Download Unit 1 Notes - Jefferson School District

Name: _______________________________________________________ Date: ______________ Pd: ____
Make sure your handwriting can be read. Complete all work in PENCIL.
Unit 1: The Number System
Math in Careers: Read page 1 of your textbook. Then fill in the blanks below.
Career: ________________________________________________________________________
1. ______________________ perform cost-benefit analysis of projects, use ________________
and ____________________ when they design the layout of infrastructure, and use
____________________ and mathematical _______________ to predict the growth and
future needs of a population. (page 1)
2. If you are interested in this career, you should take these four math classes: (page 1)
a. ____________________________________
b. ____________________________________
c. ____________________________________
d. ____________________________________
Write down the three modules that are covered in Unit 1. (page 1)
1. Module 1: _________________________________________________________________
2. Module 2: _________________________________________________________________
3. Module 3: _________________________________________________________________
Unit Project Preview (pg 2)
Use complete sentences to answer the questions below.
1. What is a real-life situation in which you would add two negative numbers?
___________________________________________________________________________
___________________________________________________________________________
2. What is a real-life situation when you would multiply two negative numbers?
___________________________________________________________________________
___________________________________________________________________________
3. What is a real-life situation when you would divide a negative integer by a positive integer?
___________________________________________________________________________
___________________________________________________________________________
Complete problems 1 and 2 on page 2 of your textbook.
1
Name: _______________________________________________________ Date: ______________ Pd: ____
Write down the Domains and Clusters that are covered in this Unit. (page 2)
1. Domain: ___________
a. Cluster
__________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
2. Domain: ___________
a. Cluster
__________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
Are You Ready (page 4)
Be sure page 4 #1-12 is done and leave in your textbook.
Reading Start-Up (page 5)
Complete the Reading Start-Up on page 5 in your textbook. Leave it in your textbook.
Vocabulary for this Unit
Absolute value
Expression
Positive number (integers)
Additive inverse
Integers
Product
Complex fraction
Model
Rational number
Difference
Negative number (integers)
Repeating decimal
Divide
Operation
Sum
Dividend
Opposites
Terminating decimal
Divisor
Pattern
Whole number
2
Name: _______________________________________________________ Date: ______________ Pd: ____
Module 1:
EQ:
_____________________________________________________
___________________________________________________________________________
___________________________________________________________________________
Watch the Real-World Video then answer the EQ.
Answer:
___________________________________________________________________________
___________________________________________________________________________
Scan the module. List the four topics you will learn in this module. (page 3)
1) ____________________________________________________________________________________
2) ____________________________________________________________________________________
3) ____________________________________________________________________________________
4) ____________________________________________________________________________________
Vocabulary for this Module
 Complete the “Reading Start-up” from page 5 in your textbook. Do not tear it out.
 Write a brief definition for each word.
Absolute value - _______________________________________________________________
Additive inverse - ______________________________________________________________
Difference - ___________________________________________________________________
Expression - __________________________________________________________________
Integer - _____________________________________________________________________
Graph - ______________________________________________________________________
Model - _______________________________________________________________________
Negative integer (number) - ______________________________________________________
Positive integer (number) - ______________________________________________________
Sum - ________________________________________________________________________
Whole number - _______________________________________________________________
Zero pair - ____________________________________________________________________
3
Name: _______________________________________________________ Date: ______________ Pd: ____
Lesson 1.1 - _____________________________________________________
Make sure your handwriting can be read. Answer all questions using complete sentences.
Standard
7.NS.1
Apply and extend previous understanding of addition and subtraction to
add and subtract rational numbers, represent addition and subtraction
on a horizontal or vertical number line diagram.
EQ
What You’ll Learn: Scan the lesson. List three headings you would use to make an outline of the lesson.
1) ________________________________________________________________________________ (p7)
2) ________________________________________________________________________________ (p8)
3) ________________________________________________________________________________ (p9)
Review of Prior Knowledge
Answer each question true or false. Prove your answer correct or provide a counterexample. Answer using complete sentences.
1. Subtraction of whole numbers is associative.
2. Division of whole numbers is commutative.
Matching. Match each example on the left to the correct property on the right. Place
the letter of the correct answer on the line next to the example.
3. 5 ∙ 3 ∙ 2 = 3 ∙ 5 ∙ 2
_____
A)
Additive Identity
4. 5 + (3 + 2) = (5 + 3) + 2 _____
B)
Associative Property
5. 5(3𝑥 − 4) = 15𝑥 − 20
_____
C)
Commutative Property
6. 4𝑎 + 0 = 4𝑎
_____
D)
Distributive Property
7. 4𝑎 ∙ 0 = 0
_____
E)
Multiplicative Identity
8. 4𝑎 ∙ 1 = 4𝑎
_____
F)
Multiplicative Property of Zero
Solve. Show each step of your work. Circle your final answer.
9. 12 + (36 ÷ 32 )
10. 30 − 2[4 + (9 ÷ 3)]
4
Name: _______________________________________________________ Date: ______________ Pd: ____
Given Notes
integers – all whole numbers and their opposites
… -3, -2, -1, 0, 1, 2, 3 …
absolute value – the distance between the number and 0, ALWAYS POSITIVE…how far the
number is from zero
symbol -- │x │
│5 │ = 5
│-5 │ = 5
│1.2 │ = 1.2
│-1.2 │ = 1.2
opposites – two numbers that have the same absolute value but have different signs…the
positive and negative of a number
5 and –5 are opposites
½ and –½ are opposites
Modeling Sums of Integers with the Same Sign
You can use colored counters to add positive integers and negative integers.
= a positive integer (yellow)
= a negative integer (red)
(See Explore Activity 1 on page 7)
You Try
Model with two-color counters.
1. 1 + 4
2. −2 + (−4)
Adding on a Number Line
Just as you can add positive integers on a number line, you can add negative integers.
Use a number line to add 2 + 3.
Steps:
1) Mark the initial term on the number line with a dot. Label the point
2) Count on the number line to find the final answer. Place a dot there. Label the point.
3) Draw a line from the initial dot to the final dot.
4) Label the line with the second term.
5
Name: _______________________________________________________ Date: ______________ Pd: ____
Use a number line to add -2 + (-3).
1) Mark the initial term on the number line with a dot. Label the point
2) Count on the number line to find the final answer. Place a dot there. Label the point.
3) Draw a line from the initial dot to the final dot.
4) Label the line with the second term.
You Try.
Use a number line to find each sum. Show your work.
1. 1 + 4
2. −2 + (−4)
(See Explore Activity 2 on page 8)
Adding Integers with a Common Sign (Example 1)
Rule: If the signs are the same, add the integers and keep the common sign.
5+3=8
6+2+1=9
-5 + -3 = -8
-6 + (-2) + (-1) = -9
You Try.
1. Add −𝟗 + (−𝟖).
2. Add 𝟏 + 𝟒.
3. Add −𝟕 + (−𝟕).
(see Explore Activity 2 on page 8)
6
4. Add 𝟏𝟐𝟎 + 𝟕𝟓