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.
Turn a graph or solved set into a story answer
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
Read the solved inequality as an inclusive upper bound, then translate it through the meaning of g. Extra guests form a nonnegative whole-number count, so discard negative and fractional values …
Preview problemTurn a contextual answer back into algebraic form
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
Translate both restrictions, because neither one alone captures the statement. “At most six” gives an inclusive upper-bound inequality for t, while “number of tickets” supplies the whole-number domain. Keep the …
Preview problemChoose the strongest contextual final answer
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
Use one reference meaning for every statement: g can be any nonnegative whole-number guest count at or below the inclusive bound. Test each wording for four features—direction, boundary inclusion, whole-number …
Preview problemChoose the best interpretation move after solving
Interpret algebraic solutions and state them as meaningful contextual answers, including restrictions or whole-number constraints when needed.
The decimal upper bound is algebraically valid, but b counts full boxes, so the interpretation step must enforce a whole-number domain without crossing that bound. Do not keep a fractional …
Preview problemRead a value from a table
Read values, trends, and meaning from tables and coordinate graphs.
Use the column headings to distinguish inputs from outputs, then locate the requested input in the left column. Stay in that same row and read horizontally to the output column; …
Preview problemRead a value from a graph
Read values, trends, and meaning from tables and coordinate graphs.
Read point A by projecting it to each labeled axis. Its horizontal position gives the x-coordinate, and its vertical position gives the y-coordinate. Write those values in x-then-y order; checking …
Preview problemIdentify a trend
Read values, trends, and meaning from tables and coordinate graphs.
Focus only on the segment between the two specified x-values and trace it from left to right. Read the y-value at each endpoint, then compare the ending output with the …
Preview problemRead a requested value or comparison from a table
Read values, trends, and meaning from tables and coordinate graphs.
Locate Thursday in the day column, then read straight across the same row to preserve the day–temperature pairing. Use the column heading to interpret the number and carry its Fahrenheit …
Preview problemCompare values from a table or graph
Read values, trends, and meaning from tables and coordinate graphs.
Two different notebook quantities point to two different rows, so keep each quantity paired with the cost beside it. Read the two costs first, decide which is greater, and subtract …
Preview problemTranslate between table-reading and graph-reading language
Read values, trends, and meaning from tables and coordinate graphs.
The table records a relationship in input–output language, while an ordered pair records the same relationship by position. Preserve that role order: the first coordinate comes from the input column …
Preview problemTurn words into table or graph language
Read values, trends, and meaning from tables and coordinate graphs.
The sentence gives two linked measurements—elapsed time and distance—but the requested ordered pair fixes which role belongs first. Match each number to its quantity, place the time value in the …
Preview problemCheck which statements are supported by a display
Read values, trends, and meaning from tables and coordinate graphs.
Treat each statement as a claim that must be checked against the table, not as a description to accept because it sounds reasonable. For a value at a particular time, …
Preview problemChoose a smart first step when reading a display
Read values, trends, and meaning from tables and coordinate graphs.
A useful first step should tell you what each coordinate of the plotted point represents before any calculation begins. Orient yourself to the horizontal and vertical quantities and their scales, …
Preview problemDescribe how a pattern changes each step
Identify a numerical pattern and write a rule that matches it.
To describe how the sequence changes, compare neighboring terms rather than only the first and last terms. Compute the change from one term to the next, repeat that check across …
Preview problemWrite an input-output rule from a table
Identify a numerical pattern and write a rule that matches it.
An input–output rule must connect the two entries within each row, not merely describe how outputs change as you move down the table. Compare every output with its paired input …
Preview problemExtend a pattern and justify it
Identify a numerical pattern and write a rule that matches it.
First identify the operation that carries each given term to the next, and confirm it works across both visible gaps. Apply that same operation once to the last given term …
Preview problemClassify the kind of pattern
Identify a numerical pattern and write a rule that matches it.
Classification depends on what stays constant from one term to the next. Test an additive description by comparing adjacent differences, and test a multiplicative description by comparing adjacent factors or …
Preview problemWrite a rule from a contextual pattern
Identify a numerical pattern and write a rule that matches it.
Translate the story by separating the amount already in the jar from the amount added during each week. A constant weekly increase contributes the weekly rate multiplied by the number …
Preview problemWrite a rule and use it
Identify a numerical pattern and write a rule that matches it.
The table must support one relationship that works for every notebook–cost pair, including the skipped input between two and four. Compare cost to notebook count row by row to identify …
Preview problemPick the rule that really fits the pattern
Identify a numerical pattern and write a rule that matches it.
A rule earns confidence by surviving several substitutions, not by matching the first pair by coincidence. Use a strategically chosen input to eliminate expressions quickly, but keep checking any survivor …
Preview problemGenerate examples from a rule
Identify a numerical pattern and write a rule that matches it.
The starting value already counts as the first requested term, so place it before applying the repeated change. Generate each later term from the most recently found term, keeping a …
Preview problemRestate a pattern rule in a requested format
Identify a numerical pattern and write a rule that matches it.
The table describes the same operation from input to output in every row, and the requested rewrite must express that operation with x and y. Compare each output with its …
Preview problemMatch rules and patterns across options
Identify a numerical pattern and write a rule that matches it.
Because several differently written rules can generate the same pattern, test every one rather than stopping after the first match. Recursive descriptions should reproduce each step from the starting term, …
Preview problemChoose a smart first move for finding a rule
Identify a numerical pattern and write a rule that matches it.
Start by examining how the outputs change as the inputs advance in equal steps; that comparison tells you what kind of rule is plausible and supplies its variable rate. Then …
Preview problemGenerate coordinates from a rule
Generate and plot ordered pairs from rules, tables, and contexts.
Treat each requested input as a separate substitution into the same rule. Keep the input as the first coordinate, compute only its matching output for the second coordinate, and repeat …
Preview problemTurn table rows into coordinates
Generate and plot ordered pairs from rules, tables, and contexts.
Each horizontal table row already contains one relationship, so translate rows one at a time instead of reading down the columns. Preserve the column roles by writing the x-entry first …
Preview problemCheck whether a coordinate pair fits a rule
Generate and plot ordered pairs from rules, tables, and contexts.
To decide whether a pair fits the rule, treat its first coordinate as x and compute the rule’s output. Compare that result with the pair’s second coordinate: equality means the …
Preview problemMake coordinates from a context
Generate and plot ordered pairs from rules, tables, and contexts.
The hourly charge is a rate, so multiply it by each requested duration to find a total rather than adding it once or treating it as a fixed total. Keep …
Preview problemPrepare contextual points for graphing
Generate and plot ordered pairs from rules, tables, and contexts.
The story combines an initial height at week zero with a fixed amount of growth for every elapsed week. Build height as the starting amount plus weekly growth times weeks, …
Preview problemChoose the coordinates that really fit
Generate and plot ordered pairs from rules, tables, and contexts.
Start with the given x-value because it determines the first coordinate and the rule determines the second. Substitute that input into the expression, compute the corresponding y-value, and then write …
Preview problemMake a plot-ready table from a rule or context
Generate and plot ordered pairs from rules, tables, and contexts.
A plot-ready list comes from applying the entire rule to each requested input, one row at a time. Multiply before adding, record x beside only its computed y, and repeat …
Preview problemTurn graphing words into coordinates or a rule
Generate and plot ordered pairs from rules, tables, and contexts.
The phrase two times x describes multiplication, not addition, exponentiation, or a constant output. Translate it into a symbolic relationship, substitute each requested x-value separately, and keep each result paired …
Preview problemMatch coordinates and plots to a relationship
Generate and plot ordered pairs from rules, tables, and contexts.
Each labeled pair must pass the same two-part check: its first number plays x, and the rule’s computed value must equal its second number. Test every label by substitution, record …
Preview problemChoose a smart first step for plotting
Generate and plot ordered pairs from rules, tables, and contexts.
Since the source gives a rule rather than precomputed points, the direct preparation is to build a small value table. Put each requested x-value in the input column, evaluate the …
Preview problemTell whether the change is additive or multiplicative
Distinguish additive change from multiplicative change in tables, graphs, and contexts.
Whether a pattern grows is not enough to classify it; the repeated operation is what matters. Compare every neighboring pair by subtraction to test for one constant added amount, and …
Preview problemFind the repeated change
Distinguish additive change from multiplicative change in tables, graphs, and contexts.
Test the sequence in its forward order. First compare consecutive differences to see whether one added amount works throughout; if those vary, compare each new term with the preceding term …
Preview problem