T1
Use a number line to show the opposite and the absolute value of a number
NS.5 & NS.6a & NS.7c
Lesson 1
Direct Instruction
Notes
How to make a number line with a minimum of -10 and a maximum of 10 -- and zero in the middle
* Pro tip: if you have a piece of lined paper, rotate it 90 degrees so that the lines are vertical
1. Draw a horizontal or vertical line (use a ruler or straightedge)
2. Add arrows: Place arrows on both ends of the line to show it continues infinitely in both directions.
3. Add tick marks (space them equally, ensure the distance between each tick mark is the same)
4. Write numbers along the line (whether you are numbering by 1s or 2s or 3s, always use the same intervals)
Note: zero does not always have to be on a number line. Whether or not to include 0 depends on the numbers you are working with.
Vocabulary
Notes
Absolute value: a number's distance from zero on the number line (distance is always positive)
The "opposite" of a number is another number that is the same distance from zero on a number line but on the opposite side of zero
Let's look at some real-life situations, work together to figure out what number is represented, place the number on a number line, and apply our new vocabulary.
(Glue this into your notebook when finished)
Direct Instruction
Notes
Instead of asking, "How far is a number from zero?", mathematicians use two vertical bars, like this: |-3|
|-3| is the same thing as asking, "What is the absolute value of -3?" Or, "How far is -3 from zero?"
What is the opposite of -25?
What is the opposite of 14?
|36|
|-8|
|5| + |-8|
|-12| + |-4|
|15| - |-6|
|-2| - |-9|
My Responsibilities
Due 9/9
1. In your notebook, make meaningful notes to your forgetful self.
2. In your notebook, do the CYUQs to a Level 3 or better and check answer before moving to next problem. When possible, draw a number line to show how you came up with your answer.
p361: 24, 25, 26, 30, 31, 32, 33, 34, 35; p359: 1, 2, 3, 7, 8, 9 (Volume 1, Ch5, L2)
3. When you don't understand, look at textbook examples (review the pages prior to the CYUQs) or search
Lesson 2
After completing the Check-your-understanding Questions, which were important for everyone to do?
On the blank side, write: First name, last name, U2T1
A. |5|
B. |-12|
* If you have time, sketch a number line to prove your answers are correct.
Direct Instruction
Notes
-3 can be read two ways: "the opposite of 3" or "negative 3"
The opposite of the opposite of a number is the number itself, e.g., –(–3) = 3,
* If we go to Starbucks and you borrow $5. What kind of number is that? Now imagine the next day I say to you, "I took away your debt." What does that mean?
|0| = 0
0 is its own opposite
Lesson 1
Direct Instruction
Notes
How to make a number line with a minimum of -10 and a maximum of 10 -- and zero in the middle
* Pro tip: if you have a piece of lined paper, rotate it 90 degrees so that the lines are vertical
1. Draw a horizontal or vertical line (use a ruler or straightedge)
2. Add arrows: Place arrows on both ends of the line to show it continues infinitely in both directions.
3. Add tick marks (space them equally, ensure the distance between each tick mark is the same)
4. Write numbers along the line (whether you are numbering by 1s or 2s or 3s, always use the same intervals)
Note: zero does not always have to be on a number line. Whether or not to include 0 depends on the numbers you are working with.
Vocabulary
Notes
Absolute value: a number's distance from zero on the number line (distance is always positive)
The "opposite" of a number is another number that is the same distance from zero on a number line but on the opposite side of zero
Let's look at some real-life situations, work together to figure out what number is represented, place the number on a number line, and apply our new vocabulary.
(Glue this into your notebook when finished)
Direct Instruction
Notes
Instead of asking, "How far is a number from zero?", mathematicians use two vertical bars, like this: |-3|
|-3| is the same thing as asking, "What is the absolute value of -3?" Or, "How far is -3 from zero?"
What is the opposite of -25?
What is the opposite of 14?
|36|
|-8|
|5| + |-8|
|-12| + |-4|
|15| - |-6|
|-2| - |-9|
My Responsibilities
Due 9/9
1. In your notebook, make meaningful notes to your forgetful self.
2. In your notebook, do the CYUQs to a Level 3 or better and check answer before moving to next problem. When possible, draw a number line to show how you came up with your answer.
p361: 24, 25, 26, 30, 31, 32, 33, 34, 35; p359: 1, 2, 3, 7, 8, 9 (Volume 1, Ch5, L2)
3. When you don't understand, look at textbook examples (review the pages prior to the CYUQs) or search
Lesson 2
After completing the Check-your-understanding Questions, which were important for everyone to do?
On the blank side, write: First name, last name, U2T1
A. |5|
B. |-12|
* If you have time, sketch a number line to prove your answers are correct.
Direct Instruction
Notes
-3 can be read two ways: "the opposite of 3" or "negative 3"
The opposite of the opposite of a number is the number itself, e.g., –(–3) = 3,
* If we go to Starbucks and you borrow $5. What kind of number is that? Now imagine the next day I say to you, "I took away your debt." What does that mean?
|0| = 0
0 is its own opposite