Making Predictions… · SHS1 Additional Mathematics

Lesson notes

Learning Objectives

Indicator: 1.4.2.LI.6 - Work collaboratively on an experiment (e.g. tossing of coins or dice) to determine the relative frequencies of events and interpret them.

By the end of the lesson, learners can:

Define relative frequency as the ratio of the number of times an event occurs to the total number of trials, using correct probability vocabulary.
Conduct a collaborative experiment (tossing coins or rolling dice) with at least 10 trials, record the outcomes accurately in a table, and compute the relative frequency of each event.
Compare the relative frequency of an event with its theoretical probability and explain, in their own words, why the two values may differ for a small number of trials.
Draw a graph showing how relative frequency changes as the number of trials increases, and interpret the trend toward the theoretical probability.
Present their group’s findings to the class, justify their conclusions using data from their experiment, and respond respectfully to questions from other groups.

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Curriculum details

Strand: Handling Data (Strand 4)
Sub-strand: Making Predictions with Data (4.2)
Content standard: 1.4.2.CS.1 - Demonstrate knowledge of basic principles of permutation and combination and interpret probability in everyday life. 1.4.2.LO.1 Explain combination and permutation, state their difference and solve basic problems related to permutation and combination. 1.4.2.LO.2 Explain the terminologies in probability orally and find the relative frequency in a given experiment.
Indicator: 1.4.2.LI.6 - Work collaboratively on an experiment (e.g. tossing of coins or dice) to determine the relative frequencies of events and interpret them.
Suggested placement: Semester 2, Week 20 (Week 40 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.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

exemplars - p.251: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page
Curriculum reference: NaCCA curriculum document, p. 250

Exemplars (from the NaCCA curriculum)

Collaborative Learning, Initiate Talk for Learning and Talk for Learning Approaches, Problem-based learning, Experiential Learning
Learning Experience: Learners discuss the relative frequencies of events, compare results with theoretical definitions of probability and what happens when terms of ordered and un-ordered arrangements and special arrangements.
Activity 1: Relative frequencies of events
Initiate Talk for Learning, problem-based and Collaborative learning Approaches to support learners in solving problems of relative frequencies of events.
Learners work in groups to perform experiments using coins, ludo dice, playing cards etc, up to about 10 trials in each case and record their findings.
Example 1: The table shows the number of times a coin is tossed and the outcome of each trial.
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 Outcome T T H T H T H H T T H T H
What is the relative frequency of (observing) heads after
- each trial ii) the experiment
Solution:
- Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 Outcome T T H T H T H H T T H T H RF 0 0 1 1 2 2 3 4 4 4 5 5 6 3 4 5 6 7 8 9 10 11 12 13 /
- = 0.46 !" Example 2: The table shows the number of times a coin is tossed and the outcome of each trial.
Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 Outcome T T H T H T H H T T H T H Trial 14 15 16 17 18 19 20 21 22 23 24 25 26 Outcome T H T T H H T H H T T T H
What is the relative frequency of (obtaining)
- Tails after the experiment
- Tails after each trial, and how does it compare to the theoretical probability of obtaining tails?
- Draw a graph to show how the relative frequencies of tails vary in the experiment.
Activity 2: Theoretical probability of an event
- Learners to establish and use the theoretical probability of an event to solve simple problems
- Learners discover the theoretical probability of an event as the likeliness of the event happening based on all the possible outcomes given by: BX#'N3 PI I&MPX3&'_N PXG;P#NO
- Probability of Event = BX#'N3 PI +POOL'_N PXG;P#NO
Example: A fair coin is tossed twice, and the result is recorded. What is the probability that (a) the first toss shows a head; (b) the second toss shows a head.
Teaching and Learning Resources:
- Ludo dice, coins, playing cards, objects in a sac or bowl.
- YEAR TWO
Assessment (1.4.2.AS.6). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.