Patterns and Relations · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.2.2.LI.1 - Explore patterns of a sequence using plane figures and continue with more terms.

By the end of the lesson, learners can:

Define a sequence as a set of numbers or objects that follow a particular pattern, and a series as the sum of the terms of a sequence.
Continue a given sequence of plane figures by identifying the pattern of change from one term to the next.
Construct a table of values from a figure pattern and use it to predict the next several terms.
Write a simple algebraic expression (rule) that describes the relationship between the term number and the term value in a figure sequence.
Create their own figure sequences using matchsticks, cardboard shapes, or drawings and state the rule that generates the pattern.

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Curriculum details

Strand: Algebraic Reasoning (Strand 2)
Sub-strand: Patterns and Relations (2.2)
Content standard: 2.2.2.CS.1 - Demonstrate understanding of patterns and relations involving sequence and series, generate strategies for algebraic formulas, and use them in solving real-life problems. 2.2.2.LO.1 Explore patterns of a sequence using plane figures and find the nth and the sum of the nth term of an arithmetic and geometric progression. Analyse, model, and solve real-life problems involving financial mathematics and exponential growth.
Indicator: 2.2.2.LI.1 - Explore patterns of a sequence using plane figures and continue with more terms.
Suggested placement: Semester 1, Week 15 (Week 15 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 201

Exemplars (from the NaCCA curriculum)

Using Talk for Learning approaches, learners discuss the meaning of sequence as a set of objects, like numbers, which follow a particular pattern, whilst series is the sum of all the items in the sequence.
Collaborative learning: In convenient groups, task learners to investigate, discuss and identify reallife patterns in the environment, including numerical and non-numerical sequences (shapes, fabric, etc.) and write the algebraic expression from the pattern. Encourage learners to justify their ideas and respect ideas from others, leading to the development of the character of tolerating others and respecting individual variance.
Example: Learners investigate and talk about: i. Seating around tables. (In a restaurant, a rectangular table fits 6 people. When two rectangular tables are put together, 10 people can be seated. Put 3 rectangular tables together, and now 14 people are seated ...).

Photograph of a wooden dining table with six chairs around it. — A photograph of a wooden dining table with six matching chairs set around it.

ii. Stacking chairs, bowls, etc., to compare the number of objects to the height of the object.

Photograph of white plastic chairs stacked in three columns. — A photograph of white plastic chairs stacked in three tall columns.

Experiential Learning: In small ability groups, task learners to use sticks, matchsticks, symbols, and numerals to create a sequence and write the algebraic expression if the sequence continues.
Example 1

A growing pattern of small circles arranged in triangles, each stage adding a row. — A growing pattern made of small open circles: a group of one, then a triangular group, then a larger triangular group, each stage adding another row along the base.

Example 2: In the match-stick pattern, a sequence is modelled with 1 side matchstick, 2 sides matchsticks and 3 sides matchsticks. Study the pattern and draw, i. The next two squares of the pattern and create a table showing the perimeter of all the squares. ii. How many matchsticks will make the 6 th square? iii. Write the rule (algebraic expression) to describe your matchsticks if the pattern continues.

Three orange squares in a row, each larger than the last. — Three squares drawn in orange outline in a row, each larger than the one before, showing a growing pattern.

Match-stick pattern
In convenient groups, task learners to find the rule for a given sequence in both direct and indirect questions. Show tolerance to each other as you share diverse ideas in your groups.
Teaching and Learning Resources:
- * Matchsticks * Cardboard
Assessment (2.2.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.