Unit Rubric: Probability
Level 1 / Level 2 / Level 3 / Level 4Problem solving
• chooses and carries out appropriate strategies to pose and solve problems involving probability (e.g., tree diagrams) / with assistance, chooses and carries out a limited range of appropriate strategies to pose and solve problems; results are rarely reasonable / with limited assistance, chooses and carries out some appropriate strategies to pose and solve problems; results are frequently reasonable / chooses and carries out appropriate strategies to pose and solve problems; results are usually reasonable / chooses and carries out appropriate strategies that produce reasonable results; may be innovative
Understanding of concepts
• shows understanding by appropriately explaining:
– predictions of probability in simple experiments
– connections between real-life statements and probability concepts / may be unable to explain:
– predictions of probability in simple experiments
– connections between real-life statements and probability concepts / partially able to explain:
– predictions of probability in simple experiments
– connections between real-life statements and probability concepts / appropriately explains:
– predictions of probability in simple experiments
– connections between real-life statements and probability concepts / in various contexts, consistently and appropriately explains:
– predictions of probability in simple experiments
– connections between real-life statements and probability concepts
Application of mathematical procedures
• uses appropriate procedures to accurately:
– use fractions to describe probability
– use tree diagrams to find and record probabilities / limited accuracy; major errors or omissions in:
– using fractions to describe probability
– using tree diagrams to find and record probabilities / somewhat accurate; makes frequent minor errors/omissions in:
– using fractions to describe probability
– using tree diagrams to find and record probabilities / generally accurate; makes few errors/omissions in:
– using fractions to describe probability
– using tree diagrams to find and record probabilities / accurate; rarely makes errors/omissions in:
– using fractions to describe probability
– using tree diagrams to find and record probabilities
Communication
• discusses procedures, results and reasoning clearly, including appropriate terminology (e.g., certain, outcome, possible, fair game, combination) / needs assistance to describe procedures, discuss results and explain reasoning; often unclear and imprecise / describes procedures, discusses results, and explains reasoning with some clarity and precision / describes procedures, discusses results, and explains reasoning clearly and precisely / describes procedures, discusses results and explains reasoning clearly, precisely, and confidently
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Name / Date Ongoing Observations:
Probability
The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning.
STUDENT ACHIEVEMENT: Probability
Student / Problem solving / Understanding of concepts / Application of mathematical procedures / Communication§ Uses appropriate strategies to pose and solve problems involving probability / § Explains predictions in simple experiments
§ Connects real-life statements and probability concepts / § Uses fractions to describe probability
§ Uses tree diagrams to find and record probabilities / § Discusses procedures, results, and reasoning clearly
§ Uses language of probability
Level 1 – very limited; Level 2 – somewhat or limited; Level 3 – satisfactory; Level 4 – thorough
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Name / DatePerformance Assessment Rubric:
At the Pet Store!
Problem solving
• chooses and carries out appropriate strategies, including tables and diagrams, to:
– solve problems involving probability
– use probabilities to design the composition of a fish tank / with assistance, chooses and carries out a limited range of appropriate strategies, with little success, to:
– solve problems involving probability
– use probabilities to design the composition of a fish tank / chooses and carries out some appropriate strategies, with partial success, to:
– solve problems involving probability
– use probabilities to design the composition of a fish tank / chooses and successfully carries out appropriate strategies to:
– solve problems involving probability
– use probabilities to design the composition of a fish tank / chooses and successfully carries out effective strategies to:
– solve problems involving probability
– use probabilities to design the composition of a fish tank (introduces some complexity to the task)
Understanding of concepts
• shows understanding by providing reasonable explanations of:
– differences between predicted probabilities and actual results
– how probabilities and number of each type of fish were determined / shows very limited understanding by giving inappropriate explanations of:
– differences between predicted probabilities and actual results
– how probabilities and number of fish were determined / shows limited understanding giving appropriate but incomplete explanations of:
– differences between predicted probabilities and actual results
– how probabilities and number of fish were determined / shows understanding by giving appropriate explanations of:
– differences between predicted probabilities and actual results
– how probabilities and number of fish were determined / shows thorough understanding by giving appropriate and complete explanations of:
– differences between predicted probabilities and actual results
– how probabilities and number of fish were determined
Application of mathematical procedures
• uses appropriate procedures to accurately calculate probabilities using fractions / limited accuracy; major errors or omissions in calculating probabilities / somewhat accurate; several minor errors or omissions in calculating probabilities / generally accurate; few errors or omissions in calculating probabilities / accurate; very few or no errors or omissions in calculating probabilities
Communication
• provides a clear presentation and explanation of results
• uses language of probability (e.g., likely, probable, outcome) / presentation and discussion are unclear and imprecise; uses few appropriate mathematical terms / presentation and discussion are partially clear and precise; uses some appropriate mathematical terms / presentation and discussion are generally clear and precise; uses appropriate mathematical terms / presentation and discussion are clear, precise, and confident; uses the most appropriate mathematical terminology
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Name / DateUnit Summary: Probability
Review assessment records to determine the most consistent achievement levels for the assessments conducted. Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying levels for each achievement category.
Most Consistent Level of Achievement*
Strand:Data Management
and Probability / Problem solving / Understanding of concepts / Application of mathematical procedures /
Communication
/Overall
Ongoing ObservationsStrategies Toolkit
(Lesson 5)
Work samples or portfolios; conferences
Show What You Know
Unit Test
Unit Problem
At the Pet Store!
Achievement Level for reporting
*Use Ontario Achievement Levels 1, 2, 3, 4.
Self-Assessment:Comments: (Strengths, Needs, Next Steps)
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Name / DateTo Parents and Adults at Home …
Your child’s class is starting a mathematics unit on probability. As adults, we use ideas of probability in everyday life when we estimate the likelihood of risks and predict future events. Many decisions, from carrying an umbrella to buying extra life insurance, are based on our understanding of probability.
In this unit, your child will:
· Use the language of probability.
· Conduct experiments and predict results.
· Use fractions to describe probability.
· Use tree diagrams to find probabilities.
· Use probability to pose and solve problems.
Probability concepts can be practised at home as well as at school. Here are some suggestions for activities you can do at home:
· Listen to weather forecasts with your child. Use words such as likely, unlikely, probable, and possible to talk about the next day’s weather. Compare the actual weather to the forecast weather. Help your child understand that meteorologists use past weather patterns to tell us what is probable, rather than certain, in the future.
· Play board and card games with your child. Compare games that depend on chance (for example, snakes and ladders) with games that depend on skill (for example, chess). Look for games that combine chance and skill.
· Talk with your child about superstitions. For instance, you might help your child realize that wishing hard or having a “lucky number” does not influence the cards you are dealt in a game.
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Name / DateBlank Spinners
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Name / Date Additional Activity 1:
Match My Meaning!
Work with a partner. Carefully cut apart these cards.
certain / will definitely happenimpossible / cannot happen
possible / could happen
probable / is likely
to happen
improbable / is unlikely
to happen
Ø Place all the cards face down.
Ø Take turns flipping over 2 cards.
Ø If the cards match (word and meaning), keep them and take another turn.
Ø The winner is the player who collects the most cards.
Ø Play 5 rounds. The grand winner is the player who wins the most rounds.
Take It Further:
Write about a situation that can be described using the words on the cards.
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Name / Date Additional Activity 2:
Animal Draw
Work with a partner.
Ø Look at the animal names listed here. What fraction of the list are
Cats? Insects? Birds? Fish?
Beetle / Fly / Mosquito / Ladybug
Crow / Eagle / Salmon / Tuna
Ø Cut apart the animal names and place them in a bag.
Ø You will pull out an animal name without looking, then replace it in the bag.
Ø Make a prediction. In 30 tries, about how many times do you expect to draw a cat? An insect? A fish? A bird?
Ø Shake up the bag. Reach in and pull out a name without looking.
Record your result and replace the name. Make 30 draws in all.
Ø Did your actual draws match your prediction? Explain.
Take It Further:
Find as many different equivalent fractions as possible to express the probability of drawing an insect.
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Name / Date Additional Activity 3:
Fold Your Tents!
Work with a partner.
You will need 20 matching squares of paper about 2 cm by 2 cm and a tray.
Ø Fold each piece of paper in half to make a small “tent.”
Ø Stand all your tents on a tray. Each tent should have the fold facing up.
Ø Shake the tray so that all the tents fall off and land on the floor.
Ø What fraction of the tents have landed fold up?
What fraction landed lying on one side?
What fraction landed standing on one end?
Ø Repeat the experiment 4 more times.
Ø Record your results each time.
Ø Based on your results, predict what fraction of the tents will land fold up after your next toss.
Ø Toss the tents once more. Count the tents that landed fold up.
Did your actual results match your prediction? Explain.
Take It Further:
Predict the fraction of the tents that will land fold up after the 10th and 20th tosses.
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Name / Date Additional Activity 4:
Robot Roundup
Imagine you are in charge of a robot factory.
Each robot needs 2 arms, 2 wheels, and a box-shaped body.
Both arms must be the same colour. Both wheels must be the same colour.
For each component, you have the colour choices shown here:
Arms: yellow or blue
Wheels: green or purple
Body: red or black or grey
Ø Use a tree diagram to find out how many different robots you can make.
Ø Draw and colour one of the robots.
Ø If you picked the components without looking, what are the chances you would create a grey robot with blue arms and purple wheels?
Take It Further:
Add another component (for example, a control panel in gold or silver) and work out how many different robots can now be produced.
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Name / DateStep-by-Step 1
Lesson 1, Question 5
Step 1 Yellow is more likely, so there are more ______sectors than red.
Red is more likely, so there are more ______sectors than blue.
Look at the first spinner on Master 11b. It has 8 sectors.
How many sectors will you colour yellow? ____ red? ____ blue? ____
Colour the spinner.
Is there a different way to colour the spinner? Explain.
______
Step 2 Blue and green are equally likely.
They cover ______sectors.
Yellow is more likely. It covers ______sectors.
Look at the second spinner on Master 11b. It has 5 sectors.
How many sectors will you colour blue? ___ green? ___ yellow? ___
Colour the spinner.
Is there a different way to colour the spinner? Explain.
______
Step 3 Yellow is certain.
Are there any blue sectors? _____ Are there any red sectors? _____
Look at the third spinner on Master 11b. It has 10 sectors.
Yellow covers _____ of the sectors.
Colour the spinner.
Is there a different way to colour the spinner? Explain.
______
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Name / DateSpinners for Lesson 1, Question 5
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Name / DateStep-by-Step 2
Lesson 2, Question 4
Vicki scores a point if the pointers land on the same colour.Alastair scores a point if the pointers land on different colours.
Make the spinners identical for each case.
Step 1 Vicki will win if the spinners are mostly one colour. Choose 2 colours.
Colour the spinners so that Vicki is more likely to win.
Step 2 Alastair will win if each spinner has 4 different colours. Choose 4 colours. Colour the spinners so that Alastair is more likely to win.
Step 3 The game is fair if the pointers are equally likely to land on the same colour or a different colour. Choose 2 colours. Colour the spinners so that Vicki and Alastair have equal chances of winning.
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Name / DateStep-by-Step 3