Name:  Mandy Reid and Mary Teague

Grade Level:  Kindergarten, 1st, or 2nd grade

Teacher Materials Needed:  Pattern blocks
Examples of shapes:
Kindergarten and 1st grade:  triangle, rectangle, square, circle
2nd grade:  parallelogram, rhombus, hexagon, pentagon, and ellipse

Student Materials Needed:  Felt or construction paper, scissors, and markers

My Mathematical Goals for this Lesson:
*Begin to assess spatial reasoning backgrounds of students in this class (how do they “see” these objects)
*Review and introduce some math ideas and vocabulary (the shapes)
*Have a beginning math activity where all students are capable of handling and not feel intimidated, yet still begin the learning process
*Enhance comparative and contrastive skills using nonstandard math terms (bigger, smaller, longer, shorter)
*Begin to appreciate the value of working in groups and talking about math
*Expand students thinking about math by incorporating music so that they have an enjoyable, physical and emotional experience with math

Related Standard Course of Study Goals/Objectives:
Kindergarten
 2.01 Recognize basic two-dimensional (plane) figures: circle, square, triangle, and rectangle. Describe their likenesses and differences and identify them in the environment.

2.02 Complete simple spatial visualization tasks and puzzles.

2.05 Use non-standard measurement of length, weight, capacity, and time.

3.01 Describe likenesses and differences between and among objects.

3.02 Sort by a given attribute; sort by own rule and explain.

 4.01 Collect data to create concrete and pictorial graphs and describe the results as a group activity.

1st Grade
2.01 Recognize, identify, and describe plane geometric figures: circle, square, triangle, rectangle.

2.02 Recognize plane geometric figures: hexagon, trapezoid, and parallelogram.

2.06 Describe and compare characteristics of geometric figures.

2.09 Use non-standard units to estimate and measure length, weight, and capacity; record results.
2.13 Solve spatial visualization puzzles and tasks; use visual memory.
3.01 Describe and compare objects by their attributes; order sets.

3.02 Sort a set of objects in more than one way; sort by own rules and explain.

4.01 Gather, organize and display information as a group activity.

Second Grade
 2.01 Describe and make plane figures: squares, rectangles, triangles, circles, hexagons, trapezoids, and parallelograms.

2.05 Use spatial visualization to solve problems; demonstrate visual memory.

3.01 Sort by one or more attributes; describe rules used.

4.01 Collect, sort, organize, and display information in charts, graphs, and tables with correct labeling.

4.02 Summarize and interpret information in charts, graphs, and tables; make predictions.

Launch:  Today we are going to be doing some exploring!  Everybody loves exploring don’t they.  You are going to begin working alone, then you will work with a partner.  After that we will come back together and discuss and work with what you found as a whole group.

Here’s what I want you to do when I give you the materials.  I want you to look at what I give you.  See if you can see anything that is the same about these objects or anything that might be different about these objects.  Do you know what the objects are?

Have the students count the sides of each shape.

Explore:  As the students work individually, walk around the room to see what they are noticing.  Then use what I find to pair up the students so that those who are getting the idea work with students who may not be noticing what I want them to notice.

Put the students in pairs and have them share their ideas with one another.  The second graders can begin to put the shapes into categories according to their characteristics.

Have each group present what they found.  Kindergarteners and first graders will do this orally and second graders can make a chart.

Once the group has presented the characteristics of the objects (what they observed), talk about the names of the shapes.  The students whether in Kindergarten, 1st, or 2nd grade should only be observing, at most, four objects at one time.   Review and practice these names by holding up a shape and having the students answer chorally.

Let the students make their own shapes out of felt or construction paper.  They can color them.  You may want your students to color code them (by making the triangle red, the circle blue, the square green).

Summarize:

Debrief the recognition of shapes and colors (colors mostly used in kindergarten) by teaching them a new song!  The kids love it and they really learn their shapes quickly by doing it to music!

Song:  “The Hokey Pokey Song”

Put your (blue) circle in, put your (blue) circle out put your (blue) circle in and you shake it all about,
You do the Hokey Pokey and you turn yourself around, that’s what it’s all about.

Continue the song until you have reviewed each shape twice.

After the song, ask them:

What was the first thing you noticed about these objects?
What shape has four sides?
Are all the shapes the same size?
Do all the shapes look the same?
What looks different between the circle and the square?
What is the same between the square and the rectangle?
Did anything surprise you when you were working by yourself?  What and why?
Did anything surprise you when you started talking to your partner?  What and why?
What did you like about this activity?  Why?

Assessment/Evidence of Learning:

While students are working in their groups I will look for
*the particular ideas and characteristics they have discovered and noticed
*how did they make their categories (did they use characteristics or colors)
*are there any similarities between the groups

During the discussion I will listen for
*individual thinking and different ideas about the shapes
*ideas about organization of the shapes
*comments about how the shapes are alike and different
*ideas about how partners helped each other
*students comparison and contrast ideas that might be “outside the box”
*how confident are my students about their ideas
*arguments made to support their ideas

Ticket out the door:  Have the Kindergarteners draw a picture of their favorite shape and walk around the room while they’re drawing and have them explain why it’s their favorite.  Then scribe for them on their piece of paper.
Have 1st and 2nd graders draw a picture of their favorite shape, and have them write why it’s their favorite.  They must use the mathematical terms discussed in this lesson.
 
 

Math Lesson:  Graphing in the 1st Grade
Part One
Spring, 2001

Name:  Mary Teague and Mandy Reid

Grade Level:  1st Grade

Teacher Materials Needed:
*One-pint size jar of M&M’s

Student Materials Needed:
*small baggies (one for each group of students) with m&m’s in them equaling the amount in the jar divided among them
*8 ½ by 11in. charts (need as many as the number of groups you plan to have)
 *worksheet to put tally marks to count the m&m’s by color

My Mathematical Goals for this Lesson:
*Begin to assess students’ prediction skills and logic of estimation.
*Assess their counting ability of more than 20.
*Have a beginning math activity that allows all students to enter the problem and feel comfortable.
*Begin to appreciate the value of working in groups and talking about math.
*Build on math concepts such as estimation and prediction, counting by tally marks, and sorting by attributes.

Related NC Standard Course of Study Goals/Objectives:
Grade 1:
1.01 Count using one-to-one correspondence to 30.
1.11 Represent numbers in a variety of ways: using tallies, building models to 100.
1.12 Estimate quantities up to 30. Recognize when solutions to problems are reasonable.
3.01 Describe and compare objects by their attributes; order sets.
4.01 Gather, organize and display information as a group activity.
4.02 Answer questions about charts and graphs.
4.03 Make predictions based on experiences.
4.04 Create concrete, pictorial, and symbolic graphs using prepared grids.

Launch:  Today we are going to make an estimate as a whole class.  Can anybody tell me what it means to make an estimate?  An estimate is a guess, for example, how many objects do you see without counting them.  So, as a class we are going to estimate how many objects we see without counting them.
 Here’s our problem.  (Pull out the jar of M&M’s).  Let the class look at it.  They can pass it around if they agree to leave the lid on the jar, don’t drop it, etc.  As they pass it around, talk about what’s in the jar.  There are different colors of m&m’s in the jar.  Then ask them how many m&m’s total do they think are in the jar?  Then have the students predict which color of m&m do they think will there be most of.  Write down their estimates and predictions on the board.
*Teacher note:  Students will not find out how many total m&m’s in the jar until the third day when the class graph is made.

Explore:  Group students in three’s or four’s.  Give each group a baggie with an equal amount of m&m’s from the jar, a worksheet to keep up with the tally marks (counting the m&m’s), and a chart to fill in with the real m&m's.
It is the students’ job to place the correct m&m in the corresponding color column.  The blue m&m would go in the column with the blue circle.  After placing all the m&m’s in the columns, the students count each m&m in each column giving the color a tally mark on their worksheet.
After they all finish recording their data and know how many m&m’s of each color they have, they put up their charts and share their data with the class.

Summarize:  Debrief how they found out how many m&m’s they had.
*Did all the groups sort their m&m’s on the charts?  Why did this help them with making tally marks?
*How did the tally marks help the students count the m&m’s?
*Did all the groups’ charts look exactly the same?  Why or why not?
*Which color had the most m&m’s produced?  Why do you think this?
*What surprised you most about this activity?

Assessment/Evidence of Learning
While students are working in groups:  I will look for
*Are students following directions for sorting, tally marks for object counting?
*Distinguishing color for color graph?
*Are they implementing cardinal principle for total m&m’s?
*How are they working in groups? Agreeable or Disagreeable?
*Are they sharing the workload?

During the discussion:  I will listen for
*Correct usage of math terms such as tally marks, sorting, and color charts
*Individuals’ confidence to share ideas, and being able to make an argument to support their thinking.  (Explaining why)
*What students notice about tally marks making counting easier.
*Comments about how this is similar and different to prior math experiences.
*Students’ comments about organizing with the color chart.

Ticket out the door:  Have students think of other items in their household that they could do this same activity with.  Write down their ideas.

 
Math Lesson:  Graphing in 1st Grade
Part Two
Spring, 2001

Name:  Mary Teague and Mandy Reid

Grade Level:  1st Grade

Teacher Materials Needed:
*Overhead Projector with clean transparency
*markers

Student Materials Needed:
*prepared grid paper (big grids)
*pencils, colored pencils, markers

My Mathematical Goals for This Lesson:
*Begin to assess their understanding and organization of graphs.
*How to read a graph.
*Students create a graph of their own and have ownership of it.
*Make connections to data gathered the day before.
*Begin to appreciate the value of working in groups and talking about math.

Related NC Standard Course of Study Goals/Objectives:
Grade 1
4.02 Answer questions about charts and graphs.
4.03 Make predictions based on experiences.
4.04 Create concrete, pictorial, and symbolic graphs using prepared grids.

Launch:
Today we are going to make a graph of the colors of the shirts of our classmates.  Without counting what color of T-shirt do you think we have the most of?  Count on the board with tally marks.  On overhead, make a pictograph of the students’ shirts. As you make the pictograph, talk about the components of the pictograph and why they’re important.   Quick discussion of what we learned from this graph.  Can graphs be useful in everyday life?

Explore:
The students will get into original groups from the day before.  Using the data recorded about the m&m’s they will individually produce a pictograph on the prepared grid portraying this information.  Students can make these colorful and intriguing.  Have students share their pictographs and place them around the room.

Summarize:
Debrief the meaning of pictographs, and how they are useful.
*How does one read a graph?
*How is a graph organized or setup?
*Discuss the uses of pictographs.  Why are they important?
*How to label the grid?  How to plug in data to the prepared grid?
*Are the students’ graphs all the same?  Why or why not?
*What surprised you most about the activity?

Assessment/Evidence of Learning
While students are working individually and with groups:  I will look for
*the particular kinds and variety of interpretations of graphs that individuals and groups have
*how individual graphs are setup
*inclusion of all the major components of pictographs

During Discussion:  I will listen for
*Connections students make with graphs in real life.
*Individuals’ confidence to share ideas and to make arguments to support their thinking.
*Connections to previous math experiences, especially to the day before.

Ticket out the door:  Take one idea from the ticket out the door the day before and do your best to make a pictograph.

 
Math Lesson:  Graphing with 1st Grade
Part Three
Spring, 2001

Name:  Mary Teague and Mandy Reid

Teacher Materials Needed:
*Overhead Projector with clean transparency
*markers
*large prepared grid for class bar graph taped to the board
Student Materials Needed:
*prepared grid paper (big grid)
*pencils, colored pencils, and markers

My Mathematical Goals for this Lesson:
*Assess their understanding and organization of graphs.
*How to read a graph.
*Students create a bar graph and have ownership of it.
*Make connections to data gathered the day before.
*Begin to appreciate the value of working in groups and talking about math.
 
 

Related to NC Standard Course of Study Goals/Objectives:
Grade 1
 4.01 Gather, organize and display information as a group activity. 4.02 Answer questions about charts and graphs. 4.03 Make predictions based on experiences. 4.04 Create concrete, pictorial, and symbolic graphs using prepared grids.
 

Launch:
Today we are going to make a graph of the colors of the shoes of our classmates.  Without counting what color of shoes do you think we have the most of?  Count on the board with tally marks.  On overhead, make a bar graph of the students’ shoes. As you make the bar graph, talk about the components of the bar graph and why they’re important.   Quick discussion of what we learned from this graph.  Can graphs be useful in everyday life?
 
 
 
 
 
 
 

Explore:
The students will get into original groups from the day before.  Using the data recorded about the m&m’s they will individually produce a bar graph on the prepared grid portraying this information.  Students can make these colorful and intriguing.

Once groups begin finishing up their bar graphs, have one group at a time come to the front and color in their results on the class bar graph.  The class bar graph will begin to build.  The assistant or yourself will have to help the students with this process.

Summarize:
Compare and contrast pictographs and bar graphs as a class discussion.
*Does the data remain the same?  Why or why not?
*What’s different about each graph?

Debrief the class graph and compare the estimates and predictions made on the first day.
*What do you notice about the class graph that might be different from the individual groups’ graphs?
*Does this graph tell us anything important?
*What were our predictions and estimations about the m&m’s in the jar on the first day?
*How has this graph become important for us finding out how many m&m’s are in the jar?  Why do you think this?
*Which m&m was produced the most? Least?  Why do you think this?

Assessment/Evidence of Learning
While students are working in their groups: I will look for
*talk that symbolizes connections (similarities and differences) between pictographs and bar graphs
*how individual graphs are setup
*inclusion of all the major components of pictographs

During the discussion:  I will listen for
*Connections students make with graphs in real life.
*Individuals’ confidence to share ideas and to make arguments to support their thinking.
*Connections to previous math experiences, especially to the two previous lessons.
*Comparison and contrast of group graphs and the class graph

Ticket out the door:  Make a bar graph out of the data used for the pictograph.

 
Math Lesson:  Graphing With 1st Graders
Part Four
Spring, 2001

Name:  Mary Teague and Mandy Reid

Grade Level:  1st Grade

Teacher Materials Needed:
*computer lab
*computer with projector
*software:  “The Graph Club” (enough CDs one for each student)
published by Richard Abrams/Tom Snyder Productions
*printer needed for computer lab

Student Materials Needed:
*previous experience with software
*basic computer skills

My Mathematical Goals for This Lesson:
*Build graphs from given data.
*Assess how well they work individually on a familiar concept.
*Assess their knowledge of graphs learned in this series of lessons.
*Plot and label data correctly on a prepared grid.
*Discussion of topic is detailed.

Related NC Standard Course of Study Goals/Objectives:
Grade 1
Math
 4.02 Answer questions about charts and graphs. 4.04 Create concrete, pictorial, and symbolic graphs using prepared grids.

Technology Competencies
3.1 Group items by different attributes using manipulatives and/or software. (SS)

3.2 Gather, organize, and display data.
 *Using technology at home.
 *Gathering, organizing, and displaying data.
 *Using word processing.
 *Exploring multimedia.
 
 
 

Launch:
Teacher does demonstration of a pictograph and bar graph using the computer software program, “The Graph Club,” on the overhead computer projector.  The program gives random variables and provides prepared grids, therefore, it is important for the teacher to model what students will do independently.

Explore:
Students will open “The Graph Club” program.  All students begin on level one of graphing.  From the data given to them through the software, they will produce a pictograph and a bar graph.  Once the student completes the graph to his/her preference, they will be able to print out a copy for them to take home and a copy to give to the teacher.  The teacher will use this copy to assess the students understanding and comprehension of graphs.  The students can put this copy on an interactive bulletin board so that they can read and study each other’s work.  It will be at their disposal for an extended period of time.

Summarize:
Once work is complete, debrief once again about graphs and their importance in everyday life.
*How can graphs benefit students?  In and out of school?
*Did working on the computer help you understand graphs better?
*Did the computer work give you practice?
*Were the graphs you made on the computer similar to the ones you made by hand?  Why or why not?  How were they similar or different?

Assessment/Evidence of Learning
While students work on computers:  I will look for
*correct plotting of data
*correct labeling of data
*using the manipulatives (mouse, data on screen, and prepared grid) and software effectively
*the quality of individual work produced by each student

During discussion: I will listen for
*Individual thinking of connections between computer activity and group work graphs.
*Individuals’ confidence about their ideas and being able to make an argument to support their thinking.
*Comments on the computer as a tool for creating and learning.

Ticket out the door:  Choose a graph off of the bulletin board that interests you.  Write down things that you learned from your particular graph.
 
 

 
Example Chart:  M&M’s could be glued on.  The actual chart could be on a half sheet of poster board so that it would be big enough for students to accurately place and line the M&M’s in the columns.

Blue                  Red                 Orange                 Yellow                Brown
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Example worksheet for tally marks.  The actual worksheet would have spaces big enough for the students to write tally marks that they could handle and keep separate.
                                                                                                                       Total # m&m’s
Blue________________________________________________          ______________
 
 

Red_________________________________________________         _______________
 
 

Orange_______________________________________________        _______________
 
 

Yellow_______________________________________________        _______________
 
 

Brown_______________________________________________         _______________
 
 

Math Lesson:  Equivalent Fractions
Spring, 2001

Name:  Mandy Reid

Grade Level:  5th grade

Teacher Materials Needed:
*dry-erase markers
*board
*knowledge about fractions and their equivalents
*fraction chart that shows fractions and some of their equivalents

Student Materials Needed:
*notebook paper
*pencil
*Math journal

My Mathematical Goals for this lesson:
*Students begin to value one another’s thoughts and ideas.
*Begin to assess mathematical backgrounds of students in this class (e.g. multiplication and division of numbers without manipulatives)
*Have a beginning math activity that allows all students to enter the problem and feel comfortable.
*Review math concepts and vocabulary such as division, multiplication, numerator, denominator
*Students see and find patterns among the equations
*Introduce equivalent fractions and why they are equivalent.

Related NC Standard Course of Study Goals/Objectives:
Grade 5
1.09 Identify equivalent decimals and fractions at the symbolic level.  Explain the equivalence.
1.13 Multiply a fraction by a whole number.
3.01 Investigate patterns that occur when changing numerators or denominators of fractions.  Model with concrete materials and extend to calculator investigations.
3.03 Use patterns, relationships, and functions occurring in computation, geometry, graphs, and other applications to make generalizations and predict results.

Launch:
Today I want you to write down all the equivalent fractions for ½, ¼, and ¾.  Use the chart on the wall.  I just want you to be looking at them and getting familiar with them.
 
 
 

Explore:
Propose the word algorithm.  Ask the students if they are familiar with it.  Then discuss what an algorithm is.  Write equations on the board. . . ½=2/4, 1/3=3/9, ¼=4/16, 1/5=2/10, 3/8=9/24, 7/10=70/100, 2/8=4/16.  Have the students work in groups of 3.  No more than three because you want them to come up with an algorithm (rule) that works with every equation.

The students’ job is to find a pattern or patterns among the equations.  Once they find a pattern, they are to come up with a rule that will help them find equivalent fractions for the given fraction.  Let them work for at least 15 to 20 minutes.

Summarize:
Discuss as a class each group’s rule.  Let them all voice their idea without saying whether it is valid or not.  Then let the students check to see if it works with all the equations.  Come up with a “class rule” (e.g. the rule that you want them to use).  The rule that you want to end up with is “Multiply the numerator and the denominator by the same number to get an equivalent fraction.”  Once you have established your “class rule,” put some fractions on the board and ask them to find an equivalent fraction.  Then continue to ask them to find four more fractions that are equivalent to a certain fraction.

¨ What did you notice about the numbers in the equations?
¨ What kind of patterns did you see?  Explain.
¨ What was your rule and how did you come up with it?
¨ How did I handle questions about mathematical vocabulary that the class might have forgotten?
¨ If a group uses a mathematical idea that I don’t see in other groups, I will ask that group to explain the mathematics to the class.
¨ How did your prior knowledge about mathematics help you come up with a rule?
¨ What surprised you most about this activity?
¨ What would have happened if I would have given you the algorithm (rule) in the beginning instead of letting you figure it out on your own?

Assessment/Evidence of Learning
While students are working in their groups I will look for:
v The particular kinds and variety of ideas that individuals and groups have
v How decisions are related to patterns and relationships between numbers
v How decisions are made among groups
v Types of patterns and relationships noticed by groups and individuals

During the discussion I will listen for:
· What students notice about patterns and relationships
· Individual thinking about working in groups
· Comments about how this is similar and different about prior math experiences
· Individual students’ engagement with the mathematics embedded in this problem.
· Individuals willing to think outside the box, do they have confidence about their ideas, and are they capable of supporting their thinking with evidence.

Ticket out the door:  (EOG Assessment work)  Put an equation on the board such as 5/9=25/45.  Ask the students if the equation is true or false.  Have them write their answers in their math journals and explain why they think this way.  Give them two more equations to solve and have them explain why.  For example, 4/8=6/32 and 8/72=16/45.  Then, after every student is finished, have them discuss the answers and why they think the answer is what it is.
 

Reflection Teaching Lesson to Strand Group
March 7, 2001

     I began my lesson expressing what I wanted to accomplish with this.  I would not tell my fifth grade students what I want to accomplish, I would simply introduce the vocabulary of equivalent fractions.  I felt that they were a little confused by the launch.  It was hard for them as teachers to understand why I would just let them “copy” the fractions from the chart.  So, I stopped to explain that all I was looking for them to do, was get familiar with what a fraction and it’s equivalent looks like.
     My peers had questions that related to the way I was presenting the information, rather than, questions about equivalent fractions.  I introduced new vocabulary to them such as algorithm.  They were to find a rule that would help them get from the original fraction to the equivalent.  They struggled because they already knew what the algorithm should be.  So, at this point, since I had seen this lesson taught, I told them about what the students in that classroom came up with.
     The level of engagement among my colleagues was one of true interest.  They were wanted to find out how this lesson worked and why it worked.  They also felt that it was important for students to come up with ideas that made sense to them.  They paid close attention so that they could imagine themselves teaching the lesson in the future.
    I learned that everyone sees lessons from a different perspective.  For instance, during explore time, a teacher could pair up groups and let each group try out the other group’s rule for finding equivalent fractions.  By teaching this lesson to other teachers, I was informed of new ideas and suggestions, and I came to the realization that other teachers can be a helpful resource.