Probability Unit Grade 5

Overall Expectations:

represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models.

Specific Expectations:

determine and represent all the possible outcomes in a simple probability experiment (e.g., when tossing a coin, the possible outcomes are heads and tails; when rolling a number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6), using systematic lists and area models (e.g., a rectangle is divided into two equal areas to represent the outcomes of a coin toss experiment).

represent, using a common fraction, the probability that an event will occur in simple games and probability experiments (e.g., My spinner has four equal sections and one of those sections is coloured red. The probability that I will land on red is .)

pose and solve simple probability problems, and solve them by conducting probability experiments and selecting appropriate methods of recording the results (e.g., tally chart, line plot, bar graph?)

Big Ideas:

The likelihood an outcome will occur can be described as impossible, unlikely, likely, or certain.

A fraction can describe the probability of an event occurring. The numerator is the number of outcomes favourable to the event; the denominator is the total number of possible outcomes.

A tree diagram is an efficient way to find all possible combinations of outcomes of an event that consists of two or more simple events.

The results of probability experiments often differ from the theoretical predictions. As we repeat an experiment, actual results tend to come closer to predicted probabilities.

In probability situations, one can never be sure what might happen next.

Sometimes a probability can be estimated by using an appropriate model and conducting an experiment.

An experimental probability is based on past events, and a theoretical probability is based on analyzing what could happen. An experimental probability approaches a theoretical one when enough random samples are used.

In this unit:

Students use probability vocabulary (impossible, unlikely, likely, certain) to describe the likelihood of different outcomes in a variety of situations.

Students find the number of possible outcomes of an event and describe the probability of a particular outcome as a fraction of all possible outcomes. They use tree diagrams, tables, area models, systematic lists and other graphic organizers to record and count all possible outcomes of an event. Students predict the probability that an outcome will occur. They conduct probability experiments and compare actual results to predicted results. (source: Math Makes Sense 5, Unit 11)

Why Are These Concepts Important?

Throughout their lives, students will make decisions in situations involving uncertainty. The abilities to understand, calculate, and predict probabilities are valuable life skills that refine and extend basic intuitions about chance events. The work students do in this unit will help prepare them for later studies of probability theory, data analysis, and statistics. (source: Math Makes Sense 5, Unit 11)

Success Criteria and Misconceptions

Success Criteria:

I can use vocabulary to clearly talk about probability experiments (likelihood, outcome, possibility, impossible, possible, unlikely, likely, certain, probability, probable, improbable, odds, chances, outcomes, combinations, permutations)

I can pose and solve simple probability problems, and solve them by conducting probability experiments

I can figure out (determine) all of the possible outcomes of a probability experiment

I can show (represent) the results in different ways (circle graph, table, tree diagram?, )

I can use fractions to show the probability that an event will occur in simple games and probability experiments

Success Criteria for Problem Solving:

I will highlight the important information in the word problem

I can make a K/W/H chart to help me find out what the question is asking me to solve

I will choose a strategy to help me solve the problem

I will try my strategy (carry out the plan)

I will check to see if my answer is reasonable

I will use math language to justify my thinking/answer

ESL Strategies

Illustrate a poster. Next to each colour (or possible outcome) print the appropriate probability statement: This outcome is likely. This outcome is unlikely, and so on. (Adapted from MMS).

Possible misconceptions:

Some students may feel they have a lucky number or colour that is more likely to be chosen. How to Help: Encourage students to discuss the concept of chance. Remind them that events are not controlled by thoughts or feelings. (from MMS)

Students may think outcomes are influenced by magic, luck, outside forces such as wind, or preference.

Students may think: past events influence present probabilities, for example, if they flip heads three times, they may think they are due for tails. How to Help: Point out that the probability never changes.

Some students may think middle values are more likely than the extremes. Students may think it is more likely to roll a 3 or 4 on a die than it is to roll a 1 or 6. In fact, when rolling one die, all six numbers are equally likely. (However, if you roll a pair of dice, middle values are most likelyfor example, with a pair of dice, rolling a 7 is much more likely than rolling a 2 or 12.) How to Help: Use a systematic list to show the difference.

Students may over-generalize from a small sample. For example, a student may flip a coin 10 times and get 3 heads. The student may predict that if you flip the same coin 100 times, it will come up heads about 30 times, rather than 50. How to Help: It is important to demonstrate that with larger sample sizes, experimental results tend to approach theoretical probability. (source: Explorelearning.com)

One of the most common is that past events influence present probabilities. For example, if you are rolling a normal six-sided die and its been a long time since youve rolled a 1, you may think you are due for a 1. But the probability of rolling a 1 never changes; it is always 1 out of 6.

Students may over-generalize from a small sample. For example, a student may flip a coin 10 times and get 3 heads. The student may predict that if you flip the same coin 100 times, it will come up heads about 30 times, rather than 50. It is important to demonstrate that with larger sample sizes, experimental results tend to approach theoretical probability.

Note: Probability is associated with games and gambling, but it also underlies many of the major decisions made by governments, companies and other decision-makers. (Explorelearning.com) Be sensitive to the fact that some Christians, such as Baptists, prohibit playing games of chance.

Lesson 1 Diagnostic and Launch Grade 5 Probability Sandra Van Elslander

Curriculum Expectations:

Overall: represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models.

Specific: pose and solve simple probability problems, and solve them by conducting probability experiments and selecting appropriate methods of recording the results.

represent, using a common fraction, the probability that an event will occur in simple games and probability experiments.

Task/Problem

To pre-teach vocabulary.

To solve a simple probability problem and express the answer as fraction, and in other ways using appropriate vocabulary.

To identify prior knowledge and areas of need (diagnostic assessment).

Learning Goal:

Solve a simple probability problem. Use vocabulary from the book (including possible, probably, and impossible) to show the answer in different ways.

Answer the question using fractions.

Part 1 Before, Minds On or

Brainstorm words about probability: Question: When you think about probability, what words come to mind? (Activate prior knowledge/ assess knowledge of vocabulary, chart answers).

Read: Thats a Possibility: A Book About What Might Happen by Bruce Goldstein.

Highlight vocabulary and add words and definitions to the chart as they occur in the text.

Questions:

From text: Whats a possibility? Could this ball knock down 12 pins in one roll? Why?

If one of these fish swims under the bridge, what kind of fish will it be? Will this bee land on a white flower? Will this butterfly land on one of the purple flowers? What colour gumball will you probably get? What prize are you most likely to get? What other prizes are probable? Which prize is improbable?

Student Success Criteria:

I can use vocabulary to clearly talk about probability experiments.

I can pose and solve simple probability problems.

I can use fractions to show the probability that an event will occur.

Part 2 During, Work on It

Stop at page 14. Ask students to answer the questions using probability language. Students work with a partner to record their answers in as many ways possible on white paper.

If the cat pounces on one ball of yarn, what color will it probably be? What other color is possible? Can you think of a color thats impossible for this cat to get? (Theres 3 blue and one yellow). With your partner, show the answer in as many ways you can. Can you show your answer using a fraction? What other ways can you also show the answer?

Questions:

How many balls of yarn are there? How m