For this experiment you will need 100 blue marbles and 25 green marbles in a paper bag.
We are going to do an experiment! Let’s try and find out, without looking in the bag and counting, whether there are more blue or more green marbles in the bag. Randomly choose four students to draw 5 marbles each from the bag. (make sure marbles are returned to the bag after each draw). Have the other students record the numbers and colors of marbles for each of the four draws.
Think – Pair-share (using the following questions)
Based on the first 4 draws, can we determine how many marbles of each color are in the bag?
Next, allow the rest of the students to choose 5 marbles from the bag (be sure to return the marbles to the bag) record the results and ask the following questions.
What are the totals for each color of marbles?
Do you think there were more marbles of one color than the other?
If so, what do you think the ratio of one color to the other might be?
Finally, open the bag and count the number of marbles of each color.
Ask the students to determine the ratio of one color to the other color?
Ask students to draw a conclusion about the ratio of blue marbles to green marbles? (The probability of drawing a blue marble is four times greater than drawing a green one.) Allow students to come up with other statements like it is more likely to draw a blue marble than a green marble. Or it is unlikely to draw a green marble out of the bag.
SMP 1 and 3
In this part of the lesson, I’m going to be introducing/reinforcing the language of probability. In the do now activity, students may have already been using words like likely, unlikely, certain or impossible. Ask them if they have ever heard these words in real life? (weather, lottery, events) Use the power point to facilitate the discussion on probability
Slide 3 shows the probability of even occurring using percents. Ask the students what they are looking at when determining probability. (I want them to see that probability is placed on a number line and that the closer to zero or 1 will determine whether an event will or will not occur). I also want them to see that probabilities can be written as fractions, decimals, or percents because of the use of a number line.
Slide 4: Using the questions from this slide have students use white boards to show their answers. This is a good way to formally assess whether or not they are getting the language of probability.
Slide 5 is a review of changing from Fractions to decimals to percents. Before showing slide 5, you could review this orally with the students to see if they can recall this information on their own. I may even use a think-pair-share to hold them accountable for the reasoning. Once you have gone through all of the conversions, show them slide 5 and have them make notes of this in their notes.
Slide 6 has them using the conversions. Again, white boards would be good to use to formally assess student understanding.
Once the direct instruction has been completed, it will be time to work with our tablemates during a Numbered Heads Together activity.
Questions 1 – 6 ask the students to determine if the probability is certain, likely, as likely as not, unlikely, or impossible. Students may come up with different responses so I’m going to be encouraging and listening to them reason out their thoughts. Before I call a color to show me their answer, I will ask them to justify their answer (SMP 3)
Questions 7 – 11 ask the students to write their probabilities as fractions, decimals, or percents. The students will need to show their work when solving these problems. I will be looking for this on their white boards when they show me their answers. If work is not shown, then they will need to tell me in writing how they figured it out.
Students will be working on coming up with a scenario that represents the following situations: certain, likely, as likely as not, unlikely, and impossible. I want them to come up with an event to represent each. Have students work alone before sharing with a partner. When students are sharing with their partners, I’m anticipating that there will be a lot of conversation about impossible and certain. When listening and advising students about when events are deemed to be certain or impossible it would be a good idea to pose a counter example. Some scenarios can be used for whole group discussion. (SMP 3)
Next, the students will be writing an equivalent to .8 as a fraction and a percent. Have them show their work to support their answer and then share their answers with a partner.