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I had never even heard of Algebra tiles until my third year of teaching.  Our school invested in a bunch of Algebra tiles, and I quickly had to learn how to use them.  I tried searching the internet to understand how to use these with my students...but I couldn't find a lot of information.  So I took some time at my desk alone with my blocks and started figuring these things out...and it was like gold.  So awesome in so many ways. Suddenly integers, solving equations, simplifying expressions, factoring trinomials, and multiplying binomials made so much sense.  When I used Algebra tiles in my classroom I was able to reach all students.  They are magic! Today I am going to share with you how to use Algebra tiles to teach multiplying binomials.  

Start by reminding your students how to find the area of a rectangle.  Connect the fact that when you multiply two factors together you also are calculating the area of a rectangle with the factors as the side lengths.  Polynomials work the same way.  If you are given the factors (x + 2) and (x + 3), those are the side lengths of a rectangle, with the product as the area.  

  • Students line up the factors to represent the length and width.  
  • Students fill in the the area with blocks that are the same length and width as the blocks on the sides of the space they are trying to fill.  
  • Once the space is filled they will have a rectangle.
  • Students will see what blocks are in the area space of their rectangle, and that's the product of the binomial factors.  


If you need some activities to practice multiplying binomials in your middle school math classroom you can check out these products below.  Click on the photo for more details.  
Factoring and Multiplying Polynomials StationsFactors and Models with Algebra Tiles Task Cards


If you don't have Algebra tiles for your classroom you can use these printable ones.

Algebra Tiles Printable FREE







Calculating the area of composite figures and shapes is an important skill for middle school math students.  Some students will pick up on this skill quickly, and others will need various methods taught to them so they understand.  Read on to learn how to teach and challenge ALL OF YOUR STUDENTS to make sense of composite area. 

Review:  Review the area of triangles and rectangles.  Make sure that students understand that height and base must be perpendicular. 

Divide:  Divide the area up into different triangles and rectangles (or parallelograms).  Students will often have different ways to divide up the composite shape.  Let them divide it up differently and compare answers. 

Negative Area:  Composite area can also be determined by taking a larger area and taking away a negative area (an area that is not actually part of the composite shape).  Take a look at the image below.  To determine the area of the L-shaped blue section, a student can determine the area of the larger square (blue) and take away the away of the negative smaller square (yellow).  This method is good to at least show to students as it will be a good skill for them to understand as they progress in mathematics. 

Problem Solving:  I ALWAYS try and incorporate problem-solving into any lesson.  With composite figures, provide shapes with sides that are not marked, but can be determined by problem-solving.  Compare Figure A and Figure B below.  To determine the area of the composite figure below, most students will determine the area of the 6 x 7 rectangle and the additional triangle.  Notice in Figure A that all dimensions to determine the area of the rectangle and triangle are given.  In Figure B the height of the triangle is not as clear.  Students would have to problem solve that the perpendicular height of the triangle is 10 - 7 = 3.  This is also a way to differentiate in your classroom.  Some students may be ready to problem-solve quicker than other students, and that is ok. 



If you are looking for a fun way to practice composite area in your classroom take a look at this fun activity.  This activity includes two versions.  One version has all the measurements listed.  The other versions has missing measurements that can be determined through problem-solving.

Area of Composite Figures Activity
CLICK THE PICTURE ABOVE TO DOWNLOAD THE ACTIVITY

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Looking for an engaging activity to help your middle school math students understand pi?  This fun discovering pi activity will do the trick. The best part of this discovering pi activity is that this helps students makes sense of pi.  They will have a concrete experience that they can draw upon to help them remember the ratio of pi as the circumference to the diameter. 

Objective:  Students will discover pi as the ratio of the circumference to the diameter of a circle. 

Supplies:  String, ruler, recording sheet, and at least 10 different cylindrical objects that you can use to measure the circumference of a circle.  If you look around your classroom or house you will be able to find a lot.   I have used cans, lids, bottles, etc...

Activity:  Students will measure the circumference and diameter of 10 circles.  Students will calculate the ratio between the circumference and diameter.  

When I have done this I have put students into groups.  Usually two students will need to help with measuring.  One to hold the object, and another student to wrap the string around. 
  
Students will measure the length of the string with a ruler.  

Another student can measure the diameter of the object. 

Measurements will likely not be exact, but encourage your students to take as accurate measurements as they can.  Have them measure at least 10 different objects.  The best way to do this is to give each group a couple of objects to measure.  Set a time limit, once the time is over, everybody passes their objects to the next group.  Students will record the object (so they can keep track of what they have done), circumference, and diameter.  After everyone has recorded the measurements of at least ten objects, have them write ratios of the circumference to the  diameter.  Then have them write their answer in decimal form, (at least to the nearest thousandth) and average their ten ratios. 

To take it one step further, I had each group write their average on the board and we took the average of all of them.  I also compared the averages of all my different classes.  Students will be amazed how close this number is to pi.  



Now that your students have a conceptual understanding of pi they will also need to be fluent with using this information to determine the circumference and area of circles.  Here is a FUN ACTIVITY you can check out so your students can become fluent with area and circumference. 


CLICK THE PHOTO TO CHECK OUT THE ACTIVITY


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Teaching in the winter is tough.  It's often gloomy outside, and the kids are either drowsy or have way too much energy.  Extra creativity is required to teaching during winter, but even more so around the holidays.  Let's face it, students (and teachers) are counting down the days until winter break, and it can be tough to keep their attention.  Here are some ideas to teach during those rough times.

1) Snowball Fight:  If you haven't tried this, you may already have your doubts just by reading the title.  But, if done correctly, students love this, and it is effective.  You can do this with various math concepts, but I will just give an example with integers.  Let's say your class is practicing integer operations. Every student needs a blank piece of paper to start.  Each student will write their own integer problem.  They then crumple up the paper, and you let them throw them around the room like a snowball fight for a set amount of time.  30 seconds usually is enough.   Set a loud timer, when the timer beeps students will grab whatever crumpled up piece of paper is closest to them, they open it up, solve the integer problem, and write a new integer problem.  To switch it up, you can tell them which operation to use.  After a set amount of time.  You let the students have another "snowball fight", set the timer and repeat the activity.  

Be clear about the process before hand, and model what it looks like when the timer beeps.  Students love this, because they get to throw paper at each other, and this is a great way to help them use their bottled up energy while practicing math.  


2)  Plan a holiday meal:  Use your local grocery ad to plan a holiday meal.  Students love looking through ads and picking out foods for their meal.  Have them total up the cost and account for sales tax.  Have them look up the sales tax for you area and apply it accordingly.  You could also have them "purchase" things like napkins, paper cups, the non-food items.  In some areas the food is taxed differently than the non-food items.  Have them apply the tax accordingly.  Compare their meals with their classmates.  

You could have them plan their meal beforehand and have them estimate cost.  Then they could calculate their percent error with the actual cost.  

They can calculate unit rates with items in the sales ad.

If the ad shows original cost and sales cost then they can calculate percent change of 10 items.  Of their 10 items, which items has the highest percent change? Which item has the lowest percent change?  

3)  Engaging seasonal problem-solving tasks:  Students love holiday activities, even middle school students.  However, you will want to keep the activities learning-based so you are not just wasting time in the classroom.  Students can differentiate between "busy work" and "effective problem-solving" work.  If you just give them busy work, most of them won't be working.  I have created 5 problem-solving tasks that are engaging, effective and easy to differentiate for the middle school math classroom. 


  • Snow Day:  This task requires students to reason through the size of a snowman and calculate the volume of the snowman.  Easier level: Students can calculate the area of the 2d snowman.  This task also includes a challenge as an extension.
  • Santa vs The Grinch:  Students calculate who wins in a sleigh race between Santa and the Grinch.  Higher level: Students use systems of equations and solve both algebraically and graphically.  Lower level:  Students reason through the task using problem-solving skills.  This task also includes a challenge as an extension.  
  • Geometric Snowflake: Students learn how the Koch snowflake is created and find the area of a stage 3 Koch snowflake. Higher level: Students use the Pythagorean Theorem to find missing side lengths. Lower level: Students use a ruler to practice measurement and find the composite area of the shape. This task also includes an extension for higher students.
  • O Christmas Tree:  Students are given equations in slope-intercept form and end points to draw on a graph.  The finished product is a work of art. Easier level:  Students use substitution to find the end points.  A challenge is also included as an extension.  Graph is included.
  • Colorful Crystals:  Students classify real numbers as whole, natural, integers, rational, or irrational.  Students then color snowflakes according to their answers.  This activity is perfect to keep students engaged before a break of with a substitute.  




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