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.
Pick a sensible unit and scale for geometry modeling
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Let both dimensional type and practical scale determine the unit. Pool capacity is three-dimensional, and its length, width, and depth are all expressed in feet, so multiplying them produces the …
Preview problemTurn context into geometry setup
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Model the patio as a flat trapezoidal region because tile covers its surface. Average the two parallel side lengths—or equivalently take one-half of their sum—then multiply by the perpendicular height. …
Preview problemPut both geometry situations into one modeling language
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Classify each context before calculating: paper covering every box face is a two-dimensional exterior measure, while a can’s capacity is a three-dimensional interior measure. Use the matching face-area and base-area-times-height …
Preview problemFind every correct geometry model in a mixed set
Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Test every statement against the physical job: wrapping paper covers all six exterior faces of a closed rectangular prism. A correct model must use three pairs of rectangular face areas, …
Preview problemFind the mean
Compute and interpret mean, median, range, and interquartile range in context.
Think of the mean as redistributing the data total equally across all observations. Add every value exactly once, count how many values contributed to that sum, and divide the total …
Preview problemFind the median
Compute and interpret mean, median, range, and interquartile range in context.
The median depends on position, so first rewrite the values from least to greatest. With an odd number of observations, locate the single middle position by leaving the same number …
Preview problemFind a measure of spread
Compute and interpret mean, median, range, and interquartile range in context.
Range measures the full distance spanned by the data, so only the true endpoints matter. Identify the maximum and minimum, then subtract the minimum from the maximum in that order. …
Preview problemMatch a data set to the right summary
Compute and interpret mean, median, range, and interquartile range in context.
Check each claimed statistic from the ordered scores instead of relying on a familiar-looking number. Use total divided by count for mean, the middle position for median, endpoint difference for …
Preview problemInterpret center in context
Compute and interpret mean, median, range, and interquartile range in context.
Add all book counts to find the class total, then divide by the number of students to redistribute that total equally. Interpret the result as books per student in an …
Preview problemInterpret spread in context
Compute and interpret mean, median, range, and interquartile range in context.
For sprint times, the full spread runs from the fastest numerical time to the slowest numerical time. Identify the minimum and maximum, subtract the former from the latter, and retain …
Preview problemChoose the most useful summary measure
Compute and interpret mean, median, range, and interquartile range in context.
First compare the ordinary price cluster with the unusually expensive mansion. A center that uses every numerical value will be pulled upward by that extreme price, while a center based …
Preview problemTurn raw data into a statistical summary
Compute and interpret mean, median, range, and interquartile range in context.
Use the ordered list once to support all three summaries. Divide the total by the data count for mean, average the two central entries because the count is even, and …
Preview problemPut both statistical summaries into one comparison form
Compute and interpret mean, median, range, and interquartile range in context.
Put Class A into the same four-statistic format already given for Class B. From the ordered data, compute total-over-count, average the two middle values, subtract endpoints, and split into two …
Preview problemFind every matching center-and-spread representation
Compute and interpret mean, median, range, and interquartile range in context.
Apply two independent tests to every ordered five-value set. The third entry must match the target median, and the last entry minus the first must match the target range; satisfying …
Preview problemRead a dot plot exactly
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
Treat the dot plot as a frequency map: each horizontal position is a score, while the height of its stack tells how many students earned that score. Because the question …
Preview problemRead a histogram
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
In a histogram, height compares frequencies, but each bar stands for a whole interval rather than one exact time. First locate the tallest bar, then trace straight down to both …
Preview problemRead a box plot statistic
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
A box plot assigns different jobs to its landmarks: the line inside the box marks the median, while the box edges mark the first and third quartiles. Read those three …
Preview problemDescribe what the display shows
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
Describe the whole histogram by checking two features separately. Pair bars equally far from the center to test whether the two sides balance, then locate the tallest bars to see …
Preview problemInterpret a display in context
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
Use two related scans of the dot plot. The mode comes from the single tallest stack, so keep the book value separate from that stack's frequency; the densest adjacent interval …
Preview problemCompare two displays
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
Consistency in the middle half is a spread question, so compare the two interquartile ranges. For each restaurant, subtract its first quartile from its third quartile, keeping the calculations parallel. …
Preview problemUse display shape to judge a claim
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
Judge each claim against both the main cluster and the tail. The tallest bars show what is typical for most deliveries, while the distance and direction of the thinning bars …
Preview problemFind every display that matches a target feature
Read and compare dot plots, histograms, and box plots to describe center, spread, and shape.
Use tail direction as the common test across all five displays: right skew means the data bunch at lower values and thin out toward higher values. Translate that idea appropriately …
Preview problemFind theoretical probability
Compute and compare theoretical and experimental probability in simple settings.
Theoretical probability starts with the complete set of equally likely faces on the fair number cube. Count how many faces satisfy the strict condition greater than four, place that count …
Preview problemFind experimental probability
Compute and compare theoretical and experimental probability in simple settings.
Experimental probability describes what actually happened, so use the recorded heads as the success count and all flips as the trial count. Put observed successes over total trials, then check …
Preview problemCompare theoretical and experimental probability
Compute and compare theoretical and experimental probability in simple settings.
Build the two probabilities from different evidence: equally likely cube faces for theory and observed even rolls for the experiment. Simplify both fractions, then rewrite them with a common denominator …
Preview problemFind an expected number of successes
Compute and compare theoretical and experimental probability in simple settings.
An expected count scales a one-roll probability up to many rolls. Multiply the number of trials by the probability of the target face, or view the trials as equal groups …
Preview problemInterpret experimental probability in context
Compute and compare theoretical and experimental probability in simple settings.
Start with the observed success rate: made free throws belong in the numerator and all practice attempts belong in the denominator. Convert that fraction to a percent so the size …
Preview problemCompare experiments using observed probability
Compute and compare theoretical and experimental probability in simple settings.
Put theory and both experiments into the same unit, such as percent. For each student, divide blue results by total spins, then find the absolute percentage-point distance from the theoretical …
Preview problemTurn an outcome model into a probability summary
Compute and compare theoretical and experimental probability in simple settings.
Because all spinner sections are equal, every color probability starts with the total number of sections as its denominator. Use each color's section count as the numerator, reduce each fraction …
Preview problemPut theory and experiment into one comparison summary
Compute and compare theoretical and experimental probability in simple settings.
Keep the two sources of probability separate and clearly labeled. Theoretical probability uses red counters over all counters in the bag, while experimental probability uses observed red draws over all …
Preview problemFind every probability scenario that matches the target
Compute and compare theoretical and experimental probability in simple settings.
Test every scenario with the same ratio: blue outcomes divided by all equally likely outcomes. Build each total by including every color or by adding blue and non-blue counts, then …
Preview problemCount outcomes in a two-step situation
Solve simple compound probability and counting problems using organized reasoning.
A complete outcome records both stages: one coin result paired with one cube result. Since every coin result can occur with every cube face, use the multiplication principle on the …
Preview problemCount favorable compound outcomes
Solve simple compound probability and counting problems using organized reasoning.
The word and requires both conditions to hold in the same compound outcome. Fix the coin result at tails, identify the cube faces strictly greater than three, and pair tails …
Preview problemFind a compound probability
Solve simple compound probability and counting problems using organized reasoning.
Find the chance of heads and the chance of an odd cube result separately. Because the coin and cube are independent and both events must occur, multiply those probabilities and …
Preview problemFind expected successes for a compound event
Solve simple compound probability and counting problems using organized reasoning.
Separate this into probability first and expectation second. Find the chance of heads and the chance of an even cube result, multiply because both independent conditions must occur, and then …
Preview problemInterpret a compound probability in context
Solve simple compound probability and counting problems using organized reasoning.
Count complete spinner-and-coin outcomes, since a play records one result from each device. Pair every spinner color with both coin faces, then identify the single pair satisfying red and heads. …
Preview problem