Iredell-Statesville Schools
Integrated Math I
Core Plus - Course 1 Unit 3 Guide
Linear Functions
Using this guide:
It is the expectation that all teachers will have their classes complete all items listed in this guide, in the order in which it is presented, and completed in the labeled time frame. At the teacher’s discretion, additional examples, problems, assignments and assessments may be added to this guide.
In the rare instance in which an investigation has already been covered, the teacher should cover the same topic and remediate or extend the students’ learning in the same time frame.
We will be seeking feedback on the guide as we progress through the year.
Here is a little about the major sections in a lesson:
LAUNCH class discussion - (You should always read the Lesson Launch section in the Teacher’s Edition.)
Think About This Situation
The lesson launch promotes a teacher-led discussion of a problem situation and of related questions to think about. This discussion sets the context for the
student work to follow and helps to generate student interest. It also provides an opportunity for the teacher to assess student knowledge and to clarify
directions for the investigation to follow.
EXPLORE group investigation
Investigation
Classroom activity then shifts to investigating focused problems and questions related to the launching situation by gathering data, looking for and explaining patterns, constructing models and meanings, and making and verifying conjectures. As students collaborate in pairs or small groups, the teacher
circulates among students providing guidance and support, clarifying or asking questions, giving hints, providing encouragement, and drawing group members into the discussion to help groups collaborate more effectively. The investigations and related questions posed by students and teachers drive the learning.
SHARE AND SUMMARIZE class discussion (Excellent section that can be used to teach student how to write/explain answers in math.)
Summarize the Mathematics (STM)
This investigative work is followed by a teacher-led class discussion (referred to as Summarize the Mathematics) in which students summarize and explain the reasoning supporting mathematical ideas developed in their groups, providing an opportunity to construct a shared understanding of important concepts, methods, and approaches. This discussion leads to a class summary of important ideas or to further exploration of a topic if competing perspectives remain. Varying points of view and differing conclusions that can be justified should be encouraged.
APPLY individual tasks
Check Your Understanding (CYU)
Students are given a task to complete on their own to check and reinforce their initial understanding of concepts and methods.
Homework
In addition to the classroom investigations, Core-Plus Mathematics provides sets of On Your Own (OYO) tasks, which are designed to engage students in applying, connecting, reflecting on, extending, and reviewing their evolving mathematical knowledge. On Your Own tasks are provided for each lesson in the materials and are central to the learning goals of each lesson. These tasks are intended primarily for individual work outside of class. Selection of homework tasks should be based on student performance and the availability of time and technology. Also, students should exercise some choice of tasks to pursue, and, at times should be given the opportunity to pose their own problems and questions to investigate. The chart below describes the types of tasks in a typical On Your Own set.
(You will see this in the Unit’s Planning Guide, as an A,C,R,E, and R appear in from of the On Your Own Assignments)
Unit 3 Planning Guide (p. 149B)Linear Functions develops student ability to recognize and represent linear relationships between variables and to use tables, graphs, and algebraic expressions for linear functions to solve problems in situations that involve constant rate of change or slope.
Topics include linear functions, slope of a line, rate of change, modeling linear data patterns, solving linear equations and inequalities, and equivalent linear expressions.
NC Math I Standards covered in this unit:
Still working on this, but coming soon!
Lesson 1: Modeling Linear Relationships
Explore: Investigation / Topic Description / Share, Summarize and Apply / Time Frame
Investigation 1: Getting Credit (p. 151)
As a way to begin the discovery process, assign problems 1-4 to individual groups of students.
(If you have already taught a linear unit, then this investigation can be done by groups, with each group doing only one problem each, then presenting their problem to the class, or each group could put their problem on poster paper and then the students could gallery walk and see all the problems.)
All students should do 5 and 6.
If problems were assigned in groups, each group could present their problem, or you could choose one paper from each group to collect and check.(You can have students write the work, and then I draw a name of the person whose paper you will collect.)
(If you haven’t done linears in Foundations, then you must do the whole investigation.) / Introduction of slope and y-intercept
Describing slope as a rate of change in context of various situations
Make sure you use the forms
y=mx + b and y=b + mx / Note: Remember that this is the minimum required for each investigation. In most cases, you will have to add to these assignments to ensure students understanding and practice.
STM p.156 or CYU p.156
Note: Much of the learning is from the STM, so this must be discussed if it assigned for HW. / 1 day
Investigation 2: Symbolize It (p.157)
Complete all parts / Recognize linear equations when written in a different form
Write linear equations given two points
Students learn how to write linear equations in y=mx + b form by investigating tables, finding the rate of change and the y-intercept. Then this is applied to just a set of two points outside of context. / CYU p.161 or OYO p.168 #2,3,4,6,8, and 9 / 1 day
Investigation 3: Fitting Lines (p. 161)
As a whole group, read the “set up” on p.161 and do problems 1 and 2. Then in groups do 3-5. Then complete the remainder of the Investigation as a whole group because students are learning how to do linear regression on the calculator.
Note: You do not need to explain the notion of residuals and how the calculator works to do the linear regression, this will be done in the statistics section later this year.
The teacher resource book has many resources for this investigation. For example, step-by-step procedure for using the calculator to get a STAT PLOT and a regression line is given. / Linear regression with a calculator and finding the line of best fit using a graph and a straight edge.
Using the regression line to predict values. / Choose from the following problems: (Note: These problems take a while, 2-5 is the most I would ever assign per night, and I give a lot of homework.)
OYO 7, 10, 11, 12(This is a good problem, because it compares paper method to the calculator method), 13, 18, 22, 27, 34, 35 (these last two problems could be used as an out of class project or “extra credit”) / 2 days
Assessments
For Investigation 1: Randomly choose one paper per group to check for correct understanding of the topic.
Write to learn as a “Ticket out the door”: How can you determine the slope and the y-intercept from the graph of a line and the equation of a line.
For Investigation 3: You could assign each group a different set of regression data which is given in context and have them make posters of their problem to display in the room.
Lesson Assessment: Lesson 1 Quiz Form B (NOTE: The quizzes, Form A and Form B are NOT equivalent and just different forms of essentially the same test. Each one assesses differently.) Choose the form that best suits the emphasis of the student learning for your class.
Vocabulary to be used in this assessment:
slope: rate of change, coefficient, mathematical models, y-intercept, constant, linear regression, NOW-NEXT RULE, slope intercept form, independent variable , dependent variable, depreciation, appreciation (inflation)
Lesson 2: Linear Equations and Inequalities
Launch: Students should start on p. 186, reading the first page and looking at all charts, graphs and data provided. The teacher then should lead a class discussion of the “Think About the Situation.” Use these questions to formatively assess the needs of your class and make adaptations as needed (You will get better at this as you become more familiar with this curriculum). This is not a time to teach concepts forgotten, only a time to assess the students’ needs. The investigations that follow will teach or reteach these concepts. You can explain to students that they should be able to figure out the complete answers when they complete the lesson.Explore: Investigation / Topic Description / Share, Summarize and Apply / Time Frame
Investigation 1: Who Will Be the Doctor (p. 188)
The whole investigation will need be completed. / Writing equations and inequalities based on a sentence and vice versa.
Using a table or graph to estimate value(s) to equations and inequalities
Solving equations and inequalities using table, graph, calculator, by hand / CYU p. 191 This could be HW, class discussion, etc.
OYO p.201 #2-3, 14, 19, 25
(#32 - 33 are optional problems) / 1 day
Investigation 2: Using Your Head (p. 191)
The whole investigation will be completed. / Using “your head” to solve equations
Solving equations by hand
Explaining answers to solutions of equations / STM p. 193
OYO p.201 #4-6 (Choose 2), 15-16
(#34 - 36 are optional problems) / 1 day
Investigation 3: Using Your Head... More or Less (p. 194)
The whole investigation will be completed. / Using “your head” to solve inequalities
When multiplying or dividing by a negative the inequality sign flips
Explaining what the inequality means and what the solution to an inequality means
Find errors in others work with solving inequalities / STM p. 196
OYO p.201 #7,8,18, 20, 21
(#17, 22, and 26 are optional problems) / .5 day - 1 day
Investigation 4: Making Comparisons (p. 197)
The whole investigation will be completed. / Comparing equations
Writing equations given a situation
Solving equations based on given information
Setting equations equal to each other and explaining what that solution means
Systems of equations
Solving systems of equations.
What does the solution of a system mean
Prove a coordinate point is a solution
Find the solution algebraically, graphically, and by a table / CYU p.200
OYO p.201 #9-10, 11-12, 23-24 (choose 1), 30-31
(#28, 32-31, and 41 are optional problems) / .5 day - 1 day
Assessment
If you don’t assign some of those problems listed above has HW or CW, they would make good test questions.
From Unit 3 Resource Masters Lesson 2 Quiz Form A :1 (all), 2(all), 3 (all) Form B : 1(all), 2(all), 3(all)
Vocabulary to be used in this assessment: equation, inequality, estimation, solution, system
Lesson 3: Equivalent Expressions
Launch: Students should start on p. 214, reading the first page and looking at all charts, graphs and data provided. The teacher then should lead a class discussion of the “Think About the Situation.” Use these questions to formatively assess the needs of your class and make adaptations as needed (You will get better at this as you become more familiar with this curriculum). This is not a time to teach concepts forgotten, only a time to assess the students’ needs. The investigations that follow will teach or reteach these concepts. You can explain to students that they should be able to figure out the complete answers when they complete the lesson.Explore: Investigation / Topic Description / Share, Summarize and Apply / Time Frame
Investigation 1: Different, Yet the Same (p. 215)
The whole investigation will be completed. / Identifying equivalent expressions and equations based on context
Write equivalent expressions and equations from a real-world situation / STM p.218 a-b
OYO p.224 #2,15,25-27 (choose two) / 1 day
Investigation 2: The Same, Yet Different (p 219)
The whole investigation will be completed.
Suggestion for covering:
Warm up: Check your Understanding (p. 218 a-d
Groups: Investigation 3 #1-3
Whole group: Notes from p. 220
Do one example from each #4-9.
Groups: Have them do the other parts of
#4-9 in their groups. / Use tables, graphs, and properties of numbers to reason about equivalent equations / STM p.223 a-c
CYU p.223 a-d
OYO p.224 #5-6,11,18-19,22 / 1 day
Assessment: Coming Soon!
Vocabulary to be used in this assessment: constant, coefficient, independent variable, dependent variable
Lesson 4: Looking Back