Math Instruction: How to Make the Most of It



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As the date for online testing approaches (Mid-May for the math portion), I've recently reflected on my teaching of math.  I've been teaching for over 30 years and have attended a great deal of inservice training for math.  Some of it has been so-so, some terrible and some completely changed my teaching and approach to math.  One of those inservice trainings that completely changed the way I teach math was the Math Their Way training I took back in the mid 90's when I was teaching first grade.  If you're not familiar with Math Their Way, click on THIS LINK.  In a nutshell, students should progress through learning stages when learning math.  This is all based on Piagetian principles of learning:  concrete level, connecting level, symbolic level and abstract level.  Even teaching 3rd grade, these principles have guided my math instruction.


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In this blog post I will show you how my daily math routine reflects not only the training I received, but some modern day reality of online testing.  My math period is 90 minutes daily (though this 90 minutes includes 30 minutes of Math RtI instruction which I fold into this 90 minute block).  I've blocked out my math period into 7 basic routines.  Of course, we all know that as teachers, routines can be interrupted and some need to be extended or shortened depending on the concept being learned.  You'll see how the Mathematical Practices are also reflected in the teaching and learning. Also, I taught the concept of perimeter for about a week before moving on to area. They were not taught simultaneously.

Correcting Homework and Review


After correcting the daily homework (usually a practice page out of the math practice book used by my district), we start with a review.  I came across this wonderful resource on TpT by Monster Wrangler Mike.  They were such a hit with my kids, I bought all of them!  They all feature a character named Goofus who is always making mistakes in math.  The students' job is to show Goofus what he did wrong.  We know how powerful it can be to have students find errors and fix them.  But it is even more powerful when a student has to explain the mistake!  I spend about 10 - 15 minutes on the review based on student needs. This daily review is very important because it solidifies the previous day's learning for those who had some confusions or for those who just forgot. I highly recommend these resources because they saved me a lot of prep time and were perfectly aligned to the the CCSS for grade 3.


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Hands-On Instruction


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The first level of math instruction is to work on the concrete level.  The concrete level is when the student can use a real object (math manipulative) and use it solve a problem.  There are no worksheets, no symbols, no word problems.  Just asking the students to use the manipulative to solve a problem that is explained orally.  The teacher can also use this time for direct instruction on how to use the manipulative to solve the problem and using the correct math language.  With area and perimeter, I used geoboards and foam tiles.  These were all supplied by the current math program my district utilizes.   I gave the students some time to just explore with the geoboards first so they could then focus on the learning later with me.  The geoboards and rubber bands are an excellent way to represent line segments that are counted for perimeter.  The foam tiles are an excellent way to represent the squares we count for area.  We practiced with multiple examples and I also had students show me 2 different shapes with the same perimeter or 2 different shapes with the same area.


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Connecting Level


Here is the most important level, IMO. Showing students how the concrete learning is now used with labels or, in this case, drawings.  Using dot paper, students copied some of their designs and labeled the perimeter or area.  Then we put away the geoboards and tiles and I had students use the dot paper to just draw shapes with certain perimeters or areas.  Students need to see the connection between the real life object on how it is represented on paper with symbols or drawings.

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Symbolic Level


This is when I begin the guided practice with the students.  Giving them a worksheet that helps the practice the procedure for either finding the perimeter or area. Are we counting or adding. Are we counting or multiplying.  Students can write equations for both adding (perimeter) and multiplying (area).  This is all symbolic.  We correct the guided practice to make sure students are not doing the procedures incorrectly before moving onto independent practice.


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Abstract Level


You're probably wondering where does the actual math book fit into this routine?  Right here! At this level.  Now the students are ready to tackle the more abstract work in their math book.  The math book becomes independent practice for them.  By this time, they have a conceptual understanding of what they are doing and can use a procedure or steps to find solutions to perimeter and area.  The example below was from a worksheet rather from the book, but it is similar.  I also assign some of the word problems as well.  But here is where I innovated.  I knew that soon my students would be taking the California version of the SBAC  called CASSPP.  So that brings in the next routine.


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Tech Integration


I wanted my students to have practice doing the same kind of math using technology while having to do similar tasks they would be asked to do on the CASSPP.  So I took the existing word problems in the math book and repurposed them as a slide in Google Slides.  I just changed the parameters and variables in the problem so it wouldn't be a repeat of the one in the book.  I created a slide for each day.  The students had to drag or use tools to figure out the solutions to perimeter and area problems.  Each problem was broken up into 3 parts (similar to CASSPP and SBAC in which math problems have a Part A and THEN a Part B).  Practicing with multiple part questions gave the students practice with using the Part A answer to solve for Part B.  Part C was usually the student having to explain how they solved the problem (again, solidifying the learning).

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Another resource I've allocated to them in Google Classroom is links to websites that have quality online games for math.  Here's one example:  http://interactivesites.weebly.com/areaperimeter.html


And if you haven't heard of LearnZillion.com, then you'll will want to explore this website as well (it's free!). High quality lessons and video lessons all aligned to Common Core Math standards.  I want to make sure that my students who need that extra support have it, so I look up videos on LearnZillion that students can watch and learn the concept again.  It's wonderful to just be able to look up a video lesson by the standard. The site also let's you share through Google Classroom, so it's a snap to assign video lessons!

Additional Resources for Google Apps


I've also created my own resources that I have used with my students as well.  Because I'm in a 1:1 school district, I have access to a Chrome Cart daily in my room.  I've created Google Slide ready resources such as, Perimeter of Shapes, that I've used for a review before a test or for more practice.  This particular resource has been created using Bloom's Revised Taxonomy:

There are 14 interactive slides for the student to practice perimeter. The slides have been leveled using Bloom’s Revised Taxonomy. 

♦ 4 Slides for Remembering
♦ 4 Slides for Understanding
♦ 2 Slides for Applying
♦ 2 Slides for Analyzing
♦ 1 Slide for Evaluating
♦ 1 Slide for Creating



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My students have really taken to using the Chrome Books for math learning and I feel confident that technology will not be a barrier when taking the CASSPP.

If you're looking for a PowerPoint to also help you with perimeter and area instruction, check out this one that is available in my store.  Here's a video clip of one of the parts.  The students enjoy the superhero theme!





Exploration and Challenges


I've also created centers and a game which I use usually before the chapter test.  This is all good review done in a fun way.

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Click HERE to go to all my Area and Perimeter resources in my store.

Don't forget to check out these Pinterest Boards.  You'll find lots of quality pins with free resources, videos, ideas, tips and strategies.  

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Click HERE to follow the Google In the Classroom.  

Click HERE to follow Area and Perimeter.





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