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* *Reflection: Developing a Conceptual Understanding
Adding and Subtracting Integers - Section 1: Do-Now

I am strongly against teaching students gimmicks inside of math classrooms. When we encourage students to “add them if they are the same” we are cheating them of an opportunity to develop their own mathematical reasoning skills. Instead, I try to rely on models (e.g., number lines) and I insist that my students use them on paper until they internalize them and can apply them to perform operations fluently.

When integers arise in my class throughout the course of the school year, I will only allow students to respond using a number line or zero pair reference. This may seem cumbersome, but the payoff for students is too large to eschew.

Early in the school year students will begin instinctively drawing number lines on the sides of their papers. By mid-year, if students are asked a more complex question such as -71-6, they are able to visualize in their head where -71 would be on a number line, then moving six spaces to the left further away from zero, yielding -77. By the end of the year, students have developed a integer intuition, and are able to complete these problems on their own.

*Is it Same-Change-Change or Change-Same-Change or...*

*Developing a Conceptual Understanding: Is it Same-Change-Change or Change-Same-Change or...*

# Adding and Subtracting Integers

Lesson 2 of 5

## Objective: SWBAT model and solve problems that ask them to add and subtract positive and negative numbers fluently.

#### Do-Now

*10 min*

As today's class begins students will complete an integer themed Do Now. After 5 minutes, we will review the answers to the Do-Now as a whole group. I will ask students to share out the methods that they used to solve each question, and I will also ask a few students to share the picture that they might have drawn to accompany each question.

A volunteer will then read the objective, **"SWBAT add and subtract positive and negative numbers".**

I will ask students to recall another word that we can use to describe positive and negative numbers (integers), and ask students to make the connection between today's objective and Do-Now that was just completed.

Integers are one of my favorite topics to review with students. By the time students reach my class as freshman, they have been inundated with many different mnemonic devices and gimmicks aimed at helping them memorize integer rules. My students can quote everything from, “keep-change-change” to “row your boat”, but they often lack a true understanding of the significance of integers and how they function conceptually in math. Consequently, the majority can name, but not recall the “rules” that they have been taught, and they OFTEN answer the integer question incorrectly.

Today's lesson is an important foundation, as students will be entering the Solving Linear Equations in the coming days.

#### Resources

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#### Guided Practice

*30 min*

I plan to group students homogeneously, in recognition of the fact that a small subset of my students are fluent with integer operations. These students will be grouped together to complete all sections of the Integer Activity together.

The remaining students will follow along with this Presentation, since I think that direct instruction will work most effectively for revision of this topic. In lieu of guided notes, I will have my students complete their work with a white board and marker as they follow along with the presentation.

Today's lesson will review the use of the **number line** and** zero pairs**. Once students have seen and considered both, I give them the option of using the method that is most meaningful to them.

I have horizontal and vertical number lines hanging on the walls in my classroom, which is suffice for many of my students. Some students also enjoy using the Building Handout, as they are then able to visualize movement on a number line on a real world example.

Students that prefer using zero pairs opt to use red and white integer chips, or by drawing white and black circles on their white boards. I created my own integer chips by printing and laminating this template, then cutting into square pieces that are about the size of my thumb.

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#### Partner Activity

*30 min*

Students will work independently or in pairs on the Integer Activity and its corresponding Map. My students really enjoyed this activity since they all ride the Metro to school each day.

If students did not start this activity at the start of class, they are usually only able to complete Part I with the time remaining. Towards the end of class, I will reveal the correct order of stations that will be visited.

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#### Closing

*10 min*

At the end of class I will ask students to share out how they could use zero pairs or a number line to solve a problem with large numbers. Students will then complete an Exit Card.

#### Resources

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- UNIT 1: Welcome Back! - The First Week of School
- UNIT 2: Linear & Absolute Value Functions
- UNIT 3: Numeracy
- UNIT 4: Linear Equations
- UNIT 5: Graphing Linear Functions
- UNIT 6: Systems of Linear Equations
- UNIT 7: Linear Inequalities
- UNIT 8: Polynomials
- UNIT 9: Quadratics
- UNIT 10: Bridge to 10th Grade