Supporting Your Student Homework Help: If your student is having trouble with a homework problem. Recommend that they utilize the Homework Help feature on the online textbook. 1-81. Rewrite each expression below without negative or zero exponents. Homework Help N a. 4 -1 7 ° x -2 Each homework help may either provide a hint, define a term, or re-direct you to review a similar problem that they have already completed in the course. Preparing for Tests: Tests are composed of both new materials from the unit, as well as material from previous units and courses of study. Generally, students can expect that the questions based on previous units may be more difficult than the questions related to the newer material since the student has had more time to practice the material. While preparing for an individual test, students should always review any study guides the teacher has provided and the chapter closure questions carefully. In addition, it may be helpful for students to look over the Parent Guide for that unit. This is available without a log in on the Parent Support page. When your Student has an Extended Absence: It is often difficult for students in any class to catch up after an illness that has kept them out of school for more than a day or two. Although the in class work is exempt when a student is absent, I would recommend that absent students still review the missed class work and ask their team or the teacher if they have any questions. Absent homework should be made up. Students can coordinate with the teacher to determine a deadline for absent work when the absence is more than a day or two. The parent guide is also helpful for catching up absent students because it outlines the key ideas, and provides additional practice. Check Points: The CPM program understands that students do not always develop a skill to a level of mastery immediately. Students are introduced to concepts that they will not be expected to have completely mastered until later units. In order to make sure that students are developing skills at the expected rate, the book provides checkpoints. If a student reaches a checkpoint, and they do not feel confident with their ability to complete that skill, they should find time to work with the teacher on that skill.
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Supporting Your Student
Homework Help:
If your student is having trouble with a homework problem. Recommend that they utilize the Homework
Help feature on the online textbook.
1-81. Rewrite each expression below without negative or zero exponents. Homework Help N
a. 4-1
7°
x-2
Each homework help may either provide a hint, define a term, or re-direct you to review a similar
problem that they have already completed in the course.
Preparing for Tests:
Tests are composed of both new materials from the unit, as well as material from previous units and
courses of study. Generally, students can expect that the questions based on previous units may be
more difficult than the questions related to the newer material since the student has had more time to
practice the material.
While preparing for an individual test, students should always review any study guides the teacher has
provided and the chapter closure questions carefully. In addition, it may be helpful for students to look
over the Parent Guide for that unit. This is available without a log in on the Parent Support page.
When your Student has an Extended Absence:
It is often difficult for students in any class to catch up after an illness that has kept them out of school
for more than a day or two. Although the in class work is exempt when a student is absent, I would
recommend that absent students still review the missed class work and ask their team or the teacher if
they have any questions. Absent homework should be made up. Students can coordinate with the
teacher to determine a deadline for absent work when the absence is more than a day or two. The
parent guide is also helpful for catching up absent students because it outlines the key ideas, and
provides additional practice.
Check Points:
The CPM program understands that students do not always develop a skill to a level of mastery
immediately. Students are introduced to concepts that they will not be expected to have completely
mastered until later units. In order to make sure that students are developing skills at the expected rate,
the book provides checkpoints. If a student reaches a checkpoint, and they do not feel confident with
their ability to complete that skill, they should find time to work with the teacher on that skill.
How to Find Additional Parent Resources:
Go to cpm.org. Then, use the Support tab to find Parent Support.
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This parent support page gives you more information about how to help your student progress through
the course. One particularly helpful feature is the parent guide which is organized by chapter. To view
the parent guide, scroll down the page and select INT1:Parent Guide. I have included the parent guide
for unit 1 so that you can review it and determine if these may be something that is useful to you and
your student.
The Parent Guide provides an alternative explanation of key Ideas along with aantonal practice problems. The Parent Guide
resources are an r , 1/ chapter and strand. The Parent Guide Is edso avallabte as a printed copy for purchase attire CPM Web
Store or accessible free beicAv.
Core Connections (English) Core Connections (Espanol) Connection Series
C:Cl: Parent Guide Ca: Gufa pare pall Js on practice adicional MCt Pa nt Guide
CC2:Parent Guide CC.Z Gula pans padres con practice adicionat MC2: Parent Guide
CC3:Parent Guide CC3: Gufa pare padres con practice acticional AC Parent Guide
CCA: Parent Guide CCA: Gila pare padres con practice adicional CAC Parent Guide
CCG: Pc rent Guide CCG: Gate pare padres con practice adicionat GC Parent Guide
CCA2Lect Guide CCA2: Gufa pate padres con practice adtclonal A2C Parent Guide
Parent Gulc.) Cat Gina pare padres con practice adicional
INT2: Parent Guide INT2: Gin pare padres con practice acliclonal
INT1 Potent Guide ma Gula pare padres con practice adiclonat
>. Core Connections Integrated 1 textbook (each student will be issued
one textbook for the school year)
> Online textbook through the Student eBook (https://sso.cpm.ore)
o Students will be given an enroll code
o Students will have a login and password
> Course Overview and Resources (http://cpm.oreint1)
o Introduction, Course Contents, Lesson Structure
o Homework Help Tool
o Parent Guide with Extra Practice
STUDY TEAM ROLES
Recorder/Reporter:
✓ Team spokesperson, shares findings
✓ Ensures each member records data
,( Reminds team to write down HW
Resource Manager
,7 Collects/returns team's supplies
✓ Calls teacher over for team questions
✓ Debriefs any absent teammates
Facilitator:
✓ Starts conversation for each task
✓ Ensures understanding of directions
✓ Organizes/assigns the team for the task
Task Manager:
✓ Enforces use of classroom norms
✓ Ensures task is completed on time
✓ Stops off task conversation
COURSE CONTENTS
0 Functions
Appendix A: Solving Equations
0 Linear Functions
0 Transformations & Solving
0 Modeling Two-Variable Data
0 Sequences
0 Systems of Equations
O Congruence & Coordinate Geom.
0 Exponential Functions
® Inequalities
O Functions & Data
0 Constructions & Closure
IN-CLASS EXERCISES are the bulk of the daily math
lessons. These exercises require students to work
with their "Study Teams" in a collaborative manner.
Each student is responsible to record their exercise
math data in their notebooks each day. Notebooks
will be evaluated throughout the course of the year.
"Notebook Checks" are unannounced to check on
the students' mathematical evidence and effort
from the in-class exercises. "Notebook Checks" may
be done individually, as a group, or one notebook
could be collected for the group. Groups are
responsible for making sure that all group members
are on track, completing the work, and recording
the groups work.
MATH NOTES are a designated area in the
fThOAND MENNS textbook at the end of each MATH N.Ttt? lesson that consolidate core
content ideas and provide definitions, explanations,
examples, instructions about notation,
formalizations of topics, and extensions or
applications of mathematical concepts. Students are
expected to copy the math notes in their notebooks.
HOMEWORK has been carefully designed to offer
students spaced practice with past material and to
help lay a foundation for future learning. Homework
for this course is identified with a "Review and
Preview" icon.
• All assignments are to be completed in a graph
composition, spiral notebook, or organized in a
binder. Work should be done in pencil.
• Title assignments: Section #, HW #, Exercise #'s
(Example: /-/-/ HW #1: 1-6 through 1-10)
• Each exercise must be completed with written
mathematical evidence and quality effort.
• Students must check their HW each night and
write correct solutions with a colored PEN next
to each problem (HW solutions are found on
classroom webpage).
• The online textbook offers homework help.
CHECKPOINTS are key homework problems
identified for determining if students are building
skills at the expected level. When students find that
they need help with these problems, worked
examples and practice problems are available in the
"Checkpoint Materials" at the back of their book.
CLASSROOM WEBPAGE contains the homework
calendar link, notes, and other pertinent resources.
http ://weage 17 . wiki s .birmingham k 1 2.mi .us/home
ENGAGE. INTERACT. PRACTICE. SMILE. SUCCEED.
LATE ASSIGNMENTS will be awarded partial credit
only and a late mark will appear in PowerSchool. An
assignment is considered late if it is not present in
the classroom when it is due. Students will not be
permitted to leave during class to collect an
assignment.
ABSENCE POLICY is that if a student is absent, they
are responsible for communicating with their Study
Team regarding classwork (it would be wise to
collect group contact info). Absent
assignments/assessments will show up as missing
and no points will appear inPowerSchool until they
are completed. Students are allowed two class
periods for each excused absence to make-up work
that was assigned on the day of an excused
absence. The return day is considered the first class
period. Students are required to submit any work
that was previously assigned and due on the day of
their excused absence on the day of their return.
Students who have an excused absence on the day
of a quiz or test will be required to make up that
quiz or test. Any assessment missed due to an
excused absence should be made up the following
day. Students who have an excused absence on a
Team Performance Task day are exempt from
completing the in class assignment. Optionally, the
student may arrange to make up the Team
Performance Task individually, if desired.
GRADING CATEGORIES are Homework (10%)
Teamwork (10%), Team Performance Tasks (10%),
93-100% A 83-87.996 B 73-773% C 63-673% and Individual Assessments (70%). 90-92.9%A- 80-823% B- 70:72.9%C- 60-62.9% D-
Extra Credit will not be provided. 88-89.9% B+ 78-79396 C+ 68-693% 13+ 59.996 & below
TYPES OF ASSESSMENTS
Team Performance Tasks: Students will complete these assessments in their study teams during a class
period. The teacher will randomly pick one group members work to score and return to the team for review.
Team Performance Tasks will be administered several days prior to the Individual Assessment. Study teams
should use the feedback from the Team Performance Task to prepare for the Individual Assessment.
Individual Assessments: Individual Assessments are announced approximately a week in advance and are
given the week following the end of a unit. In the meantime, the class will begin work on the next unit,
allowing students time to prepare for the individual test. Since we will have begun the next unit, students will
be expected to take the test on the previous unit on the day it is given, unless otherwise arranged with the
teacher in advance due to extenuating circumstances. While Individual Assessments will be spaced out
throughout the year following the closure of a unit, the Individual Assessments will essentially all be
cumulative. The Individual Assessments will be composed of both new material from the most recently
completed unit, as well as previous learned material in about equal proportions.
Cell Phones and Music
Cell phones are allowed in the classroom and are to be used only when given permission from the teacher.
Please talk to me if you have an extenuating circumstance and need to make a phone call. DO NOT feel free to
listen to music unless I have said that it is appropriate to do so. Any electronic abuse will result in teacher
taking electronic away for the rest of the day.
Additional Help
Even the best students get stuck or confused. Remember that sometimes 5 or 10 minutes of individual help
makes all the difference in understanding and learning. Please do not wait until the day of a quiz or test to get
extra help! Rather, talk to me as soon as you begin having difficulties.
• Feel free to either arrange a time in person, or contact me via email to set up a time to work together.
• There is an abundance of information online that covers most topics we'll be studying!
• The online textbook has homework help for just about every problem.
After you have reviewed the course syllabus with a parent/guardian, please sign below and return to Ms.
Weage by Friday, September 8th. Please let me know if you have any questions. This syllabus will be posted
online if you need to review it throughout the year.
Looking forward to a great year!
Student Signature:
Parent Signature:
Chapter 1
DESCRIBING FUNCTIONS 1.1.2 and 1.1.3
The main objective of these lessons is for students to be able to fully describe the key elements of the graph of a function. To fully describe the graph of a function, students should respond to these graph investigation questions:
Graph Investigation Question Sample Summary Statement What is the shape of the graph? The graph is a line/curve.
Is the function increasing or decreasing (reading left to right)?
As x gets bigger, y gets bigger, so the function is increasing.
What are the x- and y-intercepts? The graph crosses the x-axis at (2, 0) and the y-axis at (0,-3).
Are there any limitations on the inputs (domain) of the equation?
Only positive values of x are possible. Zero is also possible.
Are there any limitations on the outputs (range) of the equation? (Is there a maximum or minimum y-value?)
The smallest y-value is 0. There is no maximum y-value.
Should the points be connected? The given situation only makes sense for integer inputs, so the points should not be connected.
The more formal concepts of function and domain and range are addressed in Lessons 1.2.2 and 1.2.3.
For more infoimation, see the Math Notes boxes in Lesson 1.1.2. Student responses to the Learning Log in Lesson 1.1.3 (problem 1-27) can also be helpful.
Example 1
For the situation below, make an x y table, draw a graph, and describe the graph.
At the farmer's market, apples cost $0.50 each.
Note that the smallest possible number for the x --> y table is x = 0. You cannot buy a negative number of apples.
x (# of apples) 0 1 2 4 6 10 y (cost) 0 0.50 1.00 2.00 3.00 5.00
The graph is a discrete set of linear points because you can only buys whole numbers of apples. It starts at (0, 0) and increases from left to right. The inputs are limited to positive integers, and the outputs are 0 and multiples of $0.50.
Parent Guide with Extra Practice
0 2014 CPM Educational Program. All rights reserved.
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1. _ x+4 Y - 2
3. y=2x+1
Example 2
For the equation y = 2.x -2 , make an x y table, draw a graph, and fully describe the graph.
At this point there is no way to know how many points are sufficient for the x y table. Add more points as necessary until you are convinced of shape and location.
-2 2 3 —1.75 -1.5 0 2 6
Be careful with substitution using negative exponents when calculating values. The negative exponent moves across the
fraction bar to become positive so 2-2 = . 2/-
For example if x = -2 , y = 2-2 - 2 = - 2 = - = -1.75 .
The graph is a curve. From left to right, the function increases. The x-intercept is (1,0) . The y-intercept is (0,-1) . The points on the graph are connected. There are no limitations on inputs to the function. Outputs can be any value greater than -2.
Problems
For each equation or situation, make an x y table, draw a graph, and describe the graph.
2. Gasoline costs $4.00 per gallon. How much does it cost to buy x gallons of gas?
4. My science experiment starts with 5 bacteria and each hour the amount doubles. How many bacteria are there after x hours?
5. y = 5 - 2x 6. The product of two numbers is 12.
7. y = (0.5)x 8. My tomato plant was 5 cm tall when planted and grows 2 cm per week. How tall is my tomato plant after x weeks?
Line; intercepts (-4, 0) and (0, 2); increasing function. Inputs can be any real number. Outputs are any real number. The points are connected.
cc!
1 1 1 1
—4-2 .— 2 4 # of hours
Curve; intercept intercept and starting point (0, 5); increasing function. Inputs can be any non-negative number. Outputs are greater than or equal to 5. The graph should be several disconnected points (but there are so many it will look connected).
A ray (proportional graph); intercept and starting point (0, 0); increasing function. Inputs can be any non-negative number. Outputs are greater than or equal to 0. The points are connected.
5.
Line; intercepts (2.5, 0) and (0, 5); decreasing function. Inputs can be any real number. Outputs are any real number. The points are connected.
Curve; intercept (0, 2); increasing function. Inputs can be any number. Outputs are greater than 1. The points are connected.
Inverse variation; no intercepts, decreasing function. Inputs can be any number except 0. Outputs are any number except 0. The points are connected except at x = 0.
Curve; intercept (0, 1); decreasing function. Inputs can be any real number. Outputs are greater than 0. The points are connected.
Ray; intercept and starting point (0, 5); increasing function; Inputs can be any non-negative number. Outputs are greater than or equal to 5 (but probably also less then or equal to 180).
U-shape; intercepts (2, 0), (-2, 0) and (0, —4); decreasing for x <0, increasing for x >0. Minimum value at (0, —4). Inputs can be any real number. Outputs are greater than or equal to —4. The points are connected.
A relationship between the input values (usually x) and the output values (usually y) is called a function if for each input value, there is no more than one output value. Functions can be represented with an illustration of a "function (input—output) machine", as shown in Lesson 1.2.3 of the textbook and in the diagram in Example 1 below. Note: f(x) = 2x+ 1 is equivalent toy = 2x + 1.
The set of all possible inputs is called the domain, while the set of all possible outputs is called the range.
For additional information about functions, function notation, and domain and range, see the Math Notes box in Lesson 1.2.3.
Example 1
The inputs of a function are "x"s and the outputs are "f(x)"s Numbers are input into the function machine labeled f one at a time, and then the function performs the indicated operation on each input to determine its corresponding output. For example, when x = 3 is put into the function machine f at right, the function multiplies the 3 by 2 and then adds 1 to get the corresponding output, which is 7. The notation f (3) = 7 shows that the function named f connects the input 3 with the corresponding output 7. This also means the point (3, 7) lies on the graph of the function.
inputs x = 3
f (x) = 2x +1
f (3) =7 outputs
Example 2
a. If f (x) = x — 2 then f(11) =? f (1 1) = V11— 2
f (11) =
f (11) = 3
b. If g(x) = 3— x2 then g (5) = ? g (5) = 3— (5)2
g(5) = 3-25
g (5) = —22
c. If f (x) = 2x:35 then f(2) = ?
f (2) =
f (2) = —5
4 Core Connections Integrated I
2014 CPM Educational Program. All rights reserved.
Chapter 1
Example 3
A relationship in which each input has only one output is called a function.
g(x) is a function; each input (x) has only one output (y). g (-2) = 1, g(0) = 3, g(4) = —1, and so on.
f (x) is not a function: each input greater than —3 has two y-values associated with it. f(i) = 2 and f(i) = —2.
Example 4
The set of all possible inputs is called the domain, while the set of all possible outputs of is called the range.
In Example 3 above, the domain of g(x) is —2 x 4 , or "all numbers between —2 and 4". The range of g(x) is —1 5_ g(x) 3 or "all numbers between —1 and 3".
The domain of f(x) in Example 3 above is x —3 or "any real number greater than or equal to 3," since the graph starts at x = —3 and continues forever to the right. Since the graph of extends in both the positive and negative y (vertical) directions forever, the range is "all real numbers".
Example 5
For the graph at right, since the graph extends forever horizontally in both directions, the domain is "all real numbers". The y-values start at y = 1 and increase, so the range is y 1 or "all numbers greater or equal to V.
10. Yes, each input has one output; domain is all numbers, range is —1 y 5 3
13. No; x = —1 has two outputs; domain is —4, —3,-1,0, 1, 2, 3, 4, range is —4,-3,-2, —1, 0, 1, 2
2. f(-6) = 8
5. g(-3) = 4
8. not possible
11. No, for example x = 0 has two outputs; domain is x —3, range is all numbers
14. Yes; domain is all numbers, range is y —2
3. f(9) = 4
6. not possible
9. f(4) = —16
12. Yes; domain all numbers, range is —3 5_ y 5 3
15. No, many inputs have two outputs; domain is —2 5_ x 5. 4 range is —2 5 y 5 4
Parent Guide with Extra Practice
C) 2014 CPM Educational Program. All rights reserved.
Example 1 (2xy3)(5x2y4
Reorder:
Using law (1):
Example 2 14x2y12
7x5y7
( 14
7
Using laws (2) and (5):
2.5.x-x2 .y3 -y4 Separate:
10x3y7
X2 r 12
,5 ,7 I
2y5 2x-3y- =
x3
LAWS OF EXPONENTS AND SCIENTIFIC NOTATION 1.3.1 and 1.3.2
Laws of Exponents
In general, to simplify an expression that contains exponents means to eliminate parentheses and negative exponents if possible. The basic laws of exponents are listed below.
Scientific notation is a way of writing very large and very small numbers compactly. A number is said to be in scientific notation when it is written as the product of two factors as described below.
• The first factor is less than 10 and greater than or equal to 1.
• The second factor has a base of 10 and an integer exponent.
• The factors are separated by a multiplication sign.
• A positive exponent indicates a number whose absolute value is greater than 1.
• A negative exponent indicates a number whose absolute value is less than 1
It is important to note that the exponent does not necessarily mean to use that number of zeros.
The number 5.32 x 1011 means 5.32 x 100,000,000,000. Thus, two of the eleven decimal places in the standard form of the number are the 3 and the 2 in 5.32. Standard form in this case is 532,000,000,000. In this example you are moving the decimal point eleven places to the right to write the standard form of the number.
The number 2.61 x 10-15 means 2.61 x 0.000000000000001. You are moving the decimal point to the left 15 places to write the standard form. Here the standard form is 0.00000000000000261.
For additional information, see the Math Notes box in Lesson 1.3.1.
Example 1
Write each number in standard form.
7.84x108 = 784,000,000 and 3.72x10 3 = 0.00372
When taking a number in standard form and writing it in scientific notation, remember there is only one digit to the left of the decimal point allowed.
Example 2
Write each number in scientific notation.
52,050,000 5.205x107 and 0.000372 = 3.72x10 4
The exponent denotes the number of places you moved the decimal point in the standard faint. In the first example above, the decimal point is at the end of the number and it was moved 7 places. In the second example above, the exponent is negative because the original number is very small, that is, less than 1.
Parent Guide with Extra Practice 11
C 2014 CPM Educational Program. All rights reserved.
Note: On your scientific calculator, displays like 4.35712 (or 4.357E12) and 3.65-3 (or 3.65E-3) are numbers expressed in scientific notation. The first number means 4.357 -1012 and the second means 3.65 -10-3 . The calculator does this because there is not enough room on its display window to show the entire number.