## Counting and Pattern Tiles

These colorful tiles are excellent

in helping young mathematicians

explore concepts including:

Patterns,

Counting,

and Arithmetic

### “What can I do with these tiles?”

Read below to discover topics, activities, and discussion questions to get you started in mathematical play!

### I. Explore Patterns

- Line up the tiles to create a simple pattern. Ask your child to continue the pattern.

Pattern ideas: Green Green Yellow Green Green Yellow…

Green Blue Green Red Green Blue Green Red …

Vertical Vertical Horizontal Vertical Vertical Horizontal…

- Have your child create his/her own patterns.

Encourage your child to think about building patterns

- In a straight line horizontally
- In a straight line vertically
- In unique lines or curves
- In a grid

### II. Practice Arithmetic & Grouping

- Pour out a number of tiles of the same color (ideally green or yellow) and have your child count the tiles. (Recommended: pour at least 15 tiles.)
- If your child starts by counting one by one, that’s ok – let your child finish counting that way.
- Discuss grouping with your child – have your child make piles of tiles that are the same size. (Recommended: start with piles of 5). After all possible piles are made (plus any leftover tiles), skip count using the piles (“5, 10, 15, 20, plus three extra, equals 23.”)
- Try groupings of different sizes: piles of 2, 3, 4, etc.
- If your child is beginning to learn multiplication and is having trouble with multiplying a certain number, use these tiles to practice making piles of that number. (Ex: if your child is struggling with 9x?, practice making piles of 9.)

- Substitution: Pour out a number of tiles of the same color (green or yellow). Pour out at least 20 tiles. Again, have your child count the tiles in the way that he/she is most comfortable.
- Once again, make piles of tiles. (Recommended: start with piles of 5.)
- Now, let’s define a pile of 5 green tiles to equal 1 blue block. On a piece of paper, lay down 1 blue tile and write an equal sign next to it. Now place 5 green tiles on the other side of the equal sign. We have now defined the variable Blue Tile.
- Go back to your piles of green blocks on the table. For every 5 green blocks, remove that pile and replace with a blue tile. You will probably have some green tiles left over – that’s ok!
- Count again, now with each single blue tile = 5. “5, 10, 15, 20, 25, plus 4 extra greens is equal to 29.”

Also try:

- Pouring out more green tiles (have at least 30 total) and try defining a red block to be = 10.
- Try defining the blue and red blocks to be any values you wish (2, 3, 4, 20, etc).
- Try defining each block to be a place value. For example, say reds are thousands, blues are hundreds, yellows are tens, and greens are ones.
- What number does 2 reds, 4 blues, 7 yellows, and 2 greens equal?
- What number does 14 blues, 8 yellows, and 11 greens equal?

- Try defining the red blocks to be negative numbers, ex, -2. What would three green blocks plus one red block equal?

### III. Explore Probability, Percentages, Fractions

- Create a simple pattern of tiles (start with just using two colors).
- Ex: Green Red Green Red Green Red:
- What percentage of tiles are Green? What percentage of tiles are Red?
- What fraction of the tiles are Green? What fraction of the tiles are Red?

- Ex: Yellow Yellow Green Blue Yellow Yellow Green Blue
- What percentage of tiles are Blue? Green? Yellow?
- What fraction of the tiles are Blue? Green? Yellow?

- Ex: Green Red Green Red Green Red:
- Have your child create different arrangements and patterns using different colors. Discuss what percentage and what fraction exist of each color.
- Pick a fraction and its corresponding percentage: say, ¼ and 25%. How many different ways can you represent those values using the tiles?
- Examples of ways:
- Place down three tiles of one color and a fourth tile of another color.
- Place down four tiles, one of each color, where each tile = ¼ or 25%.
- Place down any four tiles with three having a vertical orientation and the fourth having a horizontal orientation. Or three laying down on the table and one standing up.
- Place down 20 tiles where 15 are in one color and the remaining 5 are in another color.

- Examples of ways:
- Pick four tiles: three in one color, the fourth in a second color, and place them inside a concealed box or bag. Discuss: what is the probability of reaching inside and pulling out the one tile of the second color?
- What if you add more tiles to that bag/box? How do the probabilities change?
- What happens if you draw a tile and place it back inside, VS draw a tile and leave it out of the bag? How do the probabilities for each color tile change then?

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