C1.2 Create and translate patterns that have repeating elements, movements, or operations using various representations, including shapes, numbers, and tables of values.
Activity 1: Calculated Patterns (Create a Pattern Using a Calculator)
Develop algebraic reasoning by exploring patterns using a calculator.
Give an instruction such as, "Press the [+], [5], and [=] keys. You will see the number 5 displayed."
Note: Ensure that students' calculators have the Constant Factor function.
Have people discover rules by asking questions such as:
- What will happen if you press the [=] key three more times?
- What will be the number if you press the [=] key 5 times?
- What happens next when you count in intervals of 5?
- What do you do to count in intervals of 10 with a calculator?
- Does the number 78 show up when you count by 10s?
- How many times must you press the [=] key to reach 100?
- If we count by 2, will the number 34 be in our pattern? How can you tell?
Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 66.
Activity 2: Ants in the Park
Summary
In this activity, students solve a problem using a table of values.
Materials
Small manipulatives in sufficient quantity for the class
Directions
Present the following problem to the students and ask them to solve it using a table of values. Ensure that students understand the problem.
Situation
Ants are walking to the park. On the 1st day, three ants go there. On the 2nd day, one more ant goes to the park than on the previous day. On the 3rd day, one more ant goes to the park than the day before. In fact, each day, one more ant goes there than the day before. How many ants go to the park on the 10th day?
Variation
Modify the problem by saying that four ants go to the park on the 2nd day rather than one more than the previous day, etc.
Source: adapted from J. Taylor-Cox, Workshop Algebra in the Early Years, "The Ants Go Marching… ," More Math Fun, NCTM Conference, 2005.
Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 145.
Activity 3: Guess My Pattern
Summary
In this activity, students are asked to create repeating patterns by applying specific criteria.
Directions
Allow students to work individually or in teams. Provide each student or team with a set of logic blocks. Present the problem and criteria to the students and ensure that they understand the task.
Problem
Create a non-numeric repeating pattern that meets the following criteria.
Criteria
- The pattern must be created using attribute blocks.
- Each term in the pattern must have three attributes: size, shape, and colour.
- The term in the 11th position of the pattern must be a large blue rectangle.
Ask the students to represent their pattern in a concrete way (logical blocks) and in a table of values.
Once the work is done, ask the students to circulate around the classroom to observe the different patterns created.
Then compare the different patterns with students using the following points:
- the attributes;
- the created pattern;
- the number of elements in each pattern;
- the position of each repeating term;
- the rule.
Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année, p. 147.