Making Predictions with Data

Collaborative Learning, Initiate Talk for Learning and Talk for Learning Approaches, Problem-based learning, Experiential Learning
Learning Experience: Learners to discuss the types and features of different permutations (circular arrangements, identical elements, etc.). What happens when terms of ordered and un-ordered arrangements and special arrangements.
Activity 1: Ordered and un-ordered arrangements
- Initiate Talk for Learning, Experiential and Collaborative learning Approaches to support learners to distinguish between ordered and un-ordered choices.
- Learners think-pair-square to brainstorm and discuss situations where they have to arrange a set of objects in which the order of appearance of elements of the set does not matter. For instance, APC is not different from PAC, because both sets have the same elements.
- Learners work in their groups to make presentations by comparing, contrasting and debating with other groups on ordered arrangements of items and un-ordered arrangements of items
- Learners discover/establish that the number of subsets of r elements that can be formed from elements is nCr =(n¦r)= n!/r!(n-r)!
Example 1: In how many ways can a committee of 3 members be formed from a team of 8 people? Solution 8 C 3 =(8¦3)= 8!/3!(8-3)!=56
Example 2: There are 6 different coloured cubes in a bag. In how many ways can Mawuli draw a set of 3 cubes from the bag?
Activity 2: Combination as a way of counting
- Initiate Talk for Learning, problem-based, Experiential and Collaborative learning Approaches to support learners to use combination formulas in different contexts.
- Learners explore situations where fundamental principles of counting along with the combination formula are used to solve counting problems.
- Learners find the number of ways of selecting r objects from a collection with a given condition.
Example: How many committees consisting of 2 women and 1 man can be formed from a group of 4 women and 2 men?
Solution: Task 1: Selecting 2 women from 4 women can be done in 4C2 ways.
Task 2: Selecting 1 man from 2 men can be done in 2C1 ways.
Task 1 followed by task 2 can be accomplished in 4 C 2 × 2 C 1 = 6×2 = 12 ways
Activity 3: Relationship between combination and permutation formulae Initiate Talk for Learning, problem-based, Experiential and Collaborative learning Approaches to support learners in using the relationship between combinations and permutation formulas to Solve problems Learners discover/establish that nCr =(n¦r)= n!/r!(n-r)!= nPr/r! and use it to solve problems.
Example 1: Find the value of n if i) nP 3 /nC 4 = 24/5 ii) nC 5 /nP 4 = 1/4
Teaching and Learning Resources:
- Ludo dice, coins, playing cards, objects in a sac or bowl.
- YEAR TWO
Assessment (1.4.2.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 4 Extended critical thinking and reasoning.