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.