First Lesson Plan

GRADE LEVEL:            2

DATE and TIME ALLOTMENT:               4.2.12            2:10 pm – 3:10 pm            (1 hour)

SUBJECT AREA(S):            Mathematics

GOALS

Massachusetts Curriculum Frameworks

Content Standard Measurement and Data Grade 2            2.MD

Represent and interpret data

10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories.  Solve simple put-together, take-apart, and compare problems, using information presented in a bar graph.

NCTM Standards

Data and Probability

Expectations: In pre-K through grade 2 all students should-

§  pose questions and gather data about themselves and their surroundings;

§  sort and classify objects according to their attributes and organize data about the objects;

§  represent data using concrete objects, pictures, and graphs.

TERC Standards

Ordering and representing a set of numerical data

Interpreting a data representation

Describing important features of a set of data

Comparing ways of organizing data

WHERETO

What is expected & Where the students are coming from

This lesson begins with questions regarding what the students understand about representations of data (charts and graphs), and lets the students know that we will be collecting and organizing data.

Hook all students & Hold their interest

This is an activity that actively engages students through individual tactile participation

Equip, Experience, and Explore

The students are counting pockets on their person and then using a manipulative (cubes) to represent it.

Rethink & Revise their understandings

During the small group work, I am walking around and talking with groups and individuals, using questions to provoke revisions of their thinking if they are trying something and it isn’t working out/could use some improvement.

Evaluate their work and its implications

The final portion of this lesson is a whole class regroup discussion comparing different student choices of data organization.  Students will get a chance to evaluate other students’ choices and what those choices imply about the data.

Tailored to different needs, interests, & abilities

This activity is designed in such a way that it will be accessible to kinesthetic, visual, and auditory learners.  They will touch manipulatives, write down their representations and data sets, and verbally communicate about what they are doing.

Organized to maximize engagement and effective learning

This lesson has both small group and whole group work so that the students aren’t just sitting in one place for an hour, and the lesson is not all worksheets.  It calls for active engagement.

WHEELOCK COLLEGE TEACHING STANDARDS

Standard 2. Understanding all children in their many dimensions

This standard is addressed when throughout the lesson by preparing and responding to the unique needs of every student.

Standard 3. Knowledge of content and integrated curriculum

This standard is addressed in my research prior to the lesson.

Standard 4. Educational practices that foster learning, development, and achievement in all of the nation’s children.

            Development of critical thinking, problem solving, and performance skills

This lesson is entirely centered on inquiry and investigation.  In that regard, children taking part in the learning process are given an opportunity to explore and solve.

            Active engagement in learning

This lesson engaged the student

            Communication to foster learning

This lesson engages the students in open small group dialogue.  The essential questions asked of individual children during the lesson works on their ability to communicate their understanding.

UNDERSTANDING

This lesson addresses the follow facets of understanding via the questions I will ask during various points in the lesson.

Explanation

We collected data from the 22 students in our class.  Should we have 22 towers?  Why or why not?

How many towers do you think you should have when you’re done building?

Interpretation

What does each cube stand for?

What does each tower stand for?

Application

How could we organize the pocket towers to find out more about the number of pockets people are wearing today?

Self-Knowledge

How did you organize your towers?

ESSENTIAL QUESTION

What is data?

ACTIVATE PRIOR KNOWLEDGE

To activate prior knowledge, the lesson will begin with a review from previous lessons. The students have been working on using different kinds of graphs/representations (i.e. tally chart, pictograph, bar graph).  This will help me assess and confirm what they already understand about graphs/representations.

Questions during in lesson:

What do you know about graphs and charts?

How could we organize the pocket towards to find out more about the number of pockets people are wearing today?

OBJECTIVES

1.            Students will be able to compare different ways of organizing data.

            “I can compare different groups of organized pocket towers.”

2.            Students will be able to interpret representations of numerical data.

            “I can say/show what towers and cubes stand for.”

3.            Students will be able to order a set of numerical data.

            “I can put the pocket towers in order from smallest to biggest.”

3.            Students will understand how data is collected and organized.

            “I can know how all the pocket data is gathered from the class.”

DIFFERENTIATED INSTRUCTION

I will alter the implementation of the lesson with written directions to assist the students in the class who I know have a difficult time remembering verbal directions.  The class list will also be written on the board to support the students who need visual aids to complement oral instruction.

Students will count pockets and record it.  The class will be using manipulatives (cubes) to interpret and compare data.  Manipulatives will aid kinesthetic learners understanding data, which is generally only presented to them on paper.

Advanced learners will have both manipulatives and written work, to further their mathematics communicative register.

ASSESSMENT

Students will show knowledge through ongoing assessments by observing their work.  Specifically I will look for:

How students represent the people with zero pockets?

Do students group the data?

Do students understand that each tower represents the number of pockets worn by one person?

Are students able to use their organized towards to answer the questions?

Do students know what aspects of this representation tells them the number of pockets and what aspect tells them the number of people?

IMPLEMENTATION PROCEDURES

List Materials

§  Connecting cubes

§  Chart paper (“Pocket Data”)

§  Class list

§  Pencils

Procedure

Introducing “How Many Pockets”

With the whole class sitting on the perimeter of the carpet:

·      Can someone please tell me what he or she knows about graphs and charts?

·      Today we are going to collect and organize data.  We are going to try to better understand what is data?

·      The data we will collect is on your body right now!  Let’s take a moment and everyone make a tower of cubs that shows how many pockets you are wearing.  If you count 4 pockets, you would make a tower of 4 cubes.

·      As soon as you have a tower that shows how many pockets you are wearing, bring it up and we will add it to the “Pocket Data” chart.

·      We collected data from x students in our class.  Should we have x towers?  Why or why not?

·      Let’s think about what this shows us.

·      What does this tower of 4 cubes show? 1 person has 4 pockets

·      What does each cube stand for? Pockets

·      What does each tower stand for? People

·      How many people have 2 pockets?

·      How many people have zero pockets?

Organizing Pocket Towers

Starting with the group in same setting as before:

§  We were able to gather some information about the number of pockets students are wearing today, but we could learn more if we organized the towers in some way.

§  How could we organize the pocket towers to find out more about the number of pockets people are wearing today?

§  Which towers go together?

§  How can we put the towers in order?

§  Now let’s take this a step further.  We will break into groups of 3 or 4 to create and organize your own set of pocket towers.

§  Work with your group to make a class set of pocket towers to match the set we have here.  You can use the “Pocket Data” chart to help build your set.

§  Copy the information from the chart onto the class list.

§  How many towers do you think you should have when you’re done building?

§  When you have completed

Time Chart

Introducing “How Many Pockets”	20 min
Organizing Pocket Towers	25 min
Pocket Towers Discussion	15 min

                                                                          Total: 1 hr

POST REFLECTION ON LESSON

From my summative assessment during the lesson, I felt as though all students met several of the learning objectives.  They understood how to collect and organize data; they knew how to order a set of data.  By the end of the lesson, only a select few were still really struggling with their interpretation of representations of numerical data.  I saw this when select students could not discern the difference between a cube (which represents a pocket) and a tower (which represented a whole person and his or her total pockets).  These students similarly had a difficult time comparing different organizations of data, because their concept of what they were looking at (a pocket or a set of pockets) was off.  I would want to follow up with those students by using a wide variety of data representations to practice with.