Between Never & Always - Lake Washington School District

Between Never and Always

Probability

Mathematical Emphasis
Investigation 1—Finding and Comparing Probabilities

Associating verbal descriptions with numeric descriptions of probability and understanding the meaning of the word probability
Seeing that repeating a probability experiment several times yields a variety of results
Using a probability to predict about how often an event will happen in a given number of trials
Estimating probabilities from results of actual trials
Predicting and analyzing features of distributions
Learning to add probabilities of simple events

Tips For Helping At Home
Questions To Ask:

What is the problem about? Tell me in your own words.
What did you do in class to get started?
Can you solve a simpler version of the problem?
What have you already tried? What steps did you take?
Did you show all of your work?
Does the answer make sense?
How do you know your answer is correct?

Helping At Home

Look and listen for ways probability is being used around you. Discuss these situations with your child. For example, if someone you know has entered a raffle or contest, talk about the probability of winning versus losing. Raise questions like: About how many people do you think have entered? How many winners will there be? Is there reason to believe your chance of winning is higher or lower than anyone else’s chance? These questions are both personally and mathematically interesting and provide important opportunities to “talk mathematics” with your child.

Vocabulary Terms

Center: Mid point of data, can be measured by median (score that divides data into an upper and lower half) or mode (score that occurs most often)
Expected Outcome: The expected results of probability experiment (example: a tossed penny would land heads up half the time)
Gap: A visible hole in the data, a value where there are no scores
Hypothetical Line Plot: Line plot of the expected outcome of a probability experiment
Line plot: A number line with data individually represented above corresponding numbers
Probability: How likely something is to occur
Range: The value of the difference between the lowest and highest piece of numerical data
Shape of Data: The outline or shape that data makes on a line plot or graph

Mathematics Vocabulary Web site

Mathematics Strategy—Why Doesn’t a Half-Green Spinner Spin Green Half the Time?

What does it mean to have a 1 out of 2 or 50 percent chance? Does it mean a coin always comes up heads exactly 50 percent of the time? Intuition tells us that a 1 out of 2 chance does not mean the outcome will be exactly 50 percent. We don’t expect a coin flipped 10 times to turn up exactly 5 heads to be called fair but we would be suspicious with 10 out of 10 heads.

Intuition fits into the mathematical concept of probability. The theoretical probability of landing heads up on one flip of a fair coin is 50 percent. So if a coin were flipped 10 times, the expected number of heads would be 5.

In the activities of this unit, students will work with two basic ideas. The first is that there are many times when we do not get the expected number of outcomes. The second is that although we cannot predict exactly what will happen on a single trial or even a series of trials, we can be fairly certain that if we do many series of trials, the results will have a center that is quite close to the expected number.

Source: Investigations in Number, Data, and Space: Between Never and Always. Dale Seymour, 1998. (Pages 24 and 25)

Mathematics Game—Get to Zero-Subtraction Variation

Materials

One deck of numeral cards

Score sheet for each player

Players: 1 or 2

Playing the Game

Deal out eight numeral cards to each player.

Players make two three-digit numbers with six of the cards. The goal is to make two numbers whose difference is as close to zero as possible.

These subtraction problems are written on the score sheet for round one. For example: 642 – 637 = 5. The difference is the score for that round.

Put the used cards in a discard pile and deal six new cards to each player.

For each round of play, make more numbers whose difference is as close to zero as possible. When the cards run out, mix up the discard pile and use them again.