Name:     Cam Miller and Nina Newlin                      Date: November 2003

School: Stephen Decatur Middle and Rock Hall Middle School

School Districts: Worcester County and Kent County Maryland

Title of Activity: Interesting Integers

Intended Grade Level for Activity: Seventh Grade Pre-Algebra

Duration of Activity: Four Days

Description of the Learning Activity

The rules for adding and subtracting integers (positive numbers, negative numbers, and zero) can be memorized, but unless students understand why the rules work, they may have trouble applying the rules to new situations. In this lesson, students will engage in a variety of activities that will help them to understand why the rules for addition and subtraction of integers work.  They will read to be informed, use manipulatives, use the Internet and other technology resources, and work in cooperative groups.  They will demonstrate their understanding with a final assessment that will include questions in the same format as the new Maryland State Assessments.

to top Maryland's Voluntary State Curriculum Objectives Addressed in this Activity

MATHEMATICS Standard 6.0 Knowledge of Number Relationships and Computation Students will describe, represent, or apply numbers or their relationships or will estimate or compute using mental strategies, paper/pencil or technology. Grade 7 C: Number Computation Analyze number relations and compute. a. Add, subtract, multiply, and divide integers     Assessment limit: Use one operation (-100 to 100)   READING Standard 1.0 General Reading Processes: Comprehension Students will use a variety of strategies to understand what they read (construct meaning). Grade 7 E: General Reading Comprehension 2.0 Comprehension of Informational Text: Students will read and comprehend grade-level appropriate informational texts. 1.Apply comprehension skills by selecting, reading, and interpreting a variety of print and electronic informational texts 4. Determine important ideas and messages in informational text c. State and support main ideas/ messages or arguments d. Summarize the text f. Analyze relationships between and among ideas g. Synthesize ideas from text to form new understanding   h. Explain how someone might use the text j. Explain prior knowledge that clarifies the main idea of the text

Essential Question(s) and Key Knowledge and Skills to top

Enduring Understanding: Rules can be used to solve mathematical and real world problems. There are rules for solving problems in math that are always true.   Essential Questions: What is the connection between negative numbers and the real world? What rules exist for adding and subtracting integers? How can I prove to myself that the rules are true?

Objectives to top

Students will be able to: Apply the rules for addition and subtraction of integers. Demonstrate the rules in words or symbols or both. Identify and explain a real world example using the rules for addition and subtraction of integers. Solve SRís and BCRís to demonstrate an understanding of the rules. Write a full and complete response to a BCR, including justification. Score a BCR using the rubric.

Prior Learning and Skills Required for this Activity

Prior to this lesson, teachers will have introduced the rules for addition and subtraction of integers. Students will have successfully demonstrated understanding of integers, including: Using the +/- key on a calculator to add and subtract negative numbers. Defining absolute value and finding the absolute value of an integer. Locating integers on a number line Matching positive and negative groups of integers to make zero pairs Demonstrating the addition and subtraction of integers on a number line. Students will have experience in solving SRís and in writing responses in math to BCRís and in applying the rubric to the responses.

Materials to top

Day One: Copy of pre-assessment each student ( Microsoft Word version or PDF version) Computer Lab for accessing reading sites Alternative choice students could read printed copies of the selections. Shortcut to Interesting Integers web page Graphic Organizer #1 ( PDF Version or Word Version ) Graphic Organizer #2 (PDF Version or Word Version ) Large newsprint copy of graphic organizer #2 Highlighters Large markers one per group Homework rubric - integers in the real world ( PDF version or Word version ) Day Two: Computers - preferably one per student Large Number Line Activity - (PDF version or Word version) Two-colored counter activity ( Inspiration version or Microsoft Word version or Appleworks version ) PowerPoint Interesting Integers file Interesting Integers guide ( PDF version or Word version ) Internet Explorer or Netscape Software Integers Sites Evaluation sheet one for each group 3 member (PDF Version or Word version ) Basic Power Writing example sheet - one per student ( PDF Version or Word version) Day Three Computers preferably one per student Overhead or computer projector Transparency of BCR or PDF BCR on computer Copy of BCR rubric for each student Day Four Copy of post-assessment each student ( PDF version or Word version ) Copy of BCR rubric for each student Optional Integer Card Game - one deck of playing cards for each pair of students. ( PDF version or Word version ) As read to perform a task - a copy of the directions for each pair of students As a teacher guided activity a copy of the rules on a transparency

Pre-assessment to top

Students will complete a brief assessment on integers. Adding and subtracting integers between 100 and 100 Calculator use not permitted

Procedure to top

Day One: Administer the pre-assessment (10 minutes). (Word version PDF version) State the essential questions for this unit. Divide the students into four groups.  Distribute to each group a different reading selection, a copy of graphic organizer #1, and a highlighter. ( PDF Version or Word Version ) Set the objectives for the day and the purpose for reading:  Today you will read to be informed about integers.  Each group has a different reading selection from various Internet sites that give explanations about adding and subtracting integers and using integers in real life.  Your job today is to read the selection that your group has been given, and work together to complete the graphic organizer about your selection.  Later we will jigsaw the groups, and your new group will complete a second graphic organizer summarizing the information from all four reading selections.  You now have 20 minutes to complete the reading and the graphic organizer.î While students are working, move from group to group to make sure they are clear about their task.  Use this time to make the next grouping, which will be groups of 4 students, with each student having read a different selection.  For students with limited reading or writing abilities, you may need to have some groups with five students, being sure to include two students who read the same selection. After 20 minutes, inform the students of their new groups of four and have them move into those groups, bringing with them their reading selection and graphic organizer. Distribute the large version of graphic organizer #2 each of the new groups. along with a marker  Ask each group to select one person to be the recorder, while the others use the small handout of graphic organizer #2 as a reference. (PDF Version or Word Version ) Tell the students, ìIn your new groups, each of you read a different selection.  Your task now is to pull together the information from the four selections into one summary.  AS each group member reports out, fill out any additional information in your graphic organizer. One person in each group should record the groupís information onto the large newsprint graphic organizer , You now have 15 minutes to complete the large graphic organizer.î After 15 minutes, ask each group to post its large newsprint organizer on the wall or the chalkboard. Lead a discussion of the real life examples and the wording of the ìrulesî for adding and subtracting integers. Lead the class to agreement on wording for the ìrulesî for adding and subtracting integers, which students should copy into their notebooks.  Homework: students will make flyers advertising the use of integers in the real world, using the Real World Integer Flyer Rubric - ( PDF version or Word version )   Day Two; Review the homework and discuss the studentsí sample problems. Tell students that the objective for the day is to work through a variety of activities that will help them understand why the rules for addition and subtraction of integers are true. Divide the class into three groups, based on the results of the pre-assessment.  Group 1 should be students who still need basic concepts about negative numbers clarified. Group 2 should be students who may still be unclear about the subtraction of negative numbers. Group 3 should be students who seemed to clearly understand the addition and subtraction of integers. Each group will have options, to be determined by the teacher.  Options depend on the availability of computers, software, and needs of the students. to top Group 1 Large Number Line Activity directed by the teacher (PDF version or Word version) or View Interesting Integers PowerPoint, using the guided worksheet: ( PDF version or Word version ) Group 2: Counter Activity see choices on teacher directions for doing the activity with or without computers. ( Inspiration version or Microsoft Word version or Appleworks version ) Group 3: Visit Interesting Integer Web Sites to review, using  evaluation sheet. (PDF Version or Word version ) (Group 3 needs to be directed to the counter activity, too, so that they have that in their repertoire of tools to use when answering the BCR)   Allow groups about 30 minutes to work on their activities. After this time, students from Group 2 should be paired with students from Group 1 to show them the counter activity and give the Group 1 student a chance to practice.  Group 3 students should get together to discuss the sites they visited and to select ones to share with Group 1 and 2 students the next day. Homework: students will write the rules for adding and subtracting integers with a numeric example for each rule.  Students will state which rule is the most difficult for them to remember and why, using 1-2-2-2-4 basic Power Writing. ( PDF Version or Word version) to top Day Three: Review the homework. (5 minutes) Students from Group 3 should be seated with Group 1 and 2 pairs of students to look at and complete activities on the web sites that Group 3 reviewed from the day before. (40 minutes) Lead a discussion with the entire group on the essential questions by putting this problem on the chalkboard or overhead:  5 (-2) = Ask students to determine the answer (7) and then to state reasons how they would know this answer is true without using a calculator.  They may tell you that they could use a number line, that they could show it using zero pairs, or they may quote one of the real life examples from the reading.  Model writing out an explanation for why the answer is 7. Show the BCR rubric on the overhead or on the computer projector and have students apply it to the answer previously determined. Tell students that the following school day they will take their post-assessment on integers, and on that assessment, there will be a BCR asking them to justify why they know their answer is correct. Homework: Selected problems on integer addition and subtraction from the textbook.   Day Four: Administer post-assessment ( PDF version or Word version ) Optional students play Integer Card Game in pairs. Read to perform a task activity or teacher guided activity. ( PDF version or Word version ) As a read to perform a task activity give each pair of students a copy of the game directions and a deck of cards. Have the pairs read the directions and play the game.  The teacher should circulate and observe to assess students automaticity level with adding and subtracting integers. Students may be asked to write down the problems and solutions to the problems they solve and turn in the results at the end of the game. As a teacher guided activity go over the rules and procedures for the game on the overhead projector.  Conduct a couple of sample game moves with the students.  Then divide students into pairs and proceed as above.

Synthesis and Assessment to top

1. Post-assessment 2. (Optional) Students play Integer Card Game. Teacher observes and assesses for understanding.