Year 2 Lesson Plan 15 - Simplifying
Expressions by Combining Terms
- (5 min) Mental Math
- Take 50% of 40, multiply by 2 [40]
- What is 5/8 - 1/2? [1/8]
- Take 1/3 of 900 and add 45 [345]
- Take 100% of 80 and divide by 4 [20]
- What is 150% of 60? [90]
- (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
- (Remainder of class) In-class exercise
- Hand out homework as students successfully complete the in-class exercise.
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