"Zero-ing" In On Integers

Designed by:   David K. Blackwell, Gibbes Middle School

1)  CORE CURRICULUM OBJECTIVE(S): Use concrete, pictorial, and/or abstract models to compare, order and illustrate operations on integers.   (6NA5-2)    [1.H.1]

RESTATEMENT: The student will use two colors of counters to add and subtract integers.

GRADE LEVEL: 6th       SUBJECT(S):  Math

2) OVERVIEW:    This activity can be used to introduce each operation of integers. Students will be introduced to the concept of zero pairs before beginning to add integers. They will be given two color counters. One color will represent positive integers, and one color will represent negative integers. Students will work in pairs and as individuals to complete practice in addition and subtraction integers. For their assessment, students will write a paragraph explaining in their own words the concept of zero pairs and at least one operation with integers.

3) FOCUS/ESSENTIAL QUESTION(S):

1. How can you use two color counters to add and subtract integers?

2. What is a zero pair?

4) TIME FRAME:

One 45 - 50 minute class period for addition of integers

One 45 - 50 minute class period for subtraction of integers

(These could be introductory classes for each operation.)

5) RESOURCES:

Glencoe Course 1, Pages 426 -434 (Teacher & Student Editions)

Glencoe Interactive Multimedia Software & Overhead Manipulative Resources

Two Color Counters - These can be plastic bingo circles, small pieces of construction paper, different kinds of dried beans, or the Attachments 6 & 7.     

Paper mats (These can be pieces of 9 " X 12" construction paper.) See ATTACHMENT 5.

Paper/pencil

Addition of Integers - Cooperative Activity - ATTACHMENT 1

Addition of Integers - Individual Activity - ATTACHMENT 2

Subtraction of Integers - Cooperative Activity - ATTACHMENT 3

Subtraction of Integers - Individual Activity - ATTACHMENT 4

MAT - ATTACHMENT 5

Positive Counters - ATTACHMENT 6

Negative Counters - ATTACHMENT 7

6) ASSESSMENT:

The teacher will monitor the students as they work and provide positive and corrective feedback where appropriate. The rubric below will be used to assess the students' understanding of zero pairs and how they apply to integers. The rubric should be given to the students at the beginning of the lesson.

"ZERO-ING" IN ON INTEGERS

Student _____________________    Date _________    Period ______

A written quiz or test may also be used as part of the assessment. The Richland One Grading Scale provides criteria for quizzes and tests.

7)  INSTRUCTIONAL ACTIVITIES:

DAY ONE

1. Begin the class with an overview of the lesson which includes statement of the objective.

2. Ask the focus questions and allow a few minutes for reflection and discussion.

3. Begin the lesson on zero pairs by modeling the concept with an overhead mat and overhead red and yellow counters.

4. Place 6 yellow counters on the overhead to represent +6. Place 6 red counters on the same mat to represent -6. Pair the positive and negative integers together. Remove as many pairs as you can.

5. Ask questions, such as:

* How many counters are left on the overhead?

* What is the sum of +6 and -6?

* How are +6 and -6 related?

* What is the sum of any pair of opposites?

* What is the value of zero pair?

* What happens to the value of the counters when you remove a zero pair from the mat?

6. Monitor the questions and clarify any misunderstandings.

7. Pair the students by counting 1 - 2 or by letting them turn to a person next to them. Make sure everyone has a partner.

8. Pass out Zip-lock bags that contain a laminated mat, red and yellow counters and two index cards with a negative sign on one and a positive sign on the other. (See attachments.)

9. Tell the students to take out the contents of their bags. Tell them they are going to use the index cards to answer some questions.

10. Ask the students, "What type of integer is represented by the yellow counters? The red counters?" This is a quick way to make sure all students understand which color represents what.

11. Pass out ATTACHMENT 1. Tell the students to use their counters to solve the problems. Tell them that this is a practice session. Monitor the room while the students are completing the activity. One student should record the answers to the problems. (See Attachment)

12. Have the pairs share the answers to each problem. Clarify any misunderstandings at this time.

13. Hand out an ATTACHMENT 2 to each student and let them complete the problems on their own. Provide additional bags of counters and mats at this time. (See Attachments 5, 6, & 7)

14. After students complete this activity, have students trade papers with their partners.

15. Let the partners correct the papers as you review the answers. Have volunteers give the answers.

16. REPEAT THE STEPS FOR SUBTRACTION. Use ATTACHMENTS 3 & 4.

ASSESSMENT PARAGRAPH

Students will write a first draft of the paragraph using the topic:

Zero Integers, Adding & Subtracting Integers.

1.    The draft should have a main idea sentence, at least three details, and a closing sentence.

2.    Once they complete the paragraphs, have the students trade papers and let another student edit the paragraph for spelling and grammatical errors.

3.    The students should write the final draft of the paragraph and should draw examples that show the use of counters to solve addition and subtraction problems.

4.    The paragraphs will be judged with the rubric.

Extension Activities

Once you have completed all four operations with your students, you can let students practice working with integers on the following Internet site.  http://funbrain.com/linejump/index.html

ADDITION OF INTEGERS
ATTACHMENT 1

(Cooperative Activity)

With your partner, use the mat and counters to solve the following problems involving addition of integers.

Be prepared to explain your answers during the class sharing. You can write down anything that you see occurring when you complete each task to help you in the class discussion.

ADDITION OF INTEGERS
ATTACHMENT 2 (Individual Activity)

Use the mat and counters to solve the following problems involving addition of integers.

Be prepared to explain your answers during the class sharing. You can write down anything that you see occurring when you complete each task to help you in the class discussion.

SUBTRACTION OF INTEGERS
ATTACHMENT 3 (Cooperative Activity)

Use the mat and counters to solve the following problems involving addition of integers.

Be prepared to explain your answers during the class sharing. You can write down anything that you see occurring when you complete each task to help you in the class discussion.

SUBTRACTION OF INTEGERS 
ATTACHMENT  4 (Individual Activity)

Use the mat and counters to solve the following problems involving addition of integers.

Be prepared to explain your answers during the class sharing. You can write down anything that you see occurring when you complete each task to help you in the class discussion.

ATTACHMENT 5
MAT

Make a transparency and copies of this for your students.

ATTACHMENT 6
Run copies of this in yellow for the positive counters.

ATTACHMENT 7
Run copies of this in red for the negative counters.