Math Foundations
Strengthen number sense, fractions, ratios, expressions, equations, geometry, and data—the bridge from middle-school math to high-school success.
- Problem types
- 634
- Practice variants
- 2,536
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Each problem type has four distinct practice variants. Open a preview to move among all four.
Write and solve a two-step word-problem equation
Write and solve a linear equation from a short verbal or contextual situation.
Separate the repeated ticket cost from the one-time service fee. If x is one ticket’s price, three copies of x plus the fixed four-dollar fee must make the twenty-five-dollar total. …
Preview problemWrite a comparison equation
Write and solve a linear equation from a short verbal or contextual situation.
Each plan contributes a complete cost expression, and “cost the same” means those expressions belong on opposite sides of one equation. Preserve both the variable charge and fixed charge for …
Preview problemDefine the variable before writing the equation
Write and solve a linear equation from a short verbal or contextual situation.
Keep the definition of c in view: it counts classes, not dollars. The five-dollar charge happens once, while the three-dollar charge repeats c times, and together they make the twenty-dollar …
Preview problemPick the right equation from several choices
Write and solve a linear equation from a short verbal or contextual situation.
Match every term to its role before doing any algebra: five dollars is charged once, while two dollars repeats for each download. The valid structure must add that fixed fee …
Preview problemCheck whether a word-problem solution makes sense
Write and solve a linear equation from a short verbal or contextual situation.
Model all eight seats as the sum of empty seats and the three filled seats, with x counting only the empty ones. After solving, reasonableness needs two checks: substitution must …
Preview problemCheck whether the final word-problem answer matches the question
Write and solve a linear equation from a short verbal or contextual situation.
Separate the two moments in the story before judging the conclusion: x is the initial amount, while eighteen is the total after seven stickers are added. Solving identifies the value …
Preview problemWrite an equation from a representation
Write and solve a linear equation from a short verbal or contextual situation.
Read the bar by role: x and six label adjacent parts, while fifteen labels the entire length. A part–part–whole model says the two parts add to the whole, so translate …
Preview problemTranslate sentence frames into equations
Write and solve a linear equation from a short verbal or contextual situation.
Translate the sentence in its spoken order: first double the unknown, then add five to that doubled quantity, and use “is” as the equals sign. Keeping five outside the doubling …
Preview problemMatch equations and word problems across options
Write and solve a linear equation from a short verbal or contextual situation.
Anchor every equation to the same cost structure: one six-dollar fee plus four dollars for each visit makes a thirty-four-dollar total. A matching form may state that relationship directly or …
Preview problemModel and solve a word problem
Write and solve a linear equation from a short verbal or contextual situation.
Let x count miles, then separate the fare into a six-dollar charge that happens once and a two-dollar charge that repeats for every mile. Those parts together make the twenty-dollar …
Preview problemSolve an additive one-step inequality
Solve one-step inequalities and represent solutions on a number line.
Treat the inequality like a balanced comparison and undo the added six on both sides. Adding or subtracting the same amount preserves order, so the inequality direction does not change …
Preview problemSolve a positive-coefficient one-step inequality
Solve one-step inequalities and represent solutions on a number line.
The variable is multiplied by positive four, so divide both sides by four to isolate it. Division by a positive number preserves the ordering and keeps the inequality symbol facing …
Preview problemReverse the inequality when dividing or multiplying by a negative
Solve one-step inequalities and represent solutions on a number line.
Isolating x requires dividing both sides by negative three. Negative scaling reverses order, so reverse the inequality symbol at the same moment you divide and keep the negative sign in …
Preview problemRepresent a solved inequality on a number line
Solve one-step inequalities and represent solutions on a number line.
First isolate x by undoing the subtraction on both sides; this addition preserves the inequality direction. The solved symbol then controls the graph in two separate ways: the equality bar …
Preview problemModel an additive inequality with context domain
Solve one-step inequalities and represent solutions on a number line.
Build Mia’s total as the five completed hours plus h additional hours. “At least” includes the requirement and everything above it, so use an inclusive lower-bound inequality and solve by …
Preview problemModel a multiplicative context with an inequality
Solve one-step inequalities and represent solutions on a number line.
Three dollars per person makes the total cost three times the group size, and an eighteen-dollar maximum means that product may not exceed the limit. Divide by the positive rate …
Preview problemMatch a context to the right one-step inequality
Solve one-step inequalities and represent solutions on a number line.
The backpack’s total is its current eight pounds plus w pounds added. “No more than” points toward smaller totals and includes the twenty-pound limit, so the model needs an inclusive …
Preview problemRead a number line as an inequality
Solve one-step inequalities and represent solutions on a number line.
Read the graph in two independent pieces. The open endpoint makes the comparison strict because the boundary is excluded, while the leftward ray represents values smaller than that boundary. Translate …
Preview problemTranslate inequality words into symbols and graphs
Solve one-step inequalities and represent solutions on a number line.
“At most three” includes three and every smaller number. Translate inclusion into an equality bar on the inequality symbol and a closed graph endpoint, then translate “smaller” into shading to …
Preview problemMatch an inequality across several forms
Solve one-step inequalities and represent solutions on a number line.
Solve the inequality first so the six listed values can be compared with one clear inclusive boundary. Because adding the same number to both sides preserves order, the direction and …
Preview problemChoose an inequality step and graph or set
Solve one-step inequalities and represent solutions on a number line.
Isolating x requires dividing by its full coefficient, negative four, and reversing the inequality at that exact step. Preserve the strict comparison, so the boundary remains excluded. After computing the …
Preview problemCombine like terms before solving an inequality
Solve multi-step inequalities, including reversing the inequality when appropriate.
Simplify the left side before trying to isolate x: the two x-terms combine by adding their coefficients, while the constant stays separate. Then undo the constant and divide by the …
Preview problemDistribute, simplify, and solve an inequality
Solve multi-step inequalities, including reversing the inequality when appropriate.
The outside factor multiplies the entire quantity, so either distribute it to both inside terms or divide both sides by that positive factor first. Continue by undoing the remaining addition. …
Preview problemReverse the inequality at the right multi-step moment
Solve multi-step inequalities, including reversing the inequality when appropriate.
Remove the added eight first; subtraction on both sides preserves the greater-than direction. The reversal happens only at the next move, when both sides are divided by the negative coefficient …
Preview problemSolve a multi-step inequality and graph it
Solve multi-step inequalities, including reversing the inequality when appropriate.
Solve the inequality before interpreting the graph descriptions: undo the subtraction, then divide by the positive coefficient, preserving both direction and endpoint inclusion. Once x is isolated, read the final …
Preview problemModel a multi-step context with an inequality
Solve multi-step inequalities, including reversing the inequality when appropriate.
Build the total from a twelve-dollar fee that occurs once and a four-dollar charge repeated for each student. “At most” makes forty an included upper limit, so solve by removing …
Preview problemModel and solve a grouped context inequality
Solve multi-step inequalities, including reversing the inequality when appropriate.
Treat one kit as a single group containing x pencils and two markers, then repeat that entire group four times. Keeping the parentheses prevents the two markers from being counted …
Preview problemMatch a context to the right multi-step inequality
Solve multi-step inequalities, including reversing the inequality when appropriate.
Match the cost structure first: ten dollars is fixed, three dollars repeats per rider, and “at most forty” includes the limit while pointing toward smaller totals. Solve that model with …
Preview problemTranslate a verbal multi-step inequality
Solve multi-step inequalities, including reversing the inequality when appropriate.
Translate the verbal structure in order: double the unknown, add five, and compare that result strictly with seventeen. Solve by reversing the addition and positive multiplication, so the inequality direction …
Preview problemMatch a multi-step inequality across forms
Solve multi-step inequalities, including reversing the inequality when appropriate.
Distribute three to both terms inside the parentheses, then combine the constants on that side before moving variable terms. Collect x-terms with the same subtraction on both sides and undo …
Preview problemChoose the best first step in a multi-step inequality
Solve multi-step inequalities, including reversing the inequality when appropriate.
The parentheses control the first move: distribute four across the whole grouped difference before combining any constants. Then simplify, collect variable terms, and isolate x with positive-number operations, preserving the …
Preview problemTurn a solved inequality into a context range
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
Start with the algebraic set of all values at or below the given inclusive bound. Then apply what x counts: extra guests cannot be negative or fractional, so the contextual …
Preview problemUse real-world restrictions on algebraic answers
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
Keep the algebraic result separate from its real-world interpretation. Since x counts notebooks sold, its contextual domain contains only nonnegative whole numbers; compare the given value directly with that domain. …
Preview problemUse whole-number restrictions on a context answer
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
The algebra gives an inclusive upper bound, but b counts full boxes, so only whole numbers are meaningful. Find the greatest whole number that does not exceed the decimal bound …
Preview problemFinish a contextual solve with a meaningful answer
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
Subtract the eleven students already aboard to find the inclusive upper bound on additional students. Then apply what x counts: additional students must be nonnegative whole numbers. The meaningful response …
Preview problemTurn a solved inequality into a discrete answer set
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
The solved inequality describes every numerical value at or below four and one-half, but b counts complete prize bags. Intersect that bound with the nonnegative whole numbers, excluding fractions and …
Preview problem