## Colorful 1 inch sq Area Tiles

These colorful tiles are excellent

in helping young mathematicians

explore concepts including:

Patterns,

Arithmetic,

Area, and Perimeter

### “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 …

- 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
- Or even stacking!

### II. Practice Arithmetic & Grouping

- Pour out a number of tiles of the same color 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 at least 20 tiles of the same color. To start, let’s say we pick green. 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 tile.

Extra: 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. Example: “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 Perimeter and Area

Each tile is a perfect square with 1” long edges, making each tile exactly 1inch^{2}.

- Using just four tiles…
- Create a larger square. What is the area of the square? What is the perimeter?
- Rearrange the tiles to create a 1x4 rectangle. What is the area? What is the perimeter?
- Is the area the same for both the square and the rectangle? Why or why not?
- Is the perimeter the same for both the square and rectangle? Why or why not?

- Create other unique shapes using just four tiles. Have the four tiles always touching in some way, but they can touch just at the corners. What is the area of your unique shape? What will the area always be of your unique shape when you use 4 tiles? How does the perimeter change?

- Consider dimensions:
- Use four tiles to create a 1x4 rectangle.
- Now let’s make a 4x1 rectangle. What changes? What’s the same?

Discuss: When might it matter in everyday life to distinguish the difference between something like 1x4 and 4x1? (Hint: Think of a 4x6 picture frame vs 6x4 picture frame.)

- Create more complex shapes and use estimation.
- Experiment making larger squares and rectangles. Experiment making shapes with symmetry and without. How do the areas and perimeters compare on your different shapes?
- Practice making large designs without counting how many tiles you use as you go. Once your picture is done, try estimating how many tiles you think you used. Use reasoning for your estimate. Count your tiles to verify how close you were. Remember to count in groups! Counting 1, 2, 3, 4… will take too long for larger pictures.

### IV. 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 any four tiles with 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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