HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 1

Unit 1: Operations

Students calculate a cost per goody bag by dividing the grand total cost by the number of party guests on the "Spending Your Money" activity (example: $42.84 ÷ 12 = $3.57). The planning and cost-analysis tables require students to compute totals and per-unit cost, which function as a single-number summary of the total spending across all bags.
Unit 8

Unit 8: Statistics

Students practice reading stem-and-leaf plots to find the lowest and highest values (e.g., Marco: lowest 78, highest 91) and to identify the most common value (mode: 87°). Activity questions ask students to report counts and to answer "What is the mode of the data?" and to find the fewest and largest values in given data sets. The Parent Plan and activities repeatedly have students summarize the data by reporting number of observations and identifying min/max and mode.
Students read and interpret histograms to identify the interval with the highest frequency (e.g., 12–13 has the most campers) and answer questions about which interval is most/least frequent. Students compute differences of frequencies to compare groups (example: 17 − 5 = 12 more campers in one interval than another). Students calculate the range (difference between highest and lowest values) in a stem-and-leaf activity (answer key shows difference = 16 books).
Students are explicitly told that a measure of center is "a one-number summary" and are taught how to find mean, median, and mode through examples and practice problems (Activity 1, dot plots, stem-and-leaf, frequency tables). Students compute means (including rounding), medians (odd and even cases), and modes from multiple data representations and list data values from graphs. The lesson also names range as a measure of variability and gives the procedure to compute it (subtract smallest value from greatest) in the Wrapping Up section.
The Getting Started section explicitly states, "The measures of center allow you to find a value that summarizes, or represents, all the data values in the set," and names mean, median, and mode as measures of center. The Things to Know and Answer Key define variability and list numerical measures (range, interquartile range, mean absolute deviation) that describe how data are spread. Multiple activities require students to calculate and compare measures of center (mean, median, mode) and measures of variability (range, IQR, MAD) for the same data sets (orchards, babies, snakes/lizards, box plots), reinforcing the distinction through practice.
Students compute measures of center (mean, median, mode) in the food truck example where the mean is shown as 600 ÷ 24 = 25 and the median and mode are identified as 25. Students compute and interpret measures of variability: a box plot with Q1 = 17, Q3 = 34, IQR = 17, range 6–45, and a provided mean absolute deviation (8.75) are all shown and discussed. In activities students calculate sample means (word-length and candy activities), compare sample means to the population mean, and use center and variability values to make and evaluate inferences about a population.
Students are prompted to calculate the mean of each data set (Step Three) and to calculate the mean absolute deviation (MAD) for each data set (Step Four). The materials define MAD as "the average of how far the different data values are from the mean" and provide tables where students compute distances from the mean and the MAD. Students use the mean and MAD together by computing the difference between means divided by the larger MAD to judge overlap and significance of differences between populations.
Students are asked to compute means, medians, modes, ranges, interquartile ranges, and mean absolute deviation on multiple activity pages (e.g., find the mean, median, mode, range; find interquartile range; find mean absolute deviation; create a box plot/five-number summary). Students compare measures across two data sets (Opal vs. Randall; fiction vs. nonfiction) and use differences in means and mean absolute deviations to make inferences about which population is likely to have higher typical values and which has greater variability. The Parent Plan Skills explicitly list finding quantitative measures of center (median and/or mean) and variability (IQR and/or MAD) and using these measures to describe patterns and draw informal comparative inferences about populations.
Students are instructed to compute mean, median, and mode and to calculate range, interquartile range, and mean absolute deviation (Step 4). Step 5 asks students to answer interpretive prompts such as which measure best represents the data and what the range, IQR, and MAD tell about variability. The presentation requirements require students to display the measures of center and measures of variability and to include analysis and inferences in context. The Parent Plan explicitly states that students should "Recognize that a measure of center...summarizes all of its values with a single number" and that "a measure of variation describes how a numerical data set's values vary with a single number."

3: Math

Unit 1

Unit 1: Numbers

Students compute and interpret averages in real contexts (e.g., "A company loses $60 over 5 days. What is the average daily loss?", "A hiker climbs 600 feet in 4 hours. Determine the average ascent rate per hour."). Activity pages ask students to write equations and divide totals by counts to find per‑unit (average) quantities (salary deductions, average temperature change, debt per person). The answer keys explicitly interpret quotients as average rates (e.g., −48 ÷ 6 = −8 °F per hour).
Students are asked in Phase 5 (Temperature Analysis) to calculate the temperature range from -15°C to 5°C and to compute the average daily temperature. The answer key shows students find a range of 20°C and an average of -5°C, so students perform both a measure of variation (range) and a measure of center (mean) on a numerical data set.
Unit 4

Unit 4: Probability

Students are explicitly asked to compute averages in multiple activities (e.g., Music Playlist: "To find the average, add up each of the outcomes and divide by the number of trials (20)" and activity pages include TOTAL and AVERAGE fields). In the Blue Marble and What Kind of Visitor activities students record the number of pulls/visitors per trial and are prompted to answer "On average, how many pulls/visitors did it take…?" Students also describe and compare variability qualitatively (reflection questions ask whether any trials took a long time and why).
Students calculate a probability model that assigns a single percentage to each size/color combination (e.g., 9/60 × 100 = 15%) so they summarize categories with one number. Students run simulations recording the number of rolls until a target outcome and then compute an average number of rolls across trials. Students create and use sample spaces, tables, and tree diagrams to list and organize all outcomes before summarizing them with probabilities.
Unit 8

Unit 8: Data

Students are given explicit definitions and procedures for measures of center (mean, median, mode) in the "Things to Know" and Activity 1 pages and practice calculating them on multiple data sets. The lesson defines measures of variability (range, IQR, MAD), provides step-by-step calculations (Activity 3) and worked examples (turtle ages, text messages) that show how to compute each measure. Activities and practice pages ask students to compute and interpret five-number summaries and box plots (Activity 4 and 5) and include an explicit comparative example showing two students with the same mean but different spreads to illustrate why variability matters. The Parent Plan and answer keys explicitly state that students should "recognize that a measure of variation describes how a numerical data set's values vary with a single number."
Students calculate mean, median, and mode on multiple problems (e.g., Student Quiz Scores, Snack Prices, Shoe Sizes, Books Read). Students compute measures of spread such as range, interquartile range (IQR), and mean absolute deviation (MAD) on Jumping Jacks and other tasks. Students interpret and compare distributions using IQR in box-plot comparison problems (e.g., asking which group has more consistent scores and explaining reasoning based on the IQR). The unit review sheet and parent plan explicitly list "Calculate and interpret measures of center (mean, median, and mode) and spread (range, interquartile range, and mean absolute deviation)."
Unit 9

Unit 9: Semester Exams

Students calculate mean, median, mode, and range on the Activity 1 worksheet (finding these values for given data sets). They choose between mean and median for a skewed data set with an outlier and explain why the median better represents that data, and they interpret what the median means (half the values are at or below/at or above it). In Activity 2 students compute mean absolute deviation (MAD), interquartile range (IQR), and draw box plots, answer what MAD tells about spread, and compare two classes' consistency using MAD to decide which set is more or less variable.
Students compute mean, median, mode, and range (Problems 36, 39, 40) and calculate mean absolute deviation (MAD) and interquartile range (IQR) (Problems 40, 41, 42). Students answer conceptual questions that link these calculations to interpretation: Q37 asks which measure of center best represents a skewed data set and Q41/Q44 ask what MAD and IQR tell about the spread. Problem 45 directly asks students to compare consistency of two classes using equal means but different MADs.