Mathematics Curriculum Document for 8 grade

Mathematics
Curriculum Document for 8th grade
Unit Title: Equations
Time Frame: 29 days
Grading Period: 1 and 2
Unit Number: 2
Curriculum
Enduring Understandings (Big Ideas):
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The student will know:
Most patterns and relationships can be represented
mathematically in a variety of ways.
Graphs provide a visual representation of relationships
among data.
Simplifying math operations with a standard process helps
us communicate and solve real-world situations with
consistency.
(TEACHER NOTES ON FOLLOWING PAGE)
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The difference between equations and inequalities
Properties of equality and inequality
Process for solving equations
Proportional relationships are linear and pass through the origin
Proportional relationships can be represented with the equation
y=kx
 Slope can be seen visually as a slant or steepness of a line
𝑟𝑖𝑠𝑒
∆𝑦
𝑦 −𝑦
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
 Slope is 𝑟𝑢𝑛 = ∆𝑥 = 𝑥2 −𝑥1 = ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
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2
1
Slope is the constant rate of change
Slope is the unit rate in proportional relationships
The y-intercept is the point where the line crosses the y-axis
Non-proportional linear relationships can be represented with
y = mx+b, where b≠0
 Direct variation represents a proportional relationship, y = kx
 The intersection of two graphed equations represents the solution
The student will be able to:
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Graph linear relationships*
Identify and interpret the meaning of slope in graphs
Graph proportional relationships*
Interpret the unit rate of proportional relationships as the slope
of the line that models the relationship*
 Compare different proportional relationships represented in
Unit Title: Equations
Unit Number 2
Page 1 of 7
Mathematics
Curriculum Document for 8th grade
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Teacher Notes:
New:
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8.4A - 8.4B – 8.4C – 8.5F
Extend:
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7.4A representing constant rate of change to 8.5A & 8.5B
include represent linear proportional and nonproportional situations
7.4C determine constant of proportionality to 8.5E direct
variation
6.6B write equation from table that represents the
relationship between independent and dependent
quantity and 7.7A represent and write equation
𝑦 = 𝑚𝑥 + 𝑏 to 8.5I
7.10A write one variable, two-step equations and
inequalities to 8.8A include variables on both sides.
7.10C write a real world problem given a one variable,
two-step equation and inequality to 8.8B include variable
on both sides
7.11A model and solve one-variable, two-step equations
and inequalities to 8.8C include variables on both sides
and rational coefficients
7.7 represent linear relationships verbal, table, graph,
equations 𝑦 = 𝑚𝑥 + 𝑏 to 8.9A include identify and verify
solution to systems graphically
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Unit Title: Equations
different ways
Use similar right triangles to develop an understanding of slope,
where the slope is the same for any two points on a line
Use data from a table to determine the rate of change or slope
and y-intercept in mathematical problems*
Use data from a table to determine the rate of change or slope
and y-intercept in real-world problems*
Use data from a graph to determine the rate of change or slope
and y-intercept in mathematical problems*
Use data from a graph to determine the rate of change or slope
and y-intercept in real-world problems*
Represent y=kx in tables, graphs, and equations (proportional)*
Represent y=mx+b in tables, graphs, and equations (linear nonproportional)*
Solve problems involving direct variation
Distinguish between proportional and linear non-proportional
situations using tables, graphs, and equations*
Write an equation in the form y=mx+b to model a linear
relationship from tables, graphs, numerical, and verbal
representations*
Write one-variable equations with variables on both sides that
represent problems
Write one-variable inequalities with variables on both sides that
represent problems
Write a real-world problem when given one-variable equations
with variables on both sides
Write a real-world problem when given one-variable inequalities
with variables on both sides
Model and solve one-variable equations with variables on both
sides
Identify the values of x and y that simultaneously satisfy two linear
Unit Number 2
Page 2 of 7
Mathematics
Curriculum Document for 8th grade
equations from the intersections of the graphed equations
 Verify the values of x and y that simultaneously satisfy two linear
equations
*these TEKS are addressed again in Unit 4
Essential Questions:
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Why do we follow certain procedures?
Why is it useful to represent mathematical ideas in different ways?
How do we visually represent mathematical ideas?
What do graphs represent?
Student Understanding (student friendly TEKS):
Content:
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I can write equations to represent problems. (taken from 8.8A)
I can write inequalities to represent problems. (taken from 8.8A)
I can write a real-world problem to represent an equation. (taken from 8.8B)
I can write a real-world problem to represent an inequality. (taken from 8.8B)
I can model and solve equations. (taken from 8.8C)
I can use right triangles to understand that the slope will be the same for any two points on a line. (taken from 8.4A)
I can graph proportional relationships. (taken from 8.4B)
I know the unit rate in a proportional situation will be the slope of its line. (taken from 8.4B)
I can use data from a table to determine the rate/slope and y-intercept. (taken from 8.4C)
I can use data from a graph to determine the rate/slope and y-intercept. (taken from 8.4C)
I can represent proportional situations with tables, graphs and equations. (taken from 8.5A)
I can represent linear non-proportional situations with tables, graphs, and equations. (taken from 8.5B)
I can solve problems involving direct variation. (taken from 8.5E)
I can identify the differences between proportional and non-proportional situations using tables, graphs, and equations. (taken from
8.5F)
I can write an equation to model a linear relationship. (taken from 8.5I)
Unit Title: Equations
Unit Number 2
Page 3 of 7
Mathematics
Curriculum Document for 8th grade
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I can identify and check the solution for two graphed equations. (taken from 8.9A)
Process:
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I can apply math to everyday life. (taken from 8.1A)
I can create and use a problem solving plan. (taken from 8.1B)
I can check my answer to see if it makes sense. (taken from 8.1B)
I can solve problems with different stuff. (taken from 8.1C)
I can solve problems with different resources (manipulatives, technology, etc.). (taken from 8.1C)
I can use multiple ways to communicate math ideas. (taken from 8.1D)
I can explain ways to solve math problems. (taken from 8.1D)
I can use different representations to keep information organized when solving problems. (taken from 8.1E)
I can think and talk about the relationships between math ideas. (taken from 8.1F)
I can use math language to explain and defend mathematical ideas in writing or out loud. (taken from 8.1G)
TEKS:
Content:
(4) Proportionality. The student applies mathematical process standards to explain proportional and non-proportional relationships
involving slope. The student is expected to:
(A) use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to
the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line;
(B) graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and
(C) use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world
problems.
(5) Proportionality. The student applies mathematical process standards to use proportional and non-proportional relationships to
develop foundational concepts of functions. The student is expected to:
(A) represent linear proportional situations with tables, graphs, and equations in the form of y = kx;
(B) represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0;
(E) solve problems involving direct variation;
Unit Title: Equations
Unit Number 2
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Mathematics
Curriculum Document for 8th grade
(F) distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y
= mx + b, where b ≠ 0;
(I) write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical,
tabular, and graphical representations.
(8) Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or
inequalities in problem situations. The student is expected to:
(A) write one-variable equations or inequalities with variables on both sides that represent problems using rational number
coefficients and constants;
(B) write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of
the equal sign using rational number coefficients and constants;
(C) model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and
real-world problems using rational number coefficients and constants; and
(9) Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to
develop foundational concepts of simultaneous linear equations. The student is expected to:
(A) identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the
intersections of the graphed equations.
Process:
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a
solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques,
including mental math, estimation, and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral
communication.
Unit Title: Equations
Unit Number 2
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Mathematics
Curriculum Document for 8th grade
Targeted College Readiness Standards:
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IB1, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5, VIIIB1, VIIIB2, VIIIC1, VIIIC2, VIIIC3, IXA1, IXA2, IXA3, IXB1, IXB2, IXC1,IXC2,IXC3, XA1,
XA2,XB1,XB2, XB3
Targeted ELPs:
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1E, 2C, 2D, 2E, 2F, 2G, 2H, 2I, 3B, 3D, 3E, 3F, 3G, 4C, 4D, 4F, 4I, 4K, 5B,5F,5G
Academic Vocabulary:
Language of Instruction:
Direct Variation
Proportional vs. Non-proportional
Slope
Systems of Equations
y-intercept
Coefficient
Constants
Equation
Inequalities
Linear
Multiple Representation
Rate
Unit Rate
Constant Rate of Change
y = mx + b (linear relationship)
y = kx (proportional relationship)
Instruction
Instructional Resources:
SpringBoard Course 3
Activity 9- review only as needed
Learning Plan Unit 2- Activity 10: Equations (see Resources folder for Unit 2)Includes:
Activity 10 (and supplements for inequalities)
Performance Task Unit 2
Unit Title: Equations
Unit Number 2
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Mathematics
Curriculum Document for 8th grade
Activity 11
SUPPLEMENT right triangles to develop slope
Unit 2 COMMON ASSESSMENT Part 1
Activity 12
Activity 13
Embedded Assessment 2
Activity 14
Activity 15 (Algebra TEKS- not needed)
Embedded Assessment 3 (edit #1 to “solve the system graphically”)
Unit 2 COMMON ASSESSMENT Part 2
Technology:
Career Connections/Real Life Application:
Suggested ways to incorporate technology and/or websites into the
unit.
Suggested ways to make content relevant.
Exemplar Lessons:
Research Based Instructional Strategies:
Assessment
Student self-assessment & reflection:
Unit 2 EA 2 Feedback Form
Unit 2 EA 3 Feedback Form
Unit 2 CA Part 1 Feedback Form
Unit 2 CA Part 2 Feedback Form
Acceptable evidence or artifacts:
Embedded Assessments
Performance Task Unit 2 (see O drive for official version)
Unit 2 COMMON ASSESSMENT Part 1 (see O drive for
official version)
Unit 2 COMMON ASSESSMENT Part 2 (see O drive for
official version)
Unit Title: Equations
Unit Number 2
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