HOMESCHOOL AND DISTANCE LEARNING
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3: Math

Unit 2

Unit 2: Proportions

Students plot paired data from tables and equations (e.g., Jim's earnings table, y = kx examples) and draw graphs on coordinate planes. Students test whether plotted points form a straight line and whether the line passes through the origin to decide if a relationship is proportional. Students compute and use unit rates (y/x) to check for a constant rate and compare steepness of lines to determine which rate is larger; one example includes a negative slope (temperature change) that students plot and interpret.
Students are given several graphs with plotted point pairs (for example, "Hours Worked vs. Money Earned" with points like (0,0), (8,36), (15,60) and a version with (0,0),(1,6.80),(2,13.60),...). Students are asked to determine whether those graphs represent a proportional relationship (circle proportional / not proportional) and to graph equations such as y = 4x or y = 5x, plotting points on a grid.
Students are asked to create tables and plot the number of lemons (x) against total cost (y) for multiple stores, label axes, use different colors for each store, and visually highlight the best deal. Students complete tables and graphs for cups (x) versus tablespoons of lemon juice or sugar (y), plot points on a grid, and write equations in the form y = kx, including graphs that begin at the origin. The materials include questions asking which line is steepest/least steep and what steepness tells you about price per lemon, and the parent/skills text explicitly notes deciding proportionality by graphing and observing a straight line through the origin.
Unit 3

Unit 3: Expressions

Students create graphs from tables and equations across multiple activities (e.g., Activities 4–6 and Day 3) by plotting points such as (1,4), (2,8), or (1,3), (2,6) and connecting them to form lines. Students calculate and interpret slope and unit rate using the two-point formula and by reading y at x = 1 (Activities 1 and 3). Students compare relationships on the same coordinate plane to determine which line is steeper and discuss positive versus negative slopes (examples include y = 3x, y = −3x, and various rate comparisons).
Students plot ordered pairs from tables and graph points in multiple activities (Using Tables to Find Linear Equations; Extend the Line; Solving for b) and use those points to write equations in y = mx + b. Students graph lines and compare slopes, including activities that have them graph positive, negative, and zero slopes and describe direction (Activity 3). Students convert equations to slope-intercept form, plot y-intercepts, and use slope to place additional points, practicing interpretation of slope as rate of change in real-world contexts.
Students plot paired numerical data from tables (e.g., hours vs. earnings, days vs. cost) and graph those points on coordinate planes. Students calculate slope and y-intercept from plotted points or given coordinates and write linear equations that model the bivariate data. Students compare rates of change, determine whether a relationship is proportional (passes through the origin), and identify lines with positive or negative slope.
Students fill tables of time and distance for car, train, and plane and plot those values on a shared graph (Step 2 and Step 4), and they write equations in the form y = mx for distance vs. time and y = mx + b for cost vs. distance. Students are instructed to graph all three travel methods on the same axes and answer questions about rise/run, which line is steepest, which is fastest/slowest, and whether the lines represent linear or proportional relationships. The cost activity has students write linear cost equations, graph them, and compare slopes and intercepts to decide which method is cheapest and where break-even points occur.
Unit 5

Unit 5: Functions

Students plot ordered pairs (x,y) from tables and function rules and place those points on coordinate grids (Activities 3 and 4). Students compute outputs from input/output machines, fill tables of x and y, and then graph the resulting points to form lines or curves (examples y=2x+1, y=x^2−2). Students also identify linear versus non-linear graphs and note positive or negative slope in several graph examples.
Students read data tables and line graphs (e.g., the "Reading Table" and "Silent Line") to identify the input and output, pick two points, and compute slope using the slope formula. Students extract y-intercepts from tables or graphs and write linear function rules from paired values (examples: P = 15h, C = 3h + 5). Activities require students to convert paired data into equations and to interpret direction of change (increasing or decreasing) from those points and lines.
Unit 8

Unit 8: Data

Students label axes as independent and dependent and identify which variable goes on the x- and y-axes (Activity 1 and multiple student pages). Students classify scatterplots as showing positive, negative, or no relationship and as linear or non-linear, and they identify clusters and outliers (multiple activities and the "Scatterplot Notes" pages). Students choose and draw best-fit lines, judge variability (low vs high), make predictions from a best-fit line, and analyze correlation versus causation using real-world scenarios (Best Fit Line, Making Predictions, Correlation or Causation activities).
Students are given multiple bivariate data tables and blank graphs (e.g., Hours Studied vs. Test Grade; Height vs. Arm Span; Temperature vs. Ice Creams Sold) and instructed to label axes, choose scales, plot points, and (when appropriate) draw a best-fit line. Many activity prompts and questions ask students to decide whether there is a linear relationship and to describe positive or negative association, clusters, and outliers. Matching and story-writing activities (Pick a Plot; What's the Story?) require students to interpret patterns as linear, nonlinear, random, clustered, or containing outliers. Parent/answer-key sections and wrap-up explicitly ask students to make predictions from trends and to discuss correlation versus causation.
Students repeatedly plot bivariate data and draw or read a best‑fit line (e.g., Bird Migration activity, multiple Student Activity Pages asking students to plot points and draw a line of best fit). Students write the equation of the best‑fit line in y = mx + b form (Activity 1, Graphs 5–8) and use two points to calculate slope and intercept. Students interpret the slope and y‑intercept in context and use linear models to make predictions (ice cream example, plant growth, tickets sold, and other problem pages). Some student pages explicitly label trends as positive or negative and ask students to describe the relationship in words.
Students are asked to draw scatterplots from bivariate tables (e.g., Hours of Sleep vs. Mood Rating; Hours of Video Games vs. Homework Completed; Hours of Social Media vs. Number of Texts) using blank grids with labeled axes and titles. Multiple exercises require students to identify linear vs. nonlinear relationships, determine positive/negative/no association, locate clusters and outliers, identify independent and dependent variables, assess variability, and make predictions from the scatterplots (see Exercises 5–12 and numerous blank-graph activities). The final project explicitly requires students to collect real data and create a scatterplot to display and analyze patterns of association between two quantities.
Students are instructed to draw a scatterplot: label axes, choose an appropriate scale, plot each pair of numerical values, and add a title (Part 4 scatterplot instructions). The materials prompt students to analyze the plotted points with guided questions such as "What do you notice?", "Do the dots form a pattern?", and to identify trends as positive, negative, or no trend (image and Student Activity Page). The project explicitly asks students to look for clusters and outliers and provides reflection prompts asking "Were there any outliers—points that don't follow the pattern?" and "Do your dots rise in a line? Are there clusters?" (Part 5 reflection pages and examples).
Unit 9

Unit 9: Semester Exams

Students plot bivariate data from tables (e.g., Hours vs Earnings: (0,0),(1,14),(2,28),(3,42) and Days vs Cost: (0,0),(1,75),(2,150),(3,225)) and graph those points, write equations (y = 14x, y = 75x) and interpret the meaning of the origin. Students compute slopes (including negative slopes in examples), identify y-intercepts, and write equations in y = mx + b form to interpret rate of change and starting values. Students compare steepness/rates of change across lines (e.g., deciding which line is steeper or which plan has a greater rate of change) to interpret linear association.
Students are asked to plot points and graph linear equations (e.g., questions 19, 20, 35, and 37) and an image shows a coordinate grid with plotted points and a diagonal line. Problems require students to find unit rate from points and to write equations from point pairs (e.g., find the unit rate for a line through (0,0) and (2,10); plot the line through (0,0) and (4,-8)). Students are also asked to identify positive vs. negative slope and to compare which line has a greater rate of change.
Activity 3 (Scatterplots & Linear Models) asks students to analyze three provided scatterplots, identify positive, negative, or no correlation, interpret what the relationships suggest, and explain the meaning of points being close to a line of best fit. The Parent Plan explicitly lists that students should "construct and interpret scatter plots" and should "describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association," and it also mentions informally fitting a straight line and assessing closeness to the line. The student worksheet includes prompts about correlation vs. causation and interpreting lines of best fit.
Students are given a scatter plot of hours studied (x) and test score (y) and are asked to identify the type of correlation and explain what it suggests (Question 46). Students are also asked what it means if most data points are close to the line of best fit (Question 47). The answer key identifies a positive correlation and explains that as study time increases, test scores tend to increase, and notes that the data closely follows the model so the line of best fit represents the relationship well.