Unit Overview and Unit Plan for the Seventh-Grade Mathematics - Assignment Example

Unit Overview

Content Area: Mathematics

Unit Title: Probability and Discrete Mathematics 

Target Course/Grade Level: 7

Unit Summary This unit is aimed at equipping students with the basic knowledge of permutation and combination problems  

Primary interdisciplinary connections:

Applying the multiplication principle of counting

Unit Rationale:

To differentiate  between permutations and combinations  problems

Learning Targets

Standard 4.4

Content Statement

Permutations: ordered situations with replacement (e.g., number of possible license plates) vs. ordered situations without replacement (e.g., number of possible slates

of 3 class officers from a 23-student class)

CPI 4.4.C.1

Standards 4.4

Content Statement

Applying the procedures of systematic listing, counting, and reasoning in a variety of diverse contexts.

CPI 4.4.C.3

Learning Evidence

Summative Assessment (5 days)

Learning Material: Experimental box, Smartboard, Calculator, Venn diagrams

  Teacher Resources Study Island, Textbooks Smartboard

Formative assessment

Questioning            Self and peer assessment               Observation

Discussion               Constructive quizzes                     As I see it

                                                                      Lesson plan

Content Area:  Mathematics

Lesson title: Probability

Timeframe  10hrs/5 days

Lesson components

Apply the multiplication principle of counting.

Apply techniques of systematic listing, counting, and reasoning in a variety of different contexts.

Weeks plan

Lesson

Timeframe

Lesson 1: Dependent versus independent events and permutation versus combination

1 hrs/ 1 day

Lesson 2:Order and possible outcome

1 hrs/ 1 day

Lesson 3: Counting principle and its use to establish possible outcomes

1 hrs/1 day

Lesson 4: Sample space used to establish the probability of an event happening

1 hrs/1 day

Lesson 5: Assessment test

1 hrs/ I day

Teacher’s notes

            Probability is the number of favorable outcomes concerning the total number of possible outcomes. This is established depending on the nature of the event i.e. independent or dependent as well as the presence of replacement since order matters. It is therefore very important to note that there is a huge difference between the theoretical and there experimental probability of any event. Moreover, sample spaces can be formed from possible outcomes and be determined through the application of the counting principle or permutation or combination.  

             Therefore, much emphasis should be directed to the following key terms;

1. Dependent events and Independent events
2. Permutations and Combinations
3. Experimental probability and Theoretical probability. (Tappin, 2008)

This should be done to ensure that the student understands this unit and can compute probable outcomes from an event. Furthermore, the practical demonstration should be used frequently to demonstrate the main bases of this unit. Class quizzes and homework should be a very important tool for teaching this unit to encourage self-assessment.

Objectives

DAY 1

This lesson is inclusive of an introduction which should not take more than 5 minutes. The remaining time should be distributed equally to the sub-topics as outlined in the week’s plan. At the end of this lesson, students should be able to differentiate the terms as well as be able to work out probability problems under this category.

DAY 2

            A brief discussion of the previous day’s lesson should be discussed to remind the student about the unit. In this lesson, it should be mentioned how a certain order will affect the probability of an outcome. This can be demonstrated by the use of different colored balls for students to see the order in which the colors emerge. In this lesson, permutation will also be revisited.

DAY3

This lesson is about the counting principle of probability. This principle is used to determine the many unique ways one can do something such as team selection Again dependent and independent events will reemerge in this lesson.

DAY 4

This is the last teaching lesson in this unit where the main objective is to understand the sample spaces well as conclude the team. Sample spaces are simply the set of all probable outcomes e.g. when tossing a coin the sample space is a set of tail and head. Thus, students should b able o identify various spaces under different events (Tappin, 2008).

DAY 5

This is the assessment day and a sit-in quiz will be taken by the students to evaluate their understanding of the unit. All questions will be based on the unit.