Project-Based Learning Unit Plan Overview

Unit Title: Integers in Our Daily Lives

Grade: 6^th Grade Math

Unit Essential Question(s): What are integers and where can we find them in our daily lives?
Guiding or Unit Questions: How do you multiply and divide integers? When do you need to multiply and divide integers in your daily life? How do you add and subtract integers? When do you need to multiply and divide integers in your daily life? How is a negative integer different from a positive integer? What does a negative integer mean?
Massachusetts State Standards: GENERAL STANDARD 19: Writing 19.16 Write brief research reports with clear focus and supporting detail. 19.17 Write a short explanation of a process that includes a topic statement, supporting details, and a conclusion. GRADES 5–6 LEARNING STANDARDS: Number Sense and Operations 6.N.6 Find and position integers (both positive and negative) on the number line. 6.N.7 Compare and order integers (including negative integers) 6.N.9 Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers 6.N.13 Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers. 6.N.15 Add and subtract integers, with the exception of subtracting negative integers. ENGLISH LANGUAGE PROFICIENCY BENCHMARKS AND OUTCOMES FOR ENGLISH LANGUAGE LEARNERS Understands words and phrases of grade-level academic content, including technical and abstract terms. (S.1.25) Creates media production using images, text, sound, and/or graphics. (W.5.13) Writes short accounts of personal or familiar experiences, including academic topics. (W.2.7a) Writes brief research reports with clear focus and supporting detail. (W.2.8f) Participates in classroom discussion and other academic interactions using basic and and complex sentence structures (S.3.65)
Factual Knowledge What is an integer?	Students will know: the definition of an integer the difference between positive and negative integers Places where integers are in real life
Procedural Knowledge Computing operations using integers Writing a personal narrative Word Processing	Students will be able to: add, subtract, multiply and divide both positive and negative integers write a personal narrative including mathematical equations and scenarios in which they encounter integers in their daily lives participate in the writing process by brainstorming, pre-writing, drafting, editing, writing a final draft, word processing and commenting online on peers' papers
Conceptual Knowledge When are products, quotients, sums or differences positive or negative?	Students will understand: Integers are an important part of mathematics and all throughout our daily lives. A negative integer is the opposite of a positive integer A negative sign indicates direction of movement, moving left on the number line or numbers below zero A positive added to a positive is a positive A negative added to a negative is a negative A positive multiplied or divided by a positive is a positive A negative multiplied or divided by a negative is a negative A positive multiplied or divided by a negative is a negative A negative multiplied or dived by a positive is a negative Subtracting a positive is the same as adding a negative
Technologies Word processing Blogging Online comments	Students will use: The HP laptop cart to type the stories on Microsoft word. This will give them opportunities to practice typing and digital editing using formatting and spell check. Students will also use the “track changes” function during their edits so the teachers can see their edits. Teachers will also use the “comments” option to give the students feedback on their writing Blogger.com to upload their integer stories to our classroom blog (6thgrademathsgs.blogspot.com) The website as a home-school connection, to be able to share their stories in print at home with their families on the internet The comment function on the blog website to respond to one peer's story (sign in as “studentmswaughsclass” to maintain anonymity.)
Assessments Formative and Summative Tools Rubric Drafts “My Life as an Integer Assignment Checklist”	Students will be formally assessed using a rubric from 0 to 4 as a summative assessment tool. They will be expected to include each operation (addition, subtraction, multiplication and division) in their integer story, in addition to positive and negative numbers. The story needs to be a creative narrative and not an expository essay. The students will be assessed on their mathematical computations in addition to their error-free prose. Students will be expected to submit drafts and to edit these drafts. They will edit the drafts on the computers at school or at home using the “track changes” function. Students will be expected to print their document including their tracked changes that show their edits, in addition to a final version to be graded. These drafts will stand as formative assessments and will guide future instruction if re-teaching of certain concepts is necessary. Students will assess themselves upon completion of the assignment and complete the “My Life as an Integer Assignment Checklist” prior to submitting the final draft to the teacher. There will be frequent “check lists” and check in's as the students complete their writing assignment. These checklists will allow students to monitor their own progress in addition to allowing the teacher to progress-monitor.
Number of Weeks: 4 weeks Week 1: Introduction to the assignment including brainstorming and first drafts Week 2: Rewriting and drafting process including conferencing with the teachers Week 3: Word processing and editing Week 4: Blogging and commenting on peers' posts

Project-Based Learning Lesson 1

Lesson: An Introduction to Integer Stories Week/Lesson #: 1 Amount of Time(period/days): 60 minutes, 1 math period
Guiding or Unit Questions: When do you need to multiply and divide integers in your daily life? When do you need to multiply and divide integers in your daily life? Where do you find negative integers in real life? Where do you find integers in real life?
Massachusetts State Standards: GENERAL STANDARD 19: Writing 19.16 Write brief research reports with clear focus and supporting detail. 19.17 Write a short explanation of a process that includes a topic statement, supporting details, and a conclusion. GRADES 5–6 LEARNING STANDARDS: Number Sense and Operations 6.N.6 Find and position integers (both positive and negative) on the number line. 6.N.7 Compare and order integers (including negative integers) 6.N.9 Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers 6.N.13 Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers. 6.N.15 Add and subtract integers, with the exception of subtracting negative integers. ENGLISH LANGUAGE PROFICIENCY BENCHMARKS AND OUTCOMES FOR ENGLISH LANGUAGE LEARNERS Understands words and phrases of grade-level academic content, including technical and abstract terms. (S.1.25) Creates media production using images, text, sound, and/or graphics. (W.5.13) Writes short accounts of personal or familiar experiences, including academic topics. (W.2.7a) Writes brief research reports with clear focus and supporting detail. (W.2.8f) Participates in classroom discussion and other academic interactions using basic and and complex sentence structures (S.3.65)
Materials/Technology:	Brainstorming web “My Life as an Integer Assignment” prompt “My Life as an Integer Assignment Pre-Writing Outline”
Factual Knowledge	Students will know: the definition of an integer the difference between positive and negative integers Places where integers are in real life
Procedural Knowledge	Students will be able to: add, subtract, multiply and divide both positive and negative integers write a personal narrative including mathematical equations and scenarios in which they encounter integers in their daily lives participate in a classroom brainstorming session participate in the writing process by brainstorming, pre-writing and writing a first draft
Conceptual Knowledge	Students will understand: Integers are an important part of mathematics and all throughout our daily lives. A negative integer is the opposite of a positive integer A negative sign indicates direction of movement, moving left on the number line or numbers below zero A positive added to a positive is a positive A negative added to a negative is a negative A positive multiplied or divided by a positive is a positive A negative multiplied or divided by a negative is a negative A positive multiplied or divided by a negative is a negative A negative multiplied or dived by a positive is a negative Subtracting a positive is the same as adding a negative
Outline of Steps in Lesson: The class begins with a “Do Now” on the board. The students are asked to answer the following question in their notebooks: “What is an integer?” After 10 minutes, the teacher opens up a class discussion on “What is an integer?” as a class, the students develop a comprehensive definition and the teacher writes it on the board. The teacher makes a brainstorming web with “Examples of integers in the real world” in the middle. The students then brainstorm as a class examples of integers including money, time, temperature, sports scores, height, shoe sizes, elevation and any other ideas the students can think of. If the students struggle with examples of negative integers, the teacher should prompt answers or guide the brainstorming session to make sure examples of negative integers are included. Students should copy the web into their notebooks. The teacher then introduces the assignment. Students will begin writing integer stories about where they find integers in their daily lives They will use the “My Life as an Integer Assignment Pre-Writing Outline” as a support to formulate their ideas and make sure they include equations for each operation Students will be expected to have a rough draft by the end of the week
Assessments Formative and Summative Tools	The first draft of the integer is due by Friday. Students will receive credit for turning in the rough draft. It will be editing by the teacher over the weekend and each student will conference with the teacher in the next week.

The Trip to the Antartic

One day I was getting ready to go the Antarctic to see how the temperature. So I got some warm clothes for when I get there. After I got my clothes all packed up, I went to the car and drove to the airport. I had to hurry because the plane was to leave in 1 hour.

With 10 minutes to spare I made it there right on time. When I made it to my seat I took my seat and just fell asleep because it was a long day and was very tired. It was to be 7:50pm when I got there.

I woke up and looked outside excited and when I looked out the window I saw ice and snow as far as I can see. I also saw mountains and mountains of ice everywhere. It took me a minute to find out it was cold so I opened my bag and took out my huge coat and went outside to start my research.

I took out my thermometer and stuck it in the ice and waited for 10 seconds. After 10 seconds I checked the thermometer and the temperature of the ice was -5 degrees Fahrenheit. In L.A. it is usually is 60 degrees and the difference from those two temperatures was 65 degrees. I also noticed that in each 3 minutes the temperature decreases by 15. I can write that as -15 degrees to show that the temperature was decreasing. I stayed there for 4 hours and when I woke up in the morning it was 15 degrees Fahrenheit and at nighttime it was -35 degrees. The temperature increased by 50 degrees.

At the end of the day I had all the information I needed and was ready to go back to L.A., so I came back to the plane. When I came back, I went to find some place to eat. I went to the vending machine and paid $5.00 dollars but it stole my money because the thing I wanted to buy cost $2.00 dollars and needed $2.50 dollars back. So I just went to my car and went back to house.

Integer Story of Integers

Where we could find integers in life is in the weather, time, video games, money, sea level, number line, and so much more.

For example in weather the temperature could be -5 degrees C, 6 degrees C, 3 degrees C.

An example of the number line is above.

And also examples of integers in money are: $5, $6, $3.

We could find integers anywhere, and we use them sometimes without knowing. Integers help us in some things and it helps us find out things. We use integers in our daily lives. We use them when we’re calling someone, because when we call people we dial numbers. Phone numbers are sequences of integers.

Positive and negative numbers are integers. We could find positive numbers in anything that has to do with numbers. When we add with positive you go to the right of zero on the number line. And adding with negative you go left on the number line. We could find negative numbers in the thermometer, number line, and the weather.

A negative number is any real number that is less than zero like, -5, -8, and -2. Negative numbers are also used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. And positive numbers are greater than zero like 5, 8, and 2.

When we multiply with a negative and a positive we’ll get a negative and the same thing for division. When adding with negatives you go to the left on the number line. Ex; -5+6=1

And when subtracting with negative and positives you go to the right on the number line.

Ex ; -5-6+= -11.

Integers All Around Us

In my life I see integers basically everywhere I go. Not only do I see integers, I use them in multiplication, addition, subtraction, and division.

When I go shoe shopping or just even shopping I see positive numbers for my shoe size and clothes. For example, in my sneakers it says size 5. Also my age, 13, is a positive number.

When I go to the hospital and then the doctors weigh me my weight is positive. Or if I loose weight, like 2 pounds, then I could weigh -2lbs.

We use negative numbers in weather when we talk about temperature that is below zero like -5 degrees F.

One day when I was watching TV, I saw that a golf game that was on and then I saw that the scores of the golf game were negative—they were -6 and -8.

At the store I use subtraction. If I buy something for 4 dollars and then give the cashier a 10-dollar bill, then we would be using integers because 4 and 10 are whole numbers. The cashier would take away the four dollars form the 10-dollar bill and give me the change. The cashier would give me 6 dollars I could also write that as -6 dollars.

I use addition when I use money. For example, if I had 20 dollars and 5 dollars altogether I would have 25 dollars, because 20 dollars + 5 dollars is 25 dollars.

I could use addition to see how far it is from my house to the store. On the way to the store, I would measure the distance using a positive integer, but when I go back home I will go to the negative direction. From my house to the store it is 100ft, in the negative direction it will be -100ft. I found out how many feet it is from my house to the store by using a measuring tape. To find how many minutes it takes to walk from my house to the store I would do 100/ 10 = 10 minutes or -100/10= -10 minutes.

One time 2 of my friends came over my house and I had 30 pieces of candy on the table. So I had to figure out how many pieces of candy they each would get including me. Since there was three of us I had to divide, 30/3=10 so we each would get 10 pieces of candy. If each of us had 3 boxes of cookies and 20 was in each box, then the total number of amount of cookies that we had would be 60, because 3x20 is 60.

As you can see, I use and see integers all the time in my everyday life. Integers are important because we use them to count and without integers we probably would never be able to do half the things we do today with numbers.

Going to the Bank

One day in math class, I learned about integers. Integers can be negative and positive numbers. Mr. Poremba said that negatives go to the left of the 0 and positive go to the right of the 0.

The next day, Mr. Poremba taught me how to add and subtract integers. Mr. Poremba gave me a worksheet of integers and it took me 20 minutes longer than the rest of the class to finish. I needed help on the negative and the positive sings. Then when I figured it out I knew it like that.

Five days later, my dad and I went to the bank. The bank loaned him $85. When he came back the money his account said $-85 and he only had $70. He asked me “How much money do I need?”

“You need $15, $-85 - $70=$15,” I said. So he took out his wallet and gave them $15 more.

Ten days later, he went to the bank. The bank loaned him $539. He came back the next week with $499. He asked me “How much money do I need?”

“You need $40, $539 - $499= $40,” I said. He took out his wallet and gave them $40.

When we went back to the bank it was to save money for a trip. But he again had $-85 in the bank. So he gave them $100, $-85 + $100= $15 and then dad had $15 in the bank. He wanted to save $125. He needed $110 left, $125 - $15= $110. So he added another $100. But he still needed $10 more. So he asked me for money. I had $20, so $20 - $10= $10. I gave him $10 so he can go on his trip.

I wanted to go on the trip with him. I wanted to save $144 for the trip in 12 week. So I divided $144 by 12 and I had to save $12 for each week. Twelve weeks later, I had all the money for the trip but to be sure I multiplied $12 by 12 and got $144, enough to go on the trip.

In conclusion, one place we can use integers is at the bank. I used division, multiplication, subtraction, and addition to figure out how much money my dad needs and how much my dad and I wanted to save for our trip.

It's a Money World

 

One day I woke up and my mom told me to go and buy food for our house. As I went to the store I took my list out. The list included a gallon of milk, which cost $1.89. The next one on my list was bread for $1.99, next was a pound of butter for $1.87. Then the last three on my list were 2 boxes of cereal for $4.00, flour for $ 1.92, and eggs for $ 1.99.

I took the groceries for my house and brought them to the casher. She added the milk and butter $1.89+ $1.89=$ 3.76. Then she added the cereal which was $ 4.00 then added flour $1.92. $1.92+$4.00= $5.92. Last she added the eggs and bread $1.99+$1.99= $3.98 so than she found the total cost by adding $3.76+$5.90 +$3.98 which made the total cost $13.98.

Then my mom called me on my cell phone. I was wondering what she wanted because I had bought everything on the list. She said, “Dequan take out the pound of butter because we already have one.” So I hung up and told the casher to take away the butter. $13.64- $1.87= $11.77. The total without the butter was $11.77.

The next day my mom told me to go to the store again. But this time she wanted all of us to have our own little bag of grapes. So I went down to the store and looked for them. Then I found the grapes for $1.25 each bag and I only had $20.00. I brought the 6 bags to the cashier who multiplied $1.25x6=$8.50. The total was $8.50, then she subtracted $20.00-$8.50=$11.50 was my change.

Then I had to buy a large pack of chicken for $11.50. It comes with 18 pieces and there are 6 of us in my house; I wondered how many pieces we get each. 6/18=3 so I figured out we would get 3 pieces each.

When I was leaving with the food I said to myself, “You did good, Dequan you did good.”

Integers Around the World

In my life I see many integers. For example, there are a lot of integers in weather. In the winter it can be -30 degrees F or just 30 degrees F. The difference between the two is that negative is when the weather is below zero. Another example is if you owe someone money you would take away from the money you have, which would be an integer. Example: -20 is what you have if you owe a friend, $ 20.

I thought that integers were only seen in math class. But I was wrong; there are integers everywhere. When you buy some thing there are integers. For example, once when I went to the store, and I had $10.00, I bought a cake that cost $5.00. That would take away from the money I have that would be $10-$5= $5.00.

I also see a lot of integers in the weather. Once in the news I heard that the temperature was going to go down 10 degrees F. It was 50 degrees F. So if the weather is going down 10 degrees F it is 50 degrees F – 10 degrees F =40 degrees F. But if it’s going up it would be 50 degrees F + 10 degrees F=60 degrees F. When the weather is going down it is a negative. When it is going up it is a positive. It is like a thermometer, when the temperature is cold it goes down. When it is hot it goes up. Positive is hot, and negative is cold.

Another place you can find integers is at the bank. If you have $ 1,000 and you need $500 you take $500 away from a thousand. It is $500. If you were to put that money back it would be a positive because 500 + 500 =1,000 when you’re adding it. Another place where you can find integers is in your weight. When you gain weight it is positive number, because it’s increasing. If it’s decreasing and you lose weight it is a negative. If you lose 5 pounds it can be written as -5 pounds. Integers are everywhere you go. They are present when you buy something. They measure the temperature in the weather. When you take out money from the bank you are using integers. And you use integers in measuring your weight. You can also multiply and divide integers. For example: -5x6= -30 and -35/ -7 =5. Integers are everywhere you go.

My New York Trip

One day in 4^th grade, my teacher, Miss Ortega, wanted the class to find at least 4 places you find integers over the vacation and bring it back on Monday. I thought it was going to be very hard since I was going to New York and I didn’t really know where to find integers.

So when I got home and asked my parents, “What is na integer?” and they said that it’s negative or positive whole numbers, so I said the assignment was going to be easy. When we we’re getting ready to go to New York my dad was watching the weather forecast and it said that New York weather -10 degrees F tomorrow so I wrote “-10 degrees F” down. I learned one way to find an integer is to watch the news and see what’s going to be the weather and see if the temperature is a negative or a positive number.

Three hours later we were in Conneticut and my brother was playing a game and since I was bored, I decided to watch him playing the game. He had a score of 20 points but then he got shot by one of the bad guys in the game he had a score of – 20 points. “ I wonder how much points he lost?” I said to myself. He had lost 40 points after he had got shot in the game. So I wrote in my notebook that in some games when you’re playing your score is an integer.

When we went to the store for a little break and since we were hungry my mom bought us a dozen donuts and my brother, my sister and I had to share them. I didn’t know how many each of us was suppose to get so I divided 12/ 3 and I got 4, so each person got 4 donuts out of the box.

Once we were in New York and on our way to the hotel, we stopped at a red stoplight and I saw a bunch of kids going into a school. When I look through the window I saw a teacher writing an integer word problem on the board and it said “What is -12 + 18,” and I thought that – 12 +18 would equal 6 because when I was at school back in Boston when we add a negative and a positive we started at the negative and we add up to get positive 6. When I saw it I went into my notebook and said that an integer could be in a word problem like this one.

We got to the hotel and put our suitcases away, got ready and went to downtown. We went into the supermarket to buy a snack and my mom wanted to find out how many oranges were in a bag of oranges. So I had find out how many oranges were in the package lengthwise and how many were lined up widthwise and then I multiplied 4x6 and I got 24. “There are 24 oranges in the pack,” I told my mom.

When we were done shopping at the food store, we went on the train to go to Times Square and we were thirsty so we went to the 99 Cent Store to buy some water. Inside, an old lady was arguing with the manager of the store about how she had to pay 5 dollar more for the purchase of a bunch of stuff that she had buy at the store. The screen said $-5 because she still owed $5 to the store. This argument gave me another integer, so I. So I wrote down that integers could be money, too.

At the end of the trip, my mom and I were sad to leave the Big Apple State. When we where almost home, I started to think about what had happen over the vacation and all the integers I found and when I finally got to my own house I leaned that integers are apart of my life.

Fun Filled Day of Integers

Integers are used every single day, in many different and unique ways, including weather and paychecks. When you go to the grocery store, when you get sick and need to use your thermometer, and even right in math class you use integers. It was a fun filled day when I realized that world was overflowing with integers.

It was a cold winter day and cold white snow was just overflowing the streets. To make matters worse it was -5 degrees Fahrenheit and I had to walk in the snow all the way to school. When I finally arrived at school my teacher Mr. Poremba gave me an assignment with five integer problems:

(-4)+-4, -5-(-3), (-6) x-2, and (-7)/-1

but I didn’t know how to do the problems, so my other teacher Ms. Waugh showed me a number line that said “…. -10 -9 -8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10….”. Ms. Waugh specifically said to solve (-4) + -4 start at -4 and add 4, moving 4 units to the left. I told Ms. Waugh that I didn’t understand the other problems, either. So she told me a negative take away a negative is like adding a positive, negative times a negative is a positive, and a negative divided by a negative is equivalent to a positive. For each equation I used this method because I strongly understood.

After math class was over it was time for science and Ms. Waugh had had to leave. So Mr. Poremba said loudly “Class, today we will be trying something new called weather bug. Weather bug is a website that tells you the temperature outside, the wind speed, and the chances of precipitation. Here is a handout on how to take the information on the board and write it in the table.”

As the information appeared on the board, I saw a negative sign right next to 5 degrees below Fahrenheit. I raised my hand and said “Mr. Poremba, why is that sign next to5 degrees Fahrenheit? “Mr.Poremba explained that it was there because it means that the temperature is exactly 5 degrees below zero.

As I was writing this information down the school bell rang and it was time to leave. I grabbed my jacket, coat, scarf, hat, and gloves then immediately rushed home. When I got home my dad was watching football and I heard a man say that one of the football players got tackled behind the line and he said that’s a negative. I said to my dad, “What does integers have to do with football? “ he said

“In football integers represent gains and loses,” he said.

In conclusion I saw integers in temperature, during science class, and even during math class. It truly was a fun filled day of integers.

Integers in my Life

During my life I have come across integers in many ways. In money you see integers when you take away (subtract), like if you have $10 and you subtract $5, which equals $5. If my mom gave me $10, it would be like adding $10 to the $5 and then I would have $15. Then if I were to share the money with my three cousins, it will look like 15 divided by -3 = $-5. Five dollars would be how much I owed each person. Then if I multiplied the -5 by -3, which looks like -5 times -3, it would be the $15 total.

One day I was in the mall with my cousins and I had $120. I went to GameStop and bought a game for $60, which is subtraction ($120 – $60 = $60). Then I had $60 left. Next I went to Footlocker and saw some shoes that cost $90. So I went to my mom for $40 more to buy the shoes (60 plus 40 =$100). After I bought the shoes I had $10 left. Then my cousins wanted quarters to go to an arcade, so I divided 10 by .25 cents to see how many quarters I could give them (10 divided by .25= 40). When I divided them I had 40 quarters, but they only used 20 of them. I wanted to know how much money I had left so I multiplied the value of the quarters by the number I had left, (.25 cents times 20) which gave me $5. Finally, I went to the candy shop and spent the rest of the money and ended up with $0. $5-$5=0.

What I Learned About Integers

I see integers all over, like when I’m shopping, getting paychecks, measuring height and counting money.

I see integers on the thermometer or when measuring weather. Integers are whole numbers that are either positive or negative. When I say negative, an example is (-2). A positive number is just a regular number like (2).

With integers you can add, subtract, multiply and divide. If you add integers (negative or positive), it’s really simple. If you add a positive with a positive you get a positive (5 + 5 = 10).

If you multiply a negative with a negative you get a positive (-5 x -5= 25). If you multiply a positive and a positive you get a positive (5 x 5=25). Multiplying negative and a positive you get a negative (-5 x 5 = -25). Multiplying a positive and a negative you get a negative.

Now subtracting, if you subtract a positive with a positive you get a positive (10-5 = 5). If you subtract negative and a negative you sometimes get a positive (-5 – (-5) = 0).

Doing division is simple because you follow the same rules as multiplication. If you divide positive numbers, the quotient is positive (10 / 2= 5). A negative divided by a negative get a positive (-5 /-5 =1).

If you divide, multiply, add, or subtract you get different answers:

(-5 x -5 =25)

(-5 –(-5) =0)

(-5 + -5 = -10)

(-5 / -5 =1)

It’s really fun once you get the hang of it. Especially if you have two great teachers like Mr. Poremba and Ms. Waugh.

Integers in my Life

I see many integers in my life and one place I recognized an integer was age, The first time I realized my age was an integer was when I was 12 and that’s when I first started learning about integers.

When I went to the doctor’s office they checked my weight and told my mom my height was 4 feet 9 inches and my weight was 52 lbs. My mom said that my height and weight is an integer, like my age. Also the doctor checked my temperature and it was 98.9. My temperature was not an integer because it had a decimal.

When we were leaving the doctors we saw people playing golf and I heard somebody shouting that their score was negative four. I wondered how the person’s score was negative four and my mom explained, saying that it was a bogie. Also, negative four meant that the player hit the golf ball more than one time and the last time he made it. Also in football a sack/interception could be a negative number. An interception is when the other team throws the football and you catch it and you have to run to make a touch down if nobody tackles you.

When I got home I checked the weather and it was -1 degrees Fahrenheit. I looked up my house on the map and I saw it was 76 feet below sea level, which can also been written as -76.

Then I went to the store and I bought a pattie and a soda and it equaled 5 dollars in total, which I paid with a five-dollar bill. $-5+$5=0, so then I had zero dollars.

Three Integer Stories

Junk Food Story

One day I went to the store to buy junk food. I had $15 and I bought 5 bags of chips, each cost a dollar so in total it was $5. Then I got 5 bags of starbursts and each cost $1and it was $5, afterward I bought 3 beef patties and each cost $1.50 and it was $4.50. To find my total I added $5+$5=$10 then I added $10+$4.50=$14.50, so I gave my $15 dollars to the store owner and he gave me back .50 cents and that was the time I use addition.

The Time I Bet

One time I bet with my friend that if the Celtics won he had to give me $3 dollars and if the other team won and the Celtics lost I have to give him $3 dollars. Then the Celtics lost by 7 points so I had to give him my $3 dollars so then he had $6. Then we bet if the Celtics won he had to give me my $3 dollars back, so the next game came and the Celtics won, so he had to give me my $3 dollars back. It was the same thing as subtraction and addition because he had 3 dollars and I gave my 3 dollars to him, so in total it was 6 dollars. Then I won the bet so he had to give me my 3 dollars back. That was the time I use subtraction and addition in my lifetime.

Piggy Bank

Another time when I use integer was when I check my piggy bank. I wanted to save $100. It took me 10 months to reach my goal. I wondered how much on average I had saved each month, so I divided $100 by $10 and got $10. I must have saved about $10 for 10 months.

Cookies

I went to the super market with my mom and bought a pack of cookies.

So I wanted know how much cookies are in the squared pack so I multiply the length times the width and that was the time I use multiplication in my life time.

All Around the World

Everyday when I come home from school I tell my mom what I learned each day. Today I said, “I learn about integers and that integers are numbers below 0.”

She added, “Integers are negative numbers and that they are all around you.”

Then she checked my temperature because I was feeling sick. “Your temperature is 101 degrees Fahrenheit!” she said, “Your temperature is a positive integer.”

Then I went to the hospital to get checked out because of my fever. First they checked my height, weight, and ask for my age. My height was 4’10” and my weight was 71 pounds. I told them I was 12-years-old. My mom said, “Those are also integers.” I was amazed that integers were every place I went.

On our way back from the hospital we passed a golf course and I heard someone say, “Your score is -2.”

Then we went to my brother’s football game. He played the tight end position. He got an interception and scored a touchdown. It was -65 yards for the other team.

The next day when I went to school I learned about multiplying and dividing integers. We use a number line to multiply. When I multiplied (-6x-3=18) and when I divided (18/-3 =-6).

The integers were so fun I made a book for it. I would check everyday in my book and read the stories. Every time I would see or use an integer I would add it to my story.

Math Outside of School

I’ve had many experiences with integers outside of school.

One day I was in the store with $2.00. I bought a honey bun for $0.75. I solved this through subtraction. $2.00-$0.75=$1.25. I also bought some chips for $0.50. I also used subtraction to solve that. $1.25-0.50=$0.75. And I got some Oreo cookies for $0.80. Then the clerk said I didn’t have enough money. But he let me go if I promised to pay him back. So I had -$0.50 because I owed 50 cents. The next day I returned to the shop and paid my debt so then I owed $0.

Another day the ice cream truck came by my house and I didn’t have any money. I asked my cousin if I could borrow $1.50. “I will give you the money but, you need to pay me back,” he said. So I ate the ice cream and then I had -$1.50. The next day I had the money but I didn’t give it to him. I bought 3 bags of chips for $0.50 each. I used multiplication to solve what the total amount of money I spent 3 x 0.50= $1.50. He got really mad and told me that now I have to pay him $3.00 +$1.50=$4.50. So I had -$4.50. But eventually I paid him back.

One day I was in the bookstore at school. I needed 3 notebooks so I bought 3 and then I had $2.00 left. I had to use division to see how many lead pencils I could buy. Lead pencils cost $0.50 each. $2.00/$0.50=4. I bought 4 pencils.

I learned you don’t have to be in school to use integers. They can be anywhere.

Most Common Integers

There are many integers in the world. We use integers to measure temperature, height, weight, and age. We find integers on license plates, paychecks, and money. In a bank we see integers when the bank loans you money than you owe back, like -$542. When the bank owes you they have to give you a positive number $432.Then you will owe them $110 and your account will say $-110. This is because -$542+$432=-$110.

Everyday we see integers: if it’s a whole number, negative or positive we know it’s an integer. When I first got out of school I saw integers on the cars’ license plates. Maine license plates have at least 4 digits or integers and two letters. For example, a license plate can be 5236 FE. Every car I see has a different license plate. I think the most common to find an integer is a license plate.

In sports you can see integers as the players score. In golf, you can get a negative 1 or positive 1 bogie but if you get both for a score you will get -2 because -1-1=-2. Also in football they have positive and negative lines. When someone passes the in-zone as they intercept the ball, it’s a negative yard like -60 yd x 2 interceptions=-120 yd. There are a lot of integers in sports.

There are more integers around us, like in science. Measuring wind speed uses integers. Meteorologists use thermometers to see if the temperature is negative or positive and to tell us how high the temperature is today. For example if the temperature was 50 degrees today and the next day it was 30 degrees so it had dropped 20 degrees. We can write this as -20 degrees to show it decreased.

Dollars are integers. They can be in the form of a bank check or bank account, like you have $100 and you have to split it in two you would divide $100/2=$50.

So see with your eyes and find integers day to day and you learn something new everyday about integers.

We found formulas for dividing and multiplying integers:

Positive x positive= positive

Negative x negative =positive

Positive x negative =negative

Negative x positive =negative

Positive/positive=positive

Positive/negative=negative

Negative/positive=negative

Negative/negative=positive

Example

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