Oakland Terrace Grade 5 Math

Students in Ms. Gale's class used growing geometric patterns to understand functions and to write equations to generalize the patterns.

A pattern block monster. The head is made of a hexagon, square, and two trapezoids. The monster grows by three triangles.

Students are familiar with relating growing geometric patterns to numeric patterns in earlier grades. This same activity is done in third grade. Ms. Gale presented this example to her students.

On the left, Ms. Gale's class has created a function table showing the number of blocks the monster has each year. The monster starts with just a head when it is born. Students in earlier grades are used to looking down the x-column to notice that the values (years) increase by 1. They notice that the y-column increases by 3. But a function table relates the x values to the y values. When students try to relate them, they run into a snag because they are not using multiplicative reasoning. They come up with values such as +4, +6, +8, etc. to relate the columns. Students are asked to problem solve to figure out how many blocks there would after 10 years.

She introduces the equation: 4 + 3x = y. She relates the equation to the monster, pointing out that the monster starts out with 4 blocks when it is born. Each year it adds 3 blocks.

The class then generalizes the growth of this monster which starts with 3 blocks, and grows by 2 blocks everyday.

After the students have completed these activities, other contexts for relating equations to real-world scenarios can be introduced. Perhaps a student places $20 in the lunch account. Each day, they spend $2 on lunch. So, the equation would be 20 - 2x = y. X = the number of days. Y = the $ in the account.

Indicators:
1.5.1.2 analyze patterns and generalize rules illustrated in patterns.
1.5.4.1 represent relationships using graphs and tables.
1.5.1.1 recognize, describe, and extend numerical and geometric patterns and functional relationships.