Applications of Algebra

Collaborative Learning: Learners will work in convenient groups (ability, mixed-ability, mixed gender etc.) to solve problems and present answers related to sequence and series.
Talk for Learning Approaches: Learners will brainstorm through think-pair-square and debate and discuss the types and features of sequences.
Project-based Learning: Learners will collaboratively embark on a project to develop a sequence that is relevant and applicable to real life and make presentations.
Experiential Learning: Learners will collaboratively engage in hands-on activity (learning by doing) to create sequences using objects, symbols and numerals and discuss pattern rules.
Problem-based Learning: Learners will collaboratively undertake a research inquiry into what happens when terms of sequence are summed up.
Activity 1: Sequence in real life situations Discuss sequences in the natural environment and create sequences using objects, symbols, and numerals.
Talk for Learning: Initiate TfL approaches for learners to brainstorm, debate, and discuss reasons for learning about sequence:
Example: Some important facts about sequence and series:
- The knowledge of sequence and series helps to shape our logical skills.
- Sometimes, we want to find out all the possible things out there because we want to know the most probable terms to satisfy our curious minds. Sequence and series help to settle this curiosity in us.
- Knowledge equips us with skills and strategies to find the sum of things going on even up to infinity, which is useful in scientific thesis.
Note: A Sequence is any set of objects, often numbers, that follow a particular pattern infinitely. A series refers to the description of the operation that would add all of the items in a sequence.
Collaborative and Problem-based: Learners work in small mixed-ability groups to investigate, identify and discuss real life patterns in their environment and talk about the pattern rule. For instance, have learners act out and talk about:
- Stacking cups, chairs, bowls etc., to compare the number of objects to the height of the object.

- Seating around tables: Consider a restaurant with a square table that fits 4 people. What happens when two square tables are put together, now 6 people are seated. Put 3 square tables together, and now 8 people are seated, etc. Learners may visualise this better if they are allowed to model this sequence.
Note: A rectangular table can also be used to model the sequence, but it starts with 6 seats.

- Filling something: Consider the rate at which the object is being filled, using time as the variable. An example could be a sink being filled or a pool being filled. Also, consider draining a liquid, sand, sugar, etc., out of a container with a small hole beneath.

- Fencing and perimeter: Discuss how adding a fence panel to each side of a rectangular fence would change the perimeter. For example, the first figure concept could have one panel on
each side (or change it so it is not a square). The next figure concept could have two panels on each side and so on. Each time, find the new perimeter.

- Building pyramid-like patterns, where objects are constantly increasing or decreasing, such as in seats in a stadium or an auditorium. For example, a situation might be that seats in each row decrease by 4 from the previous row.

- Negative number patterns: Think about temperature and places below sea level on Earth. Create situations like, during rainfall, the surface of the water started at 153 feet below sea level and rose at a rate of such and such per hour or diving in the ocean. 

Activity 2: Modelling instances of sequences Collaborative, Problem-based and Experiential Learning: Learners work in small mixed-ability groups and model sequences (numerical and non-numerical - using colours, cut-out shapes, objects, fabrics, sound, actions, etc.) and talk about the pattern rule. For instance,
- Learners work in smaller groups/pairs to produce/create a sequence and record their findings in tables,
- Learners in one group create a sequence and then challenge another/other groups to:
- continue or extend the pattern to include the next term;
- describe the pattern rule and record them in tables;
- write a rule that will allow you to find any large shape form.
Example 1: Study the sequence, extend it to complete the table below and answer the questions that follow.

Pattern no. 1 2 3 4 5 6 ...
No. of bottle caps 3 6 10
- Describe the pattern rule.
- Write a rule which will allow you to find the number of small pebbles in any large pebbles.
Example 2: Study the pattern, draw a picture of the next likely shapes and complete the table. Write a pattern rule which will allow you to find:
- the number of squares
- the number of joints in any large shape. 

Pattern no. 1 2 3 4 5 6 ... ... No. of squares 1 4 9
No. of joints 4 9 16
Teaching and Learning Resources:
- Cut out shapes of different colours and orientation
- Maths Technology learning apps, tools and devices
- Chalkboard illustrations
- Worksheets
- Cut-out geometrical shapes of different colours and orientation
Assessment (1.1.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall.