Students practice and apply the distributive property with explicit examples and exercises (e.g., a(b + c) = ab + ac; 5(6 + 9) = (5·6) + (5·9)) and complete problems such as 4(2+5), 3(6+1), and 6(6+7). Students use the distributive property to rewrite numeric multiplication problems into partial products (e.g., 46 × 27 = 46(20+7) ⇒ (46×20)+(46×7)) and connect that to the standard algorithm. Students are prompted to represent multiplication with a variable in a few places (for example, listing ways to represent "4 times n"), showing limited use of letters as placeholders.

Students identify and use basic operation properties in numeric contexts: the lesson shows the associative property to regroup factors when evaluating exponents (e.g., (3×3)(3×3) = 9×9) and includes a quiz activity that asks students to match examples to the commutative, associative, and distributive properties (e.g., 5(3+10) = (5×3)+(5×10)). Several practice problems require applying the distributive property numerically and recognizing properties when evaluating expressions in order of operations problems.

Students apply the distributive property to expand numeric expressions (for example 5(6+9) = 30 + 45) and are shown expansion steps. Students practice factoring numeric sums by finding and factoring out the greatest common factor (examples: 28 + 36 = 4(7+9), 15 + 21 = 3(5+7), and activity problems like 28+40, 63+54). Students use prime factorization and GCF to factor larger numeric expressions and solve word problems by writing sums as a common factor times a sum (e.g., 12(8+9+5)).

Students practice finding greatest common factors using prime factorization (activities and answer key for GCF of 36 and 56; factor trees for numbers like 140 and 250). An image explicitly shows factoring a sum of numbers (24 + 56 + 32 rewritten as 8 × (3 + 7 + 4)), and the Interactive Notebook activity directs students to use GCF to factor expressions. Multiple activities require students to list factors, use the GCF to simplify or group (e.g., simplify 18/30 and factor numeric sums), and to apply prime-factor strategies to find GCF/LCM.

Students identify and use the distributive property in multiple activities (e.g., writing undistributed and distributed forms such as 6(4 + 3) and factoring numeric sums like 84 + 120 into 12(7 + 10)). Students match and name properties of operations (distributive, associative, commutative) in a vocabulary/matching exercise. Students use prime factorization and GCF to factor numeric expressions and solve problems that require factoring and using common factors.

Students are explicitly asked (Question 5) to show the total number of goody bag items using the distributive property, with the worked example 12(5 + 3) = (12 × 5) + (12 × 3) = 60 + 36 = 96. The Parent Plan and Skills sections state that students will "use the distributive property to multiply and to factor" and give guidance to apply the distributive property in cost and item-count calculations. Prices and package-size calculations use decimal and whole-number multiplication and addition, providing practice with numerical expressions involving rational numbers.

Students set up and solve linear expressions derived from tape diagrams (for example, the answer key shows 4x + 3x = 91 for Sam and Lindy and uses 7x = 91 to find x). Several problems require writing expressions involving a common multiplier (e.g., multiplying ratio parts by a factor to reach a total, such as 5 × 15 = 75 and 6 × 15 = 90). Tables and graphs require students to interpret and extend linear relationships (e.g., plotting (1,6),(3,18),(5,30) and finding (4,24)).

Students practice identifying coefficients, variables, constants, factors, products, addends, and the number of terms in expressions (Activities 1–3 and the student pages ask learners to name the coefficient, variable, constant, and count terms). Students also practice identifying like and unlike terms and grouping matching variable/exponent forms (Activity 4 and the matching/Venn diagram exercises). Students write expressions from verbal clues that require placing coefficients and variables correctly (Activity 3 writing problems 5–8).

Students are taught to rewrite subtraction as adding the additive inverse (e.g., 12 - 4 → 12 + (-4)) and to use that form to apply properties of operations. In Activity 3 students convert an expression with subtractions into all additions (3 + (-5) + 4 + 2 + (-13)), then use the commutative and associative properties to rearrange and group positive and negative terms before simplifying. Multiple activities have students practice grouping, rearranging, and simplifying multi-term numeric expressions using these properties.

Students identify and combine like terms in multiple activities (Student Activity Page 'Combining Like Terms' and practice problems such as 8n + 9n + 14 - 10 and 5x - 2x + 7 - 2 + 4). Students apply the commutative and associative properties to reorder and group terms (Activities 3 and 4, e.g., (5a + 2a) + (6 + 3) → 7a + 9) and change subtraction to adding the opposite to enable regrouping (6x - 3 + 2x + 7 → 6x + 2x + -3 + 7). Students also match and generate equivalent expressions (card matching, strip models, and problems like x + x + 2 + 2 = 2x + 4), and they see simple multiplication-as-repeated-addition examples (2(2n) → 4n).

Students represent and expand products using the distributive property (e.g., 5(n + 2) → (5·n) + (5·2) → 5n + 10 and examples like 4(x + 5) = 4x + 20). Students simplify expressions by combining like terms and using commutative and associative properties (e.g., 5(x + 3) + 2x - 12 → 5x + 15 + 2x - 12 → 7x + 3). Students generate equivalent expressions in factored form in examples and keys (e.g., 7m + 14n = 7(m + 2n) and 24x + 18y → 6(4x + 3y)).

Students practice the distributive property and expansion when they are asked to write 12(x + 6) as 12x + 72 and to circle expressions representing area models (e.g., 3(n + 5), (3·n)+(3·5), 3n+15). Students simplify and add/subtract linear expressions by combining like terms in problems such as 2(n + 9) + 7n - 13 and 6x + 2 - 5x + 4 + 3x. Students use properties of operations explicitly by rewriting expressions using the commutative and associative properties and by changing subtraction to adding the additive inverse in several arithmetic and expression problems.

Students simplify linear expressions step-by-step in the "Prove It! Equivalencies" activity, explicitly using the distributive property, changing subtraction to adding the opposite, applying the commutative property, and combining like terms (example: 6(5 + n) − 24 − 2n → 6 + 4n). Students create Math Properties Trading Cards that require them to state and demonstrate the commutative, associative, and distributive properties with numerical and variable examples (e.g., 7(n + 3) = 7n + 21). Students practice adding and subtracting coefficients and combining like terms in tasks such as "Make a Quiz," "Create a GoFish! Game," and "Design a Book Cover," which require producing and solving expressions with positive and negative coefficients.

Students practice using addition and subtraction as inverse operations to manipulate linear expressions in equations (examples: p + 3 = 8, n + 60 = 100, 2x + 4 = x + 6). The lesson explicitly shows subtracting a variable term from both sides (2n - 7 = 3 + n → subtract n) and mentions the commutative property when explaining n + 3 = 3 + n. Several activity problems require simplifying expressions before solving (e.g., 8 + y - 2 = 14 simplified to 6 + y = 14).

Students are asked to combine like terms (for example, recognizing 5 + 3 can be combined to form 8 in 5 + 4n + 3 = 24) and to use the distributive property to rewrite expressions (examples show 3(n - 4) -> 3n - 12 and 4(2 + n) -> 8 + 4n). Student activities and step lists explicitly instruct students to "Simplify using the distributive property" and to "Use inverse operations to cancel out addition/subtraction, then multiplication/division," and practice problems include equations with decimal and fractional coefficients. Multiple worksheet problems require students to expand parentheses and combine constants before solving, and images and answer keys show these expansions and simplifications worked out.

Students solve linear inequalities by using inverse operations: they add and subtract constants (e.g., subtract 7 from y + 7 > 10), and they multiply or divide by coefficients (e.g., multiply both sides by 3 for n/3 ≤ 1, divide by 6 for 6a + 14 ≥ 20). Students simplify expressions and use reciprocals to cancel coefficients (e.g., multiply by 3/2 to solve (2/3)p ≥ 4). Activity problems require students to manipulate linear expressions with rational coefficients to isolate the variable and graph solution sets.

Students are shown and asked to rewrite two-variable equations using inverse operations, for example adding or subtracting terms to isolate a variable (2x - y = 4 rewritten to 2x - 4 = y) and dividing both sides to isolate a variable (d = 45t rewritten to t = d/45). Students practice moving terms and using inverse operations in several problems (e.g., y - 5x = 8 rewritten to y = 5x + 8, 2x + 5 = y rewritten by subtracting 4). Activities ask students to substitute values and use input/output tables after isolating the dependent variable.

Students apply the distributive property to expand expressions when solving equations such as 2(y + 1/2) = 13 (rewritten as 2y + 1 = 13) and 3(y − 4) = 6 (rewritten as 3y − 12 = 6). Students add and subtract terms to isolate variables in problems like x + 3.8 = 9.2, x − 2.4 = 7.6, and a/7 − 5 = 9. Students also rewrite and rearrange linear expressions (for example y + 5 − 2x = 6 to y = 2x + 1) and work with rational coefficients including fractions and decimals (1/2, n/3, 2.4, 3.8).

Students create and solve many linear equations and inequalities such as n + 3 = 15, 3x - 4 = 56, n/2 + 5 ≤ 9, and 2x = y, and are required to include examples using addition, subtraction, multiplication, division, fractions, and decimals. The checklist requires at least two problems that are two-step (involving addition/subtraction and multiplication/division) and at least one equation with two variables, so students practice using inverse operations and rational coefficients. Students are asked to check solutions by plugging answers back into equations or inequalities, reinforcing operational manipulation of expressions in the context of solving.

Students write and simplify linear expressions such as n + 2n = 90 and 2n + 3n = 180, combining like terms to produce 3n and 5n. Students expand and simplify expressions in context, for example interpreting 2(n - 40) as 2n - 80 when forming and solving equations. Students also simplify multi-term expressions (e.g., 12x + 6x + 4 - 5x + 4x - 10) to 17x - 6 and use inverse operations to isolate coefficients (e.g., subtracting n to get 4n = 92).

Students set up and solve linear equations from area problems (for example, 24n = 4320 to find the number of pavers and 15·n = 75 to find a missing height). The lesson shows students using multiplication, division, and multiplying by reciprocals to isolate a variable (e.g., multiplying both sides by the reciprocal of 1/2, then dividing by 5 to find a base). Students also represent area relationships with algebraic equations (for instance, 24n = 4320 and 15·n = 75) and solve for the unknown.

Students use algebraic steps to solve pi = C/d for C by multiplying both sides by d and rewriting the equation as C = πd, showing use of inverse operations and the symmetric property. Students substitute C = 2πr into Area = (1/2)·C·r and simplify (1/2)·(2πr)·r to obtain A = πr^2, applying multiplication of constants and the rule r·r = r^2. The lesson includes step-by-step algebraic replacement and simplification written as student-facing procedures and examples.

Students write and solve linear equations formed from geometric relationships (e.g., n + 2n + (3n + 12) = 180 leading to 6n + 12 = 180). Students manipulate linear expressions when solving equations such as 3n = 2n + 35 and 3n + 35 = 4n, combining like terms and subtracting terms to isolate the variable. Several problems present expressions like 2n - 15, 3n + 12, and 4n for students to evaluate and solve.

Students manipulate Euler's formula F + V - E = 2 to solve for an unknown; the lesson shows substituting values (F + 5 - 8 = 2) and then rewriting subtraction as adding the opposite (F + 5 + (-)8 = 2). The steps include combining like terms (F + (-)3 = 2) and adding the additive inverse to both sides to isolate the variable (F = 5). Additional problems ask students to use the same algebraic process to find faces or vertices from given edges and vertices.

Students are asked to simplify using the distributive property in the Basic Skills Review (e.g., 5(n + 7) = 5n + 35), so they practice expanding a linear expression. Students also plug dimensions into and compute surface-area formulas written as algebraic expressions (for example SA = 2(10×6) + 2(10×5) + 2(6×5) and SA = 2LW + 2LH + 2WH), so they evaluate and manipulate expressions with multiplication and addition of terms. Students add numeric terms that arise from expanding those formulas when they calculate total surface area (e.g., 120 + 100 + 60 = 280).

Students write and solve linear equations using variables to find missing dimensions (e.g., 54 = L × 4 1/2 × 2 simplified to 54 = 9L and solved to L = 6). The Basic Skills Review asks students to simplify the expression 4x + 3x - 9 + x + 16 to 8x + 7, which requires combining like terms. Another problem has students set up and solve a linear equation 5n + 10 = 130 (subtract 10, divide by 5) to find n = 24, demonstrating use of inverse operations and properties of equality.

Students solve simple linear equations in several places: they use Euler's formula F + V − E = 2 and solve for V (5 + V − 8 = 2 yields V = 5), and they solve 182 = 6.5 × h for h by dividing both sides to find h = 28. The practice problems also include arithmetic with fractional coefficients when computing volumes (e.g., V = 3/4 × 1/2 × 4 4/5 = 1 4/5).

Students solve and manipulate simple linear expressions in the Basic Skills Review problems: they evaluate 6p + 12 for p = 4, solve 4n - 3 = 17 (adding 3 and dividing by 4), and write/solve the inequality 4 + n ≤ 9 (subtracting 4). These tasks require using basic properties of operations (addition/subtraction and inverse operations) to isolate variables and evaluate expressions.

Students practice and apply the distributive property explicitly in Activity 2, item 2 (factoring 36 + 88 into 4(9 + 22)) and item 3 (using distribution to compute 15 × 32 as 15(30 + 2) and then adding). Students also work with factors and greatest common factor through prime factorization (Activity 2, item 1) and with least common multiple problems, which involve reasoning about factors.

Students simplify and expand linear expressions in Activity 1 Problem 4 by rewriting 3(n + 6) + 4n - 10 as 7n + 8 and by combining like terms in x + 2x + 3 + 3x - 7. Students apply the distributive property when they expand 3(n + 6) and then add and subtract like terms to produce equivalent expressions. The Parent Plan explicitly lists the skill "Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients," which signals the intended focus.

Students set up and solve linear percent equations such as 0.012 × V = $2,400 and 0.20 × I = $9,000 to find V and I, and they write equations like 1.08 × x = $212 to represent "original price + 8% tax = total." Activity problems ask students to let a variable represent the unknown (e.g., p, V, I) and solve by isolating the variable (dividing both sides). The lesson repeatedly uses the form (1 + rate)×original to represent combined terms (original + rate·original) in backward and forward percent problems.

Students calculate discounts and markups by forming and evaluating expressions like Discount = Original Price × Discount Percentage and Selling Price = Cost Price + Markup. Students perform multistep numerical operations for stacked discounts and markups and solve backward problems that set up equations such as x × (1 - 0.40) = 18 and x × 1.60 = 208 to find unknown original prices or costs. Several answer keys show students isolating x by dividing both sides of such linear multiplicative equations.

Students are instructed to rearrange and regroup terms using the Commutative and Associative Properties and then combine like terms (Activity 1, Activity 2, Activity 4), with worked examples such as transforming 3x + 5 + 2x + 4 into (3x + 2x) + (5 + 4) and simplifying to 5x + 9. Students practice expanding with the Distributive Property and then combining like terms (Activity 5), for example converting 2(n + 4) + 3n - 6 into 2n + 8 + 3n - 6 and simplifying to 5n + 2. Students also simplify multiplication of terms and write products neatly (Activity 3), for example converting 4ab × 2c into 8abc before combining like terms in later problems.

Students are shown and asked to rewrite expressions using the Distributive Property in reverse (A + AB = A(1 + B)), e.g., Selling Price = Wholesale Price + (Wholesale Price × Markup Rate) rewritten as Wholesale Price × (1 + Markup Rate). Students expand and manipulate linear expressions when solving equations, for example converting 65(1 − D) to 65 − 65D and then isolating D. Students set up and solve one-variable linear expressions such as Total Cost = 25 + 3r and 31.50 = P(1 + 0.05), performing addition, subtraction, factoring, and division with rational coefficients.

Students practice expanding using the Distributive Property (e.g., 5(x + 3) → 5x + 15 and 2(l + 6) → 2l + 12). Students practice factoring by extracting the greatest common factor with step-by-step examples (e.g., 6x + 12 → 6(x + 2) and 15x - 10 → 5(3x - 2)). Students combine like terms in multiple places (e.g., l + l + w + w → 2l + 2w and the review problem 3x + 7 + 2x + 5 → 5x + 12).

Students practice isolating y by adding/subtracting terms and dividing to convert equations into slope-intercept form (e.g., 3x + 2y = 8 → subtract 3x, divide by 2 to get y = −3/2 x + 4; 5x − y = 5 → subtract 5x, divide by −1 to get y = 5x − 5). Students work with rational coefficients and fractional slopes (examples include slopes of −3/2, 1/2, and other fractional values) when rewriting and graphing equations. Students substitute values into y = mx + b and solve for b (e.g., 5 = 2(2) + b) which requires using inverse operations to add/subtract terms.

The lesson explicitly tells students to "Rewrite and simplify expressions using the Commutative, Associative, and Distributive Properties" in the Introducing the Lesson section. A worked example is given (a + 0.05a = 1.05a) showing students how to rewrite and combine like terms. Multiple problems require students to write and solve linear equations (e.g., 30 + 10x = 80; 25 + 15x = 100; writing equations such as y = 12x + 20), which has students manipulate linear expressions with rational coefficients.

Students write linear expressions in the forms y = mx and y = mx + b (e.g., y = 60x; y = 0.15x + 31.50) and fill tables and graphs based on those expressions. The project has students set two linear expressions equal to find a break-even point (0.15x + 31.50 = 0.20x + 20.75 → x = 215), showing use of adding/subtracting terms and dividing to solve. The Parent Plan also includes an explicit example of rewriting an expression by combining like terms (a + 0.05a = 1.05a).

Students write linear equations from verbal rules (e.g., y = 2x + 3, y = 10 − 4x, y = x/5 + 2) and work with expressions that include rational coefficients. Students evaluate input/output machines and complete tables for rules given in both standard form and with parentheses (e.g., y = 2(x − 5)). Students plot and connect points for linear rules and identify linear relationships from graphs.

Students rewrite equations into slope-intercept form by moving terms and dividing (e.g., 4x + 2y = -8 → 2y = -4x - 8 → y = -2x - 4), and they apply the distributive property to expand expressions (e.g., y + 2 = -2(x - 3) → y + 2 = -2x + 6). The lesson explicitly instructs students to use distributing, moving terms, and dividing as steps to isolate y and identify the slope (examples and worked steps are provided). Students also practice adding/subtracting changes in coordinates when using the slope formula, which reinforces subtraction of linear terms in context.

Students repeatedly isolate y by adding/subtracting terms and dividing coefficients (example: 2x + 3y = 6 → subtract 2x, 3y = −2x + 6, divide by 3 to get y = −(2/3)x + 2). Activity pages (Simplify & Graph, Rewrite in slope-intercept form) ask students to rearrange standard-form linear equations into y = mx + b, which requires subtracting terms and dividing through by a coefficient. Multiple problems and answer keys show fractional coefficients (e.g., −2/3, 1/5), so students work with linear expressions having rational coefficients.

Students practice solving one-step and two-step linear equations using addition, subtraction, multiplication, and division in Activities 1 and 2. Students work with rational coefficients—fractions and decimals—in Activities 3 and 4 and multiply by reciprocals to isolate variables. The Parent Plan explicitly states students will solve linear equations "including equations whose solutions require expanding expressions using the distributive property and collecting like terms."

The lesson repeatedly teaches and has students practice the distributive property and expansion (e.g., "Things to Know" a(b+c)=ab+ac, examples 3(a+4)=21 → 3a+12 and 4(y+2)=16 → 4y+8). Multiple activity pages ask students to expand, combine like terms, and add/subtract terms to move variables and constants to opposite sides (many problems require distributing, combining, and isolating). Problems with fractions and decimals give practice applying these operation properties with rational coefficients.

Students repeatedly expand and combine like terms when they distribute in problems such as 2(3x+4)+__ = 6x+8+10 and 4(x-2)+x = 5x+__ and when they follow steps labeled "Distribute the 2" or "Combine like terms." Students also add and subtract expressions when they subtract matching terms from both sides (e.g., 3x+4 = 3x+7 leads to subtract 3x to get 4 = 7) and work with rational coefficients in tasks that include fractions (e.g., 3/2 a + (7 - a) = 2a/3 and 3/4 z). Many activity pages require students to use these operations as strategies to simplify linear expressions in order to determine the type of solution.

Students set up and solve linear equations that use addition and subtraction of terms (e.g., 25 + 15x = 130, 18x + 20 = 146). The Parent Plan explicitly states students will "solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms." The review quiz and solve-the-equation items include distributive/expansion tasks (e.g., 5(2 - 3x) = 2x - 10, 6(b + 2) - 3b = 15) and equations with fractional coefficients (3/4 x + 4 = 10).

Students are asked to convert equations into slope-intercept form by isolating y, for example rewriting 4x−2y=8 and 2x−y=4 with steps that subtract 4x (or 2x) from both sides and divide both sides by -2 (or -1) to get y=2x−4. Multiple student pages require changing standard-form equations to y=mx+b and checking equivalence by dividing both sides (e.g., showing 4x−2y=8 is a multiple of 2x−y=4). Activities direct students to compare slopes and intercepts after performing these algebraic operations to determine solution types.

Students perform expansion using the distributive property when they substitute expressions (Example 2 shows 3(x+2) → 3x+6). Students combine like terms and simplify linear expressions during substitution (steps show 2x+3x = 5x and 3x+1 = 7 → 3x = 6). Students add and subtract entire linear equations to eliminate variables (Elimination examples show adding 3x+y and 2x−y to produce 5x and elimination with multiples multiplies an equation by −2 and then adds to eliminate y).

Students write equations in slope-intercept form from two points and manipulate those linear equations algebraically (for example, setting y = y, moving terms to get 2x = -2x + 8, then combining like terms to solve 4x = 8). Students practice elimination by adding or subtracting whole equations to cancel a variable and substitution by replacing one variable with an equivalent expression. The activity pages require students to rearrange terms and combine like terms when solving for x and y.

Students set up and manipulate linear expressions when they combine like terms (e.g., substituting J+5 + J to get 2J + 5 in the Dog Walkers example). Students apply the distributive property and multiplication of expressions when using elimination (e.g., multiplying 3x+2y by −2 to get −6x−4y in the Candy Shop example). Students solve equations with rational coefficients (decimals and whole numbers) in multiple examples, including break-even and cost problems where they isolate variables and perform addition/subtraction/division to find solutions.

Students solve equations that require expanding with the distributive property (e.g., 4(2x - 3) → 8x - 12) and combine like terms (e.g., 2x + 3x, 5x - 2x + 6). Tasks include working with fractional coefficients and removing fractions using reciprocals (e.g., (3/4)x = 12, (5/6)x = 15). The parent plan and answer key explicitly instruct students to "apply the distributive property and combine like terms to simplify equations before solving."

Students write and simplify linear cost expressions in multiple activities: for housing they set up C = 1500 + m(850+150+50) and expand/combine terms to get C = 1500 + 1050m. In the phone-plan activity students simplify y = (10x + 40)/2 to y = 5x + 20, showing distribution/division across terms. In transportation and other parts students rearrange and combine terms (e.g., 225 + 0.60x = 1.25x and rewriting in standard form C - 0.60x = 225) to solve systems.

Activity 1 explicitly asks students to simplify expressions, use the distributive property to simplify (expand), and factor an expression completely. The Parent Plan gives a concrete rewriting example with rational coefficients (a + 0.05a = 1.05a) and the Activity 1 answer key shows combined and factored linear expressions (e.g., 5x + 12 and 8(4a + 1)). Student pages and problems require students to rewrite expressions in different forms and recognize equivalent linear expressions in real-world contexts.

Students are asked to rewrite and simplify linear expressions (problem 26: 4x + 9 + 6x + 1) and to distribute and simplify (problem 27: 3(y + 5) - y), which requires using properties of operations to add/subtract like terms and expand. Students are asked to factor a linear expression (problem 28: 24m + 12) and the answer key shows factoring out the greatest common factor (12(2m + 1)). Problems 29 and 30 require students to apply distribution and inverse operations when solving linear equations, reinforcing use of operational properties on linear expressions.

Students write and manipulate linear expressions in several tasks (e.g., writing y = 18h for earnings, y = 12x + 10 for rental cost, and y = 2x − 1 from the rule "Multiply by 2, then subtract 1"). Students combine like terms in the equation-writing/symbolizing task x + 3x = 28 → 4x = 28. Students also work with standard-form lines (2x + 3y = 12) to find intercepts, which requires isolating y and performing arithmetic with coefficients.

Students set up and solve a simple linear equation in Activity 3 Problem 8 by letting Angle B = x, Angle A = 2x, writing 2x + x = 90, and solving for x (combining like terms). Students in the similarity and dilation problems (Activity 1) compute missing side lengths by multiplying by scale factors, including rational factors such as 2, 1/2, and 2.5, which requires operating on linear measures with rational coefficients.

Students are asked to combine like terms and use the distributive property in Activity 1 (e.g., problems like 5(2x − 1) = 45 and 7x − 3x + 4 = 28). The Parent Plan and activity instructions explicitly direct students to expand expressions using the distributive property and to collect like terms when solving multi-step linear equations. Several problems require working with rational coefficients (fractions), for example (3/5)x = 18 and (2/3)x − 5 = 7, which involve applying properties of operations to isolate x.

Students solve and manipulate linear expressions in several problems: they combine like terms in 4x + 3x = 35 and 7x − 3x + 4 = 28, translate a verbal expression to 2x − 4 = 7, and encounter parentheses in 5(2x − 1) = 45 which requires using the distributive property or equivalent strategy to solve. Multiple equation-solving items (e.g., x + 7 = 19, 9x = 63) require adding, subtracting, or dividing terms with rational coefficients. The writing and solving of linear equations from context (tutor fee, earnings function) has students form and manipulate linear expressions.