##
* *Reflection: Connection to Prior Knowledge
Subtracting Integers - How does subtraction relate to addition? - Section 2: Explore

This was the first time I have done this inquiry activity, and it went well. When we got to the part where students are looking at the problems side by side and trying to make connections - I encouraged all students to just share what they noticed. I didn't have anyone that was real positive on a definite rule, so I just asked that they share similarities they could find between the two sets of problems - by approaching the problem that way, I was able to get more students to speak out. They shared things like - in both problems the subtraction changed to addition, the second number became the opposite, you moved the negative sign, etc. Then I instructed the students to write the problems on top of each other instead of side by side. I covered up the second term and asked what they saw - they all agreed that the first number stayed the same, but subtraction became addition. Then I covered the first term and the operation sign, leaving only the second term in view. Students said - its the opposite. That was a good segue into the rule that subtracting is the same as adding the opposite. Then I heard lots of oohs and ahs :) (I like those - they are generally good!!)

I did have a couple students that were confused, which is to be expected. I have created a very safe environment where students are comfortable asking questions, so the students did not hesitate to call me over. In helping them, students found it most beneficial to write the problems on top of one another. Often times teachers and/or students go through the problem and just change the original - but by being able to see both problems - students could easily identify if they were indeed adding the opposite.

*Inquiry Reflection*

*Connection to Prior Knowledge: Inquiry Reflection*

# Subtracting Integers - How does subtraction relate to addition?

Lesson 8 of 23

## Objective: Students will be able to subtract integers by adding the additive inverse.

#### Launch

*5 min*

**Opener: **As students enter the room, they will immediately pick up and begin working on the opener. Please see my instructional strategy clip for how openers work in my classroom (**Instructional Strategy - Process for openers**). This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is **mathematical practice 3**.

**Learning Target: **After completion of the opener, I will address the day’s learning targets to the students. In today’s lesson, the intended targets are, “I understand the relationship between addition and subtraction and I can subtract integers.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

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#### Explore

*55 min*

**Subtracting Integers Notes**: Subtracting Integers Explore Narrative The notes begin with an inquiry activity where students will be using tools strategically through the incorporation of the number line (**mathematical practice 5**). Additionally, they will be looking for patterns in repeated reasoning to develop a mathematical rule for subtraction, which is **mathematical practice 8**. They will also be making use of the structure of a problem, by recognizing that subtracting is actually adding the opposite (**mathematical practice 7**). fter the group inquiry, I will bring the class back together to develop a written rule for subtraction. I am going to address subtraction as adding the additive inverse, or the opposite. Though opposite is an easier term, it is very important that students use correct vocabulary, and I will model this for them. I will include the word opposite in the rule, however, so that students visually are able to connect additive inverse with opposite. After going over the rule, I am going to model two examples with the students, first changing the problems to addition, and then using addition rules to simplify. With this topic, it is very important that students are precise when paying attention to the signs of the numbers, **mathematical practice 6**.

**Table Practice**: Students will continue their work on subtracting integers by completing a few problems with their tables. The first few problems ask that students simply change the problems to equivalent addition problems, and then the students will move into solving. I will ask that students work individually for 5 minutes, and then collaborate with their groups. I want to give students time to persevere (**mathematical practice 1**) with the problems before their group blurts out the answers!

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#### Summarize + Homework

*5 min*

**Summary Questions: **To summarize this lesson, I am going to post 4 problems on the board, 2 addition and 2 subtraction. The students will complete these problems on the back of their opener, and then make a pile of their openers on their table for me to collect. The purpose of this activity is for me to get a grasp on who has it, and who needs more practice. I will use the data from these questions to move seats around for the next class as well as differentiate their next assignment.

**Homework:** After students complete the summary questions they will begin working on their homework assignment. Philosophy on Homework

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What exactly do you have them fill in the blanks with for the notes? Subtraction is the same as (addition) ____________ __________ ( _____________)

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###### Relative Error Spiral Lesson

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Environment: Urban

- UNIT 1: Introduction to Mathematical Practices
- UNIT 2: Proportional Reasoning
- UNIT 3: Percents
- UNIT 4: Operations with Rational Numbers
- UNIT 5: Expressions
- UNIT 6: Equations
- UNIT 7: Geometric Figures
- UNIT 8: Geometric Measurement
- UNIT 9: Probability
- UNIT 10: Statistics
- UNIT 11: Culminating Unit: End of Grade Review

- LESSON 1: Integers and Absolute Value - Are two steps forward and two steps back the same thing?
- LESSON 2: Modeling Addition - Opposites Attract, You Know?!
- LESSON 3: Integer Addition Word Problems - Can You Picture It? (Two Day Lesson)
- LESSON 4: Adding Integers - What's the Rule?
- LESSON 5: Multiple Addends - More than 2 numbers to add?
- LESSON 6: Adding Integers Review
- LESSON 7: Adding Integers Test
- LESSON 8: Subtracting Integers - How does subtraction relate to addition?
- LESSON 9: Subtracting Integers Practice - Can you subtract more than two integers?
- LESSON 10: Addition and Subtraction of Integers - DOMINOES!
- LESSON 11: Adding and Subtracting Integers - Real World Applications
- LESSON 12: Adding and Subtracting Integers - REVIEW!
- LESSON 13: Adding and Subtracting Integers Test
- LESSON 14: Adding and Subtracting Signed Fractions - Remember Those Integer Rules!
- LESSON 15: Adding and Subtracting Signed Fractions Fluency Practice
- LESSON 16: Adding and Subtracting Signed Decimals - Line Up Those Points!
- LESSON 17: Adding and Subtracting Rational Numbers - Practice Makes Perfect!
- LESSON 18: Adding and Subtracting Rational Numbers - Test
- LESSON 19: Multiplying and Dividing Integers
- LESSON 20: Multiplying and Dividing Rational Numbers
- LESSON 21: Problem Solving with Rational Numbers
- LESSON 22: Fractions to Decimals - Terminate or Repeat?
- LESSON 23: Rational Number Unit Test