## Year 2 Lesson Plan 15 - Simplifying Expressions by Combining Terms

1. (5 min) Mental Math
1. Take 50% of 40, multiply by 2 [40]
2. What is 5/8 - 1/2? [1/8]
3. Take 1/3 of 900 and add 45 [345]
4. Take 100% of 80 and divide by 4 [20]
5. What is 150% of 60? [90]
6. Take 1/2 of 1/2 of 100 [25]

2. (5 min) Rules for simplifying

In algebra, we treat variables just like we treat units of anything else. We can add and subtract variables (letters) having the same power (exponent).

```If we have:              2 apples and 3 bananas
and we add:              3 apples and 5 bananas
----------------------
Then we have:            5 apples and 8 bananas

It works with letters:   2 a  +  3 b
3 a  +  5 b
-----------
5 a  +  8 b  ```

Can you see that this is the same as: 2a + 3b + 3a + 5b = 5a + 8b ?

You cannot add or subtract different letters from each other, anymore than you can add to or subtract apples from bananas.

```
3 apples + 4 bananas
5 apples             + 6 cherries
---------------------------------
8 apples + 4 bananas + 6 cherries

with letters:            3 a + 4 b
5 a       + 6 c
----------------
8 a + 4 b + 6 c   ```

We also write it like this: 3a + 4b + 5a + 6c = 8a + 4b + 6c

Now suppose we have two variables, T and O which are multiplied together. TO is different from T and different from O and cannot be combined with either. Pretend T stands for tangerine and O stands for orange and TO stands for the fruit you get when you crossbreed a tangerine with an orange: the tangelo. We cannot combine tangelos with tangerines or with oranges. When we add them to a bowl of fruit, they are still tangelos.

```
2 tangerines + 2 oranges + 2 tangelos      2 T + 2 O + 2 TO
+ 3 tangerines + 4 oranges + 5 tangelos    + 3 T + 4 O + 5 TO
-------------------------------------      ----------------
5 tangerines + 6 oranges + 7 tangelos      5 T + 6 O + 7 TO

```

There's one more thing you need to know. If a variable is raised to a power by multiplying by itself, then it becomes a different animal and cannot be added to or subtracted from the ordinary variable.

X + X2 + X3 + 2X + 3X2 + 4X3 = 3X + 4X2 + 5X3

Find the X's and add them up. Next find the X2 and add them up. Finally, add the X3s. Think of X as a line segment, X2 as a two-dimensional square and X3 as a three dimensional cube (which they are). You can probably agree that you can't add lines and squares and you can't add squares and cubes--it just won't work! The problem above basically says:

1 line + 1 square + 1 cube + 2 lines + 3 squares + 4 cubes
= 3 lines + 4 squares + 5 cubes

3. (Remainder of class) In-class exercise

4. Hand out homework as students successfully complete the in-class exercise.