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.
image
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.
image
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.
image

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.
image
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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Turn Multi-Step Problems into Team Activities

Let me start by saying that relays are not an original idea..maybe you have been doing them for years…but they are new to me, (and i love them) so I figured I’d share in case anyone else has never tried relays with their class.

team relays

How they work:
Take a problem that requires multiple steps to solve, and break it up into however many steps you need to solve the problem.   Then break your class up into groups that are the same size as the number of steps in a problem.

For example: Multi-Step Equations

I came up with the following 5 steps:

  • distribute to clear any parentheses in the problem
  • combine like terms within each side of the equation
  • add/subtract to isolate variable terms from constant terms
  • multiply/divide to solve for the variable
  • check by substituting answer in for variable

Since it is a 5 step process, I need to break the class up into groups of 5.  (If your class size doesn’t divide evenly by 5, you can make some groups of 4).

Give the class a problem, assign each student in a group a step of the process.  Student 1 completes the first step and passes it to student 2.  Student 2 checks student 1’s work and then does step 2, etc. until each student has completed a step and the problem has been solved (and checked.). For a group of 4, student 1 will also complete step 5.

multi-step equations team relay

Repeat this process 5 times with 5 different problems, each time shifting which student starts the problem, so that by the end every student has had a turn completing each step.

I love this activity because

  • The students work cooperatively, but individually
  • The students are checking each others’ work
  • Relays really emphasize each step in a process

Make it a race if your class is competitive.  If you want to see who completed each part you can have them write in different colors.  Either have them sit in a circle if you want them to be able to help each other complete their steps or have them sit in a row if you want it to be a silent activity.

Do you use relays in your class?  If you have any tips, suggestions, or other ideas for them please share in the comments below!

If you don’t want to make your own relay and are looking for a pre-made one, I have one on writing and graphing linear equations (using point-slope and slope-intercept form) available for sale in my TpT store, which you can get to by clicking the image below.  I am planning to make several others on different topics in the near future, as well.

writing and graphing linear equations team relay pic3

Thanks for reading,

Christina

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Teaching Slope – Fun Activity Idea

Slope is an important topic for pre-algebra, 8th grade math, and algebra.  I was trying to come up with a new idea for practicing slope and I came up with the following:

I made 32 cards with ordered pairs on them.  All of the coordinates of the ordered pairs are between -3 and 3.  I plan to use these cards in a couple of different ways so I am going to print them on card stock and laminate them to keep them nice for future use.

  • Quick Entrance or Exit Activity: Give each student a card.  Have them pair up with another student and calculate the slope of the line that connects their two points.  Have the two students find the slope independently and then compare.  They should work together to identify errors if they got different answers. Then repeat with another partner.
  • “Making Slopes” Activity: Give each student a card and a worksheet (download link is below).   Put the extra cards around the room.  The worksheet specifies different slopes that the students have to make.  Students need to walk around the room and find an ordered pair that, when paired with their ordered pair, makes a line with the given slope.  (They can use other students’ ordered pairs or the extra ones around the room.  It is important that ALL 32 cards are accessible to the students so that they are able to find an ordered pair for each slope.)  Once they find one that works they need to “prove” that they are right by plugging the two ordered pairs into the slope formula (showing their work) AND by graphing the ordered pairs on a coordinate plane to show the rise/run.

Here’s an example for the ordered pair (-1, 1):

Making Slopes Activity

I am excited about the making slopes activity for the following reasons:

  • It gets the kids up, out of their seats, and moving
  • It is more of a challenge and requires higher level thinking than questions that simply ask students to find the slope of the line that passes through two points, so it should be perfect for my Pre-Algebra (advanced) math class
  • It can easily be turned into a game/contest by seeing who can find all 5 ordered pairs first or who can find the most in a given time period

I haven’t actually done the activity yet with my class but I am hoping that it goes over well.  I welcome any thoughts or suggestions for the activity in the comments.

Want to try this activity with your class? 

Download the 32 ordered pairs cards by clicking the picture below.

ordered pairs cards pic

Download the “Making Slopes” activity worksheet by clicking the picture below.

worksheet

I have a bunch of other ideas for ways to use the ordered pair cards for different lessons (not on slope), too, that I will write about in future blog posts.

 

Thanks for reading,

Christina

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A Creative Approach to Grouping in the Middle School Math Classroom

I am a HUGE fan of group work!  I love having students work together in my math classes for practice work, problem solving, review games, etc.  Occasionally I allow my students to pick their own groups, but more often than not I assign them because:

  • No students are ever left out or the last one picked when I assign them
  • I can make sure the groups are either mixed ability levels or homogenous (whatever I need for a particular class period)

I pick new groups every time we do group work because I think it’s important for the students to be able to work successfully with different people and I don’t want students “stuck” with the same people every time.  I have done different things in the past to pick random groups such as having the students count off or handing them playing cards as they walk in the room.  I also have deliberately placed students in groups.  But I was looking for a way to mix things up…

…so I have come up with the following solution:  As the students come into the classroom I will hand them a card with a math problem they need to solve (relating to what they are learning).  This problem will be in place of the typical do now problems I give them on Socrative.  Once they solve the problem, they will need to find the table labeled with the answer to their card, and sit there.  (3 other students’ cards will have that same answer), so those 4 students will be a group for the day.   (I will be walking around to assist any students who struggle with their problem).

math-in-the-middle.com|matching task cards for grouping pic1

I am pretty excited to try this and can think of a bunch of different ways to change this up.  I could have the groups be completely random by just giving each student a random card, or I can make the “random” groups fit my needs based on ability level (without the students even realizing it) by grouping the cards based on difficulty level and giving each student a card from the group that is appropriate for them.  [If I want mixed ability level groups, the 4 cards with matching answers will be 4 different difficulty levels;  If I want homogenous groups, the 4 cards with matching answers will be the same difficulty level.]

Obviously this will require a bit of prep time in advance (since I have to come up with the questions), but I plan to laminate the cards and use them every year.  I can also re-use them as a card-sorting center activity, as task cards, game cards, etc., so I think that it is worth the initial time investment.  (There are soo many different ways that I can use and re-use the cards!!)

I made my first set of these cards on one-step equations and have them set up to create mixed-ability level groups.  I color coded the cards by difficulty level – yellow include only whole numbers, blue include integers, green include fractions, and red include decimals.  As the students walk in the class, I will give the students who struggle with one-step equations yellow cards, and the students who need more of a challenge green or red.  The groups will end up with one of each color card, giving me random, but “equal” mixed-ability level groups.

math-in-the-middle.com| matching task cards for grouping pic2

You can grab this set of 32 matching task cards (to form up to 8 groups of 4) on one-step equations FREE by clicking the download links below.  (I included the color-coded cards and the same cards in black and white…feel free to download and use whichever version you prefer).

match task cards bw

Click the picture above to download the 32 matching cards in black & white (FREE)

match task cards color

Click the picture above to download the 32 matching cards in color (FREE)

Do you have any other ideas of how to use these matching cards?  Please leave me a comment with your thoughts!!

Thanks for reading,

Christina

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Coordinate Planes Freebie

Just a quick post today (to make up for my last 3 being sooo long)!

Does anyone else have students who can’t seem to draw a decent coordinate plane on a piece of graph paper?  I never would have thought that tracing a horizontal and vertical line on a piece of graph paper would be difficult for anyone to do, but I have some students who can’t seem to draw a straight line (even with a ruler)…

Obviously if the coordinate plane isn’t drawn correctly, it is impossible to graph correctly so I went online in search of a page of coordinate planes that I could print out.  I found a bunch that had 4 or 6 coordinate planes on a page but they seemed to waste alot of space to me, so I made my own sheet with 12 coordinate planes on it that I will be printing double-sided so students can use it to complete 24 graphing problems (and I can avoid the headache of having to look at problems being completed on imperfect coordinate planes.

If you have students who suffer from the same inability to draw straight lines as mine, click the image below to download and print the pdf of 12 coordinate planes.

coordinate planes

Enjoy!

Thanks for reading,

Chrisitna

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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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