April 24
Hello Cluster 4 Families!
After finishing our unit on Algebra, we spent the week before April Vacation studying different types of angles and different angle vocabulary. Once returning from break, we jumped right into our final unit on Probability and Sampling!
We will have a mid unit quiz as well as an end of the unit test per usual. This unit will lead us into the end of the school year!
Below are some lessons and student goals we have covered and will continue to cover the next few weeks:
In the first section of the unit, students learn about probability as a way to describe the likelihood of unknown events and use simulations to estimate the probability of real-world situations. In the second section, students use samples to draw conclusions about and compare populations.
-Mr. Martin
Section 1: Probability (Lessons 1–8)
Students determine the probability of unknown events and compare the results of repeated experiments and the expected probability. They also design and perform simulations to estimate the probability of multistep real-world situations.
Lesson 1 invites students to conduct their own experiments and use phrases such as “likely” and “equally likely as not” to describe the likelihood of different events.
Lesson 2 connects the concept of likelihood from Lesson 1 with probability, a measure of the likelihood of an event. Students express probabilities as numbers between `0` and `1`, and use sample spaces to help determine these probabilities.
Lesson 3 returns to experiments like those in Lesson 1. Students use repeated experiments as well as proportionality to predict the contents of a mystery bag, recognizing that the number of repeated experiments affects the accuracy of your prediction.
Lesson 4 continues the conversation about repeated experiments. Students recognize that if you perform an experiment repeatedly, the results will approach, but may not exactly match, the probability of the event.
Lesson 5 invites students to challenge their assumptions about probability tools such as coins and number cubes. Students decide whether or not an object is fair by comparing probabilities from a model to the results of a repeated experiment.
Lesson 6 extends the work of Lessons 1–5 as students make sense of probabilities of multistep events. Students use lists, tables, and tree diagrams to represent the sample space of events with multiple pennies or spinners. They then use these tools to determine the probabilities of multistep events and consider whether or not different games are fair.
Lesson 7 asks students to apply what they have learned about probability tools and repeated experiments to simulate multistep real-world events. Students use spinners and blocks in bags to simulate the chances that it rains based on probabilities from a weather forecast.
Lesson 8 extends the work of Lesson 7 as students design and perform their own simulations to estimate the probabilities of multistep real-world situations.
Section 2: Sampling (Lessons 9–15)
Students use measures of center and measures of variability from random samples to draw conclusions about and compare populations. Students also explain the purpose of sampling and which methods tend to produce representative samples. This builds on the work students did in Grade 6 analyzing data sets and distributions using mean, median, MAD, and IQR.
Lesson 9 revisits tools that students used in Grade 6 to analyze and compare sets of data. Students calculate the mean and mean absolute deviation (MAD) and use these measures to make a recommendation (MP2). They also compare and contrast data represented by dot plots.
Lesson 10 is the first of several lessons where students use samples to draw conclusions about a population. Students learn the terms sample and population and explore the advantages and disadvantages of using samples to answer a question about a population.
Lesson 11 digs deeper into techniques for gathering a sample. Students review headlines produced from different samples of data and explain whether or not a given sampling method is likely to be representative of the population.
Lesson 12 revisits proportional relationships and percentages from Units 2 and 4. Students use data from a sample to estimate the number of marigolds in a large flower garden.
Lesson 13 also asks students to use data from a sample to draw conclusions about a population, this time with quantitative data and box plots. Students estimate a measure of center of a population based on one or more samples of the population. They also explain why an estimate for the center of a population is more likely to be accurate when it is based on a random sample with less variability.
Lesson 14 extends what students learned from Lesson 13 to compare two populations based on samples. This lesson introduces the idea that you can determine if there is a big difference between two populations by looking at the difference between the centers of samples and comparing the difference to the measure of variability.
Lesson 15 wraps up the unit as students apply what they know to analyze real data about asthma rates. Students generate random samples and use them to compare the asthma rates of different places in New York.
