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Figure It Out Middle School Math and Logic : Data, Sampling, and Probability

Class
Malikai Bass M.A
Popular
Average rating:5.0Number of reviews:(276)
This problem-based math cohort is for the creative thinkers, artists, and problem solvers to build math confidence and skills at an accelerated pace suitable for gifted students while building deep foundational understanding.

Class experience

US Grade 7 - 8
4 units//20 lessons//4 Weeks
Unit 1Dot Plots and Histograms
4 lessons1 Week
Dot Plots and Histograms
 Week 1
Lesson 1
Readiness Assessment
We will begin with a readiness assessment that covers basic skills and gives a preview of course material to allow for individualization including review materials, tutoring suggestions, and enrichment based on the results of each individual learner.
Lesson 2
How can we show data on a graph?
We will represent distributions of numerical and categorical data using frequency tables dot plots and bar graphs to develop spatial understanding and prepare for future lessons.
Lesson 3
How can we use graphs to answer statistical questions?
We will continue to use dot plots to develop our understanding of center and spread and compare distributions using the structure.
Lesson 4
What is a histogram?
We will explore histograms and how they can display distributions of numerical data we will compare them to dot plots and learn to think of them in terms of shape, spread, and center. We will make comparisons between histograms to develop analysis skills.
Unit 2Measures of Center and Variability
4 lessons2 Weeks
Measures of Center and Variability
 Week 1
Lesson 5
What is the Mean?
We will understand the mean as a "leveling out" or "fair share" and then work to abstract that concept to understand the mean as a measure of center or typical value of a group. We will practice calculating the mean for different scenarios.
 Week 2
Lesson 6
What is the MAD?
We will formalize an interpretation of distances from the mean as mean absolute deviation as a measure of variability or spread and compare distributions based on mean and MAD.
Lesson 7
What is the Median?
We will consider the median as another measure of center which divides the data in half and make use of structure to understand when the median and mean are similar for a set of data and when the median might bea better choice.
Lesson 8
What is the IQR?
We will expand our work with the median to divide data into quartiles, find the Interquartile range, and construct box plots.
Unit 3Sampling
5 lessons2 Weeks
Sampling
 Week 2
Lesson 9
How can we work with larger populations?
We will understand when it is impractical or impossible to gather data about the whole population, we can use samples.
Lesson 10
What makes a good sample?
We will work to understand representative samples using dot plots and considering center, shape, and spread.
 Week 3
Lesson 11
How can we sample in a fair way?
We will compare different methods of selecting a sample and note benefits and drawbacks. We will consider bias in sampling methods and practice recognizing methods which are more likely to create representative samples.
Lesson 12
How can we estimate the measure of center for a population?
We will begin using samples to reason about populations and understand how variability impacts our certainty when reasoning based on samples.
Lesson 13
How can we make accurate predictions based on samples?
We will go beyond standards to examine accuracy of estimates for population characteristics based on samples.
Unit 4Probabilities
7 lessons2 Weeks
Probabilities
 Week 3
Lesson 14
What are probabilities?
We will assign probabilities to chance events and determine outcomes for experiments. We will understand the definitions of sample space, random, and probability.
Lesson 15
How can we estimate probabilities?
We will use dice to understand why repeated experiments can help us estimate frequencies. We will also understand relative frequency and why it does not always match the actual probability.
 Week 4
Lesson 16
How can we keep track of possible outcomes?
We will practice listing sample spaces for compound events as a primer for later studies in combinatorics using tree diagrams, tables, and organized lists.
Lesson 17
How can we work on multiple step experiments?
We will continue writing out the sample spaces with multi-step experiments and understand probability for complex events. We will practice choosing efficient strategies for problem solving.
Lesson 18
How can we design simulations?
We will understand how we can use simulations to estimate probability and create our own simulations using tools to model complex events in this culminating lesson.
Lesson 19
Bonus Day
This unit includes a bonus day that can be moved throughout the course to provide additional support on any challenging topic, pre-test review, or enrichment if no review or support is needed.
Lesson 20
End of Unit Assessment
We will close the unit with a formal assessment to confirm mastery of all the concepts covered in the unit.
This class is taught in English.
1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in
the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a
statistical question because one anticipates variability in students’ ages.
2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its
center, spread, and overall shape.
3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a
measure of variation describes how its values vary with a single number.
4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
5. Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute
deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference
to the context in which the data were gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which
the data were gathered.
1. Understand that statistics can be used to gain information about a population by examining a sample of the population;
generalizations about a population from a sample are valid only if the sample is representative of that population.
Understand that random sampling tends to produce representative samples and support valid inferences.
2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be
3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the
variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of
heights is noticeable.
4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book
Investigate chance processes and develop, use, and evaluate probability models.
5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling
a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times
I have been completed three college-level courses on common-core math instruction. I have worked as a math instructor for middle school students in a private school setting. I have ten years of experience as a math tutor including working with students from ages 5 (kindergarten) to 25 (Graduate Readiness Exam). I have served as a teaching assistant in college-level probability and statistics courses. 
Homework Offered
Learners will have one practice problem to complete each day in their math notebooks.
Assessments Offered
Learner's will receive weekly progress reports and complete a final assessment.
Grades Offered
This class is designed by an AUDHD/Dyspraxic Educator
- slides and fonts designed to support dyslexia and visual processing
- ability to type and use virtual drawing tools 
- communication aids including chat
- ND Affirming classroom
Students should have good content mastery over elementary math standards. Students should have proficiency (with or without aid) of keyboard and mouse or touch screen devices. 
Learners will need standard school supplies such as a notebook, pencil, ruler, highlighter, scissors, and tape/glue. 
In addition to the Outschool classroom, this class uses:
We will be using nearpod during this class. Students will need to click a link in chat and enter their first name or initial into the program. Students should be reminded not to use their full name. Students will also need access to scissors and may require adult supervision or support. 
Popular
Average rating:5.0Number of reviews:(276)
Profile
Hello, I have thirteen years of experience in education. As an eclectic academic learner, I had lots of opportunities to benefit others with my unique understanding and gifted perspective as a twice exceptional learner. I hold a master’s degree in... 
Group Class

$75

weekly or $300 for 20 classes
5x per week, 4 weeks
50 min

Completed by 4 learners
Live video meetings
Ages: 10-13
3-6 learners per class

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