Jessica Sullivan

Mathematics Lesson Plan

Adding and Subtracting Integers

 

 

 

Pre-Planning Questions

1. My students should know what integers are, what absolute value is, the number line and the basic principle of addition. By the time I will be teaching this lesson, my students would have already mastered absolute value. I would begin by reviewing with integers and number lines.

2. I will be covering adding integers. In adding integers, I would cover adding positive integers with other positive integers, adding negative integers together, and would begin teaching my students to add positive and negative integers. My students have a short attention span so I would not want to overwhelm them with too much at once. By introducing adding positive and negative integers, I would give the students a sneak peek to the next day’s lesson without overwhelming them.

3. In previous lessons, the students have mastered whole numbers, fractions and decimals by adding, subtracting, multiplying, dividing. Up until now, the students have been mastering these concepts, now my students will master the same concepts but with integers.

4. Since students have mastered addition, subtraction, multiplication, and division, and are comfortable with positive numbers, it will be confusing in the beginning to make sure their signs are correct. The added depth to the same concept allows for easy mistakes.

 

Lesson Plan

Teacher:  Today we will be using our number lines and integers to make new rules about addition. Up until now, we have been adding using whole numbers. Let’s remember whole numbers are zeros and positive numbers on the number line. To refresh our memory, let’s draw a number line. As I draw one on the board, please use the ruler on your desk to draw one on your paper. (Teacher will draw number line on the board. A zero will be placed in the middle with numbers 1-10 placed on the right of the zero, and numbers –(1-10) are placed on the left of the zero). As we look at our number line, we can remember that integers are numbers with a plus sign (+) to make them positive and a minus sign (-) to make them negative. Don’t be fooled by zero, it is still an integer; it just is neither negative nor positive. Let’s look at some examples.

1. (+2) + (+5)=

Teacher: Looking at our number line, where do you think we would start?

Student Responses until I am told 0.

Teacher: Putting your pencil at zero, let’s move to a positive 2. How many places would I move my pencil for this problem?

Student: Two places

Teacher: To the right or left?

Student: Right!

Teacher: Looking at our problem, we need to add 5. So how would we do this? How do you think we would do this?

Student various responses

Teacher: Starting with our pencil at positive 2 we want to add a positive 5. To do this we move our pencil 5 places to the right. What number do we land on?

Student responses: 7

Teacher: Positive or negative?

Student responses: positive

Teacher: Circle your answer on the number line and in the problem you copied.

Teacher: please notice that we added two positive numbers and our answer was also positive.

Teacher: Let’s try another one! (Teacher draws another number line just like the one in the last problem) Using your ruler, let’s draw another number line just like last time, labeling your positive and negative numbers.

1. (+4) + (+5)=

Teacher: Looking at our number line, where do you think we should start?

Student response until the number zero is said. (Would expect a correct answer).

Teacher: Now to begin our problem, what do we do?

Student responses vary, looking for “move four places to the right”

Teacher: Everyone make sure your pencil is at positive four, now what do we do?

Student responses vary, looking for “move five more places to the right”

Teacher: Now everyone make sure you move your pencil, five places to the right, if you haven’t already. Where do we end up?

Student response, looking for 9.

Teacher: Everyone circle your answer on the number line and in the problem we worked. What are the signs of 4, 5, and 9?

Student responses vary, looking for positive 4, positive 5, and positive 9.

Teacher: Let’s notice that two positive numbers yields a positive answer.

Teacher: Now let’s see what happens when we add two negative numbers. First let’s redraw our number line, just like before and label all of our numbers. Let’s look at the first problem we did, but this time we will make the numbers negative.

1. (-2) + (-5)=

Teacher: Looking at our number line, where would be the first place we start?

Student responses: 0 (they should know we start at 0)

Teacher: Looking at the problem, what is the next step?

Student answers vary, looking for negative two.

Teacher: Be sure you noticed that since it was a negative 2, we are moving the left of zero on the number line.

Teacher: Now that we all have our pencils on negative two, where do we go?

Varied student responses, looking for “move 5 places to the left”

Teacher: Correct, everyone make sure you move 5 places to the left. Why do we move to the left and not the right?

Varied student responses, looking for “because it’s a negative number”

Teacher: Since we moved five more places to the left, what number does our pencil land on?

Student response: -7

Teacher: Great! Make sure to circle your answer on the number line and in the problem we just worked. What is the sign of our answer?

Student responses vary, looking for “ negative”

Teacher: I want everyone to notice that our problem had two negative signs, and our answer was also negative. Starting to see a pattern?

Student responses vary

Teacher: Let’s try another one! Please draw another number line, just like before, label your numbers and copy down this problem.

1. (-4) + (-5)=

Teacher: Where should we begin, once we have drawn our number line?

Student responses: 0, they should understand and know this.

Teacher: Once we have started at zero, what would our next step be?

Student Reponses vary, looking for “Move four places to the left”

Teacher: Why are we moving to the left instead of the right?

Varied student responses, looking for “We move to the left because it is negative”

Teacher: With our pencils on negative four, what is our next step?

Student answers vary, looking for “move five more places to the left”

Teacher: That’s right! We are going to move five more places to the left. Everyone take there pencils and move five more places. Once you have done so, put your pencils down, so I know you are ready.  Okay class, what is our answer?

Student responses, -9

Teacher: Very good! Can anyone tell me what signs were with 4, 5, and 9?

Varied student responses, looking for “negative 4, negative 5 and negative 9”

Teacher: Notice that since we had two negative signs in the problem, we end up with our answer being what?

Student responses vary, looking for “negative”

Teacher: Does anyone see the pattern?

Students voice what they think the pattern is.

Teacher: We can notice that when we are adding two positive numbers, our answer is also going to be positive. This also works when we are adding two negative numbers, our answer will be negative. To state this as a rule, we say: When we add “like” signs, our answer is also that sign. Now let’s see what happens when we add a positive and negative number.

Teacher: Everyone draw our number line, label the numbers, and please copy this problem.

1. (-7) + (+3)=

Teacher: Okay class, where should we start on this problem?

Student expected response: 0

Teacher: Once we start at 0, what is our next step?

Varied student responses, looking for “move 7 places to the left”

Teacher: Yes, we are moving 7 places to the left because our number is negative! After we move our pencils seven places to the left, what would we do next?

Student responses vary, looking for “move three places to the right” (but not expecting very many to get this)

Teacher: Because our next number is positive, I am going to move three places to the right. We are moving to the right because we are positive number. Let’s take our pencils, place them on negative 7 and move three places to the right. Where do we land?

Varied student responses, looking for -4

Teacher: We land on negative four. Circle your answer on the number line and in the problem. What is the sign of 7 and 3?

Student responses vary, looking for “negative 7 and positive 3”

Teacher: Our signs are negative 7 and positive 3, since our signs are different, how do we know what the sign of our answer will be?

Varied student responses, looking for “ the sign of the absolute value (we have already learned absolute value) of the larger number will tell us the sign of the answer” (again, not expecting many to get this)

Teacher: This can be tricky! When we have two different signs in our problem, we use sign of the absolute value of the larger number. So in this problem, the absolute value of the larger number is negative. Therefore our answer is negative. Let’s see if this works on another example. Draw another number line, label it, and copy down this problem.

1. (+8) + (-2)=

Teacher: Okay class, where do we begin our problem?

Student response: 0

Teacher: Good, we are starting at zero and then moving where?

Varied student responses, looking for “eight places to the right”

Teacher: We are going to move eight places to the right because our problem has positive 8, right? After we move from zero to positive eight, moving our pencils to the right, we would do what?

Student responses vary, looking for “move to the left two places”

Teacher: With our pencils on positive eight, we are going to move two places to the left. Why are we moving to the left?

Varied student responses, looking for “because two is negative”

Teacher: Two is negative, so we will move from positive eight, to the left two places. Where should our pencils end?

Student responses vary, looking for “ positive six”

Teacher: We land on positive six. Circle your answer in the problem and on the number line. Can anyone tell me the sign of eight and two?

Varied student responses, looking for “ positive eight and negative two”

Teacher: So since we have a positive eight and a negative two, our signs are different. How do we know what the sign of our answer will be?

Student varied responses, looking for “ Using the sign of the absolute value of the larger number, will let us know what sign will be with our answer”

Teacher: Since we have a negative and positive sign in our problem, we will look at the absolute value of the larger number. In this problem, the absolute value of the larger number is 8, so the sign of our answer is positive. So let’s write a rule for adding integers. Write the rule in your math notebook. When we add “like” signs, our answer is also that sign. When we add “unlike” signs, we subtract and the answer is the sign of the absolute value of the larger number.

Teacher: Tomorrow we will start with this problem:

1. (-5) + (+5)=

Teacher: Look it over and we will begin with it tomorrow. I am about to hand out a worksheet that you will each need to complete for homework. You may use our rules or a number line to complete each problem.  Are there any questions?

Teacher would entertain questions. Below is the homework sheet the teacher passed out.

 

 

Homework: Adding Integers

Directions: Add the following integer problems by drawing a number line or using your adding integers rule.

 

1. (+6) + (+1) =

 

 

2. (+8) + (+2) =

 

 

3. (-6) + (-3)=

 

 

4. (-4) + (-3)=

 

 

5. (-1) + (+9)=

 

 

6. (+5)+(-9)=

 

 

7. (+6)+ (-8)=

 

 

8. (+7)+(+3)=

 

 

9. (-7)+(+9)=

 

 

 10. (-10)+(+7)=

 

 

Here is a PDF file of the lesson above: