# 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