LEARNING PROGRESSION
The class that I am using for this learning progression would be the alternative high school program that is through Ellensburg High School. This alternative program is for students who do not learn well in a traditional classroom. The students in the class are seniors and are trying to finish up their collective of evidence and take the SAT/ACT to graduate. When these students work hard and take the time to learn the concepts we teach, we reward them with teaching them a math that they want to learn like statistics.
This Learning Progression is about the basics of probability; sets, subsets, union, intersections, complements, independences, and conditional probability. The Common Core Standard for this Learning Progression are HSS-CP.A.1, HSS-CP.A.2, and HSS-CP.A3. Each standard will be covered in a day or two but after each standard there will be a benchmark assessment to check for student understanding and to see if the standard was reached.
At the beginning of each class, students will try to define a term that they will learn that day. The teacher will start the class by asking students for their definitions to be written on the board, and then the teacher will go through each of the definitions with the class to identify the correct one. At the end of each class, the students will take a formative exam (exit slip) to check for student understanding and to determine if the teacher needs to re-teach the lesson the next day. The first activity (HSS-CP.A.1), will be a concrete example that the students will use to learn about sets and subsets. The students will receive skittles and M&Ms that will be defined as the set. The students will have to separate the candy into subset. The last activity the students will receive a mathematical model and will have to create subsets from that set. The next activity the students will be doing is an activity on union, intersections, and complements. This activity will be using the previous mathematical model from the previous activity. The students will need to be able to identify unions of the subsets they created, intersections and complements. There will be a benchmark assessment after this activity for HSS-CP.A.1. The third activity (HSS-CP.A.2 and HSS-CP.A.3) that the students will be doing will be working with Conditional probability and how to use conditional probability to prove sets that are independent of each other. A worksheet will follow this activity because the students will need to practice and be able to connect the two concepts together. There will be a bench mark assessment for HSS-CP-A.2 and HSS-CP.A.3. The final activity will be a summative assessment based on the two benchmark assessment.
High School: Statistics and Probability
Cluster: S-CP: Understand Independent and Conditional Probability
CCSS.Math.Content.HSS-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
CCSS.Math.Content.HSS-CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
CCSS.Math.Content.HSS-CP.A.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
The terms entrance tasks will have the students work together to figure out how to define a word. Each group will get two of the words to define and then the teacher will assist the students to find the correct definition.
The exit exam or slip will give the students information about what they covered in the lesson. Some of these exit slips will benchmark assessments to see if the students are reaching the standards and to see if the students are aligned to the standards.
• Example problems for an exit slip would be:
o the set of odd integers has a subset of the multiples of 3 in it. True or False?
o given the set U={1,2,3,4,5,6,7,8,9} and the subsets of A={1,2,3,5,6,8}, B={2,5,6,7,8}, and C={1,4,5,6,7,9}. Find the union of A and B, the intersection of B and C, and the complement of C.
o Using the same sets as above, determine if A is independent of B.
o Write the formula for conditional probability. Find the probability of C given that B is true.
The M&M and Skittles activity could have subsets like colors. This would allow the students to create unions, intersections, and complements.
A mathematical model that could be used is the set of integers from 1 to 10. The subsets could be even, odd, prime, composite.
LESSON PLAN FOR LEARNING PROGRESSION:
Lesson Title: The Sets of Candy
Unit Title: Probability
Teacher Candidate: Megan Turner
Subject, Grade Level, and Date: High School, Statistics, 2/6/14
Placement of Lesson in Sequence
This lesson is the introductory lesson to sets and subsets. It is the concrete example for students to define a set and subsets. This lesson will be referred to during the rest of the unit as a concrete example.
Central Focus and Essential Questions
The central focus of this lesson is defining a set and being able to identify a subset within the set. The students will learn how to identify a subset given the universal set. The students will also be able to explain what a subset is and how to find it in the set. The students will also create a subset from a given set and then defend it with their knowledge and reasoning skills.
Essential questions: What is a set? What is a subset? How can I find a subset within a set?
Content Standards
CCSS.Math.Content.HSS-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
Learning Outcomes Assessment
The Learning Outcomes for the students will be
• Defining a set
• Creating subsets within the set • A worksheet that will be graded from the Skittles and M&Ms activity
• Exit slip with a true or false question
Learning Targets Student Voice
I will be able to
• Correctly identify what a set is
• Find a subset within the set given The students will work with pairs for this activity and will partake in a class discussion to find the correct definition of the terms set and subset.
Prior Content Knowledge and Pre-Assessment
The students may have prior knowledge for this lesson, but it is not required since this is the beginning of a unit.
The pre-assessment will be the entry task, where the students will have to work together be come up with a definition of set and subset.
Academic Language Demands
Vocabulary & Symbols Language Functions Precision, Syntax & Discourse
I will be able to define the terms:
• Set
• Subset
• Define and be able to provide examples of a set and subset.
Mathematical Precision:
The students will practice with Skittles and M&Ms to form subsets
Syntax:
The students will have to be able to explain their answer using correct vocabulary.
Discourse:
Students will have to work with each other to find all of the subsets.
Language Target Language Support Assessment of Language Target
I will be able to define and explain:
• A set
• A subset within a given set The students will be working pairs on this activity and will have to use the correct vocabulary and be able to explain and defend their choice. The students will have write down their choice of a subset and explain why that works.
Lesson Rationale (Connection to previous instruction and Objective Standards)
This lesson covers the first part of the Standard. The second part of the standard with the students using union, intersection, and complements will be the next lesson taught. This is a new unit so there is no connection to previous instruction. The exit slip will be graded and returned to the students before the next lesson. The exit slips will help the teacher with the data to determine if the lesson needs to be re-taught or the misconception was caught by all of the students.
Differentiation, Cultural Responsiveness and/or Accommodation for Individual Differences
The accommodation that is being made is that the students get to work with a partners during the activity.
Materials – Instructional and Technological Needs (attach worksheets used)
Skittles
M&Ms
Worksheet
White board
Markers
Exit Slip
Entry Task: Work with a partner and come up with the definition of set and subset.
Worksheet:
Name:
1. Sort the candy into colors and then write down then take a picture on your phone.
2. Then sort the candy into relative size and take a picture on your phone.
3. Create your own subset. And take a picture of it.
Given the set of even integers, find three subsets.
Exit Slip:
Name:
Given the set of odd integers. True or false? The set of all the multiples of three are in the set of odd integers.
Why?
Teaching & Instructional Activities
Time Teacher Activity Student Activity Purpose
10 minutes Entry Task on the whiteboard Entry Task To define the term set and subset.
30-40 minutes Skittle and M&M activity; assisting students Skittles and M&Ms activity To practice finding the subsets and getting a concrete example of a set and subset.
10 minutes Exit Slip and final questions Exit Slip To determine whether re-teaching is needed and to see if misconceptions are found.