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.
Choose a smart percent strategy
Use proportional reasoning to solve percent problems without relying on memorized templates alone.
The benchmark turns an awkward-looking decimal percent into a friendly fraction. Since twelve and a half percent is one eighth, the requested part of the jacket price can be found …
Preview problemCompare two signed numbers
Compare, order, and locate signed integers and rational numbers on a number line.
Because both values are negative, comparing only the digits would reverse the correct reasoning. Picture their locations relative to zero: the negative value closer to zero lies farther right and …
Preview problemOrder several signed numbers
Compare, order, and locate signed integers and rational numbers on a number line.
Least to greatest means reading a number line from left to right. Group the values first: negatives lie left of zero, zero separates the signs, and positives lie to the …
Preview problemLocate a signed number on a number line
Compare, order, and locate signed integers and rational numbers on a number line.
Read the tick spacing before matching a point label. Each interval represents one unit, and a negative target lies to the left of zero, so count the required number of …
Preview problemFind a missing value from a number line
Compare, order, and locate signed integers and rational numbers on a number line.
Point P is described by its relationship to two known endpoints, so treat it as a midpoint problem. Find the total distance from negative six to zero, take half of …
Preview problemOrder signed values in context
Compare, order, and locate signed integers and rational numbers on a number line.
Translate the context first: coldest to warmest means least to greatest temperature. Order the signed temperatures on a number line, remembering that the more negative temperature lies farther left and …
Preview problemPlace a contextual signed value on a number line
Compare, order, and locate signed integers and rational numbers on a number line.
Use sea level as zero, then separate the location into direction and distance. The word “below” determines the negative side of the scale, while one hundred twenty meters supplies the …
Preview problemReason about signed values and zero in context
Compare, order, and locate signed integers and rational numbers on a number line.
Closest to zero asks about distance, not about which signed balance is greatest or smallest. Take the absolute value of each account balance while keeping its account name attached, then …
Preview problemJudge a signed rational placement on a number line
Compare, order, and locate signed integers and rational numbers on a number line.
Judge the claim by testing the defining feature of halfway, rather than by appearance alone. Average the two negative endpoints, then verify that the proposed value lies between them and …
Preview problemShow signed-number order in a new representation
Compare, order, and locate signed integers and rational numbers on a number line.
Build the inequality chain by reading a number line from left to right. Place the two negatives first, remembering that the one with greater magnitude sits farther left, then place …
Preview problemTranslate a number line into symbolic order
Compare, order, and locate signed integers and rational numbers on a number line.
Separate the two tasks: first read the numerical tick beneath each labeled point, then order those values. On a horizontal number line, positions increase automatically from left to right, so …
Preview problemScreen a mixed set by signed-order conditions
Compare, order, and locate signed integers and rational numbers on a number line.
Treat negative one point five as a strict boundary: only values to its right qualify, and the boundary itself does not. Test every card independently, converting the fraction when that …
Preview problemChoose a smart strategy for signed rational order
Compare, order, and locate signed integers and rational numbers on a number line.
A reliable comparison begins by expressing both rational numbers in the same form. Convert the fraction to a decimal while preserving its negative sign, then compare the two locations relative …
Preview problemAdd signed numbers
Add and subtract signed numbers and explain the meaning of the sign changes.
The addends point in opposite directions, so equal positive and negative units cancel rather than accumulate. Compare their absolute values, subtract the smaller magnitude from the larger, and give the …
Preview problemSubtract signed numbers
Add and subtract signed numbers and explain the meaning of the sign changes.
Make the subtraction easier to interpret by rewriting it as addition of the opposite. The opposite of a negative number is positive, so the two signs affect both the operation …
Preview problemRewrite subtraction as adding the opposite
Add and subtract signed numbers and explain the meaning of the sign changes.
Keep the first number, change subtraction to addition, and replace the number being subtracted with its opposite. That produces two negative addends, so their magnitudes combine and the common negative …
Preview problemFind a missing signed value in an equation
Add and subtract signed numbers and explain the meaning of the sign changes.
Solve by undoing the negative seven that is added to x. Add its opposite to both sides so the opposite pair cancels on the variable side while equality stays balanced. …
Preview problemModel signed changes in context
Add and subtract signed numbers and explain the meaning of the sign changes.
Keep the two roles separate: negative three is the starting temperature, while a rise of eight is a positive change. Add the signed change to the signed start, and picture …
Preview problemCompare contextual signed-operation results
Add and subtract signed numbers and explain the meaning of the sign changes.
Treat the accounts as two separate signed-addition problems before comparing anything. For each one, combine the starting balance with its signed change, using cancellation or a move through zero to …
Preview problemTranslate number-line movement into signed operations
Add and subtract signed numbers and explain the meaning of the sign changes.
Keep the starting location separate from the direction of movement. Begin at negative four, and translate seven units to the right as adding a positive change, regardless of the start’s …
Preview problemTranslate signed context words into symbols
Add and subtract signed numbers and explain the meaning of the sign changes.
Use sea level as zero and assign signs to the two pieces independently. Starting below sea level makes the initial elevation negative, while rising makes the change positive. Add that …
Preview problemRecognize equivalent signed-operation forms
Add and subtract signed numbers and explain the meaning of the sign changes.
First rewrite subtracting negative five as adding its opposite, and record the operation’s starting value, signed change, and endpoint. Test every candidate against all three features, because sharing one number …
Preview problemChoose a smart strategy for signed operations
Add and subtract signed numbers and explain the meaning of the sign changes.
Rewrite the subtraction before comparing magnitudes or deciding a direction. Subtracting a negative means adding its positive opposite, which turns the expression into a familiar opposite-sign sum. From the negative …
Preview problemMultiply signed numbers
Multiply and divide signed numbers and interpret sign patterns correctly.
Handle sign and magnitude as two separate decisions. The factors have different signs, so the product must be negative; then multiply their absolute values to determine its size. Repeated addition …
Preview problemDivide signed numbers
Multiply and divide signed numbers and interpret sign patterns correctly.
Determine the quotient’s sign before doing the arithmetic. A negative dividend and positive divisor have different signs, so the result is negative; divide the absolute values to find its magnitude. …
Preview problemUse sign patterns in multiplication and division
Multiply and divide signed numbers and interpret sign patterns correctly.
Start with the sign pattern: the two factors carry the same negative sign, so their product is positive. Then ignore the signs briefly and multiply the absolute values to obtain …
Preview problemFind a missing signed factor or quotient
Multiply and divide signed numbers and interpret sign patterns correctly.
Undo the multiplication by dividing both sides by the signed coefficient of x. The two quantities in that quotient are both negative, so the missing factor is positive; divide their …
Preview problemModel repeated signed change with multiplication
Multiply and divide signed numbers and interpret sign patterns correctly.
Translate one day’s drop as a negative change, while the number of days is the positive repetition count. Multiplication represents applying that same signed change five times, so determine the …
Preview problemInterpret signed division in context
Multiply and divide signed numbers and interpret sign patterns correctly.
Represent the amount being shared as negative because it is debt, while the number of friends is a positive group count. Divide the signed total by that count to find …
Preview problemRead sign patterns from structured examples
Multiply and divide signed numbers and interpret sign patterns correctly.
The absolute values of the factors stay three and four in every row, so the product’s magnitude never changes. Track only how the sign pattern changes: one negative factor produces …
Preview problemTranslate signed rate or repeated change into symbols
Multiply and divide signed numbers and interpret sign patterns correctly.
Translate the descent as a negative change per minute, and treat five minutes as the positive repetition count. Multiplying those quantities models five identical changes rather than one addition involving …
Preview problemRecognize equivalent signed multiplication and division models
Multiply and divide signed numbers and interpret sign patterns correctly.
Translate the target into its precise multiplication meaning: three groups of negative four. For every representation, identify the operation, number of groups, and signed amount per group before calculating anything. …
Preview problemChoose a smart strategy for signed multiplication and division
Multiply and divide signed numbers and interpret sign patterns correctly.
A sign-first strategy keeps the two decisions from getting tangled. Because the dividend and divisor have matching negative signs, the quotient is positive; then divide their absolute values to obtain …
Preview problemEvaluate an absolute value
Interpret absolute value as distance and use it to compare quantities and errors.
Absolute value asks for distance from zero, not the signed direction of the original number. Picture negative seven on the number line and count the units between it and zero. …
Preview problemCompare absolute values
Interpret absolute value as distance and use it to compare quantities and errors.
Compare the numbers by distance rather than ordinary signed order. Evaluate each absolute value to measure how many units the original number lies from zero, then compare those two nonnegative …
Preview problemFind distance between two signed numbers
Interpret absolute value as distance and use it to compare quantities and errors.
Distance between two signed locations is the absolute value of their difference. Subtract one endpoint from the other, remembering that subtracting a negative becomes addition, and then take the absolute …
Preview problem