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Ralph Davis

Secondary 1 lesson plan

6 representations of patterns

Rows of Desks

Objective: Practice using the six representations of patterns from our class discussion.

1. Picture2. Numeric (Table)3. Graph4. Equation/ Algebraic5. Words6. Context

Materials needed:

Class paper that has been divided into 6 sections, one for each representation(one has graph paper copied into it).

Foam blocks of 5 different shapes.1. Squares2. Rhombus3. Hexagon4. Trapezoid5. Triangle

ATB: Find the point where 2 linear equations intersect. It should be at on a point with

integer values for x and y. They should use 1 of 3 methods: graphing, making a table, or

creating a system of equations. Discuss all three methods.

Main Task:

Task introduction: My room is a temporary room. I dont know what my room will

be like when they move me from this one. I have done my best to figure out the best

seating arrangements for any type of room except for one. If my room is long and skinny, I

need to know what shape my tables should be and I need to know how many students I can

fit at my tables if I arrange them end to end. Because I dont know how long my skinny

room could be I need to know how many students I can seat based on how many tables I

can fit in to my room.

Task explanation: Line the foam blocks up end to end and find a pattern to help you

find the number of seats available based on the number of tables in the room. Use your 6

representations to help you.

Task extension: How would it change your pattern or equation if I told you I could

have 2 rows in my room?

Procedure: Each group of 2-3 students works with a particular shaped block as a

desk shape. In my room I had 5 groups. My class is small so all of them had different

shapes. They are to:

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Draw a picture of each figure starting with 1 table then 2 then 3 with acorresponding value for the number of seats.

Create a table of values that matches the picture. Graph the values on the table as well as the recursive equation they discover. Derive an explicit and recursive equation for the pattern. Describe in their own words how the pattern is growing and why. Describe the context of the problem.

Homework: Students are to finish their work if they did not finish it in class. Also they are

to explore how the pattern changes if there were two rows instead of 1 long row.

Reflection on the lesson:

I came up with the idea from the videos we watched in class. I thought it would be

interesting to discuss the patterns between the equations when the desks are different

shapes. That would be later though.

As I wrote the lesson, I had in mind that using these foam blocks would help the students

have a solid idea of what they were trying to do. I feel like too many times we rely on them

to be able to use a drawing or an idea, and I think that actually having something to move

around and to count the sides of is very useful to them as an access point.

I also liked the idea of them drawing their shape out of the hat. In my class I have students

who are often stubborn about whom they work with and this provided an opportunity for

them to be forced to work with other people.

I think that I would change a few things. I would add a clearer explanation of the task after

the introduction. Several students were hung up on the fact that we dont know how long

the room is. I also think that the extension could have been crafted better. I was not sure

how long it would take for the students to finish an so I kind of threw it together at the end.

Task explanation: Line the foam blocks up end to end and find a pattern to help you find

the number of seats available based on the number of tables in the room. Use your 6

representations to help you.

Task extension: How would it change your pattern or equation if I told you I could have 2

long rows in my room? 3 long rows? Is there a way to determine how many seats areavailable for any number of rows?

The only problem that I wrote for the class was the ATB I used the equations

I believe that the task was made with higher cognitive demand because they had to

recognize the relationships between the representations in order to complete the

assignment.

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Several students tried to arrange the tables in a different array than I was thinking they

would. That is why the explanation was included in the new lesson.

The paper divided into six sections lends itself well to the progression of the task. I also

think that the lesson as a whole has some natural progressions. It will be leading to a

comparison between the patterns based on the shape of the desks.

My assessment was informal throughout the lesson. The assignment will be turned in and I

will be able to judge more accurately what each student will be able to do.