Sixth Grade - MATH
5: Math
Unit 1: Operations
Final Project
Planning a Party
The "Spending Your Money" activity (Question 1 and answer key) directs students to calculate the cost per goody bag by dividing the grand total cost by the number of guests (example: $42.84 ÷ 12 = $3.57), which has students compute a mean. Multiple planning and cost tasks require students to compute totals and then divide by 12 to find per-item or per-bag values, reinforcing this per-unit average calculation.
Unit 8: Statistics
Lesson 5
Histograms
Students read and interpret histograms to identify which interval has the most or fewest data values (e.g., camper ages and daily temperatures) and determine frequencies from bars. Students compute totals and differences by adding or subtracting interval frequencies (e.g., total campers = 17 + 18 + 10 + 5 + 2 = 52; difference between intervals = 17 - 5 = 12). Students organize raw data into intervals, create frequency tables, and construct histograms from grouped data (e.g., books read, class sizes).
Lesson 6
Measures of Center
Students are instructed how to calculate mean and median from raw data and from graphs (dot plots, stem-and-leaf, frequency tables) and complete multiple practice problems finding mean, median, and mode. Students identify distribution shape (symmetric, skewed, uniform, random) and locate outliers, and they are asked to choose which measure of center best represents a given contextual data set. The lesson also introduces range as a measure of variability and has students interpret measures of center in the context of data (e.g., which center best represents the data when an outlier is present).
Lesson 7
Measures of Variability
Students calculate mean, median, range, interquartile range, and mean absolute deviation in multiple activities (Activity 1 includes the data set 5,6,7,...,14 with a table to compute distances from the mean and MAD). Students construct five-number summaries and box plots (Activity 3 provides steps and a five-number summary template) and interpret box plots in contextual tasks (Activity 4 asks about water-company and hours-worked box plots). Students compare two data sets in context and identify outliers and overall shape (Activity 2 orchard comparison and science-club test comparisons ask for measures, which data set shows more variability, and which value is an outlier).
Lesson 8
Making Inferences
Students compute and interpret measures of center and variability in multiple places: the food truck example shows mean (600/24 = 25), median (25), and mode (25) and displays a box plot with Q1 = 17, median = 25, Q3 = 34 and IQR = 17 as well as a reported mean absolute deviation of 8.75. Students create and analyze histograms and dot plots (e.g., candy and food truck activities) and are asked to describe the overall shape (the food truck histogram is described as symmetric) and to write inferences about the data tied to the real context. In Activities 1–3 students collect samples, calculate sample means (word-length activity and candy percentages), compare sample measures to population measures, and answer reflection questions about whether their inferences matched the population and why.
Lesson 9
Comparing Populations
Students calculate the mean and the mean absolute deviation (MAD) for pumpkin and zucchini data sets and use those values to compute (difference of means) ÷ (larger MAD) to assess overlap. Students create and read box plots that show medians and quartiles for cat and dog adoptions and answer questions about range and overlapping values. Students describe overall distribution shape (symmetric, skewed, uniform), note overlap and possible outliers, and make contextual inferences (e.g., whether the farmer should use fertilizer or which pet is more popular).
Lesson 10
Unit 8 Test
Students compute measures of center and variability on multiple pages: the bagel-sales calendar asks for the median, interquartile range, mean (given) and mean absolute deviation and asks students to create a five-number-summary box plot (questions 21–25). Students calculate mean, median, mode, and range from a stem-and-leaf data set and compute mean and mean absolute deviation for Opal's and Randall's grades, using those numbers to make inferences and identify outliers. Several items require students to describe the shape of distributions (histograms, dot plots, stem-and-leaf) and to answer context-based inference questions such as which day will be busiest or what typical weeks to expect for best-seller books.
Final Project
Statistical Study
Students are prompted in Step 4 to calculate the mean, median, and mode and then to calculate range, first and third quartiles, interquartile range, and mean absolute deviation, and to create a box plot showing the five-number summary. In Step 5 students answer explicit analysis questions about the shape of the data, any outliers, which measure (mean/median/mode) best represents the data, and what the range, IQR, and MAD tell about variability. Step 6 requires students to include in their presentation the statistical question, data collection methods, the measures of center and variability (mean, median, mode, range, IQR, MAD), and analysis/inferences relating findings to the context and original hypothesis.
3: Math
Unit 1: Numbers
Lesson 7
Arctic Marine Research
In Phase 5 (Temperature Analysis) students are asked to "Find the temperature range" and to "Calculate the average daily temperature," so they compute a mean and a range. In Phase 1 students compute differences in cell counts (e.g., difference: 2.5 × 10^7 cells) and compare magnitudes of measurements, which requires quantitative comparison of datasets.
Unit 4: Probability
Lesson 3
Probability Models
Students compute numerical predictions by building probability models and multiplying probabilities by the number of trials (e.g., 1/2 × 500 = 250 heads; 1/6 × 120 = 20). Students collect experimental data (tallies for die rolls, spinner outcomes, class choices) and calculate relative frequencies/experimental probabilities for those outcomes. Students compare experimental results to theoretical predictions, note how relative frequency tends to approach predicted values as trials increase, and explain discrepancies by referencing context (small sample size, bias, recording error).
Lesson 5
Simulations
Students are asked to compute averages (means) in multiple places: the Blue Marbles reflection asks "On average, how many pulls did it take," the Music Playlist instructs students to add outcomes and divide by 20 to find the average, and activity pages include TOTAL and AVERAGE fields. Students record trial-by-trial outcomes across 10–20 trials (e.g., Pulls Until Blue, Number of Songs Listened, Trial results) and answer reflection questions about whether any trials took a long time or surprised them. Several activities prompt students to count how often a condition occurs (e.g., count trials that took 4 or more rolls and convert to a fraction/percent), which supports describing overall patterns in the data.
Unit 8: Data
Lesson 1
Statistics Review
Students calculate means and medians with step-by-step examples and practice problems (Activity 1 and Activity 2). Students compute measures of variability—range, interquartile range (IQR), and mean absolute deviation (MAD)—with worked examples and practice exercises (Activity 3 and Activity 5). Students construct and interpret box plots and five-number summaries, identify skewness, and use the IQR method to check for outliers in real-context tasks (Activity 4 and Box Plot Builders). Several practice prompts explicitly ask students to explain what MAD or IQR says about how tightly values are clustered and to compare classes or data sets in context.
Lesson 2
Scatterplots
Students label independent and dependent variables, identify positive/negative/no relationships, and classify relationships as linear or non-linear, showing they describe overall patterns. Students locate clusters and outliers and answer context-based questions about what those deviations might mean (e.g., sick student, data entry error). Students draw or choose best‑fit lines and compare graphs to judge variability visually by noting whether points hug the line (low variability) or are widely scattered (high variability).
Lesson 6
Unit 8 Test
Students calculate mean, median, and mode on multiple data sets (several activity pages and answer keys provide computed means, medians, and modes). Students compute measures of spread including range, interquartile range (IQR), and mean absolute deviation (MAD) on specific problems (Jumping Jacks, Jumping Jacks on test, and answer keys list IQR and MAD values). Students interpret box plots by comparing IQRs to decide which group is more consistent and analyze scatterplots to describe overall patterns, variability, clusters, and outliers in context (questions ask for trend identification, clusters, outlier coordinates, and contextual explanations).
Final Project
Collecting and Organizing Data
Students plan and collect numerical and categorical data, create scatterplots, and are prompted to label axes, choose scales, plot points, and draw an informal line of best fit. Students answer guided analysis questions that ask them to describe overall patterns (positive/negative/no trend), note clustering, and identify any outliers or surprising points. Students convert tally counts into percentages in a two-way relative frequency table and write one-sentence summaries describing the patterns they observe.
Unit 9: Semester Exams
Lesson 9
Data Review
Students calculate measures of center (mean and median) and simple measures of spread (range) in Activity 1, including deciding which measure of center best represents a skewed set (the 3,5,6,7,45 example) and explaining the effect of an outlier. In Activity 2 students compute mean absolute deviation (MAD), find the interquartile range (IQR), and draw box plots, and they interpret MAD and IQR to compare consistency (Class A vs Class B). In Activity 3 students describe overall patterns in context (positive, negative, or no correlation) and identify how close points are to a line of best fit and discuss outliers and relationships using contextual examples like hours studied vs test scores.
Lesson 10
Semester Exam
Students compute measures of center and spread: problems ask for mean, median, mode, range, mean absolute deviation (MAD), and interquartile range (IQR) (e.g., Problems 36, 40, 41, 42). Students draw box plots and answer what the IQR represents (Problems 43–44). Students interpret data in context by identifying the median as the best measure for the set (5, 6, 7, 8, 40) because of an outlier, explain what the median says about typical reading time, and compare class consistency using mean and MAD (Problems 36–39, 45). Students analyze overall patterns and deviations using a scatterplot (identify correlation, describe what the pattern suggests, and explain closeness to a line of best fit) (Problems 46–47).
