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.
Compare compound events or combination counts
Solve simple compound probability and counting problems using organized reasoning.
Use the same twelve-outcome coin-and-cube sample space for both events. Count heads paired with odd faces for one event, then tails paired only with faces strictly greater than four for …
Preview problemBuild an organized outcome representation
Solve simple compound probability and counting problems using organized reasoning.
Write every outcome in a consistent order, with the spinner color first and the coin result second. Hold one color fixed while pairing it with heads and tails, then repeat …
Preview problemTurn an organizer into an event summary
Solve simple compound probability and counting problems using organized reasoning.
Treat each cell of the completed table as one equally likely compound outcome, so every event uses the same full denominator. For each condition, count the cells that satisfy the …
Preview problemFind every simple compound case that matches the target
Solve simple compound probability and counting problems using organized reasoning.
Evaluate all six cases by the full two-stage event, not by a promising first step. Multiply the stage probabilities when they are independent, or count favorable leaves over total equal …
Preview problemPick out the needed information
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Begin with the requested quantity—total ticket cost—and keep only facts that can determine dollars paid. A units check points to a ticket count paired with dollars per ticket, because those …
Preview problemChoose the right operation
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Follow the roles of the quantities rather than reacting to keywords. The notebook price is repeated for every notebook, so first form the full merchandise subtotal; the coupon applies once …
Preview problemChoose a useful representation
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Let the comparison need determine the representation: four discrete pretzel quantities and their matching total costs must be visible at the same time. Use the constant per-item rate to calculate …
Preview problemMatch a context to the right setup
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Preserve the purchase structure and its units. The price per notebook combines with the number of notebooks to create a dollar subtotal, and the one dollar-valued coupon then reduces that …
Preview problemSolve while filtering out distractors
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Maya's total depends on the quantity and unit price for each ticket category. Keep the student price, adult price, and her two purchase counts; calculate a subtotal for each category …
Preview problemPick a useful strategy and solve
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Model only charges belonging to the bike rental. The hourly rate repeats for every rental hour, while the helmet fee is added once, so calculate those two parts according to …
Preview problemJudge whether enough information is given
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Audit the dependency chain before trying to calculate: arrival time needs departure time plus travel duration, and travel duration needs distance divided by a driving rate. Check the units of …
Preview problemClean up a context into a useful model
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Let C represent only the post-coupon granola-bar cost, then strip the story down to unit price, box count, and discount. The repeated box charge creates the subtotal, and the coupon …
Preview problemSort information by mathematical role
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Frame this as required seats versus available seats. Count every rider—including both students and teachers—using the stated one-seat-per-rider rule, then compare that demand with bus capacity. Ticket price and trip …
Preview problemFind every context or setup that matches the target structure
Identify relevant information, ignore distractors, and choose an appropriate operation or representation for a contextual problem.
Translate the target into an expression skeleton: a per-unit rate times a varying quantity, followed by subtracting one constant amount. Test each situation for all three roles, paying special attention …
Preview problemMatch a result to the right final answer sentence
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
Trace the units through the calculation before attaching meaning to eighteen. A ticket count multiplied by dollars per ticket leaves dollars, so the product measures money rather than tickets, hours, …
Preview problemAttach units and meaning to the number
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
A contextual result needs more than a bare value and unit. Identify what forty-two measures, keep miles attached to that measurement, and name the subject and action that produced it. …
Preview problemChoose a context-appropriate rounded answer
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
Divide the number of students by the serving capacity of one box, then interpret any remainder in context. Boxes must be whole and every student must be served, so a …
Preview problemChoose a useful reasonableness check
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
Use an estimate that preserves the purchase structure: notebook count times an approximate price per notebook. Round the unit price to a nearby whole-dollar benchmark while keeping the six notebooks …
Preview problemFinish a contextual problem with a full answer sentence
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
Build the trip total from two different cost structures: one fixed bus charge and a per-student admission charge repeated for every student. Calculate the admission subtotal first, add the fixed …
Preview problemPick the result that makes sense in context
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
Divide the student count by one bus's capacity to locate the required bus count, then apply the context rather than ordinary nearest-number rounding. Buses must be whole, and their combined …
Preview problemFind every acceptable contextual final answer
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
Establish the communication standard before evaluating the responses. Verify the quotient and the neighboring whole-bus capacities, then require an actionable whole-number decision stated with bus units and field-trip context. Reject …
Preview problemChoose the strongest complete contextual response
State a final answer with correct units, interpretation, and reasonableness justification when the context requires it.
Use a completeness checklist, not just numerical agreement. Recompute gallons by dividing distance by fuel economy, convert that amount to dollars using price per gallon, and estimate with a nearby …
Preview problem