
Written 2003 Formatted 2009 




Once students can express the ideas below they have demonstrated an understanding of the uses for negatives. The questions "Why do we need to know this?" and "How will we ever use this?" have been confronted.
What does a negative sign mean for each of these?




These can be the most confusing for students. Emphasize the language as suggested.


Addition: Put up a number line that is spaced about 1 step per number. Have a student come up and walk 5 steps then 3 more steps. Ask: "Where did he end up," and "What operation did he demonstrate?" Show: 5+3=8. Have another student walk backwards 5 steps then 3 more steps. Ask the same questions along with, "How do we represent walking backwards." Show: 5+(3)=8. Next, have another student walk forward 5 steps then backwards 3. Ask the same questions along with, "If walking then walking again was represented by addition before, how should we represent it this time?" Show: 5+(3)=2. Have student make up their own operational "rules" to describe the relationships, they have just seen. Compare their rules to each other, and to traditional rules for addition with signs.
Subtraction: Have two students stand below the number line, the first, "A," at 3, and the second, "B," at 8. Ask: "How far is it to B from A?" Make a point that the question was asked in the order "to  from." Tell A to point to B and ask, "What direction is A pointing?" Show: 83=+5. Have A and B trade places and ask the same questions. Show: 38=5. Ask: "What does the negative represent?" Next repeat these steps starting with A at 2 and B at 6. Have student make up their own operational "rules" to describe the relationships, they have just seen. Compare their rules to each other, and to traditional rules for addition with signs.
Other Negatives Lessons
Teacher Help
Demonstrate to students examples of word expressions that imply negatives. Have the students write their own word expressions, and draw their own diagrams to demonstrate negative numbers. Compare and contrast similar expressions. Be sure they practice with different types of measurements and the three different uses as shown above.
[a] An enemy airplane is flying at 12000 feet. You are flying at 8000 feet. How far must your missile rise to defend yourself? 
[b] The enemy is flying at 12000 feet. You are flying at 8000 feet. How far will his bomb drop when he tries to hit you? 
12000  8000 = 40000 
8000  12000 = 40000 
Notice the difference in signs between the two answers implies that one missile rises and the other descends. 

[c] The enemy airplane is at 12000 feet. You are in a submarine 1000 feet below sea level. How far must your missile rise to defend your self? 
Note: each problem is subtraction structured in the form: (goes to)  (comes from) = answer 
12000  (1000) = 13000 
Discuss: What is similar and different about each problem? Why? 
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