The+proposal

==‍Uses ‍standards-based assessment that is systematically analyzed and includes multiple formative, summative, and self-assessment strategies to monitor and improve instruction ==
 * ==Formative //guys, go to main (home) page, click on Math Formative Assessment 75 strategies...it will lead you to the Amazon webpage. Once you are there, click on the image of the textbook then scroll down to see all 75 strategies. So don't worry about this one. We have plenty// . I have this book so no worry.==
 * == Summative <--//we take care of this already// ==
 * =Self-assessment - I think our student voice/exit tickets do this to some extent. =

==Promotes equitable student participation and engagement special attention on (I don't know if we can touch them on rather where it is applicable): ==

Use equity sticks, pairs, small groups as well as whole class discussion

 * ==power/status issues //culture - use of games works here ==
 * ==language - again, I think working in pairs or small groups. Also allow reflection in L1 and student choice of how to represent the math. ==
 * ==disability ==
 * ==gender ==
 * ==individual interests ==
 * //maybe use Andy Coons rules? //

==//Hey Guys - are we going to write our group report on this sight, or break it up and write it in word. How about the lesson plans? We need to make some progress this week or else March is going to be ugly. (SUE) //==

__ Math topic and grade level of the mini-unit. (very brief – 1 line) __
‍‍Understanding the relationship between theoretical and experimental probability ‍‍, seventh grade.

__ Specific standards addressed in math unit: WA math standards; common core math standards. (list the standards) __
__Washington State Learning Standards__ 7.4 Core Content: Probability and Data B. Determine the theoretical probability to predict experimental outcomes.

__‍‍Common Core) Statistics and Probability 7.SP. ‍‍__ Investigate chance processes and develop, use, and evaluate probability models. 5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. 6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. 7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal. probability to all outcomes, and use the model to determine probabilities of events.

__ Why this topic is important for students to know and for you to teach (beyond the standards link). __
Here is why it is important to teach:
 * develop simulation approach to solve real-world problems--__<range type="comment" id="371125">‍‍experimental approach to probability__ ‍‍(VDW 464)
 * "it is significantly more intuitive. Results begin to make sense and do not come from some abstract rule--__experimental approach to probability (VDW 464)__
 * __"it provides an experiential background for examining theoretical model (VDW 464)__

Here is why it is important for students to know:
 * //"Informed citizens need to be numerate in data and chance and need to know how to decipher and make sense out of information that is presented in newspapers, medical reports, consumer reports and environmental studies (NCTM ).//
 * To make well informed decisions rather than relying on intuition or guessing, understanding probability enables people to be critical consumers of data//.//
 * For example, probability (chances) are all around us, e.g., weather, risks and other probability ideas are very prevalent in today's world (VDW 456)

__ <range type="comment" id="355381">‍‍Description of learning issues related to this topic : ‍‍ __

 * Students may believe theoretical probability is the true probability, and should be reflected in each trial. Otherwise they feel they are getting incorrect results.
 * Students may have difficulty defining sample space, understanding all the possible outcomes that can occur (Swedish dice article).
 * Students may have trouble conceptuallizing that the probability of an event must be between 0 and 1 inclusive.

__ Key understandings __

 * Student will develop understanding the relationship of theoretical and experimental probability
 * Student will develop understanding of a probability continuum from impossible to certain. Then students will connect the probability's vocabulary to a numerical continuum from 0 to 1 and from 0% to 100%.
 * Student will develop a understanding of "law of large number--the phenomenon that the relative relative frequency becomes a closer approximation of the actual or the theoretical probability as the size of the data set (sample) increases. " (VDW 462)
 * For simple experiment. "Chance has no memory. The outcomes of prior trials have no impact on the next." (After 5 heads in a row, the chance of a head is stil .5)
 * The representation of the probablility of an event can take the form of fractions, percents or decimals, and can move between these representations.

__** Common Confusions **__


 * "law of small number--a misconception commonly think that a probability should play out in the short term" (VDW 462). For example, students think that if a coin has had a series of heads, it is more likely to have several tails (contradicting "chance has no memory.")
 * manipulating between the representations can cause students difficulties.
 * Independent versus dependent variables.

__ Developmental Milestones __

 * As probabilities fall in the range from 0 to 1, understanding of fractions and percentages is vital.
 * The more experimental trials conducted, the closer we approach the theoretical probability, unless there is some type of experimental error.
 * Being able to identify all the possible outcomes in a sample space in order to correctly find the probability.
 * Intuition is not the same as probability.

__ Specific Strategies __

 * Introduce the spectrum of probability from impossible to certain
 * Use an experimental approach
 * Link experimental data to theorectical probabilities.

=__ Learning goals of the mini-unit: __=

__ What do you want the students to know and be able to do? How do these goals relate to specific learning issue __
> Students will understand how experimental results relate to theoretical probability and reasons why they may be different.
 * Students will know that probabilities fall in the range from impossible to certain and that translates into anything from 0 to 1 (fractions, ratios or percents all work).
 * Students will understand and be able to define all possible outcomes, sample space.

__ Brief Lesson descriptions: Provide brief descriptions of your three lesson ideas and how they connect to each other. __
__ Lesson idea #1 __ Student will group the following items (events) into one of the these catagories: Impossible, Possible or Certain Number line from zero to 1, place real life example on the number line, based on the probability from 0 to 1. Spinner activity to generate data for the class to work with. __Lesson idea #2:__ Two spinner activity (Making the most out of chance) - is it a fair game? Mapping the outcomes, sample space Certain outcomes are more likely (higher probability) __Lesson idea #3__ Two event probability. Flip of the coin followed by roll of the die. Sample space outline and experimental outcome. We are still working on the flow and how to make these activities more connected to family and community. We would welcome suggestions.

==** Assessment Draft: ** In addition to the 4-page proposal please provide a draft of the summative assessment of your mini-unit. Identify a set of math tasks/problems (**5 questions or less – think quiz**) that you believe your students should be able to solve upon completion of your instruction. __Alignment with the learning goals and your understanding of the mathematical ideas and learning issues is key here.__ ==

The assessment should help you think about the lessons you will need to design to prepare students for the assessment (i.e. proposal step 4 above). Key questions to think about:

 * ** What do I want my students to know and be able to do? **
 * == Does this assessment match what I want my students to learn? ==