Ideas for Keeping the Math Fresh in Students’ Minds

The end of the year is often a time for reviewing the math learned throughout the year, whether to prepare for state tests, final exams or cumulative projects, or just to fill the days after testing is done.  However, I have come to see how important it is to review all year long and not just wait until the end.

My first year teaching, my students seemed very receptive to my lessons, seemed to grasp the concepts, and did well on the tests I gave them after each chapter.  However, I was surprised and disappointed in the standardized test scores of some of my best students.  I realized that the problem was that once we finished a chapter and moved on to the next chapter, they never saw the material from that first chapter again and so by the time standardized tests came around they had forgotten some of the things that they used to know really well.  I learned from that experience and have since incorporated various ways to keep the math fresh throughout the year:

keeping math fresh

  • I know different teachers have different opinions on calculator usage, but my personal feeling is that once students prove that they can do something by hand, I allow them to use calculators so that they aren’t spending too much time on the computational aspect of a complex problem. However, I don’t want them to forget how to do problems by hand, so once a week I give them a “no calculator review” in place of my traditional “do now” questions.  They usually cover topics like fraction, decimal, integer, & rational number operations.  (You can read more about my No Calculator Reviews in this post).
  • After each chapter test, I give my students a cumulative review that I count as a quiz grade. It covers things from all previous units that we covered.  Students know that the cumulative quiz is coming so they know that they can’t just forget the material after they learn it.  Sometimes I allow students to use their notes for the cumulative quiz or give it as a take-home quiz, but most of the time I give it as a traditional quiz.  Not only does this encourage students to (hopefully) retain the math they are learning, but it shows me if there are particular concepts that a lot of students seem to have forgotten that I may need to revisit.
  • This is, in my opinion, the most important strategy. I give my students problems and ask them questions that require them to use skills learned previously in the year.  It is so important for students to see connections between the different units they learn, so any time I can incorporate an “old” skill/concept into a “new” one is a win in my book!  Here’s an example of a task card I made for a lesson on finding the area & perimeter of irregular figures that requires students to use previously learned skills:

irregular figure

To find the perimeter students need to use the Pythagorean Theorem and to find the area & perimeter students need to perform operations with mixed numbers, so this one problem reinforces a couple of different skills learned throughout the year.  Giving students lots of problems like this makes it virtually impossible for them to forget the math they learned earlier in the year since they are constantly using it.

 

I hope this gave you some ideas for helping students keep the math fresh!  If you are looking for ways to keep it fresh over summer break or just need a good end of year review packet, I have math review packets for students going from 5th to 6th grade, 6th to 7th grade, 7th to 8th grade, and pre-algebra to algebra I in my tpt store for $4 each.    Each packet contains detailed explanations of how to do the various types of problems, worked-out examples (showing each step), and 100 practice problems.  Click the pictures below for more information on each packet.

Slide1 math review packet new cover math review packet for 7th-8th grade pic1 Slide1

 

Thanks for reading,

Christina

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Helping Students See Their Strengths in Math

Well, it’s here.  The official turning point in the year when students and teachers (whether they admit it or not) turn their thoughts to summer.  That’s not to say that teachers are done teaching or students are done learning…but middle schoolers – especially 8th graders – come back from spring break ready for summer.

So i figured I’d share an end of year idea I had for my classes in case anyone reading this is thinking about those last days of school, too. 🙂

We’ve all had kids in our class that have shown tremendous growth over the course of the year.  We’ve all had kids who come in for extra help because they really want to understand.  Then there are the kids who are always helping their classmates who are confused, the ones who always pay attention in class, complete their homework, etc.

The problem I’ve always had is that for my school award ceremony I am required to pick 2 students from my math class to receive an award: one is the student with the highest average and the other is for a student who displayed great effort.  The issue is that there are often multiple students who I feel are deserving of the effort award but I’m only able to pick 1.

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This is such a common sense idea that I honestly don’t know how I haven’t thought to do this before…but I decided to do my own certificates in addition to the school awards.  This way I can recognize multiple deserving students.  In fact, I challenged myself to come up with a strength to recognize in each of my students so I can give every student an award.  I think that it is important for every student, especially the ones who believe that they are “bad at math”, to realize that they have potential, a skill, or talent, that can help them be successful in math.

I made awards for completing homework, participating in class, persisting in solving difficult problems, consistent effort, excellence in Algebraic thinking, outstanding critical thinking, excellence in graphing, good mental math skills, excellent overall achievement,…and many more (31 in all!).  I gave them all cute alliteration names, too, to make them more fun! 😉

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I want to show my students that I appreciate their hard work and effort. More importantly, though, I really hope this helps my students build confidence in their math skills and helps them see the strengths that I see in them.

If you like this idea but don’t want to make your own awards, you can purchase my math awards for $4 in my TpT store.  They are in editable PowerPoint form so you can type in names, and PDF form if you prefer to hand write the names.  I also included both color and black & white versions so there are options for everyone.   

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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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