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U2 Distance and Direction
T1
Direct Instruction
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.
T1
Vocabulary
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
T1
Try it
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)
T1
Direct Instruction
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?"
T1
Try it
What is the opposite of -25?
What is the opposite of 14?
|36|
|-8|
|5| + |-8|
|-12| + |-4|
|15| - |-6|
|-2| - |-9|
T1
My Responsibilities
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
T1
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T1
Entry Ticket (5 min)
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.
T1
Direct Instruction
-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
T2
Launch
On a number line showing a drive from San Francisco to Los Angeles, a landmark in San Jose would be a dot at approximately 50 miles, while a landmark near Bakersfield might be a dot at 250 miles.
We could use these two dots on the number line to answer the question, "What is the distance between Gilroy and Bakersfield on this number line?"
Draw a line with arrows. If I want to put 50 and 250 on it, do I need negative numbers? Do I need 0? What do I need? Next, change the numbers to 4 and 9. Ask, what numbers do I need? Show starting with 4, numbering by 1s up to 9. Then ask the distance and have students share both ways.
To foreshadow, write: d =
T2
Vertical Collaboration
There are two houses, one on 15 and one on 8. Graph the numbers on a number line. Then find the distance between the two whole numbers.
There are two houses, one on 36 and one on 45. Graph the numbers on a number line. Then find the distance between the two integers.
There are two houses, one on 3 and one on -5. Graph the numbers on a number line. Then find the distance between the two integers.
Graph 7 and -2 on a number line. Then find the distance between the two integers.
Graph -1 and -4 on a number line. Then find the distance between the two integers.
Graph -15 and -24 on a number line. Then find the distance between the two integers.
Graph -92 and -103 on a number line. Then find the distance between the two integers.
T2
Consolidation
There are two ways to find the distance between two numbers (a and b)
One way:
Make a number line and count the number of spaces between the two points (a and b)
* Pro tip: only make a number line for the numbers you are graphing. When you can, go by 1's (makes it easier to count)
Another way:
1. Subtract one number from the other (find the difference). You can subtract a from b, or b from a; the order doesn't matter.
2. Find the absolute value of the difference
T2
Warmup
Do the following two problems in your notebook:
1. Graph 15 and 8 on a number line. Then find the distance (d) between the two whole numbers.
2. Graph 3 and -5 on a number line. Then find the distance (d) between the two whole numbers.
T2
Discussion
To find distance:
We can count spaces (always works)
Subtract and find the absolute value of the difference of the two numbers (always works)
Adding the absolute value of the two numbers works SOMETIMES but not always... so be careful if you want to use this
T2
Summarize
There are two ways to find the distance between two numbers (a and b)
One way:
Make a number line and count the number of spaces between the two points (a and b)
* Pro tip: only make a number line for the numbers you are graphing. When you can, go by 1's (makes it easier to count)
Another way:
1. Subtract one number from the other (find the difference). You can subtract a from b, or b from a; the order doesn't matter.
2. Find the absolute value of the difference
T2
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
A. Graph 13 and 6 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
B. Graph 36 and 24 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
C. Graph 7 and -2 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
D. Graph -8 and 5 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
E. Graph -7 and -1 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
F. Graph -5 and -13 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T2
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T2
Entry Ticket (5 min)
On the blank side, write: First name, last name, U2T2
Graph 6 and -4 on a number line. Then find the distance between the two numbers. Write d=
T3
Launch
Draw a number line 0-1, break it into fifths. Label 0 1nd 1. Graph 1/5 and label it A (don't write 1/5). Ask students what number A represents. Label 1 2/5 as B (but don't write the number). Discuss.
Reminders:
Draw a visible dot on the number line to represent the number
If your number line doesn't have the number you graphed, write the number above or below the dot
T3
Vertical Collaboration
Sketch the number line. Then graph each of the three rational numbers:
Student solutions:
T3
Direct Instruction
All 'rational numbers' can be represented by a point on a number line.
Rational number: any number that can be written as a fraction (ratio) -- denominator is not zero
Integer: a whole number that can be positive, negative, or zero. Examples include -3, 0, and 7.
T3
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
Answers:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T2
Glue & Review
T3
Guided Practice
Let's make some number lines with rational numbers on them
T3
Extend
What is the value of each point if?
For each number line, start with what is given (one of the points). Use that to figure out the interval. Fill in as many tick marks as you need, then write A=, B=, C=, D=
Check answers as you're working:
A
Thursday is a Retake Day
To retake a summative assessment score in
PowerSchool that is less than 3:
1. Go to Google Classroom > Classwork. Scroll down to
find the student responsibilities for the unit and target
you are looking for (e.g. U1T1 Student Responsibilities)
2. Click View Instructions. Review the notes. Do the
CYUQs (to a level 3 or better) and check answers as
you’re working.
3. If you get stuck, review your thinking, try different
approaches, ask for help, and/or search.
4. Bring your Level 3 CYUQs to a retake day and trade
me for a retake
T3
Discuss (2 min)
After completing yesterday's extend activity, which questions were challenging? Which ones were easy?
* Please fold this in half and glue it into your notebook. It's okay that some questions will be glued.
T4
Launch
In life we say words like "Less than" or "More than" and at some point, some smart math person said, "Let's save some time and replace those words with symbols." And in addition to being able to use these symbols to compare things, now people use them when doing math, writing code, and more.
3.6 oz > weight of a letter (to mail)
spending < income
15 > 2
And we can use what we learned about number lines to prove it!
Dismiss them having them say to each other, "The bigger number is always on the right."
T4
Direct Instruction
Inequalities are symbols that are use to compare numbers.
Less than uses the symbol <
Greater than uses the symbol >
* When comparing numbers, use a number line to show your thinking and prove your answer
* The number on the right (on a number line) is ALWAYS the bigger number
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
For each problem, sketch a horizontal or vertical number line to prove your answer: p369: 15, 16, 17, 18, 19, 23; p367: 1, 2, 3, 4, 5 (Volume 1, Ch5-3)
Check answers while you are working:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T4
Reminder
* When comparing rational numbers, remember to use a number line to prove your answer.
* The number on the right (on a number line) is ALWAYS the bigger number
T4
Consolidation
Three ways to compare fractions with different size pieces (denominators):
1. Double number line -- a double number line has two number lines, one above the other, with the same starting and ending numbers but different intervals (spacing)
2. Area models (using rectangles) -- one directly above the other
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help. * Pro tip - DO NOT rotate your paper today
Click the link below to see the questions:
Answers:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
A
Retake Day
A
Retake or Prepare (35min)
Trade your CYUqs for a retake.
If unprepared, open PowerSchool and review your progress. If you have a goal that is less than 3, do the CYUqs (at a level 3) and prepare for retaking. When ready, trade me. Repeat this process until your goals are all 3's or better.
If your goals are all 3's or better OR you are done retaking, practice and review the math we are currently working on by signing into Delta Math > click Login > Sign in with Google > with your school Google Account > Fractions on the Number Line
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Direct Instruction
Start 1:22. Stop at 4:40 (before learning how to plot). B. Start again at 6:38-8:25 for how to plot an ordered pair. C. Continue until 10:13 for information on the four quadrants.
T5
Summarize
The coordinate plane is made up of an X and Y-axis
The X-axis is a horizontal number line.
The Y-axis is a vertical number line.
The X and Y-axis cross at the origin (0,0)
An ordered pair (x, y) is an 'address' on the coordinate plane.
T5
Summarize
To graph a point on the coordinate plane:
1. Start at the origin (0,0)
2. Move left or right on the X-axis (depending on whether the x value is positive or negative). Stop when you are on the x-value.
3. Next, move up or down (depending on whether the y value is positive or negative). Stop when you are on the y value and make a dot.
T5
Guided Practice
Graph and label the ordered pairs:
A: (4, -1)
B: (2, 3)
C: (-3, 2)
T5
Summarize
The two axes create four quadrants that are numbered with Roman Numerals -- counterclockwise.
The signs of the rational numbers in an ordered pair tell you which quadrant the point will be located in:
(1, 1) is in QI; (-1, 1) is in QII; (-1, -1) is in QIII; (1, -1) is in QIV
T5
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. If you need help, get help. If someone else needs help, give help. Graph and label the following ordered pairs:
A. (3, 2)
B. (-5, -3)
C. (-2, 5)
D. (3, -1)
E. (-4, 1)
F. (1, -2)
G. (-2, -2)
H. (1, 4)
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
A
Great job!
After reviewing your assessments, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
PowerSchool is up to date. You can see how your work yesterday impacted your progress toward your goals.
If you weren't able to show me you understood (score < 3), please read the comments.
You are welcome to try again. But this time, you must make a poster that teaches someone how to do the learning target you are working on. If you need help, ask for help!
T4
Entry Ticket (5 min)
Use the blank side. On top, write your first name, last, and U2T4
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Real-world Connection
T5
Explore
T5
Direct Instruction
To identify the location of a point (x, y) on the coordinate plane, start at the origin (0,0).
1. Move left OR right on the x-axis and stop above or below the point. Write down the x-value.
2. Move up OR down (parallel to the y-axis) and stop at the point. Write down the y-value.
T5
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
p399: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; p401: 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 (Volume 1, Ch5-6)
p407 1, 2, 3, 4, 5, 6, 7, 8 (Volume 1, Ch5-7)
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T4
Glue & Review
U2T4 Entry Ticket
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Entry Ticket (5 min)
At the top, write: First name, last name, U2T5
Graph and label the following:
A (3, -2)
B. (-1, -4)
C. (-3, 5)
D. (4, 2)
T6
Guided Practice
Find the distance between the two points:
A. (-2, 5) and (3, 5)
B. (4, -3) and (4, 6)
C. (-3, -4) and (-3, -1)
D. (4, -1) and (-8, -1)
T6
Summarize
IF two points share an x value,
you can find the distance between the points with either method:
1. Graph and count
2. Subtract the y-values (find the difference) and then find the absolute value of the difference
* Works for shared y-values too (just be sure to subtract the x-values)
T6
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → When needed, show your thinking in your notebook. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
Sign into Delta Math > click Login > Sign in with Google > with your school Google Account > U2T6 CYUQs
* If you come to a question that references a triangle, ignore the triangle part and focus on the two ordered pairs (points) that belong to the line (segment). See image:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T6
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T6
Review
Find the distance between the two points:
A. (-20, 3) and (-20, -6)
B. (-9, 16) and (31, 16)
T6
Challenge
Find the distance between two points:
1. El Dorado Hills is 768 feet above sea level. Folsom is 220 feet above sea level. What is the distance (in elevation) between the two cities?
2. A building sits 25' above sea level. If a submarine is 30' below sea level. How much higher is the building than the submarine?
A
Class Info
Unit 2 Test is Monday 9/29
A
Class Info
Entry Tickets vs. Tests
Entry tickets (Formative Assessments) are given after studying a learning target. They provide feedback and help you know if your learning strategies are working. They are an opportunity to know where you are before you take a test. Entry tickets get replaced by tests. They do not stay in the gradebook.
Test results (Summative Assessments) replace your entry ticket scores.
* One of the most valuable things you can do before Friday's test is to look at PowerSchool's Unit 2 Formative Assessment scores. For those Unit 2 Scores < 3, spend extra time reviewing the notes, CYUQs, etc.
A
Vocabulary
Distance: an amount of space between two things
Direction: a course along which someone or something moves
A
Summarize
Today you will receive the graphic organizer:
Complete each box by adding notes, examples, and annotations (notes that explain what is happening in your examples). Refer to your notes, CYUqs, entry tickets, vertical collaboration, Google Search, etc. Work together. Help each other.
You may use the notes you make on this graphic organizer during the test (nothing else).
A
Class Info
Test moved from tomorrow to Monday
A
Reminder
Somewhere on the graphic organizer, be sure to add the inequality symbols and words:
< less than
> greater than
Also, add a double number line example. I think it will be helpful!
A
Knowledge Application
Today, you will design your own amusement park.
Most of your work will be done on a coordinate grid.
A
Prepare
Take out your notebook and something to write with. One person, per pair of students needs a laptop. Click the link below.
Use your own notebook to show your thinking and to do your work. Work together.
C If you get stuck, use your graphic organizer.
When finished, review your thinking and correct any mistakes you made.
A
Continue
If you haven't finished your Unit 2 Graphic Organizer, work on that today! You want to be able to read and review it a few times this weekend (to prepare for Monday's test).
A
Continue
Continue working on Steps 4 and 5 of your "Welcome to My Theme Park" Project.
* I changed the directions for these steps. Please open the assignment in Google Classroom > Classwork to see the changes. Also, review my example to see how I did it for my project.
A
Test
Unit 2
A
Test Directions
Take out your Chromebook and something to write with.
DO NOT SIGN IN TO YOUR CHROMEBOOK. If you are signed in, sign out.
Click the Apps in the bottom left corner > Pear Assessment > Login with Google (sign in with your FCUSD email @student.fcusd.org)
Sign in again with @student.fcusd.org and your password > Continue
If you would like, you may use your graphic organizer. No phones, smart watches, or other electronic devices.
I will provide a piece of scratch paper. Please write your name on it. You will get it back tomorrow. DO NOT REWRITE EVERY PROBLEM. Just use the scratch paper when you need it.
Click Start Assessment to begin the U2 Test.
When finished, put your scratch paper (with your name on it) and graphic organizer in the basket in the BACK. You may read (Sora), draw, write, work on an assignment, or rest. Do not talk.
A
Were you absent yesterday?
Please raise your hand to let me know!
A
Continue
Today we will finish the Unit 2 Summative Assessment. Please take out something to write with (preferably pencil). Take everything else off or your desk.
A
Wrap-up
This is the day to finish your AWESOME theme park projects! I've updated steps 4 and 5, so let's review the revised directions now.
A
Follow up
A
Were you absent yesterday?
Please raise your hand to let me know!
A
Celebrate
After reviewing your tests, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
A
Test Corrections
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Find someone whose correctly answered a question you missed. Discuss. Ask questions. Think. Don't copy.
2. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
3. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.
A
Review
The essential standards for Unit 2 are Targets 3 and 5.
Data for T3 came from questions 8 and 9 on the Pear Assessment (computer test) and the 4 question pencil and paper test.
Data for T5 came from questions 13 and 14 on the Pear Assessment (computer test) and the 4 question pencil and paper test.
Check PowerSchool to see the proficiency level your work demonstrated.
Why, How, and What
In order to make sense of the world (DI1), students will model with mathematics (SMP4), attend to precision (SMP6), and construct viable arguments and critiquing the reasoning of others (SMP3) while discovering shape and space (CC4)
Description
Students experience absolute value on number lines and relate it to distance, describing relationships, such as order between numbers using inequality statements. (p34)
Standards
- 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
- 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
- 6.NS.7 Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.
- 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
- 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
- 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
- 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
- 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
- Source:
- 2013 CACC Math Content Standards
T1
Direct Instruction
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.
T1
Vocabulary
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
T1
Try it
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)
T1
Direct Instruction
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?"
T1
Try it
What is the opposite of -25?
What is the opposite of 14?
|36|
|-8|
|5| + |-8|
|-12| + |-4|
|15| - |-6|
|-2| - |-9|
T1
My Responsibilities
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
T1
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T1
Entry Ticket (5 min)
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.
T1
Direct Instruction
-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
T2
Launch
On a number line showing a drive from San Francisco to Los Angeles, a landmark in San Jose would be a dot at approximately 50 miles, while a landmark near Bakersfield might be a dot at 250 miles.
We could use these two dots on the number line to answer the question, "What is the distance between Gilroy and Bakersfield on this number line?"
Draw a line with arrows. If I want to put 50 and 250 on it, do I need negative numbers? Do I need 0? What do I need? Next, change the numbers to 4 and 9. Ask, what numbers do I need? Show starting with 4, numbering by 1s up to 9. Then ask the distance and have students share both ways.
To foreshadow, write: d =
T2
Vertical Collaboration
There are two houses, one on 15 and one on 8. Graph the numbers on a number line. Then find the distance between the two whole numbers.
There are two houses, one on 36 and one on 45. Graph the numbers on a number line. Then find the distance between the two integers.
There are two houses, one on 3 and one on -5. Graph the numbers on a number line. Then find the distance between the two integers.
Graph 7 and -2 on a number line. Then find the distance between the two integers.
Graph -1 and -4 on a number line. Then find the distance between the two integers.
Graph -15 and -24 on a number line. Then find the distance between the two integers.
Graph -92 and -103 on a number line. Then find the distance between the two integers.
T2
Consolidation
There are two ways to find the distance between two numbers (a and b)
One way:
Make a number line and count the number of spaces between the two points (a and b)
* Pro tip: only make a number line for the numbers you are graphing. When you can, go by 1's (makes it easier to count)
Another way:
1. Subtract one number from the other (find the difference). You can subtract a from b, or b from a; the order doesn't matter.
2. Find the absolute value of the difference
T2
Warmup
Do the following two problems in your notebook:
1. Graph 15 and 8 on a number line. Then find the distance (d) between the two whole numbers.
2. Graph 3 and -5 on a number line. Then find the distance (d) between the two whole numbers.
T2
Discussion
To find distance:
We can count spaces (always works)
Subtract and find the absolute value of the difference of the two numbers (always works)
Adding the absolute value of the two numbers works SOMETIMES but not always... so be careful if you want to use this
T2
Summarize
There are two ways to find the distance between two numbers (a and b)
One way:
Make a number line and count the number of spaces between the two points (a and b)
* Pro tip: only make a number line for the numbers you are graphing. When you can, go by 1's (makes it easier to count)
Another way:
1. Subtract one number from the other (find the difference). You can subtract a from b, or b from a; the order doesn't matter.
2. Find the absolute value of the difference
T2
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
A. Graph 13 and 6 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
B. Graph 36 and 24 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
C. Graph 7 and -2 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
D. Graph -8 and 5 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
E. Graph -7 and -1 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
F. Graph -5 and -13 on a number line. Count to find the distance (d) between the two numbers. Then subtract to show that your answer is correct.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T2
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T2
Entry Ticket (5 min)
On the blank side, write: First name, last name, U2T2
Graph 6 and -4 on a number line. Then find the distance between the two numbers. Write d=
T3
Launch
Draw a number line 0-1, break it into fifths. Label 0 1nd 1. Graph 1/5 and label it A (don't write 1/5). Ask students what number A represents. Label 1 2/5 as B (but don't write the number). Discuss.
Reminders:
Draw a visible dot on the number line to represent the number
If your number line doesn't have the number you graphed, write the number above or below the dot
T3
Vertical Collaboration
Sketch the number line. Then graph each of the three rational numbers:
Student solutions:
T3
Direct Instruction
All 'rational numbers' can be represented by a point on a number line.
Rational number: any number that can be written as a fraction (ratio) -- denominator is not zero
Integer: a whole number that can be positive, negative, or zero. Examples include -3, 0, and 7.
T3
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Click the link below. Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
Answers:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T2
Glue & Review
T3
Guided Practice
Let's make some number lines with rational numbers on them
T3
Extend
What is the value of each point if?
For each number line, start with what is given (one of the points). Use that to figure out the interval. Fill in as many tick marks as you need, then write A=, B=, C=, D=
Check answers as you're working:
A
Thursday is a Retake Day
To retake a summative assessment score in
PowerSchool that is less than 3:
1. Go to Google Classroom > Classwork. Scroll down to
find the student responsibilities for the unit and target
you are looking for (e.g. U1T1 Student Responsibilities)
2. Click View Instructions. Review the notes. Do the
CYUQs (to a level 3 or better) and check answers as
you’re working.
3. If you get stuck, review your thinking, try different
approaches, ask for help, and/or search.
4. Bring your Level 3 CYUQs to a retake day and trade
me for a retake
T3
Discuss (2 min)
After completing yesterday's extend activity, which questions were challenging? Which ones were easy?
* Please fold this in half and glue it into your notebook. It's okay that some questions will be glued.
T4
Launch
In life we say words like "Less than" or "More than" and at some point, some smart math person said, "Let's save some time and replace those words with symbols." And in addition to being able to use these symbols to compare things, now people use them when doing math, writing code, and more.
3.6 oz > weight of a letter (to mail)
spending < income
15 > 2
And we can use what we learned about number lines to prove it!
Dismiss them having them say to each other, "The bigger number is always on the right."
T4
Direct Instruction
Inequalities are symbols that are use to compare numbers.
Less than uses the symbol <
Greater than uses the symbol >
* When comparing numbers, use a number line to show your thinking and prove your answer
* The number on the right (on a number line) is ALWAYS the bigger number
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help.
For each problem, sketch a horizontal or vertical number line to prove your answer: p369: 15, 16, 17, 18, 19, 23; p367: 1, 2, 3, 4, 5 (Volume 1, Ch5-3)
Check answers while you are working:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T4
Reminder
* When comparing rational numbers, remember to use a number line to prove your answer.
* The number on the right (on a number line) is ALWAYS the bigger number
T4
Consolidation
Three ways to compare fractions with different size pieces (denominators):
1. Double number line -- a double number line has two number lines, one above the other, with the same starting and ending numbers but different intervals (spacing)
2. Area models (using rectangles) -- one directly above the other
T4
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. Check answers as you’re working. If you make a mistake, fix it. If you need help, get help. If someone else needs help, give help. * Pro tip - DO NOT rotate your paper today
Click the link below to see the questions:
Answers:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
A
Retake Day
A
Retake or Prepare (35min)
Trade your CYUqs for a retake.
If unprepared, open PowerSchool and review your progress. If you have a goal that is less than 3, do the CYUqs (at a level 3) and prepare for retaking. When ready, trade me. Repeat this process until your goals are all 3's or better.
If your goals are all 3's or better OR you are done retaking, practice and review the math we are currently working on by signing into Delta Math > click Login > Sign in with Google > with your school Google Account > Fractions on the Number Line
T4
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Direct Instruction
Start 1:22. Stop at 4:40 (before learning how to plot). B. Start again at 6:38-8:25 for how to plot an ordered pair. C. Continue until 10:13 for information on the four quadrants.
T5
Summarize
The coordinate plane is made up of an X and Y-axis
The X-axis is a horizontal number line.
The Y-axis is a vertical number line.
The X and Y-axis cross at the origin (0,0)
An ordered pair (x, y) is an 'address' on the coordinate plane.
T5
Summarize
To graph a point on the coordinate plane:
1. Start at the origin (0,0)
2. Move left or right on the X-axis (depending on whether the x value is positive or negative). Stop when you are on the x-value.
3. Next, move up or down (depending on whether the y value is positive or negative). Stop when you are on the y value and make a dot.
T5
Guided Practice
Graph and label the ordered pairs:
A: (4, -1)
B: (2, 3)
C: (-3, 2)
T5
Summarize
The two axes create four quadrants that are numbered with Roman Numerals -- counterclockwise.
The signs of the rational numbers in an ordered pair tell you which quadrant the point will be located in:
(1, 1) is in QI; (-1, 1) is in QII; (-1, -1) is in QIII; (1, -1) is in QIV
T5
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. If you need help, get help. If someone else needs help, give help. Graph and label the following ordered pairs:
A. (3, 2)
B. (-5, -3)
C. (-2, 5)
D. (3, -1)
E. (-4, 1)
F. (1, -2)
G. (-2, -2)
H. (1, 4)
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
A
Great job!
After reviewing your assessments, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
PowerSchool is up to date. You can see how your work yesterday impacted your progress toward your goals.
If you weren't able to show me you understood (score < 3), please read the comments.
You are welcome to try again. But this time, you must make a poster that teaches someone how to do the learning target you are working on. If you need help, ask for help!
T4
Entry Ticket (5 min)
Use the blank side. On top, write your first name, last, and U2T4
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Real-world Connection
T5
Explore
T5
Direct Instruction
To identify the location of a point (x, y) on the coordinate plane, start at the origin (0,0).
1. Move left OR right on the x-axis and stop above or below the point. Write down the x-value.
2. Move up OR down (parallel to the y-axis) and stop at the point. Write down the y-value.
T5
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → Do in your notebook. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
p399: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; p401: 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 (Volume 1, Ch5-6)
p407 1, 2, 3, 4, 5, 6, 7, 8 (Volume 1, Ch5-7)
Check answers as you’re working. If you make a mistake, fix it.
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T4
Glue & Review
U2T4 Entry Ticket
T5
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T5
Entry Ticket (5 min)
At the top, write: First name, last name, U2T5
Graph and label the following:
A (3, -2)
B. (-1, -4)
C. (-3, 5)
D. (4, 2)
T6
Guided Practice
Find the distance between the two points:
A. (-2, 5) and (3, 5)
B. (4, -3) and (4, 6)
C. (-3, -4) and (-3, -1)
D. (4, -1) and (-8, -1)
T6
Summarize
IF two points share an x value,
you can find the distance between the points with either method:
1. Graph and count
2. Subtract the y-values (find the difference) and then find the absolute value of the difference
* Works for shared y-values too (just be sure to subtract the x-values)
T6
My Responsibilities
1. In your notebook, make meaningful notes for your forgetful selves
2. CYUqs → When needed, show your thinking in your notebook. You chose where you want to start. If you need help, get help. If someone else needs help, give help.
Sign into Delta Math > click Login > Sign in with Google > with your school Google Account > U2T6 CYUQs
* If you come to a question that references a triangle, ignore the triangle part and focus on the two ordered pairs (points) that belong to the line (segment). See image:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
T6
Discuss (2 min)
After completing the Check-your-understanding Questions, which were important for everyone to do?
T6
Review
Find the distance between the two points:
A. (-20, 3) and (-20, -6)
B. (-9, 16) and (31, 16)
T6
Challenge
Find the distance between two points:
1. El Dorado Hills is 768 feet above sea level. Folsom is 220 feet above sea level. What is the distance (in elevation) between the two cities?
2. A building sits 25' above sea level. If a submarine is 30' below sea level. How much higher is the building than the submarine?
A
Class Info
Unit 2 Test is Monday 9/29
A
Class Info
Entry Tickets vs. Tests
Entry tickets (Formative Assessments) are given after studying a learning target. They provide feedback and help you know if your learning strategies are working. They are an opportunity to know where you are before you take a test. Entry tickets get replaced by tests. They do not stay in the gradebook.
Test results (Summative Assessments) replace your entry ticket scores.
* One of the most valuable things you can do before Friday's test is to look at PowerSchool's Unit 2 Formative Assessment scores. For those Unit 2 Scores < 3, spend extra time reviewing the notes, CYUQs, etc.
A
Vocabulary
Distance: an amount of space between two things
Direction: a course along which someone or something moves
A
Summarize
Today you will receive the graphic organizer:
Complete each box by adding notes, examples, and annotations (notes that explain what is happening in your examples). Refer to your notes, CYUqs, entry tickets, vertical collaboration, Google Search, etc. Work together. Help each other.
You may use the notes you make on this graphic organizer during the test (nothing else).
A
Class Info
Test moved from tomorrow to Monday
A
Reminder
Somewhere on the graphic organizer, be sure to add the inequality symbols and words:
< less than
> greater than
Also, add a double number line example. I think it will be helpful!
A
Knowledge Application
Today, you will design your own amusement park.
Most of your work will be done on a coordinate grid.
A
Prepare
Take out your notebook and something to write with. One person, per pair of students needs a laptop. Click the link below.
Use your own notebook to show your thinking and to do your work. Work together.
C If you get stuck, use your graphic organizer.
When finished, review your thinking and correct any mistakes you made.
A
Continue
If you haven't finished your Unit 2 Graphic Organizer, work on that today! You want to be able to read and review it a few times this weekend (to prepare for Monday's test).
A
Continue
Continue working on Steps 4 and 5 of your "Welcome to My Theme Park" Project.
* I changed the directions for these steps. Please open the assignment in Google Classroom > Classwork to see the changes. Also, review my example to see how I did it for my project.
A
Test
Unit 2
A
Test Directions
Take out your Chromebook and something to write with.
DO NOT SIGN IN TO YOUR CHROMEBOOK. If you are signed in, sign out.
Click the Apps in the bottom left corner > Pear Assessment > Login with Google (sign in with your FCUSD email @student.fcusd.org)
Sign in again with @student.fcusd.org and your password > Continue
If you would like, you may use your graphic organizer. No phones, smart watches, or other electronic devices.
I will provide a piece of scratch paper. Please write your name on it. You will get it back tomorrow. DO NOT REWRITE EVERY PROBLEM. Just use the scratch paper when you need it.
Click Start Assessment to begin the U2 Test.
When finished, put your scratch paper (with your name on it) and graphic organizer in the basket in the BACK. You may read (Sora), draw, write, work on an assignment, or rest. Do not talk.
A
Were you absent yesterday?
Please raise your hand to let me know!
A
Continue
Today we will finish the Unit 2 Summative Assessment. Please take out something to write with (preferably pencil). Take everything else off or your desk.
A
Wrap-up
This is the day to finish your AWESOME theme park projects! I've updated steps 4 and 5, so let's review the revised directions now.
A
Follow up
A
Were you absent yesterday?
Please raise your hand to let me know!
A
Celebrate
After reviewing your tests, I see that EVERYONE has been working hard and doing their best. The time you are spending thinking and working together is paying off. I am proud of YOU.
A
Test Corrections
The most important part of the test happens right now: reviewing your work and learning from mistakes.
1. Find someone whose correctly answered a question you missed. Discuss. Ask questions. Think. Don't copy.
2. On your corrections worksheet, neatly rewrite the problem, show your thinking, and circle the correct answer.
3. Before moving to the next problem, write down your mistake and what you will do to not make that mistake again.
A
Review
The essential standards for Unit 2 are Targets 3 and 5.
Data for T3 came from questions 8 and 9 on the Pear Assessment (computer test) and the 4 question pencil and paper test.
Data for T5 came from questions 13 and 14 on the Pear Assessment (computer test) and the 4 question pencil and paper test.
Check PowerSchool to see the proficiency level your work demonstrated.