Please put your test corrections in the basket in the back. No need to turn in your test with them.

After attendance, we have an assembly. Please leave your backpacks in the classroom. When we return, you will get your backpack and go to 2nd Period.

Today is a quiet, individual work day. The goal is for you to review a topics from Unit 1.

Take out your Chromebook, math notebook, and something to write with.

Click the link below to go to go to Delta Math. The first step will be to create an account. Sign up with Google. Use your school Google Account. After you create it, you will need to close Delta Math and open it again, this time signing in with your school Google Account.

Open and complete the Unit 1 Review. Start with any one of the four topics. When finished, choose another. If you don't finish in class, spend up to 20 minutes at home -- but stop after that :-)

When needed, use your notebook and pencil to work out your thinking.

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.

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)

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|

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

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.

-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

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 =

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.

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

U2T1 Entry Ticket

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.

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

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

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

After completing the Check-your-understanding Questions, which were important for everyone to do?

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=

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

Sketch the number line. Then graph each of the three rational numbers:

Student solutions:

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.

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