Here is my almost finished PreAlgebra UbD unit plan. The overall goals are for students to be able to justify decisions and choices with reason and facts. This includes a range from choosing the best deals on a shopping spree to winning a debate/argument. My students will be active in both of these things. At the end of the unit, they will be writing an argument paper and presenting it to the class in an informal debate.
If you have any questions about Understanding by Design UbD, I would go to http://grantwiggins.wordpress.com/2013/08/24/someresourcesformathteachersinneedofalittlenudgeandsomeredirection/. Grant Wiggins is at the forefront of research about UbD. We use a lot of our PD days to continue on with developing and executing UbD units successfully in our school. It is all about execution. You really have to know the big concepts you want your students to walk away with and keep that in the CENTER of your and the student's path. That is what implementing UbD really allows direction, even for more chaotic looking types of lessons.
Here is one of my plans I started in the last PD day we had... I am working on attaching the worksheets below.
Unit Plan: Ratios and Percents
If you have any questions about Understanding by Design UbD, I would go to http://grantwiggins.wordpress.com/2013/08/24/someresourcesformathteachersinneedofalittlenudgeandsomeredirection/. Grant Wiggins is at the forefront of research about UbD. We use a lot of our PD days to continue on with developing and executing UbD units successfully in our school. It is all about execution. You really have to know the big concepts you want your students to walk away with and keep that in the CENTER of your and the student's path. That is what implementing UbD really allows direction, even for more chaotic looking types of lessons.
Here is one of my plans I started in the last PD day we had... I am working on attaching the worksheets below.
Unit Plan: Ratios and Percents
Stage 1 –Desired Results


Established Goals
(Standards)

Transfer Goals


Students will be
able to independently use their learning to…
What kinds of longterm independent accomplishments are desired?
1.) Form
reasonable decisions (opinions, arguments) based off of factual information and
evidence and then be able to justify their decisions
2.) Analyze
proportional relationships and statistics and use to solve real world and
mathematical problems.
3.) Set
up proportions and decide from a variety of processes to solve for real world
problems
4.) Use
21^{st} century skills concerning responsibly research to expand
knowledge and understanding of points of interest


MeaningMaking


Understandings
Students will
understand that…
Facts and evidence make an argument strong and trustworthy. Porportional relationships and statistics relate smaller groups to bigger groups and can make an argument or fact more personal and easier to visualize. Research expands knowledge and helps a person gather evidence and facts needed to form an opinion or take a stance. 
Essential Questions
(F=Factual;
C=Conceptual; P= Provocative)
Students will keep
considering
How can I support my argument to convince others? Do I have an argument worth fighting for that can be backed with fact and evidence?
What am I trying to find, or solve in this situation?
What do I need to know to find that out, and what do I know that will help me? Is this a fact or an opinion? Can you fight for your answer? 

Acquisition of Knowledge and Skill


Students will know…
What facts and basic concepts should
students know and be able to recall?
·
Solving proportions
·
Ratios
·
Percentage conversions
·
“of” means multiply
·
Calculate percentage of amounts
·

Students will be
skilled at…
What discrete skills and processes should
students be able to use?
·
Setting up proportions
·
Identifying relationships that are proportional
·
Take percentages of wholes or figure out percentages of
parts of wholes
·
Create a problem solving strategy
·
Take surveys
·
Form hypothesis/ideas based on statistics
·

Stage 2Evidence of Understanding
Students will show their understanding by…

How
will students demonstrate their understanding (meaningmaking and transfer)
through complex performance?

Other Evidence:
Students
will show they have achieved Stage 1 goals by ...
What other evidence will you collect to
determine whether Stage 1 goals were achieved?
Assessment Task
#1 1:1 Conference about argument analysis “Argument Analysis WS” I will marking them as mastering the
content so far based on 1.) Are they able to set up proportions given certain
information, 2.) Are they able to solve proportions once set up, 3.) Do they
know that percentages are just another ratio out of 100%, and 4.) Are they
beginning to question information and statistics given to them. 5 will be
mastery meaning I can say yes for all of these and there is little teacher
prompting are guidance.
Assessment
Task #2 Ch 7 Percents Quiz 1: Students will be assessed on their
ability to…
1.)
analyze
situations where relations are proportional; 2.) set up proportions and
recognize knowns and unknowns that will lead to the ability to solve; 3.)
Analyze and draw meaning out of ratios/statistics
Assessment
Task #3 1.1 Conference about Percent Change and “Making an Argument WS”
I will be marking them as mastering the contest so fare
based on 1.) Do they identify the knowns and unkowns of the situation
successfully organize this information?
2.) Can the use the percent change formula successfully? 3.) Do they
know order of operations and solving equations? Are they beginning to
question information and statistics given to them. 5 will be mastery meaning
I can say yes for all of these and there is little teacher prompting are
guidance.
Assessment
Task #4 Argument Paper: Students will be part of brainstorming some controversial
topics that can be argued using data, reasoning, and research. Students will
make a decision about where they stand (some may have to be on the other
side, but still make the effort of walking on the other side of the line).
Students will be writing an argument paper for their particular topic given
the side that they chose/ended up with. Students will have prompts and
requirements that make them critically think in making statistics more real
to themselves and their audience of peers. They will read out their papers in
a sort of “debate” and winners will be decided.
Assessment
Task #5: Formative Test: Chapter 7 test that should be easier
compared to their argument paper. Tests on skills and ability to transfer
those skills to various situations.

I

Stage 3 Learning Plan

Summary of PreAssessment, Progress
Monitoring, and Key Learning Events

PreAssessment
KWL
Progress Monitoring
• How will you monitor students’ progress
toward acquisition, meaning, and transfer, during lesson events?
I will be checking to make sure
they are organizing their notes and their homework, so that they can use
their own work as a resource in their learning they should be able to look
back and find organized set up examples of solving proportions or be able to
look through their practice problems and see that they have practiced
processes that they can transfer to various other problems in this unit.
• What are potential rough spots and
student misunderstandings?
There are a lot of various set
ups for solving and the students will have to choose which set up they want
or which method they want to go with. Multiple ways of solving can occur, and
we should all arrive at same answer. Students will just need to be able to
JUSTIFY there process. This reasoning and justification, whether it is
writing it out or talking it out to explain their process is the observed
HARDEST thing for these students to do.
• How will students get the feedback they
need?
We will have conference and
quizzes along the way where we can both see, as a student and as a teacher,
where there are misunderstanding and understanding.
Students will be having 1:1
conferences with me. If they do not have the assignments done, they will need
to schedule an appointment outside of school time… Hopefully this will push
to get them to do their assignments on time, so they can conference with me
during class.
Learning Events
Student success at transfer, meaning, and
acquisition depends upon ...
Day 1: Introduction to percents answering essential question “How
are rates, ratios, and percentages being used?” Students will do a KWL on
percentages and Health Care in America.
They will break into groups to read an article and have a discussion
in groups about the strength of the arguments for and against. Fill out
WS #1 “Ch 7 Intro KWL and Percents Discussion”
Homework: Finish “KWL and
Percents Discussion”
Day 2: (Skip 7.1) Lesson over 7.2 “ Percents and Proportions”
Homework: Chapter 7.2 pg. pg. 337: 18,
1016 even, 24, 25
Day 2: ”Lesson over
7.3 “Percents and Decimals”
Homework: Chapter 7.3 Pg. 342 #s
1316; 2124; 2528; 33; 36
Day 3: Students will have a workday over reading an article and
applying their skills of 7.2 and 7.3 to answering prompts about making statistics
more real and personal in WS #2 “Argument Analysis” I will be conferencing with them Day 4 as part of ASSESSMENT
TASK #1 1:1 CONFERENCE
Homework: FINISH “Argument Analysis
WS”
Day 4:While I am conferencing with students about their WS#2,
students will be working on the practice quiz on Pg. 350 #216(ev);
1722.
Homework: Finish Practice
quiz and look over Argument Analysis. If did not go because you were not
done, finish and will conference Day 5. If did go, look over and make any
necessary changes. ORGANIZE BINDERS. There will also be a binder check for a
chapter 7 homework and note section.
Day 5: Finish conferencing and have Mrs. Lowe help in review activity
“Silent Library Review” working through some of the practice quiz problems.
Day 6: ASSESSMENT
TASK #2: CH 7 QUIZ (Refer to WS #3 Ch 7 Percents Quiz)
Day 7: Go over
quizzes and Lesson over 7.4 Using Dan Meyer’s Three Act “Which Deal” at http://threeacts.mrmeyer.com/duelingdiscounts/
and WS #4 Deals WS (this ws will be done with computers)
Homework: Finish Deals WS
Day 8: Lesson over
“7.5 Rates of Change”
Homework: 7.5 Pg 354 #19; 1416; 2122
Day 9: Workday on WS #5 Percent Change Argument WS
Homework: Finish WS #5
Day 10: ASSESSMENT
TASK #3: 1:1 CONFERENCE RATES OF CHANGE ARGUMENT WS; other students
will be working on brainstorming controversial/debatable topics with Mrs. Lowe.
Day 11: 1:1 Conferencing while students begin WS#6 Phase 1 of "OutlineRubric of Argument Paper
Day 12: Finish Survey/Data Collection and start transitioning into Phase 2 of Day 13 14: Work on WS #6 Argument Paper Research/Outline Phase 2/3 (1:1 conferencing on outline must be completed in these two days) Day 1517: Typing of Argument Paper WS #6 Argument Paper Outline Phase 4 Day 18: Peer Reviews Worksheets WS #1 Ch 7 Intro KWL and Percents Discussion: WS #2 Argument Analysis Practice: WS #3 Ch 7 Percents Quiz WS #4 Deals WS  This I have students do on the computers (we are going 1:1 next year) **Dan Meyer** WS #5 Percent Change Argument WS WS #6 OutlineRubric for Argument Paper I do have this template that you can print out at http://www.scribd.com/doc/217761861/Chapter7RatiosandPercents . 