Using Base 10 Blocks In Algebra.

 

When I got my teaching credentials, we didn't use manipulatives in high school.  It was never a topic and I didn't learn to use them but over time it's become more acceptable to use manipulatives in Algebra, especially for students who need the visual component.  So today, I thought I would take time to share some ways I've researched or discovered for using manipulatives in Algebra.

For working with signed numbers one can use those two colored round disks.  The ones I have are yellow and red.  I designate the red as negative and yellow as positive. This way if they have -4 + 5, they have four red disks and five yellow disks.  When they match up one red and one yellow to make zero, they are left with one yellow or -4 + 5 = 1.  One can use algebra tiles, small rods in different colors, or even a number line.  You can also use two different colored singles from the base 10 manipulatives so they have the correct number of singles for -4 and 5.  Visually they can see that there is a difference of 1.

For combining like terms, you can use those base 10 manipulatives.  The singles can make up the constant, the strips of 10 represent x and the 100 squares represent x^2.  Using two colors, one for positive, one for negative, they can combine terms and see what the total is of each term.  

Those base 10 manipulatives can be used to show binomial multiplication using the singles as ones, the 10's strips as x and the 100's as x^2.  The problem is (x +2)(x+1) like in the picture.  

The x + 2 is one 10 strip with two singles and the x + 1 is with one 10 strip and one single.  You multiply the x times x, x time one, x times one.  then you multiply 1 times x, one times one and one times one. If you count all of the parts, you end up with x^2 + 3x + 2. Side note: this visualization also works well with two digit times two digit multiplication.  You can also use these as the reverse so you set up the answer and figure out the solution.  Now if you have say (2x + 3)(3x - 2) you would have two -10 strips for one side and three - ten strips on the other with a different color for the negatives.  You could use algebra tiles but the base 10's work and you might have some of those around.

In addition, these base 10 manipulatives can be used to solve one and two step equations by using the single squares and the 10's strips.  Say you have 2x - 3 = 5.  you have a rectangle with a line about half way through.  On the left side you have two - 10 strips and three squares in the color representing a negative number.  On the right side you have five squares in the color representing positive numbers.  Using positive colored squares you add three to each side which shows how the -3 goes to zero and the other side becomes 8.  Then you can divide the 10 strips representing the x in half and divide the 8 in half so you now have x = 4

If you don't have base 10 blocks, this site has some virtual ones your students could use. I will revisit this topic in the future.  I hope this gives you some ideas. Let me know what you think, I'd love to hear.  Have a great day and a wonderful weekend.