Students practice adding and subtracting multi-digit decimal numbers throughout Activities 2–6, including numeric exercises and real-world word problems (e.g., adding costs, temperatures, masses, and weights). Students use manipulatives and videos (base-10 blocks) to model regrouping and borrowing and build foldables that describe the step-by-step addition and subtraction algorithms. The practice pages require students to compute sums and differences of decimal (rational) quantities and to answer context questions such as total spending and combined weights.

Students compute sums and differences of rational numbers in real-world contexts, for example adding pumpkin weights (17.8 + 23.15) and reducing a sprint time (26.2 − 4.05) on the Unit 1 Quiz. Students practice addition and subtraction of decimals and other arithmetic operations in multiple activities and problems that require solving contextual word problems.

Students compute and combine decimal costs for real goody-bag purchases (e.g., totaling item costs such as $14.40 + $10.08 + $18.36 = $42.84) and then interpret that total in a real-world context by comparing it to a $50 budget. Students calculate tax by converting a percent to a decimal and multiplying the purchase total (e.g., 6% = 0.06; $42.84 × 0.06 = $2.57) and then add or subtract amounts to determine under/over budget. The activity also asks students to show totals using the distributive property (e.g., 12(5+3) = (12×5)+(12×3) = 60+36), connecting numerical sums to counts of physical items.

Students practice adding and subtracting rational numbers (fractions and mixed numbers) through many word problems (e.g., guitar practice, walking distances, pie slices, recipe measurements) that ask them to compute and interpret sums and differences. Students work with number-line skills for fractions via an interactive tutorial and an activity that asks them to plot fractional points. Students also practice converting forms and using common denominators so they can compute and interpret results in real-world contexts.

Students plot and label integers on horizontal and vertical number lines (images and foldable) and are asked to mark and compare opposite numbers (e.g., mark +4 and -4). The lesson defines additive inverse as "what you have to add to that number to get zero," asks students to fill the blank "Opposites can be added to get a sum of __," and gives real-world sum examples (Paula +$8 and -$8 = $0; Simon owes -$10 then gives +$6 → -$4). Multiple activities use real contexts (temperatures, bank balances, game scores, trivia scoring with +10/−10) where students compute and interpret sums of rational numbers.

Students plot and compare rational numbers on horizontal number lines and count steps between points to find distances. They add distances from zero when points lie on opposite sides (e.g., 47 + 14.5 = 61.5 for temperature difference; 32.8 + 16 = 48.8 for platform-to-bottom distance). Students identify opposites and additive inverses (questions asking for opposites of −12, 18, etc., and a parent note explicitly calling the opposite the 'additive inverse'). The Absolute Value activity has students draw vectors from zero, name direction and magnitude, and compute absolute values of integers, fractions, and decimals.

Students plot opposite numbers on horizontal number lines (e.g., 6 and -6), draw segments from zero to each, and fold the line to show the opposites match, demonstrating equal distance from zero. Students plot points and then move them a specified number of units left/right/up/down (for example, move A left 5 and down 3) to create new coordinates, practicing translations that correspond to adding positive or negative values. Students reflect points across the x- and y-axes and write the resulting coordinates (e.g., (a,b) → (a,-b) or (−a,b)), and they trace routes on a city grid (Deon's map) that represent block-by-block movements in a real-world context.

Students plot points and then place new points a specified number of horizontal or vertical units away (e.g., plot A (2,5) then plot a point 5 horizontal units away; plot O (0,5) and the points (−12,5) and (12,5)). Students compute travel distances by adding the horizontal and vertical leg lengths in real-world contexts (bus stop example: 8 + 4 = 12 miles). The Basic Skills Review asks for the additive inverse of −19 and a number-line distance (distance from −3 to 5 = 8), and parent notes explain that distances are absolute values.

The materials include explicit problems asking students to name additive inverses (e.g., "Name the additive inverse of each number" with answers such as the additive inverse of 6 is -6). Multiple real-world word problems require students to compute sums and differences of rational numbers (rice combined, driving times, borrowing money, distances east/west, temperature changes) and interpret the results. Students are also asked to plot numbers on a number line and to plot and translate points on coordinate grids (start at a point and move units), giving practice with locating and moving between values.

Students translate real-world addition and subtraction situations into expressions such as 6 + n, n - 8, 2n + 10, and 5 + 4y, showing understanding of sums in context. Students evaluate those sums by substituting number values (e.g., n = 4 gives 4 + 6 = 10; 5 + 4(6) = 29). The lesson also asks students to write integers for temperatures (e.g., −17) and to perform arithmetic with positive and fractional numbers, showing some practice with adding and subtracting numerical values.

Students use number line diagrams throughout the lesson to start at a number p and move left or right by |q| units (examples: 12 + (-4), 3 + (-5), 6 - (-10)) and are instructed to view positive moves to the right and negative moves to the left. The lesson explicitly defines additive inverses and shows sums of opposites equal zero (for example, 8 + (-8) = 0 and many practice items asking for -(-3), -(-(-4)), etc.). Students translate subtraction to "add the opposite" (p - q = p + (-q)) and then evaluate using number lines and rules. Multiple real-world problems (bank balances, temperature changes, diving depth, game scores, money spent/earned) require students to write and interpret sums of signed quantities.

The lesson instructs students to change subtraction into adding the opposite (e.g., 6x - 3 + 2x + 7 → 6x + 2x + (-3) + 7) and to use rules for adding positive and negative numbers. It models writing negatives as additive opposites (noting 4x - 2 is the same as 4x + (-2)) and includes practice problems that require adding and subtracting signed quantities (e.g., 14 - (-8) + 9p - 6p). Students also combine positive and negative like terms in multiple simplifying activities and answer problems that involve negative values in computation.

Students are instructed to change subtraction to "add the opposite" and complete problems that rewrite and evaluate expressions that way (e.g., 18 - 5 = 18 + (-5); 20 - 36 = 20 + (-36); -14 - (-9) = -14 + 9). The Parent Plan Skills explicitly list "Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q)" and include practice with integer addition/subtraction games. Students also write and evaluate sums in real-world contexts (Tasha's shells, Zane's pay, Jeremiah's earnings, Kelsey's cookies), translating those contexts into numeric expressions and evaluating them.

The parent-skills list explicitly tells students to "Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q)," and the Prove It! Equivalencies tasks repeatedly model and ask students to "Change subtract to add the opposite" when simplifying expressions. The Make a Quiz and Design a Book Cover activities ask students to write and solve word problems that use positive and negative integers in real-world contexts (the pelican example is given). Several projects (Create a GoFish! Game, Make a Quiz, Design a Book Cover) require students to combine positive and negative coefficients and to add and subtract integers in practice.

Students solve and graph inequalities on number line diagrams in multiple activities, including plotting open/closed circles and arrows for solutions. Students write and interpret sums in real-world contexts (e.g., n + 5 < 12 for shirts, 3n - 5 ≥ 22 for chickens) and check solutions by substituting values to verify sums. The materials explicitly tell students they can use inverse operations or additive inverses to cancel addition and subtraction when solving inequalities.

Students create and solve one-step addition and subtraction equations (examples include n + 3 = 15 and x - 7 = -4) and are instructed to check solutions by plugging answers back into equations. Students are asked to represent at least one inequality solution on a number line and to include tape/hanger diagrams for some equations, which requires plotting and visual representation. Students use real-world contexts (personal facts about age, time, counts, distances) to write and interpret equations and inequalities for their "All About Me" poster.

Students work with number-line representations in the Basic Skills Review where they graph the inequality y < 2 on a number line (open circle, shading left). Students evaluate expressions that involve subtracting negatives (for example n^2 - (-5) with explanation "change subtraction to add the opposite"), showing at least some manipulation of opposites. Students also plot points with negative coordinates on a coordinate plane in the review, giving practice locating and working with negative values.

Students work with addition and subtraction of rational numbers in the Basic Skills Review (for example: 8/15 + 4/9 and 4 + 7 - 13 + 1 - (-2)). The answer key explicitly shows changing subtraction to adding the opposite for the expression with -(-2). Students also solve and graph an inequality (n + 3 < 5) on a number line.

Students compute sums and differences of frequencies in context (e.g., adding interval frequencies 17 + 18 + 10 + 5 + 2 = 52 to find total campers and computing 17 - 5 = 12 to compare age groups). Students place and read data on number lines and dot plots (e.g., class size dot plot with a number line labeled 15–30). The activities ask students to create frequency tables and histograms from given data and to interpret numerical results in real-world contexts (temperatures, salaries, campers).

Students solve contextual addition and subtraction of rational numbers (mixed-number word problems such as adding Mario's 4 3/8 and 5 3/8 hours, and subtracting fabric amounts) and perform arithmetic with fractions on the Operations with Fractions pages. Students plot points, compute distances between points, and follow directed moves on a coordinate grid (e.g., start at (-3,5), move vertically and horizontally, and find distances). Students also reflect points over axes (e.g., reflect (-2,4) to (2,4) and over the x-axis to (−2,−4)), which has them identify the opposite sign of a coordinate.

Students write and solve equations that include sums in real-world contexts (e.g., 5n + 3 = 18 for Naomi, 9n + 3 for Marie, and 4 + n ≤ 10 for Jayne), showing they form and interpret sums of rational numbers in context. Students evaluate and simplify expressions that include addition and subtraction (e.g., simplifying 3(n + 6) + 4n − 10 and x + 2x + 3 + 3x − 7). Students represent solution sets on a horizontal number line when they graph the inequality n + 2 > 5 and mark an open dot at 3 with an arrow to the right.

Students place and move from points on a horizontal number line (images and Activity 1 show a person at 2 and arrows toward zero) and are directed to "draw the movement on a number line" for scenarios such as a diver descending and then ascending. The lesson explicitly equates subtraction with adding a negative (3 - 3 = 0 and 3 + (-3) = 0) and has atom and jellybean scenarios where students write equations like 7 + (-7) = 0 and circle zero pairs. Multiple real-world contexts (money earned/spent, temperature changes, depth, debt sharing) require students to write sum equations, draw representations, and interpret the resulting totals.

Students answer explicit problems about adding opposites (Review Quiz question: "What is the result of adding a positive number and its negative counterpart, such as 5 + (-5)?" with answer key 0). Students solve and interpret contextual addition/subtraction problems (scuba diver descending 20 ft then ascending 15 ft; temperature change -2.5°F per hour for 6 hours) that require adding positive and negative rational numbers. The lesson includes a number line image (fractions between 0 and 1) which situates numbers on a horizontal line.

The review quiz (Part 1) asks students to compute operations with positive and negative numbers (e.g., 5 + 8, 7 - (-3), -4 × 6, -24 ÷ 4), and the answer key shows results that include negative sums (e.g., -15, -12). The student activity pages include real-world word problems that require interpreting sums of rational numbers in context (money/debt and temperature change problems where students must calculate totals with negative values). Several problems require students to add or subtract negatives (for example, 7 - (-3) = 10 and Jamie borrowing $5 from each of 3 friends leading to -15), demonstrating practice with signed-number sums in applied situations.

Students solve contextual addition problems with positive and negative values (e.g., the scuba diver descending 30 ft and ascending 18 ft) that require interpreting sums of rational numbers in real-world contexts. Students work with negative quantities in other contextual problems (debt, temperature change) that require combining signed numbers. Students place values on a number line (Activities 5 and related number-line diagrams) when they approximate and locate square roots, showing experience locating numbers spatially on a line.

Students perform addition and subtraction with positive and negative numbers in Phase 5: they compute the submarine's final depth after diving to -450 m and rising 175 m (requiring -450 + 175), and they compute the average daily temperature from -15°C and 5°C (requiring summing a negative and a positive number). The wrap-up and Phase 5 explicitly state that students "practiced calculations with positive and negative numbers," indicating students work with sums of rational numbers in real-world Arctic contexts.

Students are asked to compute and explain sums of opposites (e.g., "What is the sum of -6 and 6? Explain your reasoning" and similar test items with -12 and 12), which requires recognizing additive inverses. Multiple word problems place sums in real-world contexts (submarine/diver depths that change by ascent/descent, and a company profit/loss problem) where students must add positive and negative quantities to find a net value. The Parent Plan explicitly instructs students to "describe situations where opposite amounts cancel each other out to make zero" and gives a real-world example (hydrogen atom charge).

Students compute energy shortfalls by subtracting energy produced from energy needed (Task 3) and add delivery and supply costs to find total supply cost (Part 2). The activities use negative temperatures (e.g., -10°C, -4°C) and temperature differences to compute heater energy, so students work with signed rational numbers in real-world contexts. Students convert and operate with rational numbers in scientific notation (7 × 10^2 kWh → 700 kWh) when calculating fuel cells and storage needs.

Students practice forming and evaluating sums in real-world contexts by adding tax and tip amounts to original prices (e.g., Final Price = Original Price + Sales Tax; Total Price = Original Bill + Gratuity). Students compute total earnings by adding commission to a base salary (Total Earnings = Commission + Base Salary) and solve forward and backward problems that set up equations like 1.08x = total to find original prices. Multiple activity pages and answer keys require students to calculate and interpret these sums in applied situations.

Students calculate final prices by subtracting discounts from original prices (Final Price = Original Price − Discount) and solve stacked discount problems that require successive subtraction. Students compute selling prices by adding markup amounts to cost (Selling Price = Cost Price + Markup) and solve backward problems that undo markups or discounts. Students use the percent-change formula (New − Original) ÷ Original × 100 and interpret percent increases and decreases in real-world price contexts (e.g., a jacket from $80 to $100 is a 25% increase).

Students create tables and graphs of total cost versus number of lemons and write equations of the form y = kx, plotting lines that start at the origin and interpreting slope as price per lemon. Students compute and combine monetary amounts in context (calculate total cost for a gallon, divide to find cost per cup, add the disposable cup cost, apply markups, add sales tax, and add gratuity). Students set up and solve proportions and arithmetic equations to find how many lemons or pounds of sugar are needed and to compute discounted or increased prices.

Students calculate totals by adding sales tax to an original price (e.g., 40 + 2 = 42) and rewrite that sum as a one-step expression Total Price = Original Price × (1 + Sales Tax Rate). Students interpret discounts as reductions from 100% (100% − discount = percent paid) and compute discounted prices via subtraction and multiplication (e.g., 80 − 20 = 60 and 80 × 0.75 = 60). Students set up and solve equations that require adding and subtracting rational terms (for example, 48.75 = 65 − 65D then rearranging by adding 65D and subtracting 48.75).

Students set up and interpret sums in real-world contexts (e.g., t = cp + s for marker purchases and s = r(m + t) for rides), translating word problems into equations that add quantities. Students perform addition and subtraction of rational numbers when solving perimeter and cost problems (for example 54 = 2(l + 6) → 54 = 2l + 12 and subtracting 12 from both sides). Students also solve equations that result in negative or fractional solutions (e.g., 6(x + 4) = 22 gives x = -1/3), showing work with signed rational numbers in algebraic procedures.

Students write and solve equations that use sums in real-world contexts (e.g., 30 + 10x = 80 for a phone plan, 24 + 3x = 66 for theme-park spending). Students graph points including negatives (e.g., (0,0) and (3,-6)) and compute differences when finding slope, which requires performing subtraction of rational numbers. Students identify and write linear equations from contextual situations (wages, membership fees) that express totals as sums of parts.

Students compute and combine travel times and delays by adding rational numbers (for example, adding 15-minute gas stops every 200 miles, a 30-minute train layover, and airport waiting times) to find new total travel times. Students add monetary amounts (gas, food, taxes, baggage fees) to produce total trip costs and write cost equations in the form y = mx + b that include fixed fees plus per-mile costs. Students fill tables of distances over time (starting at 0) and use equations y = mx to calculate and compare distances at different times, which involves adding rates over time implicitly.

Students work with negative inputs and sums in input/output machines (e.g., Example 1: y = 2x + 6 where x = -2 is processed as 2×(-2) = -4 then -4 + 6 = 2). Exercises ask students to use the "opposite of a number" (multiply by -1) and then add (e.g., the rule "The sum of six and the opposite of a number" with y = -x + 6 and sample calculations for x = -3, 0, 5). Several worksheets require computing outputs for negative x-values and filling tables, so students practice arithmetic with negative rational numbers. Graphing activities plot ordered pairs that include negative values on the coordinate plane.

Students are asked to start at (0,0) and plot Sylvia the Sloth's climb by marking her height each hour using given rates (4 ft/hr for 3 hours, rest, then 5 ft/hr), which requires computing new positions by adding distances over time. Other scenarios (Timmy the Turtle, Bella's Balloon Ride) have students calculate heights or distances after periods of ascent, rest, or descent, so they determine successive positions after positive or negative changes. Multiple tasks ask students to translate verbal descriptions of motion into graphs and to match story segments to increasing, decreasing, or constant graph sections, engaging interpretation of cumulative changes in context.

Students create and solve real-world description cards (yellow) such as a temperature dropping 3 degrees each hour starting at 70°F, asking them to write an equation and determine the temperature after 4 hours. Students work with equations that include negative coefficients (e.g., y = -2x + 5) on blue cards and plug in values to compute outputs. Students solve table- and graph-based problems that require interpreting rates of change and applying addition/subtraction when matching representations.

Students practice adding positive and negative values to coordinates using the rule (x + a, y + b) (seen in the Translation Notes and multiple activity problems). They count steps left/right and up/down to move points on coordinate grids (e.g., translate P(2,1) five left and three up) and compute arithmetic such as 6 + (−5) = 1 and (−2) + 3 = 1 in worked examples. Students also determine translation rules from pairs of original and image coordinates (e.g., find T that maps M to M').

Students plot points and produce reflected points by changing coordinate signs (for example (x,y) → (−x,y) and (x,y) → (x,−y)) on multiple activity pages and answer keys. Students use coordinate grids to move points the same distance to the opposite side of an axis and label original and image points (A → A′), reinforcing that reflection flips a coordinate's sign. Students interact with a digital tool that has them drag points across axes and observe that the reflected point's x- or y-coordinate changes sign while the other coordinate stays the same.

Students perform translations described as moving a figure a specified number of units (e.g., "Tessa moves 4 units to the right," and translation rules like T_{2,-1}). Students apply translations by increasing or decreasing coordinates (the lesson notes that translating 2 right and 1 down increases x by 2 and decreases y by 1). Students observe reflections that change the sign of coordinates (examples show A(2,1) mapping to A'(-2,1)), and they work with sequences of moves on coordinate grids.

Students perform translations by adding constants to coordinates (e.g., "Add 3 to each x and 1 to each y" and tasks like "translate it 2 units right and 3 units up"). Students apply reflections that change the sign of coordinates (answer key shows points with negated x or y values) and perform dilations that multiply coordinates by scale factors, all on horizontal and vertical coordinate grids. Many activities require plotting original and transformed points and following step-by-step arithmetic on the coordinate axes.

Students apply translation rules such as T5,−3 to vertex coordinates, which requires adding integers to coordinate values. Students perform reflections and rotations using coordinate rules (e.g., (x,y) → (−x,y) or (−y,x)), and the answer keys show students producing negated coordinates for reflected points. Several problems ask students to compute images of points after translations, dilations, and reflections, which involves adding or negating numeric values in the coordinate pairs.

Students draw an x-axis and y-axis on graph paper and perform specified translations such as "move right 4 units and up 2 units," so they physically place shapes before and after additive shifts. Students reflect shapes across the x- or y-axis and rotate shapes around the origin, which requires changing signs of coordinates for reflected points. The activity asks students to transfer and plot original and transformed shapes on coordinate grids, giving practice with adding or subtracting values to coordinates.

Students solve many equations that require adding and subtracting rational numbers (for example, x+6=14 and x−9=5 in the one-step examples, and 3x−6=12 in two-step work). They also solve equations with fractions and decimals (e.g., (3/4)x+3=7, 0.4x+2=6.8) and check solutions by substituting back, and the problems are set in real-world contexts (repair lab scenarios, space station oxygen/navigation) that connect arithmetic operations to situations.

Students set up and interpret sums in real-world contexts (for example, writing 25 + 15x = 130 or 18x + 20 = 146 to represent sign-up fees plus monthly charges). Students revise and interpret contextual equations (e.g., the comic strip changes 10x + 40 = 120 to 10x + 40 - 20 = 120 when a sibling contributes). Students solve equations that produce negative solutions (e.g., 2x − 5 = 3x + 1 yielding x = −6), so they work with positive and negative rational results in problem solving.

Students add and subtract whole-number and negative terms when they use elimination and are explicitly shown that y + (−y) = 0 to eliminate a variable. Students perform algebraic addition of equations (adding opposites or subtracting like coefficients) and check solutions by substituting values back into equations. Students also work with negative numbers, fractions, and decimals in substitution and elimination problems, giving practice with sums and differences of rational numbers in algebraic contexts.

Students write and use sums of rational numbers to model real situations (e.g., C = 1500 + 1050m for apartment costs, C = 225 + 0.60x for car costs, and 20 = 5 + 1.5h for streaming). Students set those sums equal and manipulate them algebraically (for example 1200m = 1500 + 1050m → 150m = 1500) to find break-even points. Students interpret those numeric sums in real-world contexts (total cost = fixed fee + per-unit charge) when deciding between options.

Students identify zero pairs and write equations such as 9 + (−9) = 0 and 15 + (−15) = 0 in Mission 1, explicitly showing that a number and its opposite sum to 0. In the submarine and hiking scenarios (e.g., −12 + 7 = −5) students compute a new position after a positive or negative change and state the final position. Multiple real-world problems (temperature change, gamer losing points, debt split, and a task to create a realistic problem using positive/negative rational numbers) require students to compute sums/changes and explain what the answers mean.

Students compute sums involving positive and negative integers (e.g., "What is the sum of -18 and 27?" answered as 9) and solve a real-world integer addition problem (a submarine 350 feet below sea level rises 125 feet, answered as -225 feet). The exam includes multiple integer operation problems that require students to add and interpret signs in context.

Students apply translation rules such as (x, y) → (x + 3, y - 2) to find new coordinates and explain how the x- and y-values changed. Students reflect points across the y-axis (e.g., A(-3, 4) → A'(3, 4)) and are asked to describe the sign change in the x-value. Tasks ask students to write and use coordinate-change rules (including rotation rules like (x, y) → (−y, x)), which require adding or subtracting integers from coordinate values to represent movement on the axes.

Students solve one- and multi-step linear equations that require adding and subtracting numbers (e.g., x + 7 = 19, problems that instruct students to 'show all steps' and isolate variables). Students set up and interpret sums in real-world contexts (e.g., 'Two numbers add up to 54', ticket sales totaling $390, membership cost 25 + 15m = 100) where they write equations that express sums of quantities. Students also practice working with rational coefficients and fractions when solving equations (e.g., (3/5)x = 18, (2/3)x - 5 = 7).

Students perform coordinate translations using rules such as T_{1,-3} and T(-4,2), which requires adding positive and negative values to original coordinates. Students also carry out reflections (e.g., A(5,10) → A'(−5,10)) and translations of triangles and points, so they compute new coordinates by adding signed numbers. Several algebra problems and transformation tasks implicitly require adding and subtracting integers or negatives when finding new positions.