Linking Visual and Numerical Patterns

Experiences with a variety of patterns help students recognize order and make predictions. Physical patterns, such as clap, clap, stomp, and repetitive actions in songs, such as "Hokey Pokey," appeal to the youngest learners. Creating patterns gives students opportunities to describe what is being repeated or how the pattern grows and to explain what should come next. Teachers often use colors and shapes to help highlight numerical patterns, such as the ones created by a first-grade class that marked every fifth and tenth day during the school year on a number line and a hundred board.

See what the class did.

As students work with multiple representations of number and with counting, their knowledge of number concepts grows more sophisticated. When students place markers on hundred boards to highlight different counting sequences, they can see the relationships among the numbers and make connections between words and symbols. Linking numerical patterns to a visual display, as demonstrated in the interactive calculator and hundred board above is a way in which technology facilitates additional experiences, since students can view many different patterns in a brief time.

One Class’s Experience

As students have repeated experiences with patterns, they will be able to make and investigate conjectures about counting sequences. In preparation for celebrating the 100th day of school, a teacher had students complete hundred boards by coloring the patterns created by counting by fives, tens, and twos. She showed the students how to skip-count using a calculator so they could compare sequences on the calculator with those on the hundred board.

One pair of students began experimenting with counting by numbers other than twos, fives, and tens on their calculator. When they counted by threes, they noticed that they did not land on 100 on the display, as they did in counting by twos, fives and tens.

The teacher watched as the students removed the chips from their hundred board and started over with counting by threes. She also noticed that the students used the calculator to check the pattern. When the students repeated the work several times, she asked them to explain why they had repeated the process and what they were thinking. The students pointed out that 100 was not covered on the hundred board, as it had been in the other patterns they investigated, and they needed to check to see if they were placing the markers correctly. She encouraged them to make a permanent record of counting by threes on a hundred board and to see of they could figure out why 100 was not covered.

The teacher decided that it was important for the students to share what they were doing with the class. As a result of the class discussion, some students wondered if there were other patterns for which the markers would "go past" 100 without hitting it. This conjecture led to an investigation that continued the remainder of the year. Some students continued to use the hundred board for exploring patterns. Others enjoyed looking for patterns with the calculator, counting by twelves, fifteens, twenty-fives, and other numbers.

The students discovered that counting by fours gave 100 on the display. However, counting by sixes did not. Gradually, the students recognized that when they reached their first three-digit number, whether it was 100 or another number, their task was completed. They realized that 100 was more than ninety-something and was the smallest three-digit number.

Experiences such as these can support the development of intuitive notions about the meaning of factors and can reinforce place-value understandings.