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.
Work backward from an absolute value condition
Interpret absolute value as distance and use it to compare quantities and errors.
Read the equation as a distance condition: x must be exactly four units from zero. Distance does not specify direction, so move four units from zero on both sides of …
Preview problemUse absolute value in context
Interpret absolute value as distance and use it to compare quantities and errors.
Measure each temperature’s separate distance from zero using absolute value; ordinary signed order is not what the question asks. Compare those distances to identify which original temperature is farther, then …
Preview problemInterpret absolute value as error size
Interpret absolute value as distance and use it to compare quantities and errors.
Prediction error means the size of the gap between the predicted and actual growth, not a signed direction. Subtract the two measurements and take the absolute value so the result …
Preview problemCompare errors or deviations with absolute value
Interpret absolute value as distance and use it to compare quantities and errors.
Use the target length as the common reference instead of comparing the rods directly. Find each rod’s absolute difference from fifty centimeters, which puts an overcut and an undercut on …
Preview problemJudge a claim about absolute distance
Interpret absolute value as distance and use it to compare quantities and errors.
Test the claim by measuring distance from zero, not by looking at the signs or ordinary number order. Evaluate the absolute value of each number and compare those nonnegative distances. …
Preview problemTurn a number-line distance into absolute value notation
Interpret absolute value as distance and use it to compare quantities and errors.
Use both endpoints in the prescribed order and place their difference inside absolute-value bars. Because the second endpoint is negative, simplify the subtraction carefully as addition of its opposite. The …
Preview problemScreen a mixed set by absolute-value conditions
Interpret absolute value as distance and use it to compare quantities and errors.
Translate the condition into distance language: a qualifying entry must be exactly three units from zero in either direction. Check every listed value independently by its absolute value, including decimal …
Preview problemChoose a smart strategy for absolute value and distance
Interpret absolute value as distance and use it to compare quantities and errors.
The reference point is zero, so begin by finding each number’s absolute value rather than comparing signed order or finding the span between the numbers. Compare those two distances to …
Preview problemRead a plotted ordered pair
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Read the point in ordered-pair order: horizontal x first, then vertical y. Moving left from the origin makes the x-coordinate negative, while moving up makes the y-coordinate positive. Combine those …
Preview problemPlot an ordered pair
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Read point A by projecting it to each axis. Its horizontal position supplies the first coordinate and its vertical position supplies the second, with left represented as negative and up …
Preview problemClassify a point by quadrant or axis
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Use both coordinate signs to locate the point. A negative x-coordinate places it left of the vertical axis, and a negative y-coordinate places it below the horizontal axis. Since neither …
Preview problemInfer a point from coordinate structure
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Directly above means the two points lie on the same vertical line, so their horizontal coordinate must stay fixed. Carry point A’s x-value, including its sign, into point B and …
Preview problemMatch context locations to coordinate structure
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Translate the directions one axis at a time: west determines a negative horizontal coordinate, and south determines a negative vertical coordinate. Write x before y to form the ordered pair, …
Preview problemCompare contextual points on a grid
Plot, read, and interpret points in all four quadrants on the coordinate plane.
East-west position depends only on the x-coordinate, the first number in each ordered pair. Compare those signed horizontal values: the greater x-value lies farther right, or farther east. The equal …
Preview problemJudge a quadrant or axis claim
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Test the claim from the coordinate signs rather than the stated quadrant name. A negative x-coordinate places the point left of the vertical axis, while a positive y-coordinate places it …
Preview problemTranslate movement into coordinates
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Separate horizontal and vertical movement before writing the point. Left supplies a negative x-coordinate first, and up supplies a positive y-coordinate second. Once the ordered pair is formed, use its …
Preview problemTranslate graphed points into another representation
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Read one plotted point at a time and keep the requested label order. For each point, project horizontally to obtain x first and vertically to obtain y second, preserving every …
Preview problemScreen a mixed set by coordinate-plane conditions
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Apply both strict Quadrant Two conditions to every point: x must be negative and y must be positive. A zero coordinate places a point on an axis, so it fails …
Preview problemChoose a smart strategy for coordinate-plane tasks
Plot, read, and interpret points in all four quadrants on the coordinate plane.
Begin with coordinate order rather than the quadrant name: horizontal movement gives x first, and vertical movement gives y second. Translate left as negative and up as positive, then form …
Preview problemTranslate simple add-subtract phrases
Translate verbal phrases and short contexts into algebraic expressions.
The words “less than” reverse the spoken subtraction order. Treat n as the reference amount named after “than,” start with that quantity, and subtract nine from it. Testing a convenient …
Preview problemTranslate simple multiply-divide phrases
Translate verbal phrases and short contexts into algebraic expressions.
The operation word “quotient” signals division, and the named quantities keep their order. Make p the dividend and six the divisor, then write that relationship with a fraction bar. Reading …
Preview problemTranslate grouped verbal phrases
Translate verbal phrases and short contexts into algebraic expressions.
Build the named sum first, because “the sum of n and five” is one complete quantity. Enclose that quantity in parentheses, then apply the outside factor of three to the …
Preview problemMatch a phrase to an expression
Translate verbal phrases and short contexts into algebraic expressions.
Build the phrase in chunks: first translate “twice x” as a product. Then interpret “five less than” as subtracting five from that entire reference quantity, which reverses the spoken subtraction …
Preview problemModel a short context with an expression
Translate verbal phrases and short contexts into algebraic expressions.
Identify the rate and the quantity it repeats across: eight dollars is the cost of one ticket, and t counts the tickets. A total made from t equal eight-dollar charges …
Preview problemTranslate fixed-plus-changing contexts
Translate verbal phrases and short contexts into algebraic expressions.
Split the total into a one-time part and a repeating part. The sign-up fee appears once as a constant, while the monthly rate must be multiplied by the number of …
Preview problemTranslate comparison contexts into expressions
Translate verbal phrases and short contexts into algebraic expressions.
Use Ben’s age as the reference quantity because b represents him. Sara being five years younger means her age is five below that reference, so begin with b and subtract …
Preview problemJudge whether an expression matches a phrase
Translate verbal phrases and short contexts into algebraic expressions.
Start with the named sum, which makes x plus three one grouped quantity. The word “twice” must apply to that whole group, so parentheses are the key structural evidence when …
Preview problemTranslate a visual model into an expression
Translate verbal phrases and short contexts into algebraic expressions.
Translate every piece of the strip exactly once. Combine the three equal x-boxes as three copies of the variable, then add the separate fixed box as a constant rather than …
Preview problemTranslate structured quantity information into an expression
Translate verbal phrases and short contexts into algebraic expressions.
Read the table as a unit rate paired with a changing count. Eight dollars applies to each adult ticket, while t tells how many tickets receive that charge. Multiply cost …
Preview problemMatch several phrases and expressions by structure
Translate verbal phrases and short contexts into algebraic expressions.
Fix the target structure before checking the representations: subtract three from x first, then multiply that entire result by two. For each symbolic or verbal form, track grouping and operation …
Preview problemTranslate structured phrases and contexts into expressions
Translate verbal phrases and short contexts into algebraic expressions.
Translate from the inside outward. Group the sum of x and two first, multiply that whole quantity by three, and only then interpret “four less than” as subtracting four from …
Preview problemSubstitute into a one-variable expression
Evaluate algebraic expressions correctly using substitution and order of operations.
Substitution replaces the variable while preserving the expression’s operations. Put four in x’s place, remembering that the coefficient next to x means multiplication, then follow the usual order of operations. …
Preview problemEvaluate a grouped expression after substitution
Evaluate algebraic expressions correctly using substitution and order of operations.
Replace x with three without changing the parentheses or the outside factor. The grouping tells you to evaluate the inner sum before applying the multiplication, so preserve that structure through …
Preview problemSubstitute into a two-variable expression
Evaluate algebraic expressions correctly using substitution and order of operations.
Keep a small variable-to-value map so the two assignments are not swapped or reused. Substitute three only for a and five only for b, while retaining the coefficient attached to …
Preview problemComplete an expression-evaluation step
Evaluate algebraic expressions correctly using substitution and order of operations.
The blank asks for the intermediate line after substitution, not the final result already shown below it. Starting from three times five minus two, perform only the multiplication and carry …
Preview problemEvaluate a contextual expression
Evaluate algebraic expressions correctly using substitution and order of operations.
Interpret the rule before calculating: three is the per-mile charge, m is the miles traveled, and six is the fixed fee. Substitute the trip distance for m, multiply to find …
Preview problem