Students work with explicit input-output formulas in Phase 3, where they use N = 2^t to compute the population after 6 intervals and compare it to 3^t after 4 intervals. In Phase 3 continued, students compute the result of repeated doubling (2^10) to find the number of DNA strands after 10 cycles. These tasks require students to substitute a given input (t) into an expression and calculate the corresponding output (N).

Students identify independent and dependent variables (x as input, y as output) in Activity 1 and in multiple parent/teacher notes. In Activities 2 and 3 students work with tables of ordered pairs (x,y) and pick points on graphs to compute k = y/x, explicitly using pairs like (4,12) and (2,8). Students rewrite and interpret equations in the form y = kx, using those equations to produce outputs for given inputs.

Students identify independent (x) and dependent (y) variables, label axes, and build tables of (x,y) pairs from situations and equations (e.g., Jim's earnings, y = 12x). They plot those ordered pairs on coordinate grids, draw lines through points, and use the point (1,k) and (0,0) to find unit rates. Students also convert equations into tables and graphs (e.g., y = 4x → (0,0),(1,4),(2,8),…) and answer whether the graph shows a proportional relationship.

Students write equations in the form y = kx and t = p × n (Activity 1 and multiple student pages) and use those equations to compute outputs from given inputs (e.g., fill total cost for number of tickets or pounds). Students complete tables that pair inputs (number of items, minutes, hours) with outputs (total cost, calories burned, area painted) and use those tables to decide proportionality. Students model situations with graphs, are asked to create graphs (theme park problem, Activity 3), and interpret plotted points such as (1, 5) and the requirement that proportional graphs form straight lines through the origin (Review and Quiz items).

Students work with tables of (x,y) values and are asked to decide whether the pairs are proportional, e.g., multiple problems present x and y columns and ask if the relationship is proportional. Students plot and interpret points on graphs (for example identifying (0,0) and (1,r) and describing what those points mean) and graph equations of the form y = kx. Several tasks ask students to determine whether a graph is a straight line through the origin, implicitly treating plotted ordered pairs as input-output pairs.

Students create tables that map number of lemons or cups (input) to total cost or tablespoons (output) and label axes with number of lemons/cups on the x-axis and cost/tablespoons on the y-axis. Students plot points and draw straight lines for each store or recipe, and answer questions about steepness and which line shows the better value. Students write equations of the form y = kx and identify x as the independent variable and y as the dependent variable for proportional relationships.

Students write and use formulas that take an input and produce an output, for example Total Price = Original Price × (1 + Sales Tax Rate), Discounted Price = Original Price × (1 − Discount Rate), and Total Cost = 25 + 3r. Students plug in numeric inputs (e.g., number of rides r = 5 or original price P = 40) and compute the corresponding outputs (e.g., Total Cost = 40, Total Price = 42). Students also set up and solve equations for unknown inputs given an output (e.g., 58 = 25 + 3r and solving r = 11).

Students create tables of input x-values and compute corresponding outputs y (for example, filling tables for y = 3x, y = 2x, y = 1/2 x) and then plot each pair as points on a coordinate grid. Students map real-world inputs to outputs (hours → earnings, time → distance, pounds → cost) and plot points such as (0,0), (1,10), (2,20) to show the relationship. Students also turn graphs into equations by selecting a point (x,y), computing k = y/x, and writing y = kx, which treats the graph as a set of ordered input-output pairs.

Students create tables of (x,y) values, plot those ordered pairs on coordinate grids, and draw lines for relationships like y = mx. Students use equations in the form y = mx to compute an output y for each input x and repeatedly identify the unit rate as the value of y when x = 1. Students compare graphs and equations to determine which input-output mappings produce larger outputs (steeper slopes).

Students repeatedly write and plot ordered pairs for intercepts (e.g., (3,0), (0,-2)) and complete activities that require identifying x- and y-intercepts as coordinate points. Activity pages ask students to graph lines from given intercepts and to derive intercepts algebraically by setting one variable to zero, connecting equations (e.g., 2x+4y=8, y=5x+10) to specific coordinate points. The Parent Plan explicitly states that students will "interpret the equation y = mx + b as defining a linear function, whose graph is a straight line," linking equations to the idea of a linear function and its graph.

The Parent Plan explicitly says students will "Interpret the equation y=mx+b as defining a linear function," and multiple activities ask students to pick x-values from tables, compute corresponding y-values, and write y=mx+b (Activity 7 and related student pages). Students repeatedly plot points from tables or ordered pairs and draw the line (Activities 5–7), and real-world problems label x as the input and y as the output (Activity 8). Instructions also ask students to use tables, graphs, and equations interchangeably to represent relationships.

Students work with tables that map inputs (hours, days) to outputs (earnings, cost) and answer questions about whether the relationship is proportional. Students plot ordered pairs on coordinate grids, find slope from two points, and write linear equations in slope-intercept form (y = mx + b) that represent input-output relationships. Several tasks ask students to identify whether a graph passes through the origin and thus represents a proportional (through-origin) relationship.

Students fill tables that map time (hours) to distance (miles) for car, train, and plane and complete entries for times from 0 to 4 (or 0 to 6) hours, showing a single distance value for each time input. Students write equations in the form y = mx and y = mx + b for these relationships (distance = speed × time; cost = rate × distance + fixed cost), directly expressing a rule that produces an output from a given input. Students plot those table values on graphs (Distance vs. Time and Total Cost vs. Distance) so they create ordered pairs and draw the corresponding lines for each mode of travel.

The lesson gives explicit Number Assignments (e.g., Music Playlist: digits 0–3 = Pop, 4–6 = Country, 7–8 = Rap, 9 = Instrumental) and similar mappings for visitors and book types. Students roll a die or use digits, apply that mapping to determine a genre or visitor/book type, and record the digit alongside the resulting category in data tables ("Numbers Rolled" and the corresponding outcome). These tasks require students to use a single rule that maps each input digit to one categorical output repeatedly across trials.

Students are given the definition that a function assigns exactly one output for every input and are repeatedly shown examples where a repeated input with different outputs is not a function (tables, ordered pairs, and mappings). The lesson has students use mapping diagrams and ordered pairs and asks them to decide whether given ordered pairs or tables represent functions. The lesson explicitly connects input/output pairs to graph points, telling students that every input/output pair becomes a point (x,y) on the coordinate plane and has them plot points from rules and tables. The Vertical Line Test is taught and applied to graphs to determine whether a graph represents a function.

Students plug given x-values into equations (for example y = 2x + 4 and y = x^2) to compute y-values and fill tables, producing explicit (x,y) pairs. Students plot those ordered pairs on coordinate planes (points marked like (-1,-1),(1,1),(2,3),(3,5)) and describe the graph as a straight line or a curve. The Parent Plan and examples interpret y = mx + b as defining a linear function and give A = s^2 with points (1,1),(2,4),(3,9) as an example of a non-linear relationship.

Students label axes with independent and dependent variables (e.g., x = time, y = height) and are asked to plot points using coordinate pairs (for example, "Start at (0, 0)" for Sylvia the Sloth). Students plot and connect dots for scenarios (Sylvia, Timmy the Turtle, Bella the Balloon) and translate step-by-step descriptions into points and line segments on a coordinate grid. Students match graphs to real-world situations and describe how the y-value changes as the x-value changes, showing an input–output relationship in context.

Students practice treating x as an input and y as the corresponding output when they fill tables (e.g., complete the table for y = 3x + 1) and when they compute y for given x values (e.g., find y when x = 4 for y = x + 2). Students are asked to decide whether given sets of ordered pairs or graphs represent functions on the cumulative quiz (e.g., determine whether (1,2), (2,3), (1,4) is a function and whether a graph is a function). Multiple activities require converting between graphs, tables, points, and equations y = mx + b, which has students produce ordered pairs and match inputs to outputs.

Students are introduced to the idea that "a function rule tells us how one quantity changes based on another" and that it "always has an input, an output, and a rule that connects them." The lesson defines input and output explicitly and has students name variables (e.g., let c = number of chores, A = total amount) and write functions in the form output = slope × input + starting value. Students read tables and graphs (e.g., a table of hours vs. pages and graph points like (0,5), (1,8), (2,11)), identify corresponding coordinates, compute slope and intercept, and write the matching function equations. Multiple activities require converting between story, table, and graph representations so students practice mapping each input value to its single output in concrete examples.

Students work with equations that explicitly name x as the input and y as the output (for example, y = -3x + 100 where x is weeks and y is amount of money). Students identify points on graphs (e.g., (0,0) and (30,2)) and use those ordered pairs to compute slope (Δy/Δx). Students read and construct tables of input/output values (time vs. position or balance) and convert real-world dates/times into numeric x-values to find corresponding y-values. Many activities require comparing representations (graph, table, equation, verbal) by matching x-values to y-values and computing rates of change.

Students are asked to decide whether a table represents a function by checking repeated x-values with different outputs (Question 1 and its answer explanation). Students must explain in their own words what it means for a rule to be a function (Question 2 and the answer key stating "A function gives one and only one output for each input"). Students apply the vertical line test to graphs to determine function status (Question 5 and its answer). Students read and write ordered pairs and intercepts (multiple problems ask for y-intercepts and x-intercepts written as (0,3), (4,0), etc.), and they translate between tables, graphs, and equations in many items.

The Parent Plan explicitly states "Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output." Students create Red, Green, Blue, and Yellow cards that ask "Is this a function?" using graphs, tables, equations, and real-world descriptions. Green card instructions tell students to draw tables with x- and y-values and to decide whether the relationship is a function, and Red/Yellow cards require students to analyze graphs and descriptions for function behavior. Students also write answer keys and check answers while playing, providing practice in identifying input-output relationships across representations.

Students use the algebraic translation notation Ta,b → P'(x + a, y + b) and apply it to specific points and shapes (for example, translating M(6,-2) to M'=(1,1) and X(0,0), Y(2,0), Z(1,2) to X'(-4,1), Y'(-2,1), Z'(-3,3)). Student activities require computing new ordered pairs after applying given translation rules (many exercises ask for the translated coordinates or the translation that maps originals to images). The lesson repeatedly has students perform and record mappings from original coordinates to single image coordinates using the (x,y) → (x+a,y+b) format.

Students apply explicit coordinate rules written in mapping form (e.g., (x,y) → (x,−y), (x,y) → (−x,y), (x,y) → (y,x), (x,y) → (−y,−x)) and use those rules to produce reflected points and shapes. Activities require students to plot original points and then compute and plot the reflected coordinates (labeling originals and primes), and answer tables that record 'before' and 'after' ordered pairs. Digital and hands-on tasks have students drag or move points and observe the single corresponding reflected point produced by the rule.

Students work with explicit coordinate rules written as mappings, for example (x, y) → (−y, x), (x, y) → (y, −x), and (x, y) → (−x, −y). Students apply those rules to given input ordered pairs in examples and problems (e.g., M(6, −2) → M'(2, 6); A(1,2) → A'(−1, −2)) and plot both original and image points. Activity pages ask students to write the new coordinates and label the image with a prime symbol, reinforcing the input→output calculation for each point or shape.

The lesson gives an explicit mapping rule: "If the original point is (x, y), the new point should be: (x × scale factor, y × scale factor)." Students repeatedly compute new ordered pairs from given original ordered pairs (tables and examples showing Original Coordinates → New Coordinates and calculating scale factors). Activity pages require students to enter original coordinates and calculate corresponding new coordinates and then plot those ordered pairs on a coordinate plane.

Students apply coordinate transformation rules in multiple problems (e.g., rotation rules chart and exercises that ask students to rotate, reflect, translate, and dilate points and triangles). Several items ask for an explicit translation or rotation rule (for example, find T_{a,b} that maps A to A' and use rules like (x,y) → (−y,x) listed in the answer key). Many activities require computing image coordinates from given input coordinates and plotting the corresponding ordered pairs.

Students graph linear equations in slope-intercept form (y = mx + b) and plot specific points such as (0,3), (1,5), and (2,7). The materials state that "every single point on this line is a solution to the equation" and have students identify and record intersection points as coordinate pairs (for example (1,3) and (2,3)). Students verify solutions by substituting ordered pairs into equations to show both sides are true.

Students plot lines from two given points and write each line's equation in slope–intercept form (y = mx + b). Students substitute x-values into those equations to find corresponding y-values and identify intersection points as ordered pairs (for example, finding that (1, 4) makes both equations true). Students label and estimate intersection points on graphs and record solutions as (x, y).

Students define variables x and y and write equations in slope-intercept form (y = mx + b) for real situations (e.g., cost = rate × quantity + fixed amount). Students solve those equations and report solutions as ordered pairs (for example, (5, 150) and (30, 35)). The lesson prompts students to create graphs of both lines to ‘see a picture of the solution,' linking equation outputs to plotted coordinate pairs.

Students repeatedly write equations that map an input variable to an output (e.g., C = 1200m, C = 1500 + 1050m; C = 225 + 0.60x; C = 5 + 1.5h) and complete tables of values for those equations (phone plan table). Students graph those equations on coordinate grids with labeled axes and plot the lines, then use the graphs to identify break-even/intersection points. In the phone-plan activity students simplify and compare two expressions to find that they produce the same line, noting that for every x the cost y is the same.

Students label the x-axis as the independent variable and the y-axis as the dependent variable (Activity 2 Step 1) and repeatedly work from tables of paired data to plot points (e.g., Hours Studied vs. Test Grade, Height vs. Arm Span, Temperature vs. Ice Creams Sold). Students are instructed to "plot the points" and "plot each time of day as one dot," so they practice creating graphs from ordered pairs. Many activity questions ask students to interpret the plotted points and make predictions based on the input (x) and corresponding output (y).

Students plot data points on scatterplots and draw or use a best‑fit line, then write the line in slope‑intercept form y = mx + b (Activities 1 and Bird Migration). Students identify independent and dependent variables and interpret slope and y‑intercept in words (multiple student activity pages and parent plan examples). Students substitute specific x values into the linear equation to produce predicted y values (ice cream example: substitute x = 10 to get y = 70).

Students are asked to plot and analyze many sets of ordered pairs (for example the table with pairs (1,10),(2,8),(3,6),(4,8),(6,5) and the Hours of Social Media vs Number of Texts table) and to draw scatterplots on blank grids with labeled axes. Multiple items require students to identify the independent and dependent variables (e.g., Study Time vs Test Scores, Hours Practiced vs Performance Score) and to predict an output for a given input (e.g., predict texts for 9 hours of social media, predict homework at 8 hours of gaming). Students also match or write linear equations for scatterplots (e.g., choose between y=2x+4 and y=4x+0; write y=4x+2), which treats y as an output dependent on x.

Students collect paired numerical measurements (for example, number of jumping jacks and heart rate) and record each participant as a row in a numerical data table. They are instructed to plot each pair of values on a scatterplot, label axes, choose scales, and plot dots or X's for each data pair. The Part 4 and Part 5 pages guide students to read the plotted points and describe the relationship between the two quantities.

Students graph linear equations (e.g., "Graph the equation y = 6x"), label points, and are asked explicitly what points like (0,0) and (1,6) represent in context. Several activities require matching tables to equations (e.g., y = 10x, y = 3x) and identifying the constant of proportionality, which has students generate outputs from given inputs. The Parent Plan and activities repeatedly ask students to write equations, create tables, and explain what a point (x,y) means in a real-world situation.

Students plot ordered pairs from tables and graphs (e.g., (0,0), (1,14), (2,28)) and graph linear relationships, directly connecting inputs (hours, days) to outputs (earnings, cost). Students write equations in the form y = mx and y = mx + b from tables and graphs and identify slope and y-intercept as rate and starting value. Students interpret points (for example, what (0,0) means) and translate between tables, equations, and graphs for proportional and linear relationships.

Students graph lines (e.g., graph y = 4x; plot the line through (0,0) and (4,-8)) and interpret slope and proportional relationships. Students work with tables that map x to y (e.g., x:1,2,3 to y:5,10,15) and find the constant of proportionality and write equations like y = kx. Several items ask for unit rates and describe how y changes when x increases, linking inputs and outputs numerically and visually.

Students examine tables of ordered pairs (e.g., (0,2), (1,5), (2,8), (1,7)) and are asked to declare whether the relation is a function and explain that the input x = 1 has two different outputs. Students explain in their own words what a function means (what happens to each input and why it matters) and select the statement "Each input has exactly one output." Students use the vertical line test on graphs and plot or identify points and intercepts (e.g., finding the x-intercept (4,0), y-intercept (0,4), and graphing y = 3x − 2 and points like (−1,−3), (1,1), (3,5)).

Students practice graphing linear equations in slope-intercept form (e.g., graph y = x - 3 and y = -2x + 1) and compute slope from two given points. Students solve systems by graphing and identify the intersection point as the solution, and they solve systems algebraically where ordered pairs (x,y) are produced as solutions. Several activities require plotting lines on coordinate grids and interpreting those plotted points as solutions to equations.

Students use the vertical line test (question 7 and answer key) to decide whether a graph represents a function, write a context-based function y = 10x for earnings (question 8 and answer key), and graph equations such as y = 2x − 4 and plot points/intercepts ((0,4), (4,0)) from tables (questions 3, 4, 6 and associated tasks). The exam also gives a table of (x,y) pairs for finding an x-intercept and asks students to identify intercepts as ordered pairs, so students work directly with input-output pairs when graphing and interpreting functions.