Sample Lesson Plan


GAIN AND LOSS

Purpose: To add integers in realistic gain and loss situations.

Why: Addition is a common operation with a set of numbers.

What you need: You will need pencil and paper.

What you do:

Activity A: Play It

Below you will find a series of eight plays of football. Use a number line to visually show what happened in these plays. Fill in the chart to show the total number of yards gained or lost from the start.

Example: Player one carried the ball for 6 yards in the first play. The play would look like this: 

The team then received a penalty for false start and lost 5 yards. The penalty would look like this on the same number line: 


Begin with 0 on the provided number line. Working on the same number line, use arrows to show the moves from the last stopping point and give the resulting position from the starting point 0.
1. 1st play gain 4 yards position = _________
2. 2nd play gain 10 yards position = _________
3. 3rd play penalty 10 yards position = _________
4. 4th play gain 7 yards position = _________
5. 5th play lost 13 yards position = _________
6. 6th play gain 6 yards position = _________
7. 7th play gain 9 yards position = _________
8. 8th play lost 4 yards position = _________


9. A first down is received if the team has a net gain of 10 yards in 4 plays. Did the team have a first down in the first 4 plays? _______

10. Create you own series of 4 plays. Trade papers with another student and have them show your plays on a number line.

Activity B: Subatomic Particles

Protons are found in the nucleus of an atom; protons have a positive electric charge. Electrons are found surrounding the nucleus of an atom; electrons have a negative electric charge. Since they have opposite charges, one proton and one electron paired together result in a charge of zero, i.e., they neutralize each other.

In the following activities, a shaded circle represents a positive proton and an open circle represents a negative electron, each inside an atom. Follow the first example to give the resulting electrical charge.
   

On another sheet of paper, draw an atom model of protons (shaded circles) and electrons (open circles) that would give the following net charges.
9. + 5
10. - 3
11. - 6
12. + 2

Activity C: Stock It

Although integers do not include fractions, negatives and positives can be used with fractions, as is done in the stock market. Begin with one share to invest in the stock market. Choose two stocks in which to invest. After you have chosen your stocks, watch the papers carefully and record your gains or losses for 3 days. An example of a gain is +1 3/8 and an example of a loss is -1/4. The fraction represents the fraction of a dollar change in the value of the stock. An example is given. Note: 5/8 = $.625 or $.63 rounded to the nearest cent.
Stock Beginning
Amt.		 Day 1
Change		 Day 2
Change		 Day 3
Change		 Total
Change		 Amt of
Change		 Cent
Change
A T & T 1 share +3/8 +1/8 -1 1/8 - 5 loss of 5/8 dollar loss of $.625
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _

Activity D: Score It

Three people are playing the game of rummy. They score points for runs (at least 3 cards of the same suit in order, i.e., 9, 10, J) and sets (at least 3 cards of the same number or face) that they lay down. They lose points for cards still in their hand when another person lays down all cards. The table shows the points laid down and the points left in the hand for each player for each hand. Compute points for each hand and the running total score. Two hands are completed for Erica. Who wins?
Erica 1 2 3 4 5 6 7
Points Gained +60 +100 +50 +15 +40 +75 +30
Points Lost -15 0 -50 -50 -15 -65 -70
Points in Game +45 +100 _ _ _ _ _
Running Score +45 +145 _ _ _ _ _
Selena 1 2 3 4 5 6 7
Points Gained +55 +90 0 0 +45 +60 +100
Points Lost -55 -15 -40 -55 -25 -80 -5
Points in Game _ _ _ _ _ _ _
Running Score _ _ _ _ _ _ _
Robert 1 2 3 4 5 6 7
Points Gained +30 +25 +40 +10 0 0 +110
Points Lost -15 -25 -10 -40 -35 -70 0
Points in Game _ _ _ _ _ _ _
Running Score _ _ _ _ _ _ _

In the set of integers, additive inverse is a term used for two numbers that add together to give zero. Find three examples in the rummy game in which the points gained and the points lost in a hand are additive inverses of each other:
Name: _______________ Hand: ___________
Name: _______________ Hand: ___________
Name: _______________ Hand: ___________

In the set of integers, additive identity is a term used for a number which when added to any other number does not change it. What number of points results in no change in the score? _______

Activity E: Sum-marize It

Any language, including the language of mathematics, includes operation rules and properties which, if we know them, make it a better and easier tool for communication. Think about the activities you have done in this lesson. Then write these rules for adding integers. Try to use "absolute value" in your definitions.
  1. . Example: 3 + 5 = _________
    To add a positive integer to a positive integer you _________________ __________________________________________________________________
    and the answer will be (positive, negative).
  2. . Example: - 3 + - 5 = ________
    To add a negative integer to a negative integer you ________________ __________________________________________________________________
    and the answer will be (positive, negative).
  3. . Examples: - 3 + 5 = ________ 3 + - 5 = _____________
    To add a negative integer to a positive integer you _______________________
    __________________________________________________________________
    and the answer will be positive or negative depending on
    __________________________________________________________________
  4. . If you add integers, does it matter what order you add them? _____ Give examples to justify your answer.
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