Sunday, March 30, 2014

Pre-Algebra Percentage UbD Unit


Here is my almost finished Pre-Algebra 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/some-resources-for-math-teachers-in-need-of-a-little-nudge-and-some-re-direction/.  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)

Ratios and Proportional Relationships 6.RP
Understand ratio concepts and use ratio reasoning to solve problems. (6.RP.A)

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." (6.RP.A.1)


2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."1 (6.RP.A.2)


3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (6.RP.A.3)

Transfer Goals
Students will be able to independently use their learning to…

What kinds of long-term 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 21st century skills concerning responsibly research to expand knowledge and understanding of points of interest

Meaning-Making
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 2-Evidence of Understanding
Students will show their understanding by…
Performance Task(s):
How will students demonstrate their understanding (meaning-making 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 Pre-Assessment, Progress Monitoring, and Key Learning Events
Pre-Assessment
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: 1-8, 10-16 even, 24, 25
Day 2: ”Lesson over 7.3 “Percents and Decimals”
Homework: Chapter 7.3 Pg. 342 #s 13-16; 21-24; 25-28; 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 #2-16(ev); 17-22.
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 #1-9; 14-16; 21-22

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 15-17: 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/Chapter-7-Ratios-and-Percents .







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