Pattern blocks are colored geometric shapes. While each blocks is a different shape, they all share the same side length (except for the red trapezoid which has one side equal to twice the common side length). Because shapes share a common side length, they can be put together to form interesting patterns. A set of pattern blocks will contain some or all of the following shapes:
Except for the square and small rhombus, each pattern block can be made from small triangles. This means that the areas of the shapes are proportional, a relationship that supports the illustration of various mathematical concepts. Pattern blocks offer a hands-on way to learn fractions, mixed numbers, operations on fractions, patterns, ratios, proportions, congruence, similarity, lines of symmetry, and more.
Virtual manipulatives, such as Brainingcamp's Pattern Blocks Manipulative, empower users to do things that are difficult or impossible with physical manipulatives. Blocks can be toggled from solid to transparent to more easily see when stacked pattern blocks overlap. Convenient triangular or coordinate plane grids make it easy to work with pattern blocks. A handy snapping feature makes it easy to align pattern block edges.
A fraction is a number that names a part of a whole. If a yellow hexagon represents a whole, notice that it take 3 blue trapezoids to make a yellow hexagon. 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 blue trapezoids model the fraction 3/3. Now remove one blue trapezoid to model the fraction 2/3. Remove another trapezoid to model the fraction 1/3. Remove 1 more trapezoid to model the fraction 0/3.
If a yellow hexagon represents a whole, then two blue rhombi represent the fraction 2/3. Notice that four green triangles are equivalent to two blue rhombi. Since four green triangles represent the fraction 4/6, the fractions 2/3 and 4/6 are equivalent.
If a yellow hexagon represents a whole, use blue rhombi to make the fractions 1/3, 2/3, and 3/3. Think about what fraction comes next in the pattern. The next fraction is 4/3. A fraction where the numerator is greater than the denominator is called an improper fraction. Improper fractions can be written as a mixed number with a whole and a fraction. So 4/3 can be written as the mixed number 1 1/3.
Adding Fractions (like denominators)
If a yellow hexagon represents a whole, adding 1/6 and 4/6 can be modeled by combining 1 green triangle with 4 green triangles. The result is 5 green triangles, so 1/6 + 4/6 equals 5/6. To add fractions with like denominators, just add the numerators.
Adding Fractions (unlike denominators)
If a yellow hexagon represents a whole, adding 1/2 and 1/3 can be modeled by combining one red trapezoid with one blue rhombus. Try to model 1/2 and 1/3 as equivalent fractions using a common block type. Using green blocks, the fractions 1/2 and 1/3 can be modeled as equivalent fractions 3/6 and 2/6. The sum of 3/6 and 2/6 is 5/6, so 1/2 + 1/3 equals 5/6.
If a yellow hexagon represents a whole, model the subtraction 2/3 – 1/3 by starting with two blue rhombi to represent the first value, 2/3. To subtract 1/3, remove one blue rhombus. One blue rhombus remains so 2/3 – 1/3 equals 1/3.
Multiplication can be thought of as the first number telling how much to take of the second number. To model 1/2 × 1/3, place a blue rhombus to represent 1/3 (assume a yellow hexagon represents a whole). Next take 1/2 of the blue rhombus. A green triangle is 1/2 of a blue rhombus, so 1/2 × 1/3 equals 1/6.
Division can be thought of as finding how many times the second number fits into the first number. To model 1/2 ÷ 1/3, find out many times 1/3 fits into 1/2. The 1/3 block fits into the 1/2 block one full time and one half time, so 1/2 ÷ 1/3 equals 1 1/2.
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.
Ratios and Proportions
A ratio is a comparison of two numbers. Place five green triangles and one yellow hexagon on the workspace. The area of the green triangles to the area of the yellow hexagon can be written as the ratio 5:6. Next double the number of blocks to create the ratio 10:12. A proportion is an equation that shows that two ratios are equal. The ratios 5:6 and 10:12 form a proportion because their ratios are equivalent. The cross products of proportions are equal.
Congruent figures have the same size and shape. Create a figure using a combination of blocks. Then try and make the same shape using a different combination of blocks. If the new blocks can completely cover the original blocks, the figures are congruent.
Similar figures have the same shape, but may be different sizes. For figures to be congruent, the lengths of corresponding sides must have the same ratio. The shapes in the triangular patterns are similar to each other. The shapes in the trapezoidal pattern are not similar to each other because the lengths of corresponding sides do not have the same ratio.
Lines of Symmetry
A line of symmetry is a line that cuts shapes into two identical figures. Using a coordinate plane, place a group of connected pattern blocks immediately to the left of the vertical y-axis. Next place pattern blocks on either side of the line to create a symmetric figure.