Milwood Magnet School
Biotechnology Magnet Curriculum
Math 8
Unit 3, Guide 1
Understanding by Design: 6-page Template, page 1
Unit Title: Alternative Energy & Medical Biotechnology (first half) Grade level: 8
Subject/Topic Areas: Frogs Fleas and Painted Cubes - representing quadratic
relationships
Key Words: function, parabola, quadratic relationship, factored form (product),
expanded form (sum), distributive property, quadratic expressions, factoring, roots, line
of symmetry, vertex, vertex form, intercept, maximum value, minimum value
Designed by: Jennifer Pinckney & James Roth
Time Frame: 5 weeks (MP 3 weeks
4-6 & MP 4 week 1-2)
School District: Kalamazoo Public Schools
School: Milwood Magnet School
Brief Summary of Unit (including curricular context):
In this unit students will be introduced to quadratic relationships by looking at tables,
graphs, and equations. They will make connections between the patterns presented in
each representation. Equations will be examined in both expanded and factored form.
(This particular guide of this unit does not have direct ties to the thematic topic of Cap
and Trade, however look for creative ways to support the theme as you explore these
concepts.)
Unit design status:
(Review use)
□ Complete template pages – Stages 1, 2, and 3
□ Completed blueprint for each performance task
□ Completed rubrics
□ Directions to students and teachers
□ Materials and resources listed
□ Suggested accommodations
□ Suggested Extensions
Status: □ initial draft (date _______ )
□ Peer reviewed
Notes:
□ Content reviewed
□ Revised draft (date __________)
□ Field tested
□ Validated
□ Anchored
Milwood Magnet School
Biotechnology Magnet Curriculum
Math 8
Unit 3, Guide 1
6-Page Template, Page 2
Stage 1 – Identify Desired Results
Established Goals:
A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions
including inversely proportional relationships (y = k/x); cubics (y = ax 3); roots (y = √x ); and
exponentials (y = ax , a > 0); using tables, graphs, and equations.*
A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth,
describe how changes in one variable affect the others.
A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable.
A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs, and vice versa; in
particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic
function.
A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x-axis and the
coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with
leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9; y = – x2; y = – (x – 3)2.
A.FO.08.07 Recognize and apply the common formulas:
(a + b) = a + 2 ab + b2
What
(a – b)understandings
2 = a2 – 2 ab + b2 are desired?
(a + b) (a – b) = a2 – b2 ; represent geometrically.
2
2
A.FO.08.08
Factor simple quadratic expressions with integer coefficients,
A.FO.08.09 Solve applied problems involving simple quadratic equations.
Students will understand the…
Tables, graphs, and equations of quadratic functions can be used to represent/understand patterns
and characteristics.
What essential questions will be considered?
How do outside factors impact decision making?
Scaffolding Questions:
How are graphs, equations, and tables related and what information can be gathered from
each?
What real world examples can be represented by quadratic functions?
What are the similarities and differences between linear and quadratic functions?
What key knowledge and skills will students acquire as a result of this unit?
Students will know…
The differences between different types of
functions (i.e. quadratic, linear, exponential)
How roots and x-intercepts are related.
How to determine if a solution is correct or
incorrect.
Solve various problems using factoring, roots,
and graphs.
Understanding of what a change in one variable
does to the other variable in a quadratic
Students will be able to do…
Graph functions of all types
Make connections between functions using
tables, graphs, equations
Apply common formulas for multiplying
binomials
Determine roots and their relationship to the xintercepts of a graph
Factor quadratics
Solve quadratics with roots and/or by factoring
and verify solutions
Milwood Magnet School
Biotechnology Magnet Curriculum
Math 8
Unit 3, Guide 1
6-Page Template, Page 3
Stage 2 – Determine Acceptable Evidence
What evidence will show that students understand?
Unit Test
* Complete a Performance Task Blueprint for each task (see next page)
Other Evidence (quizzes, tests, prompts, observations, dialogues, work samples):
Bell Work, Vocabulary, Summary, Class Discussion, Binder (Investigations),
Quizzes/Check-Ups
Student Self-Assessment and Reflection:
Exit Slip, Reflections
Milwood Magnet School
Biotechnology Magnet Curriculum
Math 8
Unit 3, Guide 1
6-Page Template, Page 4
Performance Task Blueprint
Supplement to Stage 2 performance task
What understanding and goals will be assessed through this task?
Writing quadratic equations in factored
and expanded form.
Identify quadratic functions by looking at
tables, graphs, and functions
What criteria are implied in the standards and understandings regardless of the task specifics?
What qualities must student work demonstrate to signify that standards were met?
Student can fluently move between
representations of quadratic function.
Students can justify why a table, graph,
or equation is quadratic or linear.
Through what authentic performance task will students demonstrate understanding?
What student products and performances will provide evidence of desired understandings?
Weekly probes
Unit Test
By what criteria will student products and performances be evaluated?
Milwood Magnet School
Biotechnology Magnet Curriculum
Math 8
Unit 3, Guide 1
6-Page Template, Page 5
Stage 3 – Plan Learning Experiences and Instruction
Consider the WHERETO elements:
WHERETO elements:
W – Introduce performance task at beginning of unit so as instruction and learning
occur they can be connected, and recorded, as tools for the task.
H – Performance task has a real world connection. While not every student may be
able to relate to farming, framing the context from a business perspective gives
students an accessible practical application.
E – Using textbook examples as their experiences have students reflect on how the
content they are working might apply to the project.
R – Performance task is planned for two days. Day two begins with questions that
arose from Day one’s work. Based on the discussion students have the opportunity to
revise their work,
E – This summative assessment is the foundational knowledge for solving
simultaneous linear equations by substitution and combination. So based on their
results students will be able to reflect on their strengths and weaknesses and use that
information to help them prepare for the second part of the unit.
T – The integrated assessment which pulls content from the four core areas of
instruction allows students to determine the format and content of their final project.
O – Graphic Organizer created for students to keep final product together.
Milwood Magnet School
Biotechnology Magnet Curriculum
Math 8
Unit 3, Guide 1
6-Page Template, Page 6
Stage 3 – Plan Learning Experiences and Instruction
Marking Period 3
Day 18
FFPC 1.2 (Day 2)
Day 16
FFPC 1.1
Day 17
FFPC 1.2 (Day 1)
Day 19
FFPC 1.3 (Day 1)
• Begin an introduction
• Make connections
• Write an equation that
to quadratic
relationships
by looking at a table and
graph
between the patterns in a
table and graph of a
quadratic relationship
• Use tables and graphs to
predict the fixed
perimeter and maximum
area for a family of
rectangles with a fixed
perimeter
describes the
relationship between the
length and area of
rectangles with a fixed
perimeter
• Use a quadratic equation
to describe the graph
and table of a quadratic
relationship
• Use the equation, graph,
and table to solve
problems about quadratic
relationship
Day 21
Distributive Property
Review
Day 22
FFPC 2.1
Day 23
FFPC 2.2 (Day 1)
• Introduce the concept of
• Continue the
equivalent quadratic
expressions
exploration of equivalent
quadratic expressions of
the form ax2 + bx
• Represent a quadratic
relationship in expanded
and factored forms as two
equivalent ways to
write an expression for
the area of a rectangle
that has been subdivided
into two
rectangles
Day 24
FFPC 2.2 (Day 2)
use calculator to view
graphs
Day 20
FFPC 1.3 (Day 2)
Day 25
FFPC 2.3 (Day 1)
• Expand the context of
area of rectangles to
write equivalent
quadratic expressions for
the
area of a rectangle x2 +
bx + c
• Use the area model to
review the Distributive
Property
• Use the area model and
Distributive Property
to multiply two binomials
Milwood Magnet School
Biotechnology Magnet Curriculum
Math 8
Unit 3, Guide 1
Day 26
FFPC 2.3 (Day 2)
Day 27
FFPC 2.4 (Day 1)
Day 28
FFPC 2.4 (Day 2)
Day 29
Quiz
Day 30
Flex Day
• Use the area model and
Distributive Property
to rewrite an expression
that is in expanded
form into an equivalent
expression in factored
form
Day 1
FFPC 2.5 (Day 1)
Day 2
FFPC 2.5 (Day 2)
Marking Period 4
Day 3
FFPC 2.5 (Day 3)
Day 4
FFPC 4.1
Day 5
FFPC 4.2
• Make a connection
• Make a connection
• Make a connection
• Examine patterns of
• Examine patterns of
between a quadratic
equation in
factored/expanded form
and its graph
• Predict the shape and
features of a graph from
the expanded and
factored form of a
quadratic
equation
between a quadratic
equation in
factored/expanded form and
its graph
• Predict the shape and
features of a graph from
the expanded and factored
form of a quadratic
equation
between a quadratic
equation in
factored/expanded form
and its graph
• Predict the shape and
features of a graph from
the expanded and factored
form of a quadratic
equation
change associated with
quadratic situations that
are represented by
equations in expanded
form, such as the height
of a ball over time that is
thrown in the air
• Predict the maximum or
minimum point from
an equation, graph or
table
change associated with
quadratic situations that
are represented by
equations in expanded
form, such as the height
of a ball over time that is
thrown in the air
• Predict the y-intercept
from an equation, graph
or table
• Interpret the
information that the yintercept
represents
Day 6 Flex Days
Day 7 Flex Days
Day 8 Flex Days
Day 9 Unit Test
Day 10 Unit Test