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3.0A.A .1
Common Core State Standards for Mathematics.
SMP1
SMP2
SMP4
SMP5
SMP6

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"Learning Styles." Learning Styles. N.p., n.d. Web. 27 Feb. 2017. <https://www.nde-ed.org/TeachingResources/ClassroomTips/Learning_Styles.htm>.

Dolan, Dan, Jim Williamson, Mari Muri, and Calvin T. Long. Mathematics Activities for Elementary Teachers. Boston: Pearson, 2015. Print.

"The History of Negative Numbers." The History of Negative Numbers. N.p., n.d. Web. 02 Mar. 2017.

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OK class lets go over our answers.
1)  6-9=
group 1 what's the answer?
-3 dollars that's correct.
2)  7-8=
group 2 what did you get for this?
-1 dollar Good job!
3)  4-6=
group 3 what answer did you get?
-2 dollars excellent job.
4)  2-5=
group 4 your up, what did you get?
-3 dollars great! I am really proud of all of you.
5) 3-4=
group 5 do you have and answer?
-1 dollar that's right.
Ok we are  going to go over the answers for 6, 7 and 8.
6) 1-7= -6 dollars
7) 5-6= -1 dollar
8) 3-9= -6 dollars

Its time for your lunch break. I want you to put your name at the top of your papers and pass them to the fromt.

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Now I am going to give you some problems to do. I want you to break up into 5 groups. Work together on these problems. You have 10 minutes and then we will go over the answers together. I am also going to add the dollar symbol to these questions and I want you to answer them in dollars. This is to help you understand what happens when you try to spend more money than you have.
1)  $6 - $9=?
2)  $7-8=?
3)  $4 - $6=?
4)  $2 - $5=?
5)  $3 - $4=?
6)  $1 - $7=?
7)  $5 - $6=?
8)  $3 - $9=?
I want each of you to write down the problem and answer ok.

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Ok here we go. I know you all will do great. I will show you a few examples first.
remember this is just to see if you can visualize it in your head. Try to think of the number line. I will give a few examples to get you started.
5-5=0
that is an easy one.
Now lets try to figure out
5-6=
think of your number line remember on the right side of the zero are positive numbers and on the left side are negative numbers.
Your know that 5-5 = 0 now think about going left of the zero and thinking about those numbers. So what do you think 5-6 would be? I will give you a hint it is the first negative number after zero.
Yes (-1) is right.
How about 2-4=?
Does any one know the answer. Go ahead Tim. Excellent the answer is (-2)

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Let's  start off by refreshing our memory and doing a few subtraction problems that I know you can do ok.
5-3=2,  6-3=3,  8-1=7, 4-3=1
Now lets do some together raise your hand if you know the answer.
5-3=? yes Susie you are correct the answer 2.
7-4=? good job Daniel the answer is 3.
9-2=? no Sally its not 6 but you are close think about it? Great it is 7.

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Did you all understand this worksheet? Do you have any questions? We will do some  more problems with number lines later. OK. Lets move on.

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As far back as 200BC the Chinese were using a rod system to keep count of debt. By using red rods to represent positives and black rods to represent negatives. If you were selling silk on the silk road that would be income and would be represented by a positive red rod, but if you were buying silk worms in the town of Yangmie that would be a bill or money you have spent and that would be represented by a black rod.

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Introduction to Negative Numbers; Third Grade Lesson, by Delane Dunagan

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Introduction to Negative Numbers; Third Grade Lesson, by Delane Dunagan

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OK class lets try to do some subtraction problems using numerical representation. For this exercise lets try not to use number lines or visual representation. Are you ready? (Dolan...Chapt5,activity3)

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Let's o over the answers.

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Ok now I want you to match up one negative red star with one positive blue triangle and tell me what you have left over. Do you have negatives or positives and how many?  You can draw a circle around each match. Here is a hand out. We will go over the answers when you are done.

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Let's  move on to what we can call a visual representation. We will use red stars to represent negatives and blue triangles to represent positives .  In this example I have drawn some red stars and  blue triangles. How many negatives did I draw? Yes 6 is the correct answer. Now how many positive triangles do you see? Good job 5 is correct. (Dolan...chapt5,activity1)

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Ok, now let's go over  the answers. I asked you to find negative 5 and 1 on the first two number lines. On the second two number lines I wanted you to show me a positive 3 and 7.

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OK students here is a hand out with four blank number lines. I want you to use a red marker and draw an example of a negative 5 and a negative 1 on the first two lines. Then use a blue marker to draw a positive 3 and a positive 7  on the last two lines. Remember the left of the zero is negative and the right of the zero is postive. you have 5 minutes and then we will go over the answer.

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This is a number line it is one way you can show your work when using negative numbers. Here is an example. I drew four number lines. The zero is in the middle and on two lines I used a red marker and drew to the left of the zero. On the other two lines I used a blue marker and drew to the right of the zero. (Dolan....chpt.5, activity2)

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5. Alas,we hear the voice of reason! Mic drop

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5. Alas,we hear the voice of reason! Mic drop

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19th century mathematicians decide to revisit the ‘laws of arithmetic’ there has got to be an end to this negative number nonsense. They are successful and here we are today so lets get this party started. Who wants to leave home and pay bills? Like you really have a choice.

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4. Wow! Did the paying the bills concept really take that long to travel from india to the uk?

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4. Wow! Did the paying the bills concept really take that long to travel from india to the uk?

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Let's  jump ahead to 1758, Francis Maseres and  a pal named William Friend (yes that is his real name). Had the opinion that negative numbers did not exist. These two were obviously trust fund babies and knew nothing of real world transactions. You could say William Friend was not friend to negative numbers and probably never talked to his accountant.

There were others that were cool with negative numbers and believed they could be used in calculations as long as they could be removed at the same point where they appeared.

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The mathematician Brahmagupta lived in 7th century India. He is known for coming up with the first set of rules to be used when dealing with  negative numbers. Perhaps there was conflict among the young adults and “the been-there-done-that, have-the-receipt-to-prove-it” old adults. Rules needed to be made to help the young learn the consequence of buying that new scarf called a dhoti in India and then not having enough money to by some bonda which is a potato dish in India. The new scarf is pretty to wear, but what happens when it is lunch time and you do not have enough money. What if you had $6 and you bought the scarf for $4. You would only have $2 left for lunch and your lunch cost $3. You are not going to have enough money for lunch. Today we are going to figure out how much money you would need. The way we do that is to look at negative numbers.

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1.Negative Numbers: How Can There be Something Of Nothing?!?

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1.Negative Numbers: How Can There be Something Of Nothing?!?

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Did you know that you can add and subtract negative numbers. Today we are going to learn about negative numbers and how you can use them.