Color tiles are 1" square tiles that come in assorted colors (typically red, green, yellow and blue). While incredibly simple, color tiles can be used to learn a broad range of math topics. Color tiles provide a concrete and hands-on way to mode math concepts such as area, perimeter, patterns, algebra, operations, fractions, square numbers, and more.
Virtual manipulatives, such as Brainingcamp's Color Tiles Manipulative, include convenient background grids and snapping, along with 9 color options. The virtual color tiles manipulative also has a place value mode where each of the nine tiles has a place value label of 0.0001 to 10000.
Counting and Cardinality
Using color tiles, model and write the numbers 0-10. Count the numbers 0-10 and understand that each successive number refers to a quantity that is one larger.
To find 3 + 4, place 3 of one tile color and 4 of another. There are 7 tiles in total, so 3 + 4 = 7. Explore how many other ways two numbers can be summed to make 7. To find the missing addend in the sum 3 + ? = 5, place 5 tiles of one color and then cover 3 of them with tiles of a different color. It would take 2 more tiles to cover the 5 tiles, so the missing addend is 2.
To find 8 – 5, place 8 tiles of one color and then remove 5 of the tiles. There are 3 tiles remaining, so 8 – 5 equals 3. The subtraction can also be modeled by placing 8 tiles of one color, and covering 5 of those tiles with another color. There are 3 tiles that are not covered, so 8 – 5 equals 3.
Multiplication can be thought of as the first number telling how much to take of the second number. To model 5 × 4, make 5 groups of 4 tiles. The total number of tiles can be found by skip counting. There are 20 tiles in total, so 5 × 4 equals 20. Multiplication can also be modeled by creating a row of 4 tiles, and then making 5 rows. There are 20 tiles in the array, so 5 × 4 equals 20.
Dividing 12 by 3 is like finding how many groups of 3 can be made from 12. It is the same as counting how many times 3 can be subtracted from 12 or finding how many rows of 3 can be made from 12. Using any of the methods, 12 ÷ 3 = 4.
Create repeating nonnumeric patterns and have students describe and extend the pattern. Next create a numeric pattern. Have students create a table to identify and describe the pattern.
Area and Perimeter
Area is the number of square units needed to cover a figure. A unit square is one unit long and one unit high. Perimeter is the distance around a figure. If the side length of a tile is 1 unit, then a tile has an area of 1 square unit and a perimeter of 4 units. Place 6 tiles beside each other to make a figure with an area of 6 square units and a perimeter of 14 units. Using another 6 tiles, make a staircase figure with an area of 6 square units and a perimeter of 12 units. Notice that figures can have the same area but different perimeters.
Make a bar with 2 red tiles, and 3 blue tiles. A fraction is a number that names a part of a whole. The top number in a fraction is called the numerator and the bottom number is called the denominator. The denominator represents the number of equal-sized pieces in a whole unit. The numerator represents the number of pieces made by the part. So the red tiles represent the fraction 2/5 and the blue tiles represent the fraction 3/5.
Factors, Prime Numbers, and Composite Numbers
To find the factors of a number, find all the different rectangles that can be made with a number of tiles equal to that number. The length and width of any such rectangle is a factor of the number. A prime number is a whole number greater than 1 whose only factors are 1 and itself. A composite number is a whole number that has more than 2.
Assign different place values to different colored tiles. To model 347, place three 100 tiles, four 10 tiles, and 7 one tiles. To model the addition 347 + 26, place an additional two tens tiles and 6 ones tiles. If there are 10 or more of any tile color, regroup by exchanging ten tiles for 1 tile of greater place value. After regrouping there are three 100 tiles, seven 10 tiles, and three ones tiles. So 347 + 26 equals 373.
Use color tiles to make bar graphs of collected data. Label the bars along the x-axis.
Square Numbers and Square Roots
A square numbers is the product of a number and itself. To find 3², model multiplying 3 by itself with an array that is 3 units high and 3 units wide. There are 9 tiles in total, so 3² = 9. The square root of a number is the number that when multiplied by itself equals the original number. To find the square root of 16, place 16 tiles in a square shape. Each side is 4 tiles long, so the square root of 16 is 4. To find the square roots of 20, try to place 20 tiles in a square shape. Since 20 tiles cannot form a square, the number 20 is not a perfect square. Since 20 makes a square greater than 4×4 but smaller than 5×5, we can estimate the square root of 20 as a number between 4 and 5.
Ratios and Proportions
A ratio is a comparison of two numbers. Place 2 red tiles and 5 blue tiles. The number of red tiles to blue tiles can be written as the ratio 2:5. Next double the number of tiles to create the ratio 4:10. A proportion is an equation that shows that two ratios are equal. The ratios 2:5 and 4:10 form a proportion because their ratios are equivalent. The cross products of proportions are equal.