# Understanding by Design - DOC by 55s6rHF

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6-page Template, page 1

Unit Title: Medical Biotechnology                      Grade level: _7

Subject/Topic Areas: Math/Linear Functions – Unit 4 (continued linear from Unit 3B)
Key Words: linear equation, ax + b = c and ax + b = cx + d, solution, real numbers, expression,
first degree, variable

Designed by: Diane Rogers                              Time Frame: 6 weeks

School District: Kalamazoo Public Schools              School: Milwood Magnet School

Brief Summary of Unit (including curricular context):
This guide will explore how to generate and solve linear equations from a given context
as well as how to identify and interpret key elements of linear functions such as
intercepts, starting point, slope, rate of change, etc. The guide will also focus on
simplifying expressions and symbolic manipulation of expressions and equations of the
first degree.

Unit design status:      □ Complete template pages – Stages 1, 2, and 3
(Review use)

□ 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 _______ )        □ Revised draft (date __________)

□ Peer reviewed       □ Content reviewed   □ Field tested   □ Validated    □ Anchored

Notes:
6-Page Template, Page 2
Stage 1 – Identify Desired Results

Established Goals:
A.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) – 5x + y, or x(x+2) and justify
using properties of real numbers.

A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points on the graph, and
express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change.

A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.

A.FO.07.13 From applied situations, generate and solve linear equations of the form
ax + b = c and ax + b = cx + d, and interpret solutions.

A.PA.07.03 Given a directly proportional or other linear situation, graph and interpret the slope and intercept(s) in terms of the original
situation; evaluate y = mx + b for specific x values, e.g., weight vs. volume of water, base cost plus cost per unit.

A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and
volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees
Fahrenheit; distance and time under constant speed.
What understandings are desired?

Students will understand that…
Equations are models that help us interpret data and/or a situation.
Multiple representations of linear functions provide rich information to interpret a
situation and make predictions for the future.

What essential questions will be considered?
How do we use data to communicate?
 What information can be found in a linear equation?
 What information is found in each representation?
 When is one representation more useful?

What key knowledge and skills will students acquire as a result of this unit?
Students will know…                                                    Students will be able to do…
 How one variable effects another                                      Generate an equation from a given
 The components of equations in                                           situation
various forms such as y = x + b, y =                                Analyze the equation for the
mx, y = mx + b, y = ax+ b, ax + b = c                                  relationship between the variables
and ax + b = cx + d                                             Calculate a result given the value of
     How to symbolically manipulate simple                              one variable in an equation
linear expressions and equations
6-Page Template, Page 3

Stage 2 – Determine Acceptable Evidence
What evidence will show that students understand?

Students will be given three equations from the Math-a-thon pledge plans. They will
analyze which plan would yield the most profit for the fundraiser. Students will use their
symbolic manipulation skills as well as their knowledge about the components of a linear
equation to find a solution for the problem. The three plans will include two that are
equal but look symbolically different.

* Complete a Performance Task Blueprint for each task (see next page)

Other Evidence (quizzes, tests, prompts, observations, dialogues, work samples):

Math binder – homework assignments, vocabulary notes, partner quiz, class work notes
on Investigation 3

Student Self-Assessment and Reflection:

Math reflection –p. 69 in Moving Straight Ahead
Think, pairs, share
Summary discussions – whole group
Exit pass
Warm ups

6-Page Template, Page 4

Supplement to Stage 2 performance task
What understanding and goals will be assessed through this task?

Identify components of an equation –                Compare 3 plans and evaluate which plan
slope as a rate of change, intercepts,              raises more money, evidence shown for
variable relationships                              reasoning – table of values, graph, and/or

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?
Accurate table, graph, or equation used to          Clarify the relationships between the
explain answer, Appropriate symbolic                given variables; thorough explanations
manipulation used to prove answer

Through what authentic performance task will students demonstrate understanding?
St. Jude Children’s Research Hospital called Milwood Magnet School with a problem that
we need your help to solve. The hospital officials were very impressed with your previous
work on the pledge plans, but they wanted to know which plan was the best for raising
money. St. Jude’s has given us three plans that we need analyzed.

You are asked to compare and contrast the three plans and decide which plan will raise the
most money for the hospital. Included in your solution must be an explanation of your
mathematical reason.

What student products and performances will provide evidence of desired understandings?

Students will submit a written
explanation that includes their
mathematical reasoning for the best plan.

By what criteria will student products and performances be evaluated?
The table, graph or equation must be                The analysis of the plans must compare
labeled correctly and use appropriate               and contrast the values of the number of
intervals and scale. Symbolic                       problems completed and the money
manipulation must accurately show that              raised.
two plans are equal.
6-Page Template, Page 5
Stage 3 – Plan Learning Experiences and Instruction

Consider the WHERETO elements:

W – Where are they going? Why are they learning this? What is required?
Students must know how to interpret equations given a real world context. Students will use
symbolic manipulation (for both expressions and equations) in every mathematics course to
solve applied problems. At the 7th grade level problems are only of the first degree and are at
most 3 step. Students need to understand the distributive property as a tool for solving these
problems

H – How will you Hook the students? (through inquiry, research, problem-solving, and experimentation)
The context for balancing equations involves money. Each pouch contains the same number of
coins and each side of the equation needs to remain balanced. As students solve the problem,
they are looking for how many coins equal each pouch.

E – How will you provide opportunities will for student to Explore and Experience the Big
Ideas and concept? How will you equip them for required performances?
Students will work through Investigation 3 in Moving Straight Ahead that explores the
concepts necessary for this unit. Various Application, Connection, and Extension problems
will be assigned as class work and homework that provide students will time to practice skills
and solidify their understandings.

R – Provide opportunities for student to Rethink, Rehearse, Revise and Refine their work based
on feedback.
Students collaborate throughout the investigation and have opportunities to display work and
refine based on information gathered in class discussion.

E – How will students Evaluate their work and set future goals?
During the performance task, students will receive feedback based on the analysis of which
plan is a better “deal” for the walker/cause and the donor. Students will also evaluate their own
understanding of the mathematical concepts by answering the Math Reflection questions.

T – How is the lesson Tailored to address student interests and learning styles?
the investigations, the problems include real world situations such as cell phone plans, plans for
hiring a DJ, etc. Each investigation is organized so that students can access some part of the
lesson tasks. Students will be exposed to other students’ thinking during the summary portion
of each lesson.

O – How is it Organized to maximize engagement and effectiveness.
Students are required to produce products such as tables, graphs and equations for various
contextual problems. These items will be displayed and students will be asked to explain
characteristics of the model as well as asked to make inferences and/or interpret the models to
solve applied problems. This unit is very active and requires teams of people to collaborate in
order to accomplish a task much like the work place of the 21st Century.
6-Page Template, Page 6
Stage 3 – Plan Learning Experiences and Instruction

Monday                   Tuesday                  Wednesday                Thursday              Friday
1                        2                        3                        4                     5

Review y=mx+b            Inv. 4.1                 Inv. 4.1                 Inv. 4.2              Inv. 4.2

**See notes below for
this week.

6                        7                        8                        9                     10

Review for Quiz on 4.1   Quiz on 4.1 and 4.2      Inv. 4.3                 Inv. 4.3              Inv. 4.4
and 4.2

11                       12                       13                       14                    15
Supplemental Lesson      Supplemental Lesson
Inv. 3.1                 Inv. 3.2              Project Research Day
Find slope using         Find solutions from a                                                   See lesson plan
coordinates.             table, graph, and
y  y1          equation.
Slope  2
x 2  x1
16                       17                       18                       19                    20
Supplemental Lesson      Supplemental Lesson      Supplemental Lesson   Project work day
Inv. 3.3                                                                                         See lesson plan
Solving One-Step         Solving Two-Step         Solving Two-Step
Equations                Equations                Equations
21                       22                       23                       24                    25
Project Due
Inv. 3.4                 Inv. 3.5                 Review Investigation 3   Project work day
Check-Up                                       Review
26       27           28           29           30

Review   Assessment   Assessment   Re - Teach   Re - Teach
Content Area: Math                                                                                   Grade: 7th

Lesson/Activity: Birth Defects Research

Lesson Duration: 1 class period (58 minutes)

Resources/Materials: lap tops or computer lab,

Objective: (Students-friendly language-reference the GLCE the objective is related to)

Students will research information on birth defects including the rates, characteristics, history, causes, and prevention in the U.S, China, and India.

A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.

A.FO.07.13 From applied situations, generate and solve linear equations of the form
ax + b = c and ax + b = cx + d, and interpret solutions.

Action Steps to Deliver the Lesson:

Birth Defects Research
To begin this lesson, discuss birth defects and propose thoughts and ideas about the rates of birth defects in different countries. Why would one
country have a higher birth defect rate over another? Instruct students that they will be researching different birth defects and their rates in
different countries. Allow 5-10 minutes.

Students should research the rates of certain birth defects (Spina Bifida, cleft lip or Palate, Heart Defects, Excessive digits or missing limbs,
etc.) in the U.S, India, and China. Their research should include a description of the characteristics of the birth defect (such as how it affects the
body, how it progresses, and the life expectancy). In addition, students should research and gather information about the history, causes,
prevention and treatments of birth defects in China, India and the United States. Students should record their information in their notebooks.
Allow 40-45 minutes.

With 5 minutes to go, bring the class back together and ask for students to share their findings. Which country had the highest birth defect rate?
The lowest? Why do they think this is?
Content Area: Math                                                                                   Grade: 7th

Lesson/Activity:

Lesson Duration: 1 class period (58 minutes)

Resources/Materials: Birth defect research, access to a computer

Objective: (Students-friendly language-reference the GLCE the objective is related to)

A.PA.07.03 Given a directly proportional or other linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y
= mx + b for specific x values, e.g., weight vs. volume of water, base cost plus cost per unit.

A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container
with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant
speed.

Action Steps to Deliver the Lesson:

Rates of Birth Defects

To begin this lesson, have the class decide on a birth defect from a country to use in order to create a table, graph, and equation as a whole class. Also,
briefly summarize student ideas regarding how the trend may affect the countries population in the future. (Are there enough cases annually to
significantly affect an entire country?) Allow 15-20 minutes.

Then, instruct students to use their birth defect rates and information to make a table, graph, and/or an equation.
Students can select one birth defect for all three countries to compare. Their analysis should include a table, graph, and/or equation for each country, in
addition to a brief paragraph regarding the trends and the comparisons between the U.S., India, and China.

OR

Students may select to compare ALL the birth defects in ONE country. Their analysis should include tables, graphs, and/or equations for the rates of ALL
birth defects in a particular country. They should include a brief summary of observable trends and a prediction regarding how these trends will affect
future populations.

Allow 25-30 minutes.
With 5-10 minutes left of class, bring the class back together and ask for student volunteers to share some of their findings.

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