To get an idea of the students’ knowledge about geometric patterns, the teacher will assign several heterogeneous groups and offer each group to discuss different patterns. The teacher will ask students to imagine that they are communicating with each other on the phone or Skype and describing to each other the pattern that they see. To define a particular pattern, it will be necessary to use the following questions: what does the pattern look like? Is the pattern growing or shrinking? How is it possible to describe this pattern to other group members to recreate it only from words? The groups discuss the patterns for 5-7 minutes and then share them with the rest of the class, asking other groups to recreate the patterns they describe.
Definition and Representation of Geometric Patterns
The teacher will ask students to work in pairs to cope with the task of using different patterns. Since students are just beginning to get acquainted with geometric patterns, the question will be open-ended: do you see the pattern? After that, choose any method and try using it to represent the pattern. Students, divided into pairs, will tell the class their opinion orally. During the discussion, the teacher will provide the class with another pattern for analysis, but this time it will be completely different. Students will work with this pattern, again choosing any method, and the result of their work should be ways of expressing a geometric pattern. Then, students will be offered a discussion concerning the method of representing a numerical pattern using diagrams. The teacher can evaluate students during discussions and work with representations of geometric patterns. For consolidation, students will be offered a similar to the previous task.
Terms Determination in a Numerical Pattern
The teacher will form groups and assign each of them its number, and there will be a list of cards on the blackboard under each group number. Special cards with images of unusual geometric patterns will be prepared for students on the blackboard. To understand the new topic as best as possible, groups of students will need to determine which term number and its value coincide with a certain card. Once the task is completed and the students demonstrate their method, they will attach the completed assignment to the board and take the next one. Next, students will need to create their cards with patterns for each type of pattern representation (words, table, graph). This friendly math game will allow students to develop teamwork skills and the teacher to evaluate this work and abilities. For consolidation, the groups will swap the cards to complete the task of the other group.
Creating a Geometric Pattern
Now students will work individually to create at least three shapes that follow the pattern. Students will be encouraged to be creative to build their geometric pattern using any forms they want. The basic rules for pairs of students will be as follows:
- Start drawing two circles, then double each element and subtract 1 to get the next element.
- Draw the first three shapes of the pattern.
- Create the appropriate value table.
- List the coordinates from the table and apply a pattern to the grid.
Each pair of students will evaluate the task of the other pair and, possibly, suggest making changes. For consolidation, students will try to determine and present their pattern independently. Students should first choose the method that seems most convenient to them and then present the pattern in a table or diagram. It is necessary to monitor the learning process in the classroom carefully and not miss which students did not understand the topic. In many respects, the student’s progress depends on the teacher (Lee et al., 2018). The teacher can finish the lesson by giving students an open-ended question: what do they think about the types of geometric patterns and methods of building and representing them.
Reference
Lee, Y., Capraro, R. M., & Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. International Electronic Journal of Mathematics Education, 13(2), 75-90.