them for graphing.  I have been using these ones from EAI Education for a few years now and love them!  They are thin and lightweight and barely take up any room.  If you don’t want to invest in a good set of mini whiteboards you can always make your own.  My first year of teaching I took a piece of cardstock and a printed out coordinate plane and put them in page protectors.  I taped them shut, and had my own little makeshift whiteboards.  The nice thing about the homemade ones is that since they are in 3 hole punched page protectors, students can each keep one in their binders (if they are using binders) and always have them on hand.  I use old rags as erasers for the whiteboards, but paper towels or actual whiteboard erasers work, too.

 

I hope you found this list helpful.   Do you have any must-haves for your middle school math classroom that weren’t on my list?  Please share!  I will send a FREE set of my Algebra alphabet set to the first 2 people to comment (be sure to leave an email address for me to send it to).

 

Thanks for reading,

Christina

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