Using A Pattern to Solve A Problem

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Objective

SWBAT identify structures and patterns that can help them to solve problems.

Big Idea

Patterns are prevalent in all levels of math. Common Core Standards expect students to be able to use structure - like that found in repeating the patterns of odd and even numbers or counting by 5s or 10s - to solve problems (MP7).

Warm Up

15 minutes

Today I will be asking students to find patterns in puzzles and pictures. I hand them a sheet of paper that looks as follows:                  

                W

              I     I

           N    N    N

       T     T     T     T

    E    E     E     E     E

R     R     R     R     R     R

 

I also display the page on the White Board.

I ask them what they see in the paper? Are there any patterns that they notice? (Students will probably notice that the word winter runs down each side. They will also see rows of letters). After they have shared there ideas I go back to the word winter. Do they see it anywhere else on the page except the two sides? Could they connect the letters to make the word winter if they went in order but in any direction?  I ask if anyone could come up and draw a path to winter other than down the 2 sides. I let one student try. Now I ask students to see how many paths they can mark on their paper. They may use the letter more than once. They should do each path in a different colored pencil color so they can count how many paths they find. We compare the number of paths found. This is a warm up for students. I give them just 5  minutes to find the paths. I acknowledge when we stop that there may be more paths but that they have all found some of the paths. I am building an awareness of patterns with this warm up. 

This exercise can be done with other words written in the same format. Try snow or cold  instead for a less complicated version of the puzzle. 

The next puzzle requires addition of adjoining numbers or numbers directly above and below one another. I hand out the page and ask students what is the same or different from the first  puzzle? (numbers, not all the same numbers  in the same row, doesn't make a word).

Students may understand the pattern and want to add another row to the puzzle on their own. This is an excellent way for students to demonstrate their understanding of the pattern of the puzzle.Extending the Pattern

Gingergbread houses

25 minutes

Today I begin by displaying the coordinate grid on the smart board (or you could draw one on an easel page). I show students the letters across the bottom and numbers down the side and say, if I wanted to find D2 what might I do? I ask for a volunteer to come up and show me where D2 might be. We touch the D row and the 2 row and where our fingers meet we color in the D2 square. I repeat this with G4. (You can also tell students this is like the game Battleship for those who may have played before.) This is another way that students must attend to the structure of the grid as they solve the problem (MP7) and attend to the activity with precision (MP6) in order to color in the squares correctly.

I tell students that today they will do the same thing on their papers. They will read the direction such as D2, figure out what color it should be, and then color in that square.

 I allow students to partner up. I provide them with the page that gives them a coordinate grid, and the directions that tell students how to divide and color each square on the grid.  Students work together to read the coordinates, find the correct squares and color them appropriately. The resulting drawing is a gingerbread house. 

This activity can be found at http://www.mathwire.com/seasonal/gingerbreadhouse2.pdf.

During the activity, I circulate around the room, helping groups color in 1 or 2 squares until they are able to find the squares on their own. I find that by helping students get started on the design, they are then able to continue on their own.