Murray


 * Understanding By Design Lesson Template**

Students will know… |||||| ** Skills ** Students will be able to… || __**How was it creating this lesson?**__
 * Title of Lesson |||| Ratios || **Grade Level** ||||  6 ||
 * Curriculum Area |||| Math || **Time Frame** ||||  1 week, 80 minutes per day ||
 * Developed by |||||||||| Tracey Murray ||
 * ** Identify Desired Results (Stage 1) ** ||
 * **Content Standards** ||
 * **4.1.2 B**** .4. ** Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.
 * 4.1.2 C.**** 3 ** . Explore a variety of strategies for estimating both quantities and results of computation.
 * 4.4.6 B. **** 1 ** . Determine probabilities of events. Event, complementary event, probability of an event. Multiplication rule for probabilities. Probability of certain event is 1 and of impossible event is 0. Probabilities of event and complementary event add up to 1
 * 2. ** Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag). Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked. Given data obtained experimentally, what is the likely distribution of items in the bag
 * 3 ** . Explore compound events.
 * 4 ** . Model situations involving probability using simulations (with spinners, dice) and theoretical models.
 * 5. ** Recognize and understand the connections among the concepts of independent outcomes, picking at random, and fairness.
 * 4.5 A. **** 1. ** Learn mathematics through problem solving, inquiry, and discovery.
 * 4.5 C. **** 3 ** . Recognize that mathematics is used in a variety of contexts outside of mathematics. ||
 * ** Understandings ** |||||| ** Essential Question(s) ** ||
 * **Overarching Understanding** |||| **Overarching** || **Topical** ||
 * Students will learn the basics of ratios and the difference between ratios and fractions. They will explore and utilize the information with classroom activities and real life questions and situations. They will learn how to use ratios in comparing two quantities. |||| When will I use ratios in real life? What professions will I use ratios to compare two quantities? Can ratios help me gather important and essential data? || How many blue marbles are there to red marbles? How can I explain this to my group and class? What else can I make ratios out of besides marbles? ||
 * **Related Misconceptions** ||
 * Students can misconceive that ratios are fractions, when in fact they really aren’t. They will try to treat them as fractions at first, but will learn that they are meant to compare two quantities and to not have to be simplified completely like fractions do. This is very good! ||
 * ** Knowledge **
 * The meaning of rations, when to use them, how to use them, how to compare them, and how to utilize the information outside the classroom. |||||| Work in a group setting and discuss ratios. They will come up with ides on how to further engage in ratios and present their thoughts to the class after doing the classroom activity. ||
 * ** Assessment Evidence (Stage 2) ** ||
 * ** Performance Task Description ** ||
 * **Goal** |||||||||| To gain understanding of ratios and apply them outside the classroom. ||
 * **Role** |||||||||| Students will discover all aspects of ratios from the instructor and by participating in a group activity. ||
 * **Audience** |||||||||| The students, 6th grade. ||
 * **Situation** |||||||||| Students will be given various cups filled with different color marbles and be asked to give the ratios of some of the specific colors and record their findings. They will then be able to discuss where they will see this outside the classroom, what kinds of things they can make ratios of. Will this be done in groups? How will you know if everyone understands the concept? ||
 * **Product/Performance** |||||||||| The end result will be the record sheet for the teacher to look over and assess and of course the group discussion with the class to check for understanding. ||
 * **Standards** |||||||||| See above. ||
 * ** Other Evidence ** ||
 * Students will show the teacher a basic understanding of the computation and creation of ratios from the worksheet. This will be evident once it is checked. In the discussion, the teacher will be looking for understanding on where they believe ratios exist outside the classroom, where they may have seem them, why they are important, and most of all how they can use them to gain information about something. ||
 * ** Learning Plan (Stage 3) ** ||
 * ** Where are your students headed? Where have they been? How will you make sure the students know where they are going?** |||||||| My students are headed toward making inferences about ratios and thinking outside the box. They have been learning fractions and now ratios will be something new, and they can compare and contrast fractions and ratios. I will check for understanding throughout the lesson, constantly asking questions and checking their work. I will also formally assess them with a test or a quiz following the lesson at some point. ||
 * **How will you hook students at the beginning of the unit?** |||||||| My anticipatory set will be asking them to make a comparison to the boys and girls in the class. They will then make a fraction out of it, and I will discuss how this LOOKS like a fraction, but it really isn’t. I will then introduce ratios and their basic concepts. ||
 * **What events will help students experience and explore the big idea and questions in the unit? How will you equip them with needed skills and knowledge?** |||||||| The classroom activity I have planned will have different colored marbles in cups, and they will be asked to make ratios on the given colors. They will also discuss real life situations where they may use or have seen ratios. ||
 * **How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?** |||||||| I will have them talk to each other as a group and reflect on what they have learned. They will then discuss as a whole class with the teacher the importance of ratios and how they are used in every day life. ||
 * **How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?** |||||||| I will have them put on an index card on a scale from 1 to 10 how well they understand the lesson and it’s concepts. I will also ask them to list how and why ratios are used and important. This will be handed into me before they leave class so I can read through them later. ||
 * **How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?** |||||||| I will differentiate my instruction by making some of the cups have less marbles in them to make the ratios simpler. I will also pair up some of my advanced learners with my lower level learners to help promote their motivation. I will also keep this as hands on and thought provoking as possible to involve all learners in being creative. ||
 * **How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students?** |||||||| I will use proper pacing and wait time for my students to discuss and come up with valuable answers. I will also give them ample group time to finish the activity as best as they can while I walk around and offer my help and advice to all groups. ||
 * ==**REFLECTION**==

I thought it was fun, and I loved how it was structured. It's very similar to my curriculum I just worked on last year with the math curriculum committee. I love doing hands-on things with my kids!


 * __What difficulties did you encounter?__**

I was a little confused with the setup. As you said, this is different to how we learned things originally, but I got the hang of it. The last few questions were great because it got me thinking really heard about the lesson. I thought that some of the earlier questions were very repetitive.


 * __Did you like the format? What are additional questions you now have?__**

I liked the format eventually, and I believe it's easy to work with once you get the hang of it. What I wanted to ask is how can this be incorporated into all subjects, and have you had a problem using this format in your district? It could be looked at by other teachers as something that doesn't make sense, when it actually does. I think it's important that teachers as well as administrators are constantly exposed to new ways of learning, teaching, planning, and assessing, and I found this truly useful.

For your first shot at this I think you did well. You need to be careful to think with the end in mind and to dedign assessments that show students levels of understanding and not just be what Wiggins calls an activity designer.

I found it initially difficult to follow, but that was only because you used a different format than I did. I like your hands on activities and also your group work. I feel in Math class students at times learn better while working in groups than whole class instruction. You seem to have grasped the concept fairly well. Ron Kucheruck

Tracey- For a structure you did well with this and had good EQ. The part where you need a bit more elaboration is the assessment. What does a sophisticated vs. naive understanding of ratios look like? How would a student individually demonstrate how they understand rations with the marbles and how would they transfer this to a real-life sitation or knowledge to another form? BB

Tracey, I enjoyed this lesson as it is teaching the students using hands on manipulatives. I also really liked your student self-assessment procedure. I have used a system similar to that in my classroom and have found that it is very helpful to know where the students feel they are as compared to how we as teachers may view them. With this self assessment, I think you could include a wrap up activity that would be completed individually to show understanding. Since much of their lesson is being completed in groups, it would be important to have some type of individual work to know which level of understanding each student has reached. Maybe they could choose one of the "real life" ratio examples you will be discussing to create a few sample situations with fake questions and answers. This could be done on paper or in some other (more creative) format. - FG

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