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.”