Sixth Grade - MATH
5: Math
Unit 8: Statistics
Lesson 3
Frequency Tables and Dot Plots
Students create and read frequency tables and dot plots for categorical and numerical data (several activities ask them to organize values into frequency tables and draw dot plots). Students reorder numerical data from smallest to largest and identify the shortest and tallest values (dog heights example) and they count frequencies to find the most and least common responses (questions asking which meal, score, or exhibit is most/least popular). Students use dot plots to see where data points concentrate (questions about where most players go to bed or which weather type has greatest frequency).
Lesson 4
Stem-and-Leaf Plots
Students create and interpret stem-and-leaf plots (Activity 2) by ordering data, constructing stems and leaves, and adding a title. Students identify minimum and maximum values and count observations in ranges (questions asking for lowest/highest, how many sessions < 60, how many ≥ 65, how many total sessions). Students also identify the mode and note where most data fall (e.g., "Most high temperatures were in the 80's" and "temperature 87° was the most common").
Lesson 5
Histograms
Students read and interpret histograms by identifying which interval has the most or least data (e.g., asking "Which age range has the most campers?" and identifying the 12–13 interval). Students compute frequencies, totals, and differences from histogram bars (e.g., adding interval frequencies to find the total number of campers and computing 17 − 5 = 12). Students create histograms from raw data (organize values, make frequency tables, and draw histograms) and practice choosing appropriate intervals and bin sizes.
Lesson 6
Measures of Center
Students calculate mean, median, and mode from graphs and data lists (Activities 1–3 and multiple Student Activity Pages) by adding, ordering, and counting data values. Students classify distribution shape as symmetric, skewed, uniform, or random (Day 2 activities and 'Exploring Distribution Shapes' pages) and use dot plots, stem-and-leaf plots, histograms, and frequency tables to find measures of center from those displays. Students identify and discuss outliers and how an outlier can skew the mean, and they are asked to choose which measure of center best represents a given data set in context (Activity 4).
Lesson 7
Measures of Variability
Students calculate measures of center (mean, median, mode) and measures of spread (range, interquartile range, mean absolute deviation) on multiple student activity pages. Students construct and label box plots using five-number summaries and answer explicit questions about the shape of distributions (symmetric or skewed) and identify outliers. Several activities require students to compare two data sets using measures of center, variability, and the shape of the distribution.
Lesson 8
Making Inferences
Students create dot plots and histograms from sample data (candy activity, food truck sales) and are prompted to describe the overall shape (the food truck example explicitly states the distribution is symmetric). Students compute measures of center (mean, median, mode) in the food truck example and find sample means in the candy and word-length activities. Students compute and interpret measures of spread (range, interquartile range shown on a box plot, and mean absolute deviation) and use box plots to display variability.
Lesson 9
Comparing Populations
Students describe overall shape by labeling distributions as symmetric, skewed, or uniform (e.g., questions asking for distribution shape of 10- and 11-year-old heights and dot-plot shape prompts). Students create and read dot plots and box plots to view distributions and identify medians and quartiles (box-plot activity comparing cat and dog adoptions). Students compute measures of center (means) and measures of spread (range and mean absolute deviation) and use the ratio of difference of means to the larger MAD to assess overlap and relative separation of two populations.
Lesson 10
Unit 8 Test
Students calculate measures of center (mean, median, mode) on multiple activities (e.g., questions asking for mean, median, and mode; Opal's and Randall's means). Students compute measures of spread (range, interquartile range, mean absolute deviation) and create box plots and five-number summaries (calendar bagel data, best-seller weeks, box-plot task). Students identify and describe overall shape of distributions using dot plots, histograms, and stem-and-leaf plots (questions asking whether distributions are symmetric, skewed, or uniform and tasks comparing shapes and sampling variability).
Final Project
Statistical Study
Students formulate a numerical statistical question and collect data, then organize it into dot plots or histograms and draw a box plot. They compute measures of center (mean, median, mode) and measures of spread (range, interquartile range, mean absolute deviation) and identify outliers. In Step 5 students explicitly answer prompts about the shape of the data, which measure best represents the data, what the measures of variability tell them, and make inferences about the population.
3: Math
Unit 1: Numbers
Lesson 7
Arctic Marine Research
Students compute an average daily temperature and a temperature range in Phase 5 (find the temperature range from -15°C to 5°C and calculate the average daily temperature). Students compare cell measurements and cell densities in Phase 1 by converting measurements, determining which is larger, computing how many times larger one is than the other, and finding the difference in cell counts. These tasks require students to calculate center (average) and spread (difference/range) for small sets of values.
Unit 4: Probability
Lesson 3
Probability Models
Students collect and record data from chance experiments (rolling a die in three rounds, spinning spinners, class choice tallies, and surveys) and compute relative frequencies and probabilities from those counts. Students compare experimental results to theoretical predictions, note how relative frequency changes with more trials (Law of Large Numbers), and build probability models from observed counts (e.g., choir/band/orchestra, spinner color counts). Students also analyze discrepancies and consider causes such as small sample size or bias.
Lesson 5
Simulations
Students run repeated trials in multiple activities (Blue Marble, Music Playlist, What Kind of Visitor, The Library Hunt) and record numerical outcomes in data tables. Students compute averages in at least two activities (Music Playlist and other pages showing TOTAL/AVERAGE) and are asked reflection questions about unusually long trials, which prompts consideration of variability. In The Library Hunt, students count how often a condition occurs and convert that frequency to a fraction and percent, providing practice describing how often outcomes occur.
Final Project
Happy Tails Dog Shelter
Students compute counts and percentages for each size/color combination (e.g., 9/60 = 15% for Medium White) and fill a probability model table listing the probability of each outcome. Students sum category probabilities to find totals (e.g., total probability of medium dogs = 30/60 = 50%, total white dogs = 14/60 ≈ 23.33%) and identify the most likely size/color combination. Students run simulations and compare observed frequencies to the probability model, reinforcing understanding of how the data are distributed across categories.
Unit 8: Data
Lesson 1
Statistics Review
Students calculate and interpret measures of center (mean, median, mode) in Activity 1 and related practice pages, with step-by-step examples and exercises. Students compute measures of spread — range, interquartile range (IQR), and mean absolute deviation (MAD) — with worked examples and practice problems in Activity 3. Students construct and interpret box plots, identify the five-number summary, and determine overall shape (symmetrical, skewed left/right) and outliers in Activity 4 and Variability Practice. Several practice items ask students to compare distributions (e.g., which class is more consistent) and to describe variability and skewness in context.
Lesson 2
Scatterplots
Students identify and label clusters and outliers and practice locating them on scatterplots (Activities 2 and multiple student pages). They classify relationships as positive, negative, or none and as linear or nonlinear, describing the overall pattern or shape of bivariate data. Students draw and choose best‑fit lines described as running through the "middle" of the points and compare variability by judging how closely points cluster around that line (low vs. high variability).
Lesson 3
Constructing a Scatter Plot
Students plot bivariate data and are asked to describe overall shape and association (e.g., positive/negative, linear/nonlinear) by answering questions like "Is there a linear relationship? How do you know?" Multiple activities ask students to identify clusters and outliers and to describe trends and make predictions from scatterplots. The Weather Watch and several answer keys explicitly have students note whether points rise or fall, identify clusters, and point out outliers. The lesson also has students choose ranges and scales for axes, which requires noticing the span of the data when setting up a graph.
Lesson 6
Unit 8 Test
Students repeatedly compute measures of center (mean, median, mode) in multiple problems (quiz scores, snack prices, heart rates, shoe sizes, books read). Students compute measures of spread (range, IQR, MAD) and compare IQRs to judge which group is more consistent using box plots. Students analyze overall shape features by identifying clusters, outliers, linear vs. nonlinear patterns, and variability in scatterplots and by matching scenarios to graph shapes; the final project asks students to collect data and create a scatterplot and a two-way relative frequency table to display distributions.
Final Project
Collecting and Organizing Data
Students create and analyze scatterplots where they are asked to note whether points "are clustered," form an "upward-slanting pattern," and to identify outliers and trends (positive/negative/linear/nonlinear). Students build two-way relative frequency tables, convert tallies to percentages, and answer which category combinations have the highest or lowest percentages and whether there are zeros or surprises. Reflection prompts ask students to "look for patterns," "look for surprises," and to describe clusters or whether points "spread all over," which directs attention to aspects of a distribution's shape.
Unit 9: Semester Exams
Lesson 9
Data Review
Students compute measures of center (mean, median, mode) and range in Activity 1, including deciding which measure of center best represents a data set when an outlier is present. Students calculate measures of spread in Activity 2 (mean absolute deviation and interquartile range) and draw box plots showing minimum, Q1, median, Q3, and maximum. In Activity 3 students identify clustering, outliers, and types of association in scatterplots and interpret closeness to a line of best fit.
Lesson 10
Semester Exam
Students compute measures of center (mean, median, mode) and range in problems 36 and 39 and identify which measure of center best represents a skewed data set in problem 37. Students calculate measures of spread including MAD and IQR in problems 40 and 42 and answer interpretive questions about what MAD and IQR tell about spread in problems 41 and 44. Students draw a box plot (problem 43) and compare consistency of two classes using mean and MAD in problem 45. A scatterplot task (problem 46) and questions about closeness to a line of best fit (problem 47) ask students to interpret the overall relationship shape in bivariate data.
