Elementary Algebra

Click here for the syllabus.

Virtual Manipulatives
The following are links to computer games that will help reinforce some of the concepts that are often difficult for students to learn. Give them as shot. If you have trouble working them, or if you don't understand them, please don't hesitate to contact me at cmathers@northampton.edu (after trying the instructions link at the top of the page).

Virtual Manipulative: Fractions
To do something like add 5/6 to 3/4, most students realize that you need to get a common denominator. And that usually means multiplying the first fraction by 2/2 etc. But they don't usually understand what that really means. Try this link to help you visualize what it means to change (for example) 5/6 to 10/12.

This applet will help you really understand what we're really doing when we change a fraction to something equivalent.

Virtual Manipulative: Adding Integers
For a fun and educational way to review adding positive and negative numbers (or perhaps really understand for the first time), try the applet at this link.

For some reason, it doesn't seem to do anything at first click, so just click again.

Click the Instructions button at the top for help.

Virtual Manipulative: Subtracting Integers
One concept that always seems to persist as a source of confusion for students is the idea that subtracting a negative can turn out positive??? For example 2 - (-3) = POSITIVE 5??? How does that happen. Try this virtual manipulative to help with understanding this. If it works for you, think of it whenever you're uncertain in the future. You'll notice that when you get to the second step, it only delivers plus and minuses in pairs. That is because while we might want some positives there to "take away", the only mathematical sound way to do it is to counteract each positive with a negative (ie, adding something equivalent to zero doesn't effect the overall value).

Virtual Manipulative: Solving Simple Linear Equations
Remember that algebra is about trying to figure out what value(s) x could be replaced with, so that we'd have a true statement. For example, to solve x + 2 = 5 would mean to figure out what value(s) x could be so that adding 2 to it would equal 5. That mathematical sentence can only be true when x is exactly 3. In that example, we can easily figure out what x must be by just thinking along those lines "I can clearly see that 3 is the number that x could be replaced by". However, when problems start getting more complicated, like 2 + 4(1 + x) = 18, the answer isn't so easy to see (and of course, they can get WAY more complicated than that). This is why we learn about adding/subtracting/multiplying/dividing the same quantities to both sides, getting us to an x = some # (ideally).

The applet at this link illustrates these ideas, by thinking of the middle of a balance as the equals part, and we add and subtract different weights to each side.

Algebra Balance Scales - Negatives
This link is similar to the previous one, except it includes helium baloons to represent negatives (think about why).


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Faculty Web Sites > Charles Mathers > Elementary Algebra Click here for the syllabus. Virtual Manipulatives The following are links to computer games that will help reinforce some of the concepts that are often difficult for students to learn. Give them as shot. If you have trouble working them, or if you don't understand them, please don't hesitate to contact me at cmathers@northampton.edu (after trying the instructions link at the top of the page). Virtual Manipulative: Fractions To do something like add 5/6 to 3/4, most students realize that you need to get a common denominator. And that usually means multiplying the first fraction by 2/2 etc. But they don't usually understand what that really means. Try this link to help you visualize what it means to change (for example) 5/6 to 10/12. This applet will help you really understand what we're really doing when we change a fraction to something equivalent. Virtual Manipulative: Adding Integers For a fun and educational way to review adding positive and negative numbers (or perhaps really understand for the first time), try the applet at this link. For some reason, it doesn't seem to do anything at first click, so just click again. Click the Instructions button at the top for help. Virtual Manipulative: Subtracting Integers One concept that always seems to persist as a source of confusion for students is the idea that subtracting a negative can turn out positive??? For example 2 - (-3) = POSITIVE 5??? How does that happen. Try this virtual manipulative to help with understanding this. If it works for you, think of it whenever you're uncertain in the future. You'll notice that when you get to the second step, it only delivers plus and minuses in pairs. That is because while we might want some positives there to "take away", the only mathematical sound way to do it is to counteract each positive with a negative (ie, adding something equivalent to zero doesn't effect the overall value). Virtual Manipulative: Solving Simple Linear Equations Remember that algebra is about trying to figure out what value(s) x could be replaced with, so that we'd have a true statement. For example, to solve x + 2 = 5 would mean to figure out what value(s) x could be so that adding 2 to it would equal 5. That mathematical sentence can only be true when x is exactly 3. In that example, we can easily figure out what x must be by just thinking along those lines "I can clearly see that 3 is the number that x could be replaced by". However, when problems start getting more complicated, like 2 + 4(1 + x) = 18, the answer isn't so easy to see (and of course, they can get WAY more complicated than that). This is why we learn about adding/subtracting/multiplying/dividing the same quantities to both sides, getting us to an x = some # (ideally). The applet at this link illustrates these ideas, by thinking of the middle of a balance as the equals part, and we add and subtract different weights to each side. Algebra Balance Scales - Negatives This link is similar to the previous one, except it includes helium baloons to represent negatives (think about why).