Subtraction with Integers for Real-World Problems
In this lesson, students will apply subtraction with integers to solve real-world problems, exploring concepts through examples like calculating elevations. Essential questions, warm-up activities, and reviewing absolute values are included to reinforce understanding.
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Presentation Transcript
Lesson Subtract Integers
[OBJECTIVE] The student will explore subtraction with integers and apply this understanding to solve problems in mathematical and real world situations.
[MYSKILLS] Addition and subtraction of whole numbers Number line Addition of integers
[ESSENTIALQUESTIONS] 1. Explain how to subtract integers using algebra tiles. 2. Describe the process we can use to take away the second number in the subtraction problem if there are not enough algebra tiles. 3. Will the following problems have the same solution? 4 6 and 4 + ( 6) Justify your answer.
[Warm-Up] Begin by completing the warm-up for this lesson.
SOLVE Problem Introduction SUBTRACT INTEGERS
[LESSON] SOLVE The highest elevation in North America is Mt. McKinley, which has an elevation of 20,320 feet above sea level. The lowest elevation in North America is Death Valley, which has an elevation of 282 feet below sea level. What is the difference between these two elevations?
[LESSON] SOLVE S Study the Problem Underline the question.
[LESSON] SOLVE The highest elevation in North America is Mt. McKinley, which as an elevation of 20,320 feet above sea level. The lowest elevation in North America is Death Valley, which as an elevation of 282 feet below sea level. What is the difference between these two elevations?
[LESSON] SOLVE S Study the Problem Underline the question. This problem is asking me to find the difference between the elevations.
Reviewing Absolute Value 5 5 0 What is the range of number values on the number line? negative five through positive five Identify zero on the number line.
Reviewing Absolute Value 5 5 0 Negative Positive Describe the change as we move from zero to the right on the number line. Describe the change as we move from zero to the left on the number line.
Reviewing Absolute Value 3 spaces 5 5 0 Negative Positive Identify the number of spaces from the zero in the positive direction. 3 spaces
Reviewing Absolute Value 3 spaces 5 5 0 Negative Positive Identify the position on the positive side of the number line. 3
Reviewing Absolute Value 3 spaces 3 spaces 5 5 0 Negative Positive Identify the number of spaces from the zero in the negative direction. 3 spaces
Reviewing Absolute Value 3 spaces 3 spaces 5 5 0 Negative Positive Identify the position on the negative side of the number line. 3
Reviewing Absolute Value If the number of spaces from zero in both directions is 3, explain why one of the points is 3 and the other is a negative 3. When we move to the left we are moving in the negative direction; when we move to the right we are moving in the positive direction. The distance moved is 3 spaces for both.
Reviewing Absolute Value Identify what this concept is called. Absolute value Explain what absolute value means. Absolute value is the distance a number is from zero on the number line.
Reviewing Absolute Value What is the absolute value of 3? 3 What is the absolute value of 3? 3
Reviewing Absolute Value 5 Positive 4 What is the value of ? ? 4 spaces 3 2 1 0 4 What is the value of ? ? 4 spaces 1 2 3 4 5 4 Negative
Reviewing Absolute Value The absolute value of a number is always a __________ value because the absolute value represents the distance from _______ on the number line and a distance cannot be a _________ value. positive zero negative
Concrete and Pictorial SUBTRACTING TWO POSITIVE VALUES
Subtracting Two Positive Values 4 1 = What is the problem asking us to find? The difference of positive 4 and positive 1 Explain how we can model the problem using unit tiles. Place four yellow tiles on the space.
Subtracting Two Positive Values 4 1 = What are some terms we can use to describe subtraction? Take away, remove, cross out What do we want to take away from the four yellow tiles? 1 yellow tile
Subtracting Two Positive Values 4 1 = Let s show how to take away 1 yellow tile.
Subtracting Two Positive Values 4 1 = What do we have left after we take the one yellow tile away? 3 yellow tiles What do you notice about the color of the tiles? They are all yellow.
Subtracting Two Positive Values 4 1 = Let s draw a picture of the 4 yellow tiles in the box below Problem 1 and talk about how to show subtraction. Cross out 1 yellow tile with an X.
Subtracting Two Positive Values 4 1 = Y Y Y Y We can also model using Ys. How can we model taking away one Y? Cross out 1 Y.
Subtracting Two Positive Values 4 1 = Y Y Y Y Explain the color of the tiles. All the same color
Subtracting Two Positive Values 4 1 = Y Y Y Y What operation did we use? Subtraction
Subtracting Two Positive Values 4 1 = 3 Y Y Y Y What is the difference? 3 yellows = 3
Subtracting Two Positive Values 4 1 = 4 3 4 5 6 3 2 1 4 5 2 6 1 0 Explain how to model the first value of positive 4. Draw a line in the positive direction to the right from the zero to the 4.
Subtracting Two Positive Values 4 1 = 1 4 3 4 5 6 3 2 1 4 5 2 6 1 0 Explain how to model subtracting the 1. Draw a line starting at the 4 and then moving one space in the negative direction.
Subtracting Two Positive Values 4 1 = 3 1 4 3 4 5 6 3 2 1 4 5 2 6 1 0 What is the difference of 4 and 1? 3
Subtracting Two Positive Values 5 4 1 = 3 4 3 2 1 0 4 Explain how to model the first value of positive 4. 1 2 3 4 5 Draw a line in the positive direction up from the zero to the 4.
Subtracting Two Positive Values 5 4 1 = 3 4 1 3 2 1 0 4 Explain how to model subtracting 1. Draw a line from the 4 one space in the negative direction which is down. 1 2 3 4 5
Subtracting Two Positive Values 5 4 1 = 3 4 1 3 2 1 0 4 What is the difference of 4 1? 3 1 2 3 4 5
Subtracting Two Positive Values Describe the relationship between subtraction and addition. They are opposite operations.
Subtracting Two Positive Values Compare the horizontal number lines for Problem 1. The number lines look the same.
Subtracting Two Positive Values 1 4 3 4 5 6 3 2 1 4 5 2 6 1 0 How can you represent the number line model above with addition? 4 + ( 1) = 3
Subtracting Two Positive Values 1 4 3 4 5 6 3 2 1 4 5 2 6 1 0 What conclusion can you make based upon the horizontal number line models? Subtraction is the same as adding the opposite.
Subtracting Two Positive Values 1 4 3 4 5 6 3 2 1 4 5 2 6 1 0 How can we write the two problems? 4 1 = 3 corresponds to 4 + ( 1) = 3
SUBTRACTING TWO NEGATIVE VALUES
Subtracting Two Negative Values 4 ( 1) = What is the problem asking us to find? The difference of negative 4 and negative 1 Explain how we can model the problem using unit tiles. Place four red tiles on the space.
Subtracting Two Negative Values 4 ( 1) = What are some terms we can use to describe subtraction? Take away, remove, cross out What do we want to take away from the four red tiles? 1 red tile
Subtracting Two Negative Values 4 ( 1) = Let s show how to take away 1 red tile.
Subtracting Two Negative Values 4 ( 1) = What do we have left after we take the one red tile away? 3 red tiles What do you notice about the color of the tiles? They are all red.
Subtracting Two Negative Values 4 ( 1) = Let s draw a picture of the 4 red tiles in the box below Problem 2 and talk about how to show subtraction. Cross out 1 red tile with an X.
Subtracting Two Negative Values 4 ( 1) = R R R R We can also model using Rs. How can we model taking away one R? Cross out 1 R.
