Kevin HallArlington, Virginia, US,

January 18, 2010

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Building from concrete (pictorial) to abstract (computational), this multi-day lesson teaches integer addition with a combination of whole-class and small-group inquiry. It introduces a new pictorial representation of integers, combining the best of the number lines and algebra tiles approaches.

- Education > General
- Education > Instructional Design
- Mathematics > General
- Mathematics > Algebra

- Grade 6
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TIME: This lesson will probably take 2-3 class days.
PREREQUISITES: None.
CONTEXT: I recommend teaching integer addition at least 2 weeks prior to integer subtraction. The procedure for subtraction involves turning the problem into an addition problem and then computing the answer. If students haven't yet mastered addition, working with subtraction will cause them to confuse everything they've learned about addition. So (although your textbook might not do it this way), teach addition and then move on to something else for a while. Come back for subtraction when students are so good with addition that they can do simple problems automatically.

**Group Size:** Small groups

**Learning Objectives:**

Students will:

- Understand and explain why additive inverses have opposite signs.
- Use pictures to represent and answer integer addition problems.
- Understand and explain a computational procedure for integer addition problems.

How can we model integer addition with a simple picture?
Can we find patterns in integer addition problems that make them easier to solve?

**Materials:**

Student handouts. It is also strongly recommended that you make transparencies of the student handout, to display on the projector.

**Procedures:**

**Before class:**

- Make copies of student handout (1 per student).
- Print out answer key for yourself.
- Download and open the PowerPoint file for the drill questions in #8. When the class gets to #8, you want to seamlessly transition into the drill practice and PowerPoint, without a lot of dead time.

- Hand out student packets.
**Hook.**Hook students by saying that this unit will culminate in a game called "Attack & Defend: The game of integers". Explain that in order to succeed in the game, we have to know how to add integers.- Begin with a whole-class discussion of "What Are Integers". Ask students for examples and non-examples of whole numbers. Then ask a student to say any number out loud, and challenge the rest of the class to identify it as a whole number or non-whole number.
- Repeat procedure to list examples and non-examples of integers.
**Real-world connection.**Ask students where negative numbers come up in real life. Examples include: debt, negative temperatures, feet below sea level, losing yards in a football game, etc. If students struggle to come up with ideas, prime the pump. For example, you could say, "If $2 represents two dollars that you have, what would -$2 represent?- Complete rest of first page as a whole class, using as much interactive discussion and student-generated explanation as possible.
**Real-world connection.**Point out to students that opposites cancel out. For example, if the football team gains 6 yards in one play, and -6 yards in the next play, what the overall result? Then let students try #1 (on 2nd page) on their own and share their answers with the class.*Be sure to introduce the pictorial representation of opposites canceling out*(by drawing lines through pairs of opposites--see answer key for an example).- Continue working through #7, using as much student input and student-generated explanation as possible.
**Formative assessment.**When you get to #8, show the PowerPoint drill practice slides. Let students practice while you walk around the room, praising and coaching them on their work. Use this time to get a sense of whether students understand enough to continue in small groups. Use a remote mouse "clicker" to show the answers slowly, step-by-step, as you walk around. If students are not successful with these questions, do some more examples as a class before letting small groups work independently.- Let students continue with the "Small-Group Inquiry" section in groups.
- This lesson will probably stretch over several days. At the beginning of Day 2, start with a Bellwork assignment reviewing the pictorial representation of integer addition (like #8) and asking students to do a few simple problems without drawing the picture (by imagining the picture in their heads).

The first formative assessment is #8. Bellwork on Day 2 is another formative assessment, to give you an idea of what they've retained from yesterday. During small group work, teacher should be walking around, listening to students and observing the level of understanding they show. The game of Attack & Defend will also give the teacher time to observe student understanding in small groups. Finally, a quiz on integer addition should give students a summative assessment of what they've learned.

**Answer Key or Rubric:**

Answer Key document is attached.

**Attached Files:**

3.6aIntegerAddition--Packet-v.2.docx | |

3.6aIntegerAddition--Key.docx | |

3.6aIntegerAddition--DrillA.pptx |

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