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.
Identify and compute percent change
Calculate percent increase and decrease and explain what the percent measures.
We’ll first compare twenty-four and thirty to identify the direction of change, then find the numerical difference. Percent change uses the original twenty-four as its denominator, so we’ll divide the …
Preview problemComplete a percent-change structure
Calculate percent increase and decrease and explain what the percent measures.
The table marks one hundred twenty as the original base and one hundred fifty as the new amount, with the labeled percent change missing. We’ll determine the direction, subtract to …
Preview problemInterpret percent change in context
Calculate percent increase and decrease and explain what the percent measures.
This response needs four connected pieces: direction, percent change, numerical change, and original attendance. We’ll identify two hundred as the starting base, subtract to find how many people were added, …
Preview problemCompare percent changes across contexts
Calculate percent increase and decrease and explain what the percent measures.
A larger dollar increase does not necessarily mean a larger percent increase because the stores begin at different prices. We’ll find each price change, divide it by that store’s own …
Preview problemUse percent change to describe a situation
Calculate percent increase and decrease and explain what the percent measures.
The direction and above-or-below judgment come from comparing this month’s average with last month’s original seventy-two. We’ll subtract to find the point change, divide by the original average, convert to …
Preview problemCheck whether a percent-change answer makes sense
Calculate percent increase and decrease and explain what the percent measures.
We’ll evaluate the student’s claim independently by identifying ninety as the original value and seventy-two as the new value. After finding the amount lost, we’ll divide that loss by the …
Preview problemTranslate percent change into a ratio or equation
Calculate percent increase and decrease and explain what the percent measures.
The required ratio is change divided by original, so the starting forty-eight-dollar price must be the denominator. We’ll subtract to find the dollar increase, write that change over forty-eight, simplify …
Preview problemRead percent change from a representation
Calculate percent increase and decrease and explain what the percent measures.
The table establishes thirty-two as the before value and forty as the after value, while the arrow identifies the direction. We’ll subtract to find the change, divide it by the …
Preview problemScreen for correct percent-change representations
Calculate percent increase and decrease and explain what the percent measures.
We’ll establish the club’s actual change first and compare it with last year’s original membership. That target ratio lets us test every percent claim, equation, and whole-to-whole statement without accepting …
Preview problemChoose a smart percent-change strategy
Calculate percent increase and decrease and explain what the percent measures.
A valid percent-decrease strategy must compare the price drop with the original ninety-six-dollar price. We’ll identify the strategy that follows that structure, subtract to find the drop, divide by the …
Preview problemApply a percent discount
Solve discount, markup, tax, tip, and simple interest style percent problems.
Twenty-five percent off describes the amount removed from the original eighty-dollar price, while the question asks for what remains. We’ll calculate the discount amount, subtract it from the original, and …
Preview problemApply a percent markup
Solve discount, markup, tax, tip, and simple interest style percent problems.
A markup is an added percent of the original forty-eight-dollar cost, not the final price by itself. We’ll find twenty-five percent of the original, add that markup to the starting …
Preview problemApply tax or tip
Solve discount, markup, tax, tip, and simple interest style percent problems.
The twenty-percent tip is based on the thirty-six-dollar meal, but the requested total includes both amounts. We’ll convert the rate, calculate the tip from the before-tip price, and add it …
Preview problemSolve a simple interest problem
Solve discount, markup, tax, tip, and simple interest style percent problems.
Simple interest keeps the principal unchanged, so the structure is principal times annual rate times time in years. We’ll convert six percent to a decimal, substitute five hundred dollars and …
Preview problemInterpret one percent application in context
Solve discount, markup, tax, tip, and simple interest style percent problems.
The sales tax is calculated from the forty-five-dollar pre-tax rental price, while the requested amount is the total after tax. We’ll convert eight percent to a decimal, find the added …
Preview problemCompare percent-application scenarios
Solve discount, markup, tax, tip, and simple interest style percent problems.
The discount rates apply to different jacket prices, so the larger rate does not automatically create the greater dollar savings. We’ll keep each rate paired with its own price, calculate …
Preview problemUse a percent application to find a final amount
Solve discount, markup, tax, tip, and simple interest style percent problems.
Thirty percent off names the discount removed from the original one-hundred-twenty-dollar price, not the final amount paid. We’ll calculate the discount, subtract it from the original, and keep dollars attached. …
Preview problemCheck reasonableness in a percent application
Solve discount, markup, tax, tip, and simple interest style percent problems.
We’ll first compare the claimed tax with ten percent of the fifty-dollar jacket to establish a reasonable bound. Then we’ll identify the pre-tax price as the base, convert eight percent …
Preview problemTranslate a percent application into an equation
Solve discount, markup, tax, tip, and simple interest style percent problems.
A total-cost multiplier must include the full original price plus the seven-percent tax. We’ll combine one hundred percent and seven percent, convert that total rate to a decimal, and multiply …
Preview problemRead a percent application from a receipt or table
Solve discount, markup, tax, tip, and simple interest style percent problems.
The receipt’s subtotal is the whole on which the six-point-two-five-percent tax is based, while the requested amount is the completed total. We’ll convert the rate, calculate the tax from thirty-two …
Preview problemScreen for correct percent-application representations
Solve discount, markup, tax, tip, and simple interest style percent problems.
A percent-off situation has two different outputs: the discount removed and the sale price that remains. We’ll find the discount from the original price, derive the sale price both by …
Preview problemChoose a smart percent-application strategy
Solve discount, markup, tax, tip, and simple interest style percent problems.
A valid sales-tax method applies the rate to the original sixty-four-dollar price and then adds the tax because the question asks for total cost. We’ll identify the method with that …
Preview problemWrite a ratio from words
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
A ratio preserves the order of the quantities named, so red must occupy the first position and blue the second. We’ll match each marble count to that order and write …
Preview problemInterpret a written ratio
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
The quantity names and ratio terms must be aligned in the same left-to-right order. We’ll pair the first number with green beads and the second with yellow beads, then read …
Preview problemDistinguish part-to-part from part-to-whole
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
The phrase girls to all students compares one group with the entire class, so we first need the whole rather than the boys count alone. We’ll add both groups, classify …
Preview problemCompare two ratios
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
Both ratios describe red marbles per blue marble, so the comparison must hold the blue quantity constant. We’ll rewrite each ratio as a fraction, scale them to the same number …
Preview problemModel a context with a ratio
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
The ratio must preserve the quantities and order named, so juice comes first and water second. We’ll attach each cup count to its ingredient, place those counts in juice-to-water order, …
Preview problemCompare contextual ratios
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
The mixes use different amounts, so comparing only the raisin counts would ignore how many peanuts accompany them. We’ll write both relationships as raisins divided by peanuts and compare the …
Preview problemCheck what a ratio is measuring
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
We’ll label the two numbers before judging the student’s claim: four counts blue tiles, while nine counts every tile in the basket. Then we’ll read the ratio in order and …
Preview problemTranslate a ratio into a new form
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
The display gives separate red and blue bead counts, and both requested forms must keep red first and blue second. We’ll translate the same ordered relationship into words and colon …
Preview problemWrite a ratio from a diagram
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
Two different ratios are requested, so we’ll count circles and squares once, add them for the whole, and then build each comparison separately. Circles-to-all uses the circle count over the …
Preview problemScreen for matching ratio representations
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
Every match must preserve cats first, dogs second, and the same multiplicative relationship as two to five. We’ll test direct notation, labeled notation, each table row, and the picture, then …
Preview problemChoose a smart ratio setup strategy
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
We’ll decide whether the requested ratio is part-to-part or part-to-whole, then use that classification to evaluate what the first step must produce. After forming the ratio in the named order, …
Preview problemFind a unit rate from whole numbers
Compute and interpret unit rates, including rates with fractional or decimal quantities.
Miles per hour tells us both the division order and the target denominator: miles divided by hours, scaled to one hour. We’ll divide the full distance by the elapsed time, …
Preview problemFind a unit rate with decimals
Compute and interpret unit rates, including rates with fractional or decimal quantities.
Dollars per pound means total cost divided by total pounds, even though both values contain decimals. We’ll set up that quotient, multiply dividend and divisor by the same power of …
Preview problemFind a unit rate with fractions
Compute and interpret unit rates, including rates with fractional or decimal quantities.
Cups per batch means divide the total flour by the number of batches, not multiply the two quantities. We’ll rewrite one and one half as an improper fraction, divide by …
Preview problem