Teaching Math with Manipulatives

We all know students learn better by doing.  Here are a few tips for teaching math with manipulatives.  First off, always remember that is easier for the students to actually handle and manipulate objects than to imagine a situation.  We know it takes more effort and more planning for these types of lessons, but we also know it is worth it.  To cut down your planning time, we have some materials ready for you.

Teaching Substitution with Manipulatives

Substitution arises very often in mathematics.  Here is a trick for teaching it right the first time.  Your students will better understand "plugging in."


Given y = 4x + 2, find y when x = 3.

This is a very basic example for using substitution.  Instead of just substituting 3 for x and solving, we want the students to physically plug in 3 for x.  Remember, we are teaching math with manipulatives here.

At the board, write...


     y = 4x + 2   y = ? when x = 3

Now, the only manipulatives you will need for this activity is some colored index cards (red or pink show up very well), a few markers, and some magnets. (Tip:  you can cut up kitchen magnets into small squares.)

Give a student an index card (already cut in half), a magnet, and a black marker.  Have that student write the value of x on the card.  In this case, the card should have a 3 written on it.

The student should then go to the board and put the pink card on top of the x, where you have x = 3 written.  The board should look like...



Placing the 3 on top of the x physically shows that the x is "worth 3."  By doing this, you are also reiterating that an equal sign establish balance in an equation, and doesn't necessary mean "an answer."  View our page on the math property of equality for more details.

Now have the student take the 3 and plug it into the equation.  This is where we are really teaching math with

manipulatives, They physically plug in the 3, with an understanding that it is "worth" that amount.

       Math Manipulatives

Notice that I also put in a multiplication dot.  Now would be a good time to remind the students that 4x really means four times x.  Now, all the student must do is simplify the right side of the equation.

Substitution Manipulative  

This activity is great for engaging students, and of course teaching math with manipulatives.  It really helps the students to learn substitution. 

Want more free math teaching tools to help improve your teaching skills? 

How would you like to incorporate math jeopardy! into teaching math with manipulatives?  Check out GRADE-A's cool math games!

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