First-graders can explore algebraic relationships using pattern blocks. In this activity, they will learn to recognize a pattern, and extend it. You will need a set of pattern blocks per student. Set up a short pattern with the pattern blocks. Remind the students of the names of the various shapes. Tell the students to duplicate the pattern, and extend it by two blocks. Work to increase the pattern extensions.
This activity can be used in first, second or third grade. Increase the complexity according to the age of the students. You will need a set of pattern blocks for every student, grid paper and crayons or colored pencils. Divide the students into four groups. The groups will complete the activity one at a time. Pile all the pattern blocks in a single pile. Tell the first group to grab a handful of pattern blocks, and make a bar graph of the blocks they took. Demonstrate how to make the bar graph with the shapes (or colors) of the blocks plotted on the x-axis, and the quantity on the y-axis. They can color each bar a different color to increase the readability of the graph. Increase the complexity according to the age of the students. Younger students might just count the number of each shape. Older students can graph both number of each shape, and the colors.
This activity develops the concept of patterns that grow for third- and fourth-graders. Each student needs 12 squares, 12 trapezoids and three triangles. Build a tree with pattern blocks using one square as the trunk. Place a trapezoid on top of the trunk, and a triangle on top of the trapezoid. Tell the students this is a tree on its first birthday. Build a second tree using two squares on top of each other for the trunk. Place a trapezoid on top of the trunk, and another trapezoid on top of the first. Top the tree with a triangle. Tell the students this is the same tree on its second birthday. Ask the students to build the tree on its third, fourth and fifth birthdays.
Tell the students to make a chart by folding a piece of paper vertically four times. Flatten the paper. Label the far left column "Birthdays." Label the next three columns "Square," Trapezoid" and "Triangle" respectively. The last column should be labeled, "Total Number of Blocks." The first line is birthday "1." Under the square, write "1 +"; under the trapezoid, write "1 +"; u nder the triangle, write "1 = ." Write "3" in the "Total Number of Blocks" column. Ask the students to fill in the remainder of the chart representing the blocks used for each birthday of the tree.
Introduce the terms constant and variable. Ask the students to look at their charts and tell you if they notice any patterns. Ask them what things stayed the same.
For this activity for third- and fourth-graders, tell the students to visualize 100 square pattern blocks in a row. Ask them to tell you what the perimeter is (100 + 1 + 100 + 1), and what the area is (100 x 1 squares²). Ask the students to visualize in squares. How would they find the perimeter, and area? Build several other figures that could be copied in two, three or four extensions. Ask how many pattern blocks would be used in each of these extensions.