Pi Day: Original (& Free) Ideas for Celebrating in Algebra I

Like most math teachers I love Pi Day!  I mean, who doesn’t love a day where you eat pie and celebrate math?!  I have always done a bunch of fun pi related activities with my students on Pi Day (you can read all about them and grab a Pi Day word problem freebie in this post from a couple of years ago), but the activities I usually do are geared towards 5th – 8th grade (pre-algebra) kids and aren’t really relevant to my Algebra I kids since area and circumference of circles are not in the Algebra curriculum.

So, I have set out to find ways to tie Pi Day into Algebra concepts and have come up with the following activities:

  1. Pi Day Literal Equations:  Literal Equations are a topic I teach towards the beginning of the year in Algebra I.  It is one of the harder concepts we do at the beginning of the year so I think Pi Day is the perfect time to revisit and review them.  I made a worksheet with a bunch of Geometry formulas that involve pi to have my students solve for pi.  I made it a bonus to see how many of the formulas students can identify.  The first student/group to finish and the student who correctly identifies the most formulas get prizes!  (Download the worksheet by clicking the image below).solve for pi pic
  2. Systems of Pies: Have students work with a partner to write a system of equations about pies.  Then have students walk around the room and solve each other’s systems of equations using the methods of their choosing.
  3. Pi Day Attack Review Game: Have each group draw a pie cut into 5 slices.  Ask students review questions on ANY Algebra I topic.  When a group gets an answer right, they can attack two different pies by “eating” a slice (coloring it in).  The last pie with any slices remaining is the winner!  (I wrote a detailed blog post about Attack here that you can read for a better explanation of the game and rules).

image

I hope this has given you some useful ideas for making Pi Day a success in your Algebra class!  What other activities have you done that bring Pi Day into the Algebra I classroom?

Thanks for reading,

Christina

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Fun Christmas Ideas for the Middle School Math Classroom

One of the things I like best about teaching in a Catholic school is the ability to celebrate religious holidays like Christmas with my students so I am always looking for ways to incorporate the fun of the season into my daily classes.  Here is a collection for some of my favorite Christmas activities that go along with topics that I teach in December:

Equation Writing

I write 2-step equations on little slips of red paper, fold them and stick them in a stocking.  I write different Christmas “things” (like Christmas trees, presents, stockings, reindeer, etc.) on little slips of green paper and stick them in a different stocking.

2 step equation writing christmas

I have the students partner up.  One student from each pair reaches into the 1st stocking and picks a red slip while the other student picks a green slip from the 2nd stocking.  They then have to work together to write a word problem about the thing that’s on their green slip that could be solved using the equation from their red slip.  It’s a great, critical thinking activity!

2 step equation writing christmas example

(If you’re in need of a bulletin board display, have them write their problem on nice paper, make a drawing that goes along with it and then have them solve the problem below it – makes a great Christmas math display)!

Percents

I made this quick self-checking sheet a couple of years ago to review finding the percent of a number.  Students start at the bottom and work their way up.  They know if they did the page correctly if their last answer matches the number in the star.  I use it as a warm-up around Christmas time with my 6th graders – it only takes a few minutes to complete and students (and teachers who don’t want to spend time checking/grading papers) love the self-checking aspect of it!  Grab it for free by clicking the picture below.

tree wksht pic2

(I have a set of Christmas percent word problem task cards for $3 in my TpT store, if you are interested, as well.  They are fun and challenging word problems that really make the students think Click the picture below if you are interested in them.)

christmas task cards pic2

Use sale ads:  Have students calculate the percent of discount for an ad that lists the sale price and original price of an item.  Have them calculate the total price of something including sales tax.  Tell them they get an additional 20% off the sale price and ask them how much something will cost…..the possibilities are endless!

Systems of Equations

Systems are my absolute favorite topic to teach in Algebra!  I love everything about them – but my absolute favorite is systems of equations word problems!  I always teach this topic in December and years ago I made this Christmas word problem activity.  It’s FREE, so just click one of the pictures below to download the resource – it is one of my absolute FAVORITE resources and my students have fun with it every year.  Students answer the word problems – there is a good variety of different types of systems of equations word problems – and then plot their answer on a coordinate plane.  At the end, they connect the ordered pairs in alphabetical order, which makes a Christmas tree.

christmas freebie pic2 christmas freebie pic4

Those are just a few of my favorite ways to bring the fun of the season into the topics I teach in December.  Please feel free to share your own Christmas math ideas by leaving me a comment!

 

Thanks for reading,

Christina

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Hands-On Integer Operations (Part 3: Multiplication & Division)

Multiplying and dividing integers are, in my opinion, the hardest operations to teach to students and it took me a few years before I found a good way to have these operations make sense to students.  After I am confident that my students are comfortable adding and subtracting integers, I move on to the final two operations.  (Click here for my post on teaching integer addition.  Click here for my post on integer subtraction.)

I begin with a class discussion of what multiplication means.  Once the students are able to tell me that multiplying means “grouping,” I pull out the two-color counters again…

I start with a positive x positive:  2 x 3.  We discuss how this means “make 2 groups of 3”.  The students show me this with their counters and get 6 as an answer.

pos x pos

I move onto a positive x negative problem: 2 x (-3).  This means “make 2 groups of -3”. The students are able to do this easily with the two-color counters, as well, by making 2 groups of 3 red counters to get an answer of -6.

pos x neg

Now we get to harder questions:  negative x positive and negative x negative.  I ask the class “if a positive times a number means to make groups, what do you think a negative times a number means?”  Then we come up with the idea that a negative times a number must mean to take away groups.

So we do a negative x positive problem: -2 x 3, which means “take away 2 groups of 3”.  Obviously the students can’t take away groups when there are no groups to begin with, so I ask the students what to do.  Because they are familiar with having to add zero pairs to take away numbers from our lesson on subtraction, the students are able to tell me that I will need to first make 6 zero pairs and then take away 2 groups of 3 yellow counters, leaving them with 6 red counters, or -6.

neg x pos

Finally, we move onto a negative x negative problem: -2 x (-3), meaning “take away 2 groups of -3”.  The students are able to figure this one out on their own based on the last example, so they again add 6 zero pairs, but this time take away 2 groups of 3 red counters, leaving them with 6 yellow counters (positive 6) as their answer.

neg x neg

I give the students problems to try on their own and then we come up with our formal rules for our notebooks:

Same signs:  multiply the absolute values of the numbers and make answer positive

Different signs:  multiply the absolute values of the numbers and make answer negative

Coming up with “real-world” examples for adding and subtracting integers is easy – you can use elevators moving up and down, temperatures rising and falling, and gains and losses in football.  It was much harder for me to come up with a “real-world” example for multiplication to give my students, but I finally have one that I am happy with that makes sense to the students and that I can use to show all 4 types of multiplication problems!

temp

  • Positive x Positive: It is 0 degrees outside.  The temperature is rising 2 degrees every hour.  What will the temperature be in 5 hours?  [The students know to do 2 x 5 = 10 degrees, so they are multiplying the rate the temperature is changing, which in this case is positive since the temperature is rising, by the time, which is also positive since I am talking about the future]
  • Negative x Positive: It is 0 degrees outside.  The temperature is dropping 2 degrees every hour.  What will the temperature be in 5 hours?  [-2 x 5 = -10 degrees – the rate is negative since the temperature is dropping, and the time is positive]
  •  Positive x Negative: It is 0 degrees outside.  The temperature rises 2 degrees every hour.  What was the temperature 5 hours ago?   [2 x (-5) = -10 degrees – the rate is positive, since the temperature is rising, but the time is negative since I am talking about going backwards in time]
  • Negative x Negative: It is 0 degrees outside.  The temperature drops 2 degrees every hour.  What was the temperature 5 hours ago?  [-2 x (-5) = 10 degrees – both the rate and the time are negative]

 

I teach dividing integers just by using the inverse of multiplication.  For example, I give the problem -24 ÷ 4.   Since they already know multiplication of integers rules they simply ask themselves 4 x ? = -24, so the answer must be -6 since a positive x negative = negative.

Students then come to the conclusion that multiplication and division use the same rules since they are inverses.

Once the students understand the rules, they have no problem solving multiplication and division problems, as they find multiplying & dividing integers to be easier than adding and subtracting.  I have them complete worksheets and/or play review games with them for practice and then I move on to practicing all 4 operations together the next day.

Click the image below to download a FREE page students can add to their notebooks  for a quick reference on integer operations.

int ops rules

If you are looking for more resources on integer operations, check out my Integer Bundle, which includes 21 (differentiated) worksheets, 4 games, and 3 sets of task cards.

integer bundle pic1

I would love to hear how other teachers teach integer operations, especially real-world examples for multiplication and/or division.  Please leave a comment if you would like to share!

 

Thanks for reading,

Christina

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Unit Analysis in the Middle School Math Classroom

After a long break (due to craziness in my personal life and some technical difficulties with the blog)…I’m happy to be back blogging!

I’m going to jump back into blogging with a post about Unit Analysis…

unit analysis in the  middle school math classroom

I hate teaching customary system conversions the traditional way!  No matter how many times you explain to students that you multiply when converting from a larger unit to a smaller unit and divide when converting from a smaller unit to a larger one, there are always students who mix the two up.  And then when teaching students to convert rates, it’s a whole new process…

So, I prefer to teach Customary conversions with unit (or dimensional) analysis.

Here are a few of the reasons why I love unit analysis:

  • It’s ALWAYS multiplication (no need to figure out which operation to use)
  • It reinforces fraction multiplication skills
  • The same process can be used for converting rates (no need to learn a new skill)
  • Students get it (and like it)!!

 

Here is an example of a simple unit analysis problem:

Convert 7 miles to yards.  (This example is done with the assumption that  students do not know that there are 1,760 yards in a mile;  If they do know this, it is only a one-step unit analysis problem).

basic unit analysis

 

When I teach unit analysis I always have a discussion with the students on why it works.  It sometimes takes some encouragement, but students are eventually able to come to the realization that each fraction (other than the starting one) equals one since the numerator and denominator are equivalent.  Therefore, unit analysis ‘ works’ because they are just multiplying by 1 over and over again, which doesn’t change anything (as we know from the multiplicative identity property).

I typically start the lesson with a simple fraction multiplication problem to review cross-simplifying.  That makes the transition to cancelling out the “yd” in the numerator with the “yd” in the denominator easy for the students.

I always tell them that they know they are done when the only word remaining is the one they are asked for.

When I give the students rate conversion problems the next day they are able to solve them using unit analysis, as well.  It just sometimes takes some gentle reminding that every fraction should equal one (the numerator should equal the denominator) and then they are good to go, even for “hard” problems like the one below!

converting rates unit analysis

Thanks for reading,

Christina

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