Students are asked to compute a per-unit rate in a verbal word problem: "If Dwayne was paid $78 for washing 5 cars, determine how much he earns per car." The answer key shows the division and gives the unit rate $15.60 per car. The quiz and its answer explicitly require students to find the amount earned per one car from a given total and quantity.

Students solve word problems that produce unit-rate answers by dividing totals by counts (for example, $850 ÷ 4 = $212.50 weekly earnings; 135 oz ÷ 2 oz per cup = 67 cups). Several problems require finding a per-unit quantity by division (e.g., groceries per week, ketchup servings, crackers per bag). The answer key shows these division calculations explicitly.

Students compute a unit cost when Question 1 on the "Spending Your Money" page asks them to divide the grand total cost by 12 to find the cost per goody bag (example: $42.84 ÷ 12 = $3.57). Students complete and use the planning table that multiplies items per bag × 12, determines packages needed, and multiplies packages × price to get total cost for each item. The lesson provides an example calculation that explicitly shows computing total cost and then dividing by the number of guests to obtain a per-bag value.

The Parent Plan lists understanding the concept of a unit rate a/b associated with a ratio a:b and using rate language. Students write and interpret ratios in three forms (words, colon, fraction) including several unit-type ratios with denominator 1 (e.g., 3:1, 4:1) and complete word problems that scale quantities (bread, cleaning solution, blueberry pies). Students practice forming equivalent ratios and simplifying ratios (e.g., 9:6 to 3:2), which reinforces the numeric relationship between quantities.

Students make and use tables of equivalent ratios and plot the pairs on coordinate-plane graphs (e.g., Leo/print job, Leo/lemons: (1,6),(3,18),(5,30) with the point (4,24) highlighted). Students use double number lines and problems that require scaling rates (e.g., 2 sodas for $5 to find cost of 6 sodas; 2 sandwiches every 3 minutes to find time for 12 or 40 sandwiches). Multiple activities ask students to fill missing values in tables and to compute corresponding values from graphs and diagrams (e.g., key chains: (5,2),(15,6),(30,12); hamburgers/drinks scaled from 5 to 75).

Students compute unit rates from verbal descriptions and ratios by writing the ratio as a fraction and dividing (e.g., 216 miles/4 hours → 54 miles per hour; 156 calories/12 chips → 13 calories per chip). Students use diagrams (double number line and tape diagrams) and equivalent-ratio methods to produce unit rates and unit prices (several activities and worked examples show these methods). A data table (Uri's hours vs. calories) is provided and students are asked to create a graph from it and answer rate questions, and multiple problems ask students to find unit price from given quantities and prices.

Students work with percents described as a rate per 100 and set up equivalent ratios (e.g., 15/100 = part/whole) using double number line diagrams and bar models. Students translate verbal percent problems into equations (for example, 32 = 0.64x and part = percent × whole) and solve for unknowns in those equations. Several activities ask students to create and use double number line diagrams and to solve problems by finding equivalent ratios or by rewriting percents as fractions/decimals.

Students are given and use unit conversion ratios written as unit rates (for example, 1 ounce ≈ 28.35 grams, 1 inch = 2.54 cm, 1 foot = 12 inches) and are instructed to choose the appropriate given ratio from verbal descriptions. Students set up and solve conversion problems by forming equivalent ratios and by using double number line diagrams, scaling the unit rate (e.g., 1 in → 2.54 cm scaled to 10 in → 25.4 cm). The activity problems require students to determine the unit conversion ratio from a word problem and apply it to compute answers.

Students are asked to "Calculate a unit rate and a unit price" and the matching exercise defines "Unit rate" as a ratio showing amount per single unit. Multiple problems require students to compute unit rates from verbal descriptions (Braden: miles per hour; peaches: dollars per pound; florist: price per rose; candy machine: pieces per minute; printer: pages per minute). Students also complete tables and plot graphs for proportional situations (apple–pie table and graph) and use tape diagrams and double number lines for ratio problems (model cars, Farmer Ned, conversions).

Students collect product data in tables and compute unit prices by setting up a ratio of price to number of units (e.g., $3.38 ÷ 13 oz = $0.26/oz) and record the unit price in the data tables. Students use dimensional analysis and series-of-ratio diagrams to convert units (gallons → fl oz) so that unit prices are comparable. The activities and answer key ask students to find and use unit rates (price per unit) in verbal problems (coupon savings, currency conversion) and to mark the best buy in their tables.

Students write and interpret expressions of the form k·n (examples: 5n for $5 per car, 20n for minutes practicing, 36n for cookies in n boxes) and are asked to identify constants and variables (circle variables, underline constants). The lesson explicitly labels constants in word problems (e.g., "The constant is 12" for Carlee's board games; "The constant is the number of pencils in a pack" in the pencil example). Activity pages and answer keys require students to translate verbal descriptions into algebraic expressions that include a fixed multiplier and a variable.

The Basic Skills Review includes a rate problem in which students divide 42 push-ups by 3 minutes to compute a unit rate (14 push-ups per minute) and then use that unit rate to find how many push-ups could be done in a different number of minutes (the answer key shows scaling to 70 push-ups in 5 minutes). The answer key explicitly shows the division to get the unit rate and expresses it as 14 push-ups per 1 minute.

Students convert verbal situations into multiplicative expressions such as y(6 + 4 + 8) = 18y for Cesar's fruit baskets and form expressions like 5n for Tessa's purchases, showing a multiplier relating quantity to total. Several word problems and answer keys present expressions of the form k·variable (for example 18y, 5n, 3n) and require students to evaluate those expressions for given values. The lesson also has students rewrite and simplify expressions that expose the multiplicative factor (e.g., 2n + 3n → 5n).

Students draw tape diagrams for equations like 2n = 8 and divide the total into 2 equal groups to find n = 4. Students use hanger diagrams and inverse operations to solve expressions such as n/3 = 5 (n = 15) and check solutions by substitution. Students also translate verbal multiplicative relationships into equations (e.g., "Five times what number is 40" → 5n = 40) and solve for the unknown.

Students are asked to use variables to represent dependent and independent quantities and to write equations such as d = 65t (motion at constant speed). Activities ask students to create tables based on equations, list and graph ordered pairs, and identify how y changes as x increases or decreases. The lesson includes examples and practice forming equations from verbal scenarios (word problems) that produce relationships like 3n + 4 = 19.

The lesson defines a unit rate and gives explicit equation and verbal examples (Tonya driving: d = 45t and the text stating the unit rate is 45 miles per 1 hour). It reiterates that "the value that defines the relationship is the number per single unit in the ratio" and points to 45 as that value. Multiple proportional examples are given in equations and word problems (y = 15x for cookies, 10x = y for pay, 5x = y for biking) and each of these is shown with tables and graphs that display the constant multiplier.

Students are asked to create at least one two-variable equation with a corresponding table and a written description of the relationship (e.g., "as x increases/decreases, y ______"). The project includes a sample proportional equation 2x = y with the verbal description "practice piano (y) twice as long as soccer (x)" and asks students to solve for one variable given the other. The plan requires inclusion of a tape or hanger diagram for an equation and a table for the independent/dependent variable equation, which prompts students to represent the relationship in multiple formats.

Students are asked in the Basic Skills Review to use equivalent ratios to determine how many gumdrops a machine makes in 1 minute given 208 gumdrops in 4 minutes (208:4 → 52 gumdrops per minute). The answer key explicitly treats this as a unit-rate calculation (208:4 = 52:1). This problem presents a verbal description of a proportional relationship and requires computing the per‑one (unit) quantity.

Students measure die-cut circles and record circumference and diameter in a table, then compute the quotient c/d for each circle (Activity 1). Students use algebraic steps and equations to derive and use C = πd and C = 2πr to calculate circumference (Activity 2). The lesson gives verbal descriptions that pi is the relationship of circumference to diameter and includes diagrams labeling radius, diameter, and circumference.

Students compute and identify scale factors from verbal descriptions and diagrams (for example, Mia's Garden where 8 cm/2 m is simplified to 4 cm/1 m and is described as "each group of 4 centimeters represents 1 meter"). Students set up and solve proportional equations (e.g., 1 in/5 ft = 6 in/n ft) to find the constant relating drawing measure to actual measure. Worksheets ask students to find the scale factor from pairs of corresponding measurements (triangles, trapezoids, circles) and to express the scale factor as a ratio and as a percent.

Students compute scale factors from diagrams and verbal descriptions (e.g., find the reduction scale factor for the bird's nest by comparing diameters: 4/12 = 1/3). Students apply a given scale factor (1/3) to redraw a rectangle and compute the corresponding scale factor for perimeter (3/1) and area (9/1). Students find an enlargement scale factor for a kite from a diagram and actual dimensions (5:1).

Students are asked to create a scale drawing of a shape based on a given scale factor using a laminated grid and to reproduce a scale drawing at a different scale (Activities: Create a Scale Drawing; Parent Plan: Reproduce a scale drawing at a different scale). The planning and station setup steps require students to specify and use a scale factor when designing the scale-drawing station and its problem/answer cards.

Students are asked to find a unit price in a word problem: Evie bought a 24-ounce bottle for $3.12 and the answer key shows computing the unit price $3.12 ÷ 24 = $0.13 per ounce. Another money example (Michael buying 2.5 pounds of grapes at $1.58 per pound) uses a per‑unit price in context, indicating students work with rates in verbal descriptions. The Basic Skills Review includes solving for a unit rate from a verbal/contextual situation.

The Basic Skills Review includes a verbal-rate problem (600 miles in 8 hours) that has students compute miles per hour (75 mph). The candy sampling activity has students write part-to-whole ratios (e.g., 3:10) and convert those ratios to percentages, which requires finding a unit fraction or rate for each color. Additional percentage problems (e.g., "64 is what percent of 200?") ask students to compute a rate as a percent, reinforcing unit-rate reasoning in verbal/numeric contexts.

Students solve rate word problems that require finding unit rates from verbal descriptions, e.g., dividing 310 miles by 5 hours to get 62 mph and dividing $6.12 by 3 pounds to get $2.04 per pound. Students work ratio problems that involve scaling ratios (Jane makes 3 necklaces every 5 minutes and must find time for 15 necklaces) and write ratios in multiple forms (3 to 4, 3:4, 3/4). The parent/skill sections explicitly note that students may solve #6 and #7 using division and that they will practice ratio and rate reasoning.

Students read and write word problems that state a rate (e.g., "Marie makes $9 per hour" and "Naomi earned $5 for each hour"), and they write and evaluate expressions/equations such as 9n + 3 and 5n + 3. Students solve for unknowns in those equations (for example, substitute hours to compute earnings or solve 5n + 3 = 18). The activities thus have students work with numeric rates embedded in verbal descriptions and translate them into algebraic equations.

Students calculate and apply scale factors in diagrams (Activity: enlarge a triangle by a 2/1 scale factor and find the new side lengths). Students determine a scale factor by comparing corresponding parts of two rectangles (4/12 = 1/3) and use that ratio to relate dimensions. Students solve a verbal proportional problem about percent enlargement (800% larger) and compute the resulting height from the given postcard measurement.

Students compute totals from per-unit rates in verbal descriptions (e.g., "temperature drops by 2.5 degrees per hour" and then find the decrease after 3.5 hours). Students calculate unit rates by dividing totals by units in real-world contexts (e.g., −72 ÷ 6 = −12 monthly deduction; 600 ÷ 4 = 150 feet per hour). Several activities ask students to write equations and interpret quotients in context (e.g., average daily loss, debt per person), requiring identification of a per-unit value.

Students encounter verbal rate descriptions written in scientific notation (for example, a fire hose delivering 1.2 × 10^3 liters per minute, a delivery truck driving 2.5 × 10^2 miles a day, and machines producing units per hour). Students perform calculations that scale those rates (for example, multiplying 1.2 × 10^3 liters/min by 60 to find liters per hour and multiplying miles per day by number of days). Multiple word problems and activities require students to work with ‘per‑unit' quantities presented in words and in scientific notation.

Students compute energy use per hour, per day, and per year for each location (Task 1), showing conversion of a per-hour rate into daily and yearly totals. Students calculate solar and wind outputs per day and per year for specified numbers of panels and turbines (Task 2), and they use given unit values such as "$2.50 per kg" and "$50 per meter of radius" from the supplies data to compute total costs. Students convert the fuel-cell quantity 7 × 10^2 kWh to 700 kWh and use that unit energy value to determine how many fuel cells are needed (Task 3).

Students set up and solve proportions from verbal descriptions and equations (e.g., 3 blue/2 red = x blue/12 red → x = 18; 2 books/3 days = 24 books/n days → n = 36). Multiple activities ask students to convert real-world descriptions into labeled fractions and solve for missing values (car travel, tickets, apples, paint coverage). Students also check if relationships are proportional by simplifying fractions to see if they are equivalent (Is it Proportional? activity).

Students calculate unit rates from verbal descriptions and equations throughout the lesson (e.g., $9.60 ÷ 12 = $0.80 per pencil; 300 miles ÷ 5 hours = 60 mph). Students use diagrams and labeled fraction expressions to find unit rates and constant ratios (e.g., 3/4 miles ÷ 1/2 hours → 3/4 ÷ 1/2 = 1.5 miles per hour, with step-by-step KCF shown). Students set up and solve proportions as equations to find per-one quantities (recipe and scaling examples showing 2 cups/4 people = 0.5 cups per person and using multiplication to scale). The curriculum also asks students to create and compare real-world scenarios and interpret unit-rate conclusions from pictorial examples (sunscreen, tile packs, streaming plans).

Students compute k = y/x in explicit teaching statements and the "Things to Know" section. In Activity 2 students find k from multiple tables (e.g., (4,12),(7,21),(9,27)) and decide if the relationship is proportional. In Activity 3 students pick points on lines that pass through the origin and use k = y/x to identify the constant from graphs. In Activity 5 and Day 3 word-problem activities students rewrite equations into y = kx and extract k, and Activity 6/7 require finding k from verbal descriptions and diagrams (e.g., liters per minute, dollars per hour).

The lesson repeatedly defines and uses the unit rate as k in y = kx and explicitly tells students that the unit rate is the y-value when x = 1 and can be read at the point (1, k). Multiple activities ask students to find the unit rate from graphs (e.g., asking "If proportional, what is the unit rate?" for Graphs 1–6), from tables (Jim earns $12 per hour → y = 12x and k = 12), and from given equations (examples y = 4x, y = 5x, etc., with k identified). The comparing activities and answer keys require students to compute and compare unit rates from equations, tables, graphs, and word problems (e.g., 65 mph, $5/week, $8 per t-shirt).

Students are asked to compute unit rates and identify the constant of proportionality in multiple places (e.g., Review Quiz Questions 1, 2, 6, and Problem 9 where d = 4.5t and a table with x:2,4,6,8; y:10,20,30,40 prompt identification of k). Activities require students to write equations in y = kx or t = p×n form from verbal descriptions (movie tickets, pizza, calories, painting), and to solve for k (e.g., t = 12n, c = 8m, d = 4.5t). Students interpret graphs (Water Tanks filling, question about the point (1,5), and other graph items) and complete tables to determine whether relationships are proportional and to extract the unit rate.

Students use multiplicative formulas such as Sales Tax = Price × Tax Rate, Tip Amount = Original Bill × Tip Percentage, and Commission = Total Sales × Commission Percentage and practice converting percent rates to decimals and multiplying to find amounts. Students set up and solve equations that expose the constant multiplier (for example, 1.08x = 212 to find a pre-tax price) and solve problems that require finding a rate from amount and base (for example, determining commission rate from commission earned and total sales). Several activity problems ask students to compute tax/tip/commission rates or to work backward to find original amounts, which requires isolating the multiplicative constant.

Students use formulas that multiply a quantity by a percent-as-decimal (e.g., Discount = Original Price × Discount Percentage; Markup = Cost Price × Markup Percentage) and practice converting percents to decimals and applying those multipliers in examples. Students solve forward and backward multiplicative equations (e.g., 100 × 0.20 = 20; x × 1.20 = 72) and compute factors such as 0.70, 1.60, or 0.85 to find final or original prices. Students complete problems that require using these constant multipliers repeatedly, including stacked discounts and markups followed by further percent operations.

Students are given and use the equation I = Prt (Simple Interest Formula) and fill in its parts (I, P, r, t). Students solve example problems that rearrange the formula to find the annual interest rate (r), e.g., r = 250/5000 = 0.05 = 5% and r = 540/9000 = 0.06 = 6%. Students work with verbal scenarios (deposits, loans) that describe proportional relationships between principal, rate, time, and interest.

Students are asked explicitly to find constants of proportionality in tables (e.g., Unit 2 Review Q5 and Unit Test Q5 ask for the constant from given x–y tables). Students identify constants from equations (questions asking "What is the constant of proportionality in y = 7x?" and prompts to write equations y = (k)x for given k). Students determine unit rates from graphs and points (problems asking what (0,0) and (1,r) mean, and tasks to find unit rate from plotted points like (0,0) and (2,8)). Students extract unit rates from verbal/word problems and real-world descriptions (price per shirt/muffin, map scale, recipe ratios, and cost vs. items scenarios).

Students compute unit prices directly ("Use unit rate formula to calculate the price per lemon", find $ per pound of sugar by dividing total cost by 2, and compute $ per cup by dividing total cost by number of cups). They create and complete tables of number of lemons/cups versus total cost and graph those tables, label axes, and are asked to compare line steepness to determine price per lemon. Students write equations in the form y = kx for the recipe (answer key shows y = 2x and y = 1.5x) and use those equations and graphs that start at the origin to model proportional relationships.

Students rewrite two-step percent situations as one-step multiplicative equations such as Total Price = Original Price × (1 + Sales Tax Rate), Discounted Price = Original Price × (1 − Discount Rate), and Selling Price = Wholesale Price × (1 + Markup Rate). They compute and use the numeric multipliers (e.g., 1.05, 0.75, 1.50) in worked examples and practice problems, and they solve equations by dividing by these multipliers to find original prices. Students also interpret verbal descriptions (e.g., "100% + 5% = 105% → 1.05") and fill in blanks that require recognizing the one-step factor.

Students write and use equations that include unit multipliers in word problems, for example defining t = cp + s with c = cost per pack ($4) and solving 15 = 4p + 3 to find p. Students also define r = cost per ride ($2) and use s = r(m + t) to compute total cost and to solve for an unknown number of rides. The lesson repeatedly uses formulas like P = 2(l + w) and factoring/ distributive-property examples that pull out a common numeric multiplier (e.g., factoring 2 from perimeter expressions).

Students are taught to find the unit rate by dividing y by x (Things to Know; Activity 2 and Activity 4 instructions), and they practice this with graphs (e.g., earnings $10/hour graph, Graphs A–E in Finding the Unit Rate). Students create and use tables from equations (Day 2 Activity 3: make a table for y = 3x, y = 2x, y = 1/2 x) and turn graphs into equations by picking a point and computing k = y/x (Turning Graphs into Equations). Students also work with verbal descriptions and real-world scenarios (e.g., 120 miles in 3 hours; price per pound examples) and compute the unit rate from those descriptions.

Students are given explicit rules such as "The unit rate is always the y-value when x = 1" and "In the equation y = mx, m is both the slope and the unit rate." Activities require students to find unit rates from equations (e.g., identify m in y = 2x), from graphs (check y at x = 1 or use the two-point slope formula), and from tables (divide y by x to get a unit rate). Multiple student activity pages and word problems (faucets, marbles, driving data, recipes) ask students to compute and compare unit rates and to write or graph equations like y = mx based on given rates.

Students pick lattice points on graphs, draw right triangles, count rise and run, and simplify the rise/run fraction to find slope (e.g., +4/+4 = 1) as shown in Steps 1–3 and the Student Activity pages. The Things to Know box and formula m = rise/run explicitly give students a method to compute the constant ratio between vertical and horizontal change. In Activity 2 students set up proportions comparing rise and run for different triangles to show the ratio is constant and use yes/no checks to identify when triangles (and points) are collinear.

Students are taught that y = kx is the form for proportional relationships and that y = mx + b reduces to y = mx when b = 0. Students practice finding slope (m) as the rate of change from two points and from tables (m = change in y / change in x) in Activities 5 and 7. The lessons include explicit tasks that convert tables to equations (Using Tables to Find Linear Equations) and graph proportional examples such as y = 2x and verbal scenarios with no base fee (e.g., selling bracelets: earn $2 per bracelet → y = 2x). Students also graph and interpret lines in multiple representations (tables, equations, graphs, and verbal descriptions) while identifying the slope/unit rate.

Students are asked to determine whether relationships are proportional from tables (e.g., babysitting, car rental, dog walker, lawn care) and to write the equation, identify the slope, and give the y-intercept for those tables. Multiple problems require reading graphs and finding the slope (unit rate), extending lines to find the y-intercept, and writing the equation in y = mx (+ b) form. The answer keys explicitly label slopes and equations for proportional cases (e.g., "Slope = 10, y-intercept = 0, Equation: y = 10x"), and review instructions state students should "Interpret unit rates and slopes from tables and graphs."

Students fill a distance-versus-time table for car, train, and plane speeds and use those values to compute distances at each hour. Students write equations in the form y = mx (e.g., y = 60x, y = 80x, y = 400x) and graph the three lines, then answer questions about rise/run for the train and which line is steepest. In the cost activity, students write cost equations in the form y = mx + b, identify the slope m as cost per mile, and answer which method has the steepest slope and which has the highest fixed cost.

Students record counts in tables for 10, 50, and 100 spins and convert those totals into experimental probabilities expressed as fractions, decimals, and percents. Students use the equation Prediction = Experimental Probability × 600 to scale their experimental probability (e.g., 0.59) to predict counts out of 600, and an image/example shows the calculation 0.59 × 600 = 354. The student activity pages provide columns for totals, experimental probability (decimal/percent), and predicted spins out of 600, so students practice moving between a table of counts, a numeric unit-rate (probability per one spin), and an equation that uses that rate.

Students compute probabilities as a ratio (favorable outcomes/total) in many activities (e.g., Roll of the Dice: P = 1/6 and predictions 1/6 × 30, 60, 120). In Making Predictions and Probability Models, students build probability tables from counts (e.g., 16/34 for choir) and then use that probability to predict expected counts by multiplying by the number of trials. In Non-Uniform Events students calculate experimental probabilities from counts (e.g., 29/50 for red) and compare those ratios to theoretical probabilities derived from diagrams (7/12 for red).

Students compute sample proportions and convert them to decimals/percents and apply them to populations (e.g., 14/60 = 0.233 → 0.233 × 1143 ≈ 266; 18/50 = 0.36 → 0.36 × 350 = 126). Activity pages provide tables, bar graphs, and verbal descriptions from which students extract counts and compute the proportional rate (examples include survey tables and bar-graph questions in Making Inferences). Several problems ask students to find a fraction or percent representing a part of a sample and then scale that rate to a larger population.

Students are directed to compute rate of change using the formula (y2 - y1)/(x2 - x1) in tables and to check whether the difference between y-values stays the same as x increases by 1. Students complete activities that fill tables from given equations (e.g., y = 2x + 4 and y = x^2), calculate ∆y/∆x, and decide linear vs nonlinear. Students also examine graphs (including y = 2x and y = x^2) and label them as straight lines or curves, and an answer key lists slopes and rates of change for those examples.

Students interpret and match linear graphs that show a constant rate (e.g., Graph B: "Constant Increase" described as "earning the same amount of money every hour"). Students plot positions from verbal rate descriptions (Sylvia the Sloth: 4 ft/hour for 3 hours, then 5 ft/hour later; Timmy the Turtle: meters per minute segments) and connect points to show steady-rate segments. Students identify whether a graph is straight (linear) or curved (nonlinear) and note sections that increase at a constant rate.

Students calculate slope from graphs, points, and tables using the formula m = (y2 - y1) / (x2 - x1) (Activity 4 and multiple student pages). Students identify the slope m directly from equations in slope-intercept form y = mx + b and practice rearranging standard form to find m (Activity 6). The lesson includes a ‘Slope from a Table in 3 Simple Steps' activity where students pick two rows from a table and compute the change in y over change in x to find the slope.

Students repeatedly find the slope m using m = (y2 - y1)/(x2 - x1) from graphs, tables, and pairs of points (Activities: Graph to Equation, Table to Equation, Slope from Two Points). The Table to Equation example with x = 0, 5, 10 shows students computing m = 1/5 (miles per minute) and converting it to a unit rate (12 miles per hour). Several problems explicitly ask students to identify the y-intercept when x = 0 in tables and to write equations in y = mx + b form, including cases where b = 0.

Students repeatedly find the rate of change (slope) from verbal descriptions (e.g., Liam earns $6 per chore → A = 6c + 12 and Sasha earns $10 per hour → T = 10n + 20). Students calculate slope from tables (the reading table shows pages increasing by 15 per hour, yielding P = 15h) and from graphs (bike rental graph: y-intercept 5 and slope 3 → C = 3h + 5). The cooking activity and some tasks include relationships that start at zero (e.g., serving-based ingredient functions like F = 0.5s and Table 3 with point (0,0)), where students write functions that are proportional (through the origin).

Students compute rates from verbal descriptions (e.g., Alex: 1.5 miles per 30 minutes → 0.05 miles/min) and from graphs by finding slope using two points (Bella: using (0,0) and (30,2) to get ~0.067 miles/min). Students find slope and y-intercept from equations (e.g., y = -3x + 100 gives slope -3 and starting value 100) and compute slopes from tables (Taylor's table → -3.5). Multiple activity problems ask students to compare rates and starting points presented as graphs, tables, equations, and written descriptions.

Students calculate and interpret rate-of-change from tables (e.g., train distance table with distances 60, 120, 180, 240 and the answer "Rate of change = 60 miles per hour"). Students read unit rates from verbal descriptions and write equations (e.g., "E = 12h" or "E = 15h" for hourly earnings). Students identify and compare rates from graphs and equations (e.g., determining which streaming service increases fastest per month, finding slope from y = -2x + 5, and identifying slope from plotted lines).

Students create red graph cards that ask for slope identification and whether a graph is linear or a function. Students make blue equation cards that require identifying slope and y-intercept and matching equations to situations. Students make green table cards that ask them to identify slope from a table and write an equation for a table, and yellow description cards include real-world rate problems (e.g., "Emma earns $10 for each hour") asking students to identify the rate of change and write equations from stories.

Students are taught that similar shapes have corresponding sides that are proportional and that a scale factor is the number that compares the size of one similar shape to another. The lesson shows how to compute a scale factor with numeric lengths (for example, scale factor = 6 ÷ 3 = 2) and uses equations to find missing side lengths (for example, x = 10 ÷ 2 = 5). Multiple student activity pages ask learners to find scale factors and solve for unknown sides using proportional relationships in diagrams.

Students compute the scale factor by dividing new coordinates or lengths by original ones in multiple worked examples (e.g., A(1,2) → A'(2,4) giving factor 2; side CB = 3.6 → C'B' = 3.6×3). The lesson gives and uses the equation new length = original length × scale factor and shows solving for the scale factor (k = new ÷ original). Students read and analyze diagrams and coordinate graphs to check whether x and y values are multiplied by the same constant, and they complete tables mapping original to new coordinates with the associated scale factor.

Students are asked to identify scale factors and perform dilations in multiple problems (e.g., determine x when a 5×5 square is dilated by scale factor 3, dilate triangles by factor 2, and perform a 0.5 dilation then reflect). Several problems give original and image coordinates (e.g., triangles with A(2,3) and A'(4,6)) requiring students to compute the multiplicative factor between corresponding coordinates. Answer keys explicitly list scale factors and resulting side lengths, showing students practice using a constant multiplier on lengths and coordinates.

Students translate verbal phrases with "per" or "each" into coefficients in equations (e.g., Mr. Patel: 3c for $3 per pound; phone plan: 29.99 + 0.15t = 47.24; Jason runs 1.5 miles per day represented by 1.5d = 36). The lesson explicitly tells students to look for words like "each" and "per" when writing an equation and to turn a sentence into a math equation, and multiple real-world problems use unit-rate language that students convert into multiplicative terms.

Students write and solve linear equations in forms such as y = 30x and y = 2x + 15 and use those equations to compute per-unit values (e.g., peach rings = $4 per pound; cherry sours = $3.85 per pound; popcorn = $4.00, soda = $3.50). Student activity pages and answer keys prompt students to define variables, write systems from verbal descriptions (prices, rates, fixed fees), and solve for the numeric rate in the equations. Break-even examples (Sparkle Clean vs. Shiny Solutions; CinemaNow vs. StreamMore) explicitly isolate and equate the rate terms so students solve for the per-unit/hour/movie value.

Students compute slope from two points in multiple graphing problems (e.g., find slope through (2,3) and (4,7); find slope through (1,2) and (5,10)). Students work with linear equations in slope-intercept form (e.g., graph y = 2x - 1 and identify slope and y-intercept) and solve systems that produce unit prices (e.g., ticket-price systems and word problems that give per-item or per-hour rates such as $2 per cup). Several graphs explicitly label slopes and students find intersections that require comparing constant rates (e.g., parallel lines with same slope).

Students write cost equations from verbal descriptions (e.g., Dormitory: C = 1200m; Rideshare: C = 1.25x; Meal Plan: C = 80w) and complete tables of values (phone plan table and monthly cost comparison) that show consistent per-unit changes. Students graph those equations (graphs provided for housing, rideshare vs car, streaming, meal plans, phone plans) and are prompted to calculate slopes and y-intercepts (e.g., "identify fixed costs and slope (cost per week)" and graph to find intersections). In multiple activities students set up equations from words, compute and compare unit costs (per month, per mile, per hour, per week), and use the slope or the coefficient of x to compare options.

Students repeatedly plot data from provided tables onto graphs and draw best-fit lines, practicing reading rates of change from scatterplots. One example explicitly states "Each additional hour studied corresponds to approximately a 10% increase in test grade," which names a unit-rate style relationship in a verbal/graph context. Students also make predictions (e.g., expected grade at 8 hours) based on the observed per-unit change.

Students identify slope from a best-fit line by picking two points and computing m = (y2 − y1)/(x2 − x1) and then write equations in y = mx + b form for scatterplots (example solution finds slope = 1 and b = 5). Students interpret the slope in words as a unit change (e.g., "for every 1°F increase, 2 additional ice cream cones are sold") and use the equation to make numerical predictions (substituting x = 10 to predict sales at 70°F). Multiple activity pages ask students to choose the equation matching a plotted line, write an equation from a plotted line, and explain slope and y-intercept in context. The bird‑migration task asks students to record data in a table, plot points, compute a rate of change from two points, form a linear equation, and make a prediction from that model.

Students compute relative frequencies by dividing counts by totals (Relative Frequency = frequency of an event / total number of events) and create two‑way relative frequency tables (for example, 18/90 = 0.20). Activities ask students to convert frequency tables into row- or column-based relative frequency tables, label values as decimals or percentages, and compare proportions across groups (e.g., comparing 20% of bikers vs 25% of drivers). Several tasks require students to read values from tables and use those proportions to answer which group is more or less likely to exhibit a trait.

Students are asked to construct and interpret scatterplots, including fitting a straight line and assessing linear association (Parent Plan: "Know that straight lines are widely used to model relationships... informally fit a straight line"). The Parent Plan also tells students to "Use the equation of a linear model to solve problems, interpreting the slope and intercept." Student pages prompt students to draw a line of best fit on scatterplots and to analyze whether points form an upward or downward trend.

Students compute unit rates and identify constants of proportionality in multiple places: Activity 1 asks students to find unit rates from word problems and to write a real-world proportional scenario with its unit rate. Activity 2 has students match tables to equations, determine whether relationships are proportional, and identify k (constant of proportionality) when writing proportional equations. Activity 3 requires students to determine the constant of proportionality from a table, graph the equation y = 6x and interpret points like (0,0) and (1,6), and identify which graphs are proportional and their k values. Activity 4 includes a map scale problem (1 inch = 6 miles) that asks students to use a diagrammatic scale to find a unit rate.

Students work with tables (babysitting and car rental) that ask explicitly "What is the slope (unit rate)?" and to write equations (Activity 2). Students read and interpret graphs and are asked whether the graph passes through the origin and what that implies about proportionality (Activity 2 and images). Students find slopes and write equations from points, tables, and graphs (Activity 3), and they translate verbal descriptions such as "tutoring service charges $40 per hour" and delivery or job pay descriptions into equations and identify the slope/unit rate (Activities 2, 3, and 4). The parent plan and answer keys explicitly connect unit rate to slope and show students writing proportional equations of the form y = kx.

Students compute unit rates from verbal descriptions in problems 14 (4/5 mile in 1/2 hour) and 15 (18 miles in 3 hours). Students identify proportionality and find the constant of proportionality in a table in problem 17 and are asked to write an equation given k in problem 18. Students determine unit rates from graphs in problems 19 and 20 (including lines through the origin and y = 4x) and problem 34 asks for unit rate and equation from a word problem.

Students calculate slope (rate of change) from two points and from equations (e.g., find slope from (2,1) and (6,9); identify slope from y = -1.25x + 5). Students write functions from verbal descriptions that give a unit rate (e.g., write y = 18h for $18 per hour) and interpret the slope as amount per unit in context. Students work with a table of points that includes (0,0),(1,5),(2,10) and find and compare the rates of change for those functions.

Students compute scale factors in multiple tasks: they find the scale factor when a triangle with side 5 corresponds to one with side 10 and use it to calculate the other sides, and they compute a scale factor of 15 ÷ 6 = 2.5 to resize a triangle. Students perform dilations on coordinate grids (e.g., dilate Triangle LMN by a scale factor of 3 about the origin and record L'(6,3), M'(12,3), N'(9,9)). Several items explicitly ask students to identify the "Scale Factor" from diagrammed dilations and to decide enlargement versus reduction.

Students calculate slope from two points (Activity 2 asks them to find slopes for (3,2) & (7,10) and (-2,4) & (-8,-8)). Students graph lines given in slope-intercept form and identify slope and y-intercept (they graph y = x - 3 and y = -2x + 1). Students translate verbal descriptions into linear equations and extract per-unit rates from those equations (e.g., taxi fare 6 + 2m, gym 25 + 15m), which lets them identify the rate-of-change in contextual problems.

Students analyze scatterplots and are asked to interpret lines of best fit and strength of linear relationships (Activity 3). The Parent Plan lists that students should use the equation of a linear model to solve problems and interpret slope and intercept. A linked resource titled "Write an Equation for a Line of Best Fit" is provided, indicating some focus on linear equations.

Students convert a verbal description into an equation in problem 8 ("You earn $10 per hour"), and the answer key gives y = 10x, showing identification of the unit rate from a verbal context. Students compute slopes (problem 5, slope = 2) and graph linear equations (e.g., graph y = 2x − 4), and they work with a table of x–y pairs (problem 4), all of which are contexts where a constant rate could be determined.