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
Page 16 of 18
Each problem type has four distinct practice variants. Open a preview to move among all four.
Find every matching area representation
Use area formulas for rectangles, triangles, parallelograms, trapezoids, and composite figures.
Classify each region by the structure of its area formula, not merely by whether base and height appear. Rectangles and parallelograms use one direct product of a base and its …
Preview problemUse angle-pair totals
Use angle facts and diagram structure to find unknown angle measures.
Begin with the relationship word, because it determines the total the two angles must make. Supplementary angles fill a straight angle, so represent the unknown as the part that completes …
Preview problemUse vertical-angle equality
Use angle facts and diagram structure to find unknown angle measures.
At an intersection, position matters before arithmetic. The target lies directly across the vertex from the labeled angle, so the pair is vertical rather than adjacent. Vertical angles are equal …
Preview problemUse line and full-turn angle totals
Use angle facts and diagram structure to find unknown angle measures.
The diagram partitions all the space around one point into three nonoverlapping sectors. Since those sectors make a full turn, add the two known measures and the unknown to the …
Preview problemUse shape angle totals
Use angle facts and diagram structure to find unknown angle measures.
Use the figure’s invariant before working with the particular numbers: every triangle’s interior angles share the same total. Combine the two known measures first, then treat the third angle as …
Preview problemUse angle facts in a real situation
Use angle facts and diagram structure to find unknown angle measures.
Separate the door’s current opening from the right-angle target. The question asks for additional movement, so model the current angle plus an unknown increase as the target rather than reporting …
Preview problemRead the structure of the diagram first
Use angle facts and diagram structure to find unknown angle measures.
Read the rays before using the labels: the two angles share a side, while their nonshared sides point in opposite directions along one line. That structure makes an adjacent straight-line …
Preview problemTranslate angle words into angle structure
Use angle facts and diagram structure to find unknown angle measures.
Treat the straight path as one whole angle, then view the extra ray as dividing that whole into two adjacent, nonoverlapping parts. Angle addition says the measures of the parts …
Preview problemTurn angle words into a solve-able setup
Use angle facts and diagram structure to find unknown angle measures.
Translate “supplementary” into a total before building the equation. Preserve each angle measure exactly as stated, add the numerical angle and the variable expression as the two parts, and set …
Preview problemFind every angle fact that fits
Use angle facts and diagram structure to find unknown angle measures.
Map each label’s position relative to the given angle before testing any statement. The directly opposite angle inherits the given measure through vertical-angle equality, while either adjacent angle completes a …
Preview problemAdd the areas of all prism faces
Find and interpret surface area of prisms and cylinders.
Surface area is an inventory of the prism’s exterior faces, not a measure of the space inside. Pair the two length-by-width faces, the two length-by-height faces, and the two width-by-height …
Preview problemAdd the face areas from a net
Find and interpret surface area of prisms and cylinders.
A net changes the arrangement of the faces but not their total area. Group the six visible rectangles into matching dimension pairs, multiply each rectangle’s side lengths, and double each …
Preview problemAdd the circle tops and the wrapped side
Find and interpret surface area of prisms and cylinders.
Inventory a closed cylinder as two circular bases plus one curved side. The bases contribute two copies of circle area, while unwrapping the side makes a rectangle whose length is …
Preview problemRecognize a complete surface-area setup
Find and interpret surface area of prisms and cylinders.
Judge each setup against the complete exterior of a closed cylinder. It must contain two circle-area terms for the bases and a separate circumference-times-height term for the curved side. A …
Preview problemUse prism surface area for covering
Find and interpret surface area of prisms and cylinders.
Wrapping paper covers the box’s exterior, so include all six faces of the closed rectangular prism. Form the three distinct rectangular areas from pairs of dimensions, double each for its …
Preview problemUse cylinder surface area for covering
Find and interpret surface area of prisms and cylinders.
First match the paper to the surface it actually covers: the label wraps around the curved side but excludes both circular ends. Unwrap that side into a rectangle with length …
Preview problemDecide which outside parts really matter
Find and interpret surface area of prisms and cylinders.
Build the setup from the surfaces that exist and are painted, rather than automatically using a closed-prism formula. The open box contributes one bottom, two long side faces, and two …
Preview problemTurn a solid into a surface-area setup
Find and interpret surface area of prisms and cylinders.
Imagine unfolding the closed prism to expose its six rectangular faces. Each pair of dimensions creates one face type, and each type occurs twice on opposite sides, so write three …
Preview problemPut both surface-area situations into one comparison form
Find and interpret surface area of prisms and cylinders.
Compare the solid and the net by inventorying their faces rather than their layouts. If both contain the same two copies of each dimension pair, they must share one surface-area …
Preview problemFind every matching surface-area representation
Find and interpret surface area of prisms and cylinders.
Use the target as an exact test and evaluate every representation independently. For prisms and nets, count each included rectangular face once; for a closed cylinder, include both circular bases …
Preview problemMultiply the three rectangular-prism dimensions
Find and interpret volume of prisms and cylinders using correct units.
Volume counts the unit cubes filling the prism. Multiply length by width to find how many cubes fit in one horizontal layer, then multiply that base count by the number …
Preview problemUse base area times height
Find and interpret volume of prisms and cylinders using correct units.
A prism repeats the same base region through its perpendicular height. Since the base area is already supplied, use it directly as the amount in one layer and multiply by …
Preview problemUse circular base area times height
Find and interpret volume of prisms and cylinders using correct units.
Treat the cylinder as identical circular layers stacked through its height. First find one layer’s area by squaring the radius and multiplying by pi, then multiply that base area by …
Preview problemRecognize a correct volume setup
Find and interpret volume of prisms and cylinders using correct units.
A valid cylinder-volume setup must show circular base area multiplied by height. Put the radius, not the height, in the squared factor, retain pi as part of the base area, …
Preview problemUse volume for inside-space contexts
Find and interpret volume of prisms and cylinders using correct units.
The phrase “inside space” signals a three-dimensional capacity rather than an exterior covering. Model the rectangular box as layers by multiplying its length and width for one layer, then multiply …
Preview problemUse cylinder volume for capacity
Find and interpret volume of prisms and cylinders using correct units.
Capacity asks for the can’s interior space, so build the cylinder from a circular base area extended through its height. Square the given radius, multiply by pi for one layer, …
Preview problemDecide whether the situation needs volume
Find and interpret volume of prisms and cylinders using correct units.
Translate the manager’s question into the feature being measured before naming a formula. How much water the tank holds refers to all three-dimensional space inside it, not material covering the …
Preview problemTurn a solid into a volume setup
Find and interpret volume of prisms and cylinders using correct units.
Start from the general structure that volume equals base area times perpendicular height. For a cylinder, the base is a circle, so express its area using the squared radius and …
Preview problemPut both solids into one comparable volume form
Find and interpret volume of prisms and cylinders using correct units.
Put both solids into total cubic centimeters before comparing. Multiply all three prism dimensions for one volume, and preserve the pi factor while multiplying the other solid’s given base area …
Preview problemFind every matching volume representation
Find and interpret volume of prisms and cylinders using correct units.
Test every representation against the target in cubic units. Use three dimensions or base-area times height for prisms, interpret a count of unit cubes directly, and use circular base area …
Preview problemIdentify what the context is asking to measure
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Start by classifying the feature the paint covers. It spreads across every exterior face of a three-dimensional box, so the needed quantity must total several two-dimensional regions rather than measure …
Preview problemMatch the context to the right formula
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Match the formula to the surfaces the paper must cover. A closed can contributes two circular ends plus one curved side; the ends use two copies of circle area, while …
Preview problemLabel the answer with the right kind of units
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Use the reference container to determine both unit type and scale. Each counted bottle contributes one unit of liquid capacity, so multiply the bottle count by the capacity per bottle …
Preview problemModel and solve a short geometry context
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Fencing follows one complete trip around the circular garden, so model a boundary length rather than the region inside. Because the supplied measure is the diameter, use the circumference form …
Preview problemModel a flat-region geometry context
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Mulch covers the flat region inside the triangular bed, so the model must measure area rather than boundary length. Multiply the base by its perpendicular height, then apply the triangle’s …
Preview problemModel a solid-object geometry context
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Inventory only the painted surface shown: the curved side is included, while the open top and unpainted bottom are excluded. Unwrap that side into a rectangle whose length is the …
Preview problem