##
* *Reflection: Diverse Entry Points
Using A Pattern to Solve A Problem - Section 1: Warm Up

Patterns and geometry often take a different type of understanding than computation and operations. Children who quickly grasp computational operations often struggle with the more visual patterns and geometry.

Today one of the children who struggles with computation suddenly saw the computation pattern that was laid out in the puzzle. While everyone else was still trying to figure out how the triangle worked, she had completed it and was trying to create her own row based on the pattern. She had to think about the computation involved, but she had clearly figured out how the puzzle worked and was forging ahead, well ahead even of the children who are usually the first to complete a math assignment.

When we moved forward to the Gingerbread house, she again quickly grasped how the coordinates worked and she was half way through the directions when her classmates had not even finished the first 4 or 5 directions.

I often see this happen with the geometry and fraction units as well. This type of math is more visual and almost artistic in nature, and it is always a different group of students who excels at it.

This is an important case for not grouping children in permanent groupings. Different children have different strengths so be careful to watch for those children who may struggle in one area and shine in another. Respect the diversity of their skills, and support all the levels of learning that a child may show.

*Different Understandings*

*Diverse Entry Points: Different Understandings*

# Using A Pattern to Solve A Problem

Lesson 1 of 14

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

#### Warm Up

*15 min*

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

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#### Gingergbread houses

*25 min*

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.

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Using A Pattern to Solve A Problem
- LESSON 2: Skip Counting Patterns
- LESSON 3: Extending Partners of 10 and 100
- LESSON 4: Patterns in Larger Numbers
- LESSON 5: Larger Numbers: A Tie to Social Studies
- LESSON 6: Doubles and Halves are Patterns Too
- LESSON 7: Smiley Faces and Up
- LESSON 8: Put It Together and Take It Apart
- LESSON 9: Pets, Pets and More Pets
- LESSON 10: Larger Number Patterns
- LESSON 11: Let's Review
- LESSON 12: Patterns in Nature
- LESSON 13: Writing and Solving Number Stories
- LESSON 14: Trimester Assessment Day