Making Predictions with Data

Collaborative Learning, Initiate Talk for Learning, Talk for Learning Approaches, Problem-based learning, Experiential Learning:
Learning Experience: Learners to establish different ways of counting, inquire into what happens when elements are repeated in an arrangement and explore different ways of counting Activity 1: Application of fundamental principles of counting ordered and unordered arrangements.
Initiate Talk for Learning, Experiential and Collaborative learning Approaches to support learners to use the fundamental principles of counting to solve problems.
Learners think-pair-share to brainstorm and collaboratively work with examples to recognise that if a task can be accomplished in m different ways and following this task, a second task can also be accomplished in n ways, then the first task followed by the second task can be accomplished in m×n ways.
Example 1: Akwesi has 5 pairs of trousers and 8 shirts. Assuming that each pair of trousers can be worn with each shirt, how many trousers-shirt outfits does he have?
Solution: For each pair of trousers, Akwesi has 8 shirts. Therefore, he has 5×8 = 40 different trousersshirt outfits to choose from.
Example 2: An eatery serves three different corn dishes (banku, akple and kenkey) and four different types of cold local drinks (asana, lamugin, soobolo, and pitoo). How many different different meal-witha-drink can you order as a customer?
Example 3: How many numbers of 3 different digits can be formed by choosing from the digits 1,2,3,4 and 5?
Solution: Task 1: Choosing the hundred's digit, we can do this in 5 ways. Task 2: Choosing the ten's digit, we can do this in 4 ways since one digit is fixed as a hundred digit. Task 3: Choosing the one's digit, this can be done in 3 ways because two digits are fixed as hundred and ten digits, respectively. Therefore task 1, followed by task 2, followed by task 3 can be accomplished in 5×4×3=60
Activity 2: Arrangements with repetitions
- Problem-based learning-learners in their groups work together to investigate and report on what happens if elements of sets are repeated in an arrangement.
- Here are some stimuli to guide learners.
Example 1: How many numbers of 3 digits can be formed by choosing from the digits 1,2,3,4 and 5 if the digits can be repeated?
Example 2: The ID numbers of WASSCE candidates consist of one capital letter (from the English alphabet - i.e. A -Z), followed by 3-digit number containing repeated digits; for example, A-000 is an ID number. How many such ID numbers can be formed?
Teaching and Learning Resources:
- Ludo dice, coins, playing cards, objects in a sac or bowl.
- YEAR TWO
Assessment (1.4.2.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.