Operations & Word Problems
79 problem types
Multiplication as Equal Groups
Count sticks needed via multiplication Operations
Multiplying by one and by zero Operations
Division as the Inverse of Multiplication
Dividend equals divisor times quotient Operations
Division as repeated subtraction Operations
Find the total first, then divide Operations
Larger dividend gives larger quotient Operations
Dividing by a whole number is multiplying by its reciprocal FractionsNumber system
Use how multiplication and division undo each other Number systemRatios
Multiplicative Comparison and Unit Rate
Find the per-unit-weight rate first OperationsMeasurement & data
Fraction of a number: divide then multiply FractionsOperations
Distance grows in proportion to time Measurement & dataOperations
Find the value of one unit Base-ten numbersOperations
How many times the unit quantity OperationsBase-ten numbers
Speed is distance per unit time Measurement & dataOperations
Decimals convert small units to larger ones Base-ten numbersMeasurement & data
Express smaller units as larger using fractions FractionsMeasurement & data
Slope of a time-distance line graph is speed Measurement & data
Change the unit using a decimal Number systemRatios
Find the daily gap between a clock and true time Number systemRatios
Find the unit amount RatiosNumber system
Find the unit amount first Number systemRatios
Set the whole job to 1 and write a day's work as a fraction RatiosNumber system
Proportion and Proportional Division
Scaling both terms keeps the ratio RatiosExpressions
Equal heights make the area ratio the base ratio GeometryRatios
Work Backwards to Recover a Start Value
Undo more/less to find original length Measurement & data
Recover the unknown, then recompute Operations
Reverse the operations to find the start Operations
Skip-count backward to the start Base-ten numbers
Reverse decimal operations to recover the start Base-ten numbers
Undo a wrong decimal operation to recover the start Base-ten numbers
Name the unknown with a symbol and build an equation ExpressionsGeometry
Symbolize the unknown, then build an expression ExpressionsOperations
Apply a Newly Defined Operation
Evaluate a custom-defined operation symbol Operations
Set up an expression and compute in order Operations
Solve shape-coded products in order Operations
A new symbol can define a custom operation Operations
Define a custom operator and evaluate it Operations
Evaluate a newly defined operation symbol Operations
Find Two Unknowns from Sum and Difference
Find two lengths from sum and difference Measurement & data
Combine sum and difference of two weights Measurement & dataOperations
Find a rectangle side via one unknown Measurement & dataOperations
Reduce to one unknown to solve OperationsBase-ten numbers
Set up one-unknown equation for capacities Measurement & dataOperations
Set up an equation with one unknown angle Measurement & data
Eliminate to find two decimals from sum and difference Base-ten numbers
A balanced scale means both sides are equal Expressions
Write it as an equation with a single unknown ExpressionsNumber system
Name both unknowns and write two equations Expressions
Add or subtract equations to eliminate unknowns Expressions
Track a Quantity Through Changes
Add poured water to find total capacity Measurement & data
Bouncing ball rises a fraction of its fall FractionsOperations
Find container weight after adding or removing Measurement & data
Net fill rate is inflow minus outflow Measurement & dataOperations
Use weight differences to find the empty container Base-ten numbersMeasurement & data
Moving some across leaves the total unchanged ExpressionsRatios
Use what was poured out to weigh the container Number systemExpressionsRatios
Get Closest to a Target Value
Choose digits for sum nearest a target Base-ten numbersOperations
Smaller error means a better weight estimate Measurement & data
Closest number may be above or below target Base-ten numbers
Build the decimal closest to a target from cards Base-ten numbersFractions
Place consecutive whole numbers to sum decimals Base-ten numbers