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 a unit rate inside a representation
Compute and interpret unit rates, including rates with fractional or decimal quantities.
The highlighted row asks for the ounces paired with one bottle, so we need to scale a complete row to a bottle count of one. We’ll identify the factor that …
Preview problemInterpret a contextual unit rate
Compute and interpret unit rates, including rates with fractional or decimal quantities.
The phrase bottles per minute fixes both the quotient order and the target of one minute. We’ll divide the bottle total by the elapsed minutes, carry the units through the …
Preview problemCompare contextual unit rates
Compute and interpret unit rates, including rates with fractional or decimal quantities.
A lower total price or a larger bag alone cannot establish the better buy because the ounce amounts differ. We’ll divide each bag’s price by its own weight to create …
Preview problemCheck a claimed unit rate
Compute and interpret unit rates, including rates with fractional or decimal quantities.
The claim is about dollars for one notebook, so we’ll test it against the full purchase before calculating a replacement. First multiply the claimed per-notebook cost by six and compare …
Preview problemTranslate a rate into unit-rate form
Compute and interpret unit rates, including rates with fractional or decimal quantities.
Cost per ticket means the expression must place total dollars over the number of tickets. We’ll use that unit order to write the division, calculate the cost attached to one …
Preview problemRead a unit rate from a display
Compute and interpret unit rates, including rates with fractional or decimal quantities.
The missing row asks for dollars paired with exactly one apple. We’ll take any complete row, divide its cost by its matching apple count, and place that dollars-per-apple value in …
Preview problemScreen for matching unit-rate representations
Compute and interpret unit rates, including rates with fractional or decimal quantities.
Every statement must represent the same cost relationship as twenty-four dollars for six notebooks. We’ll establish dollars per notebook by dividing cost by quantity, then test each statement’s value and …
Preview problemChoose a smart unit-rate strategy
Compute and interpret unit rates, including rates with fractional or decimal quantities.
Each proposed strategy should end in dollars per one ounce, so we’ll track the units through every operation. We’ll check whether the weight is expressed in ounces before total dollars …
Preview problemScale a ratio up
Generate and justify equivalent ratios using scaling, tables, and diagrams.
An equivalent paint ratio must preserve both the red-to-blue order and the multiplicative relationship between its terms. We’ll apply the given scale factor to the red amount and the blue …
Preview problemScale a ratio down
Generate and justify equivalent ratios using scaling, tables, and diagrams.
Scaling a ratio down keeps the term order but replaces both terms with smaller equivalent amounts. We’ll divide the first and second terms by the same specified factor, rather than …
Preview problemComplete an equivalent ratio pair
Generate and justify equivalent ratios using scaling, tables, and diagrams.
The first terms correspond to each other, and the second terms correspond to each other, so one scale factor must connect both pairs. We’ll divide the new first term by …
Preview problemCheck whether two ratios are equivalent
Generate and justify equivalent ratios using scaling, tables, and diagrams.
Equivalence requires one multiplicative factor to map both positions, not merely two larger numbers or matching additive changes. We’ll compute the factor from six to ten, then test that exact …
Preview problemScale a contextual ratio
Generate and justify equivalent ratios using scaling, tables, and diagrams.
The mixture must keep concentrate first, water second, and preserve the same flavor as the two-to-five recipe. We’ll compare the target concentrate amount with the original concentrate amount to find …
Preview problemMatch a context to an equivalent ratio
Generate and justify equivalent ratios using scaling, tables, and diagrams.
Every candidate must be compared in raisins-to-nuts order, because reversing the labels changes the relationship. We’ll divide each candidate’s raisin amount by three and its nut amount by four, looking …
Preview problemUse an equivalent ratio in context
Generate and justify equivalent ratios using scaling, tables, and diagrams.
The target changes the red paint amount, but an equivalent mixture must change the white paint by the same multiplicative factor. We’ll divide the target red amount by the original …
Preview problemCheck an equivalent-ratio claim
Generate and justify equivalent ratios using scaling, tables, and diagrams.
The rows list juice first and water second, so their corresponding entries can be tested directly. We’ll find the factor from four parts juice to ten, apply that same factor …
Preview problemShow equivalent ratios in a table or diagram
Generate and justify equivalent ratios using scaling, tables, and diagrams.
The table’s column factor applies to the entire red-and-blue pair, while the row labels preserve which quantity belongs in each blank. We’ll multiply the red entry and the blue entry …
Preview problemRead an equivalent ratio from a display
Generate and justify equivalent ratios using scaling, tables, and diagrams.
A ratio from the table must use two entries from the same row and follow the requested juice-to-water order. We’ll read the juice entry first and its paired water entry …
Preview problemScreen for equivalent-ratio representations
Generate and justify equivalent ratios using scaling, tables, and diagrams.
We need every representation that preserves both the red-to-blue order and the value of four to six. We’ll simplify the reference ratio, test each standalone ratio and statement against that …
Preview problemChoose a smart equivalent-ratio strategy
Generate and justify equivalent ratios using scaling, tables, and diagrams.
A valid strategy must connect five cups of nuts to the twenty-cup target and preserve the nuts-to-dried-fruit relationship. We’ll carry out each proposed method far enough to see whether both …
Preview problemComplete a ratio table entry
Use ratio tables and double number lines to solve missing-value and scaling problems.
The two entries in each row form a matched apples-and-dollars pair, so both quantities must scale together. We’ll compare three apples with twelve to find the multiplicative factor, apply that …
Preview problemFind a missing value on a double number line
Use ratio tables and double number lines to solve missing-value and scaling problems.
Values at the same vertical tick form a proportional cups-and-servings pair. We’ll use a labeled pair to divide servings by cups, giving the number of servings for one cup, and …
Preview problemScale a ratio pair to a target value
Use ratio tables and double number lines to solve missing-value and scaling problems.
The given and target columns must represent the same notebook-to-cost relationship, even though ten is not a whole-number multiple of four. We’ll create a convenient intermediate pair by halving both …
Preview problemIdentify a correct ratio table or double number line
Use ratio tables and double number lines to solve missing-value and scaling problems.
A correct table must preserve juice first, water second, and the two-to-five relationship in every column. We’ll compare each juice entry with two to identify its column factor, then test …
Preview problemSolve a contextual ratio-table problem
Use ratio tables and double number lines to solve missing-value and scaling problems.
The target column pairs twenty people with an unknown rice amount, so we’ll scale from a complete column rather than mix entries. We’ll find the factor from ten people to …
Preview problemSolve a contextual double-number-line problem
Use ratio tables and double number lines to solve missing-value and scaling problems.
The evenly spaced ticks show that each one-hour move must add the same distance on the miles line. We’ll use a labeled aligned pair to identify miles per hour, then …
Preview problemCompare represented proportional scenarios
Use ratio tables and double number lines to solve missing-value and scaling problems.
A fair comparison uses the same input, so the five-day column is the anchor in both plan tables. We’ll read the data amount paired with five days for each plan, …
Preview problemCheck a ratio table or double number line for validity
Use ratio tables and double number lines to solve missing-value and scaling problems.
Every notebook-to-folder column must be a common-factor copy of three to seven; several correct columns cannot excuse one mismatch. We’ll identify the factor used by each notebook entry and test …
Preview problemConvert between a ratio table and a double number line
Use ratio tables and double number lines to solve missing-value and scaling problems.
Converting the table changes the layout, not the proportional pairs or their labels. We’ll place cups of concentrate on one line and pitchers on the other, keep every table column …
Preview problemRepresent a proportional relationship
Use ratio tables and double number lines to solve missing-value and scaling problems.
Servings per cup determines the division order: use the servings value over its aligned cups value. We’ll calculate that quotient from one vertical pair on the double number line, then …
Preview problemScreen for matching proportional representations
Use ratio tables and double number lines to solve missing-value and scaling problems.
Every matching card must preserve rice first, servings second, and the two-to-five relationship in every displayed pair. We’ll test all rows of both tables, all aligned ticks on both number …
Preview problemChoose a smart table or number-line strategy
Use ratio tables and double number lines to solve missing-value and scaling problems.
The target is exactly fifteen notebooks, so a useful method must reach that quantity rather than overshoot or stop at a nearby row. We’ll evaluate whether each strategy preserves the …
Preview problemCheck proportionality from a table
Determine whether a relationship is proportional from a table, graph, equation, or context.
Proportionality in this table depends on a constant cost per cup, not equal dollar jumps between successive rows. We’ll divide each total cost by its matching cups of rice and …
Preview problemCheck proportionality from an equation
Determine whether a relationship is proportional from a table, graph, equation, or context.
A proportional equation has one constant multiplier in the form y equals k times x, with no separate amount added or subtracted. We’ll match the given equation to that structure, …
Preview problemCheck proportionality from a graph
Determine whether a relationship is proportional from a table, graph, equation, or context.
A proportional graph must satisfy two conditions together: one straight-line rate and passage through the origin. We’ll inspect whether all plotted points lie on a single line, verify that zero …
Preview problemClassify mixed representations for proportionality
Determine whether a relationship is proportional from a table, graph, equation, or context.
Each representation needs its own proportionality test. We’ll compare output-to-input ratios in the table, look for an added term in the equation, check whether the graph passes through the origin, …
Preview problem