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 close decimals
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
This comparison comes down to place value, not the number of visible digits. We’ll write the decimals with matching places, scan from left to right, and stop at the first …
Preview problemOrder large whole numbers
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
This is an ordering problem built on place value. We’ll compare the numbers from the highest place to the right, grouping any that stay tied, and then break those ties …
Preview problemPick the best benchmark match
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
Closeness to a benchmark means distance, regardless of whether a number lies below or above it. We’ll find each number’s positive distance from eight and compare those distances. The number …
Preview problemRound for a reasonable estimate
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
Rounding to the nearest tenth depends on two adjacent place values. We’ll identify the tenths digit, inspect the hundredths digit as the deciding digit, and use the five-or-more rule to …
Preview problemCompare contextual decimal quantities
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
The key is interpreting the context before comparing the decimals: a faster finish means less elapsed time. We’ll line up the race times by place value, find the smallest one, …
Preview problemEstimate in context by rounding
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
This is an estimate, so the original prices are inputs to simplify before we add. We’ll round each price to the nearest whole dollar using the cents, then add only …
Preview problemJudge a number against benchmarks
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
This is a distance-to-a-benchmark question. We’ll place the bottle amount between the two benchmarks, measure how far it is from each endpoint, and compare those two distances. The endpoint with …
Preview problemCheck a rounding claim
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
To test the student’s claim, we need to round independently rather than trust the stated result. We’ll locate the tenths digit, use the hundredths digit to decide whether it stays …
Preview problemConvert number forms before comparing
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
The two quantities are not yet written in the same form, so place value is the bridge. We’ll turn the named ones, tenths, and hundredths into one decimal, then compare …
Preview problemInterpret a number line for magnitude
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
The number line gives both scale and order. We’ll use the one-hundredth tick spacing to calculate the value of each labeled point, then read the points from left to right …
Preview problemConvert, order, then estimate
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
This problem has two linked tasks: put unlike representations on a common scale, then compare their spacing. We’ll convert every value to a decimal, align the place values, and order …
Preview problemDefend the most reasonable estimate
Compare, order, and estimate whole numbers and decimals using place value and magnitude sense.
The task is to build a defensible whole-dollar estimate. We’ll round every price to the nearest dollar, add those rounded amounts, and use that sum as the benchmark for the …
Preview problemEstimate a sum with rounding
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
This sum is meant to be estimated at the whole-number level. We’ll round each addend independently by looking at its tenths digit, then add the two rounded values instead of …
Preview problemEstimate a product with specified rounding
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
The estimate depends on rounding each factor to the particular place named for it. We’ll use the tens digit to round the larger factor to a hundred and the ones …
Preview problemEstimate a quotient with a specified compatible dividend
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
This quotient is estimated by replacing only the dividend with the specified nearby compatible number and keeping the divisor unchanged. We’ll split that compatible dividend into easy multiples of the …
Preview problemEstimate a percent amount with a specified benchmark
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
Instead of calculating nineteen percent exactly, we’ll use the nearby twenty-percent benchmark. We can find ten percent of two hundred forty by dividing by ten, then double that amount to …
Preview problemEstimate a contextual total with a specified rounding rule
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
The question is whether an estimated purchase total stays within a fixed budget. We’ll round all four prices to the nearest dollar, add every rounded amount, and compare that estimate …
Preview problemEstimate a contextual product with specified factors
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
Because the cans come in equal groups, the total is modeled by multiplication. We’ll replace the box count and cans-per-box count with the specified benchmark factors, multiply those easier numbers, …
Preview problemEstimate a contextual quotient or percent with a specified benchmark
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
A percent discount is a fraction of the price, not a dollar amount by itself. We’ll apply seventeen percent to the specified sixty-dollar benchmark, either as a decimal or as …
Preview problemUse an estimate to check an exact answer
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
The claim is judged by a benchmark and a tolerance, so we need two separate comparisons. We’ll calculate the twenty-percent benchmark, find the positive gap between it and the claim, …
Preview problemRewrite an expression using specified benchmarks
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
This estimate keeps the addition structure but replaces each addend with a nearest-hundred benchmark. We’ll round the two addends separately, preserve the plus sign between their replacements, and add the …
Preview problemUse a specified benchmark-percent rewrite
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
The percent is being decomposed into familiar parts, but every part still applies to the same whole. We’ll find ten percent, use it to build five percent, find one percent …
Preview problemUse estimation to choose the best answer
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
Since seventeen percent lies between ten percent and twenty percent, its discount on a positive price must lie between the corresponding dollar amounts. We’ll calculate those lower and upper bounds …
Preview problemEstimate a multi-step result with specified benchmarks
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.
The bill estimate must keep all three parts: food, tax, and tip. We’ll add the specified benchmark amounts, measure the positive gap between that estimate and the reported total, and …
Preview problemEvaluate without grouping symbols
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
This expression is about operation priority, not simply reading from left to right. We’ll complete the multiplication first, rewrite the entire expression with that product in place, and then handle …
Preview problemEvaluate with one grouped part
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
The parentheses make the grouped sum one complete factor. We’ll evaluate that group first, replace it with its value, multiply before subtracting, and only then finish the outer difference. Working …
Preview problemEvaluate with exponents
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
The exponent has the highest priority here and represents repeated multiplication of its base. We’ll evaluate that power, substitute its value without changing the surrounding expression, then multiply before adding. …
Preview problemEvaluate a layered expression
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
This expression has nested grouping, so we’ll peel it from the inside out. First evaluate the parentheses, then finish the bracket, and treat that completed bracket value as one factor. …
Preview problemEvaluate a bundled context expression
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
The story contains two kinds of equal groups: complete bundles and extra stickers. We’ll find the cost of one whole bundle before multiplying by the number of bundles, find the …
Preview problemEvaluate an exponent in context
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
The squared term represents the area of the square patio because both side lengths are the same. We’ll interpret the exponent as two factors of the side length, calculate that …
Preview problemEvaluate a subtotal-then-adjust context
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
The story has a repeated earning amount followed by two separate adjustments. We’ll multiply to find the tickets from the wins, add the bonus to form a subtotal, and then …
Preview problemCheck a grouped-expression claim
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
We can judge the claim only after evaluating the expression independently. We’ll simplify the parentheses first, multiply the grouped result by the outside factor, and add the remaining term last. …
Preview problemRewrite the first valid step
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
This task asks for one valid rewrite, not the completed evaluation. We’ll identify the single operation with highest priority, simplify only that grouped part, and copy every other number and …
Preview problemConvert a solution plan into an expression
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
The words describe a sequence of operations, so the expression must protect the first result for later use. We’ll group the initial sum, multiply that whole quantity by four, and …
Preview problemCompare two structured expressions
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
The two expressions use the same numbers but different grouping, so we must evaluate each structure on its own. We’ll complete the parenthesized sum in the first expression, use multiplication …
Preview problemSelect the right model and evaluate it
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.
Both fees occur every month, so one month’s complete cost must include both of them. We’ll group the base fee and device fee, then multiply that monthly total by the …
Preview problem