A Seventh Grade Unit Plan

Intriguing IntegersWhy do they do what they do?

And, what do they do?

Deb BradleyUNCC –MAED 5040

Fall 2009

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Table of Contents

General Information…………………………………………………………………

Unit Goals……………………………………………………………………………….

Desired Results………………………………………………………………………

Acceptable Evidence………………………………………………………………

Scope and Sequencing…………………………………………………………..

Instructional Resources………………………………………………………….

Lesson Plans…………………………………………………………………………

Reflection……………………………………………………………………………..

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General Information

Intriguing IntegersWhy do they do what they do?

And, what do they do?

This is a mathematics unit for a 7th grade math class.Class Composition: 18 studentsBoys/Girls: 6 boys/12 girlsRacial profile: 3 Black students

2 Hispanic students13 White Students

Education profile: This in a lower/middle performing math class. One child is repeating the class and on a behavioral IEP. Two other students are on IEP for mathematical learning disabilities.

The class periods are 80 minutes long. This unit will cover 7 days.

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Unit designer: Deb Bradley

Unit Goals

This unit teaches students to compare, order, add, subtract, multiply, and divide integers. Students will learn to graph ordered pairs and solve one step equations with integers.

This unit specifically addresses North Carolina Standard Course of Study

Competency Goal 1:1.02     Develop fluency in addition, subtraction, multiplication, and division of rational numbers.

a. Analyze computational strategies.b. Describe the effect of operations on size.c. Estimate the results of computations.d. Judge the reasonableness of solutions.

1.03 Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

http://www.ncpublicschools.org/curriculum/mathematics/scos/2003/k-8/35grade7

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The National Teachers Council for Mathematics states that by the end of middle school students need to be able to develop meaning for integers and represent and be able to compare quantities with them.

Content specific learning outcomes: Students will be able to compare and order integers Students will be able to add, subtract, multiply, and

divide integers Students will be able to identify and graph ordered

pairs on a coordinate plane Students will be able to solve one step equations with

integers

Prior Knowledge: Students must know how to add, subtract, multiply, and

divide whole numbers. Students need to know vocabulary words: whole

number, expression, graph, solve, equation, order Students should understand the Order of Operations Students should be able to evaluate expressions with

variables Students should be able to use inverse operations to

solve equations Students should know the words for operations such as

sum, difference, and product

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Desired Understandings

Essential Question:What numbers are less than zero and how do we compute with them?

Enduring Understandings:1. How does one work with negative integers?2. How are positive and negative integers alike?

Different?3. Do the Commutative and Associative Properties

work the same with integers as they did with whole numbers?

4. Where do we see negative integers in the world and how are they used?

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Determining Acceptable Evidence

Diagnostic: Students will be evaluated to determine what they know prior to the unit. This information will be used to direct the instruction in the class as well as to individual learners.

Formative: Students will be evaluated in the classroom as they work independently and in small groups. They will play games to demonstrate concepts, keep journals, solve puzzles, and work on a banking project. Homework

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assignments will be used to determine where additional time on instruction needs to be spent.

Summative: There will be a unit test at the end of the unit.

Scope and Sequence

Day 1: Introduce integers and absolute value. Be able to put integers on a number line. Be able to evaluate integers and determine what numbers are larger than others.

Day 2: Introduce a coordinate plane, quadrants, and ordered pairs. Have students graph ordered pairs on a

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coordinate plane. In class have students use a coordinate plane as a grid for a map of their neighborhood.

Day 3: Teach students how to add integers (Lesson Plan attached)

Day 4: Teach students how to subtract integers (Lesson plan attached)

Day 5: Teach students how to multiply and divide integers

Day 6: Teach students how to solve equations containing integers

Day 7: Review unit. Students work in class on checkbook project using webquest

Day 8: Summative Unit test

Instructional Resources:

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"Grade 7." North Carolina Public Schools. Web. 12 Nov. 2009.

<http://www.ncpublicschools.org/curriculum/mathematics/scos/2

003/k-8/35grade7>.

Holt Middle School Math Course 2. Austin: Holt, Rinehart and Winston,

2004. Print.

"Number and Operations." National Council of Teachers of

Mathematics. Web. 13 Nov. 2009.

<http://www.nctm.org/standards/content.aspx?id=7564>.

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Day 3 Lesson PlanAdding Positive and Negative Integers

ACTIVATE: One day lesson: The lesson will begin with the teacher verbally throwing out simple addition problems for the students to answer. (Examples are 4+5=, 2+8=, 3+6=) She will ask the class to define the words: Whole numbers, Integers, Associative and Commutative Properties. If a student does not know the definitions of these terms or can not give an example the student will be asked to

record the term in their “Personal Mathematics Vocabulary Journal” (An outline of this journal is attached) This allows each individual learner to determine their needs as the students who are already comfortable with this information do not need to record the definitions. However, as the teacher I would encourage most students to record these definitions to study later.

The teacher will then throw out a problem with a negative number and ask if such a problem could exist and how one could solve it. She will write this problem on the smart board. (Example 4 + (-3) =)

ACQUIRE: Using a Think, Pair, Share activity the teacher will ask the students to think quietly to themselves about how such a problem could be solved. She will then ask groups of three to share their ideas quietly together. These groups will be selected randomly as they will simply be the three students sitting closest together. There will be 6 groups total. The teacher will then ask each group what their answer was and how they arrived at that answer. Each answer will be written on the smart board. Without giving the correct answer she will ask each group to share how they arrived at the answer and record that using a mathematical representation on the board. She will ask the class as a whole which answer they think is correct. She will then review how the groups with the correct answer arrived at their answer. There will be a class discussion on ways to solve addition problems with negative integers.

The teacher will introduce Absolute Value (student will be encouraged to write this in their Personal Mathematics Vocabulary Journal) and show what his means using a number line. She will demonstrate adding positive and negative integers using a number line to show

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what is happening as we perform this operation. Additive Inverse will be defined at this time.

Again randomly the class will be divided into 9 groups of 2 students. The students will be given a worksheet (attached) and red and black counters. They will be told that red represents negative numbers and black represents positive numbers. The students will be asked to work with their partner to solve the problems on the worksheet. They can use the strategies discussed previously or they can solve the problems using the counters to help if they wish. They will not be told how to use the counters allowing them to come up with their own strategies for solving these addition problems. The teacher will walk around the room observing the methods used to solve the problems and redirecting if necessary. She will note students who seem to be struggling and those who obviously understand the concept.

Once most of the groups are done with the worksheet the class will go over the problems on the smart board with each group getting an opportunity to work at the smart board to explain their method of working a problem. The teacher will ask for questions or observations.

APPLY AND ADJUST: The teacher will now select groups based on her observations of the understanding of each student of the concept being taught.

Group 1 (lower learners) will work with the teacher with the red and black counters on more addition problems using the Beat Me to the Top exercise.

Group 2 (middle learners) will work with a friend in their group or alone to solve the Beat Me to the Top exercise

Group 3 (High level learners) will work in pairs or individually to solve the Sum Fun puzzles. When they are done with those puzzles or if they feel they need more of a challenge, they can work on the Addition Integer Logic Puzzle.

As a wrap up we will discuss how this is applicable to our lives. The teacher will ask for ideas about where we see this type of math everyday. These applications will be listed on the smart board.

The final activity will be for the students to use their math journal to solve a checkbook problem and write about how they solved the problem. Each student will be given a copy of a check book page and a list of five transactions to record. They will be asked to find the final balance in the checkbook and explain how they arrived at the balance in their journal. Students who are still struggling with this concept will be given whole dollar amounts on their assignment so that they can concentrate on the concept and worry less about the math. The rest of

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the students will be given more realistic numbers. This will be homework if not completed in class.

ASSESS: Learning will be assessed by teacher observations, classroom activities and puzzles, and the final checkbook journal activity. This plan teaches to three levels of learners by allowing time for the teacher to re-teach the necessary concepts to the lower learners while the middle and upper level learners are challenged through other activities and puzzles. The Addition Integer Logic Puzzle in particular is challenging.

The final checkbook activity will allow the teacher to see how each student is working on these problems while showing the students a real world application. By commenting in the journals the teacher can continue to direct the learning of each student.

Day 4 Lesson PlanObjective: Subtracting Positive and Negative Integers

ACTIVATE: Class will start with a review of adding positive and negative integers that was taught the previous day. This will be done as a warm up on the smart board. Teacher will write problems on the board for students to solve in their Math Journal.

1. -2+6=2. -3+(-4)=3. 7+(-5)=4. 3+(-4)=5. -6+(-1)=6. -6+1=

Teacher will then ask students how to subtract a greater number from a lesser number. Is it possible? We will relate this to borrowing money. If you want to buy something for $8.00 but only have $5.00 you would have to borrow $3.00. The mathematical representation would be written on the board. 5-8=-3. Now if we were to pay back $2.00 we are actually subtracting a -2. So now our debt is -1.

(-3-(-2) =-1)At this point the teacher will pass out two different colored pieces of paper (for simplicity I will use red and blue). She will ask five people with blue paper to come to the front of the room and stand to the right

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of a line. She will ask 8 students with the red paper to come to the front of the room and stand to the left of the line. The students are to stand facing the class in a line. We are going to pretend that this is a tug of war game. Because there are more reds they will be able to pull the blues over the line one at a time. As the blue is pulled over the line they will pair up with a red and the pair will return to their seats. At the end there will be only 3 reds left. We will talk about how this represents a number line and the center line is zero.

In groups of 5 the teacher will have the students think about how to apply the same tug of war example above to the next example problem above (-3-(-2) =-1) Teacher will circulate around the room and observe and help where needed. After a few minutes the teacher will ask one group to demonstrate how they worked this problem and then ask the rest of the class if this is how they acted out the problem. Through class discussion we will come up with the idea that subtracting an integer is the same as adding the opposite. We will talk about how to represent this mathematically.

Students will be divided into groups of 2 and given a worksheet and red and black counters. They will be told that red represents negative number and black positive. The students will be asked to work the problems on the worksheet with their partners. They can use the strategies discussed previously or they can solve the problems using the counters to help if they wish. They will not be told how to use the counters allowing them to come up with their own strategies for solving these addition problems. The teacher will walk around the room observing the methods used to solve the problems and redirecting if necessary. She will note students who seem to be struggling and those who obviously understand the concept.

APPLY AND ADJUST: The teacher will not select groups based on her observations of the understanding of each student of the concept being taught.

Group 1 (lower learners) will work with teacher using red and black counters to practice more subtraction problems. This group will also use the Dominos Subtracting Integers activity to reinforce understanding.

Group 2 (middle learners) In pairs, students will be directed to play the Dominos Subtracting Integers game

Group 3 (High level learners) Student will play the Dominos Subtracting Integers Game with a partner or do the Number Tiles worksheet individually.

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As a wrap up we will discuss how this is applicable to our lives. The teacher will ask for ideas about where we see this type of math being used. We will list these applications on the board.

Students will be assigned a webquest using addition and subtraction of positive and negative integers. They will be allowed to work in pairs. Time will be given in class to work in the computer lab. Some work will need to be done outside of the classroom as homework. The webquest asks the students to explore global warming by looking at minimum and maximum temperatures from 5 places around the globe over a period of time. Students are to average these temperatures and determine if they think the world is getting warmer, staying the same, or cooling.

Webquest site: http://sites.google.com/site/extremetemps/

ASSESS: Learning will be assessed by teacher observations, classroom activities and puzzles, and the webquest activity.

Personal Mathematics Vocabulary Journal

Word/Concept Definition Example

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Adding Positive and Negative Integers Worksheet

8 + 3 =

8 + (-3) =

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5 + (-9) =

-4 + -6 =

2 + (-12) =

-5 + 3 =

-7 + (-2) =

-7 + 2 =

6 + (-4) =

9 + (- 12) =

Beat Me to the Top Activityhttp://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade07/goal01/objective1.02/1.02-tasks/1.02-beatmetothetop.pdf

Addition Integer Logic Puzzlehttp://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade07/goal01/objective1.02/1.02-tasks/1.02-addintegerlogic.pdf

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Sum Fun Puzzlehttp://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade07/goal01/objective1.02/1.02-tasks/1.02-sumfun.pdf

Dominos Subtracting Integers Activityhttp://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade07/goal01/objective1.02/1.02-tasks/1.02-dominoessubtractintegers.pdf

Number Tiles – Integer Operationshttp://www.dpi.state.nc.us/docs/curriculum/mathematics/middlegrades/grade07/goal01/objective1.02/1.02-tasks/1.02-numberintegeroperations.pdf

Reflection

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We use positive and negative numbers everyday in our daily living. In this unit I tried to show the students just how many times we see these operations. At the same time, adding and especially subtracting positive and negative integers can be a very difficult topic to understand. In my lesson plans I worked to reach all learners. I did this by using different strategies to present the material. I tried to let the students get an understanding of the concepts by allowing them to work out and share ideas about what we were learning. I gave them activities tailored to their understanding levels that were fun so that the students could see that learning math is fun. Using the “Personal Mathematics Vocabulary Journal” gives the students the ability to look back on the lesson and review the notes and applications that we discussed.

I hope the students enjoy this unit like I have enjoyed designing it.

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