Home School Life Journal

Home School Life Journal ........... painting by Katie Bergenholtz
"Let us strive to make each moment beautiful."
Saint Francis DeSales

Patterns on Tiles and Cubes

"The ability to see patterns is an essential element in understanding mathematics and is closely connected to the ability to think logically."
-Mathematics...A Way of Thinking, Robert Baratta Lorton

I made a pattern with tiles, and invited him to predict and build the next step.
"See how many steps of my pattern you can make with your tiles without checking each new step with me. Keep adding steps until you have run out of tiles.
Then I cleared our tiles away and began a new pattern. He watched while I made a few patterns and then he could predict the next pattern.
"Most learning consists of observing closely what has already happened, and from that trying to project what will happen. The most reliable the  patterns, the better the predictions. More difficult or less regular patterns lead to more tenative predictins."
-Mathematics...A Way of Thinking, Robert Baratta Lorton

Patterns do not have to grow. It may change direction, or it may grow to a certain height and then decrease in size in an equally predictable manner.

I then let him make up a pattern using the tiles and when he had a pattern he liked, I showed him how to record it on graph paper. These recordings could then be kept and used as puzzles for others to solve.

Once we tired of creating patterns with tiles, we went on to cubes.

We labeled the patterns with letters.
We recorded them on graph paper.

Then we analyzed the patterns. Do all the patterns look the same?  How many different kinds of patterns could we make? Can you make a pattern with the cubes having the same patterns going up and across?
If I give you a piece of graph paper colored in, can you build the cube pattern from which it was made?

"The mathematical experiences that lie ahead are based on the belief that patterns form the core of all mathematics. The search has just begun."
-Mathematics...A Way of Thinking, Robert Baratta Lorton



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5 comments:

  1. I love the follow on activity of graphing it. I need to work on my kids graphing skills.

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  2. I am a strong believer in looking for patterns everywhere. Great work on trying to predict your pattern - interesting idea!

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  3. I love your blogs! You are a very amazing mom and teacher. Wish I had found you when my kids were younger because I know it would have changed my mind on teaching with text books. While I use them scantly I still use them and I use CM stuff but not all the way. Love gleaning from all the fabulous cooking you do at your house.

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  4. We love playing with pattern blocks. I love your idea of graphing them.

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  5. This is wonderful Phyllis! I guess you have done tanagrams? That is what this reminds me of. I bet your kids are just so awesome to talk to. They seem to know so much! I love the way you HS.

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