Sensim Math · Depth
Advanced math problem types, adapted to the Common Core. — 237 problem types · 2,267 generated practice variants across 233 archetypes
2-2
48 problem types
3-1 51 problem types
3-2 48 problem types
4-1 43 problem types
4-2 47 problem types
Count numbers built from digit cards 4.NBT.A.2 · take
Compare numbers with an unknown digit 4.NBT.A.2 · take
Find a number from digit clues 4.NBT.A.2 · take
Count ways to make an amount with coins 2.MD.C.8 · adapt
Carry ten units to the next place 4.NBT.A.24.NBT.A.1 · take
Skip-count backward to the start 4.NBT.A.2 · take
Find the constant skip-count step 4.NBT.A.2 · take
Ten hundreds make one thousand 4.NBT.A.22.MD.C.8 · adapt
Different factor pairs, same product 3.OA.B.54.OA.B.4 · take
Bound an inequality at equality 3.OA.A.43.OA.C.7 · take
Recover the unknown, then recompute 3.OA.A.43.OA.B.6 · take
Guess-and-check a legs problem 3.OA.A.33.OA.D.8 · take
Count groups several equivalent ways 2.OA.C.43.OA.A.1 · take
Multiplying by one and by zero 3.OA.B.53.OA.C.7 · take
Find a number satisfying product bounds 3.OA.A.43.OA.C.7 · take
Solve shape-coded products in order 3.OA.A.43.OA.D.8 · take
Count sticks needed via multiplication 3.OA.A.13.OA.A.3 · take
Gaps are one fewer than the objects 2.MD.B.5 · adapt
Cut a rectangle into a grid of cards 2.G.A.23.MD.C.7 · adapt
Find one handspan from measured counts 2.MD.A.12.MD.B.5 · adapt
Undo more/less to find original length 2.MD.B.5 · adapt
Subtract the overlap from total length 2.MD.B.52.MD.A.4 · adapt
Ribbon around a box: four equal parts 2.MD.B.53.MD.D.8 · adapt
Smaller unit, more measured counts 2.MD.A.1 · adapt
Find two lengths from sum and difference 2.MD.B.5 · adapt
Convert to one unit, then compare lengths 2.MD.A.14.MD.A.1 · adapt
Compare hours first, then minutes 2.MD.C.7 · take
Find a future date using days per month 1.MD.B.3 · adapt
Elapsed time between two clock times 3.MD.A.12.MD.C.7 · take
Reason about a fast or slow clock 3.MD.A.1 · take
Reach the next hour, then add the rest 2.MD.C.73.MD.A.1 · take
Read a mirrored clock, then find elapsed time 2.MD.C.73.MD.A.1 · take
Read the hour when the hand is between 2.MD.C.7 · take
Weekdays repeat every seven days 2.NBT.A.2 · adapt
Read totals and differences from a graph 2.MD.D.103.MD.B.3 · take
Find the value of one grid interval 3.MD.B.3 · take
Set the scale, then complete the graph 3.MD.B.3 · take
Solve graph values step by step from clues 3.MD.B.33.OA.A.3 · take
Complete a table from its graph and back 2.MD.D.103.MD.B.3 · take
Total equals the sum of the rows 2.MD.D.102.OA.A.1 · take
Compare two data sets in one graph 2.MD.D.103.MD.B.3 · take
Find the rule of changing clock times 4.OA.C.53.MD.A.1 · take
Complete addition and multiplication tables 3.OA.D.9 · take
Find the rule of a growing block stack 4.OA.C.54.OA.A.3 · take
Multiplication table folds to equal cells 3.OA.B.53.OA.D.9 · take
Sum a repeating number sequence 4.OA.C.53.OA.A.3 · take
Find shape and color repeats separately 4.OA.C.5 · take
Use the seven-day weekday cycle 4.OA.C.5 · adapt
Bigger addend, bigger sum 3.OA.A.43.NBT.A.2 · take
Choose digits for sum nearest a target 3.NBT.A.23.NBT.A.13.OA.D.8 · take
Sum consecutive numbers via the middle 3.OA.D.93.NBT.A.22.NBT.A.2 · take
Recover hidden digits using regrouping 3.NBT.A.23.OA.A.42.NBT.B.7 · take
One number, many addition expressions 3.NBT.A.23.OA.A.4 · take
Big digits in high places 2.NBT.A.43.NBT.A.2 · take
Overlap shrinks the total length 2.MD.B.53.OA.D.8 · adapt
Ten in a place carries forward 2.NBT.A.13.NBT.A.2 · take
Reduce to one unknown to solve 3.OA.D.83.NBT.A.23.OA.A.4 · take
Count all shapes hidden in a grid 1.G.A.23.OA.D.9 · take
Count segments between points on a line 4.G.A.13.OA.D.9 · take
Base perimeter from multiple views 3.MD.D.8K.G.A.34.MD.A.3 · adapt
Find a side from equal perimeters 3.MD.D.84.MD.A.33.OA.A.4 · adapt
Side lengths from overlapping rectangles 3.MD.D.84.MD.A.33.OA.D.8 · adapt
Perimeter of the nth figure by rule 4.OA.C.53.MD.D.83.OA.D.9 · adapt
Perimeter plus tiles needed to build it 3.MD.D.84.MD.A.33.OA.A.3 · adapt
Perimeter by tracing every side 3.MD.D.84.MD.A.3 · adapt
Numbers divisible by several are common multiples 3.OA.B.63.OA.C.7 · take
Dividend equals divisor times quotient 3.OA.B.63.OA.A.4 · take
Division as repeated subtraction 3.OA.A.23.OA.A.3 · take
Narrow candidates by divisibility conditions 3.OA.B.63.OA.C.7 · take
Find the total first, then divide 3.OA.D.83.OA.A.3 · take
Larger dividend gives larger quotient 3.OA.A.23.OA.A.3 · take
Objects versus gaps when spacing along a line 3.OA.A.33.OA.D.8 · adapt
Recover side length from number of cut pieces 3.OA.A.33.MD.D.8 · adapt
Place digit cards for largest or smallest product 3.NBT.A.33.OA.B.5 · take
Estimate a product to solve an inequality 3.NBT.A.33.OA.D.8 · take
Evaluate a custom-defined operation symbol 3.OA.D.83.OA.B.5 · take
Recover missing digits from column carries 3.NBT.A.33.OA.B.5 · take
Overlaps are one fewer than the strips 3.MD.D.83.OA.D.8 · adapt
Write a growing pattern as an expression 3.OA.D.93.OA.D.8 · take
Find perimeter path length by multiplication 3.MD.D.83.OA.A.3 · adapt
Find right and wrong counts from total score 3.OA.D.83.OA.A.3 · take
Reduce relations to a single-unknown equation 3.OA.D.83.OA.A.3 · adapt
Reverse the operations to find the start 3.OA.D.83.OA.A.4 · take
Sum distances and times across legs 4.MD.A.24.MD.A.13.MD.A.1 · adapt
AM and PM make a 24-hour day 3.MD.A.1 · take
Match units before comparing path lengths 4.MD.A.14.MD.A.22.MD.A.4 · adapt
Distance grows in proportion to time 4.MD.A.23.OA.A.3 · adapt
A drifting clock accumulates daily error 3.MD.A.13.OA.A.3 · take
Total length is the sum of its parts 4.MD.A.14.MD.A.22.MD.B.5 · adapt
Speed is distance per unit time 4.MD.A.23.OA.A.3 · adapt
Time regroups in base sixty 3.MD.A.1 · take
Compare decimals from the highest place down 4.NF.C.7 · take
Compare fractions sharing numerator or denominator 3.NF.A.3 · take
Ten tenths make one whole 4.NF.C.64.NF.C.5 · take
Place big digits high to maximize a decimal 4.NF.C.74.NF.C.6 · take
A fraction is a count of unit fractions 4.NF.B.33.NF.A.1 · adapt
Fractions require equal partitioning of the whole 3.NF.A.13.G.A.2 · take
Find fractions between two on the number line 3.NF.A.23.NF.A.3 · take
The whole is one; find the remaining fraction 3.NF.A.13.NF.A.3 · take
Set up an expression and compute in order 3.OA.A.33.OA.D.8 · take
Consecutive integers around a middle value 3.OA.D.93.OA.D.8 · take
Place big digits high for largest product 3.OA.C.73.NBT.A.3 · take
Estimate a product to bound an unknown 3.NBT.A.33.OA.C.7 · take
Posts versus gaps on lines and loops 3.OA.A.33.MD.D.8 · adapt
Deduce missing digits in a multiplication 3.OA.C.73.NBT.A.3 · take
Recover the original number from a wrong product 3.OA.A.43.OA.C.7 · take
Sum of evenly spaced numbers equals middle times count 3.OA.D.93.OA.C.7 · take
Adjust the total to leave no remainder 3.OA.A.33.OA.C.7 · take
Exact division means remainder zero 3.OA.C.73.OA.B.6 · take
Count posts via length divided by spacing 3.OA.A.33.MD.D.8 · adapt
Fill long-division blanks from the known 3.OA.C.73.OA.B.6 · take
Perimeter as side length times side count 3.MD.D.83.OA.C.7 · adapt
Recover the dividend from quotient and remainder 3.OA.B.63.OA.A.4 · take
Find a rectangle side via one unknown 3.MD.D.83.OA.A.4 · adapt
Remainder must be less than the divisor 3.OA.B.63.OA.C.7 · take
Segment through chained centers as radius multiples 3.OA.C.73.G.A.1 · adapt
Diameter is twice the radius 3.OA.C.73.G.A.1 · adapt
Rectangle sides are multiples of the diameter 3.OA.C.73.G.A.1 · adapt
Center to edge distance is the radius 3.MD.D.83.G.A.1 · adapt
Perimeter splits into radius arcs and straight parts 3.MD.D.83.G.A.1 · adapt
Perimeter of shape joining circle centers 3.MD.D.83.OA.C.7 · adapt
Perimeter of shapes from tangent circles 3.MD.D.83.OA.C.7 · adapt
Find each radius and diameter from segments 3.OA.C.73.G.A.1 · adapt
All radii in one circle are equal 3.MD.D.83.G.A.1 · adapt
Polygon side equals sum of two radii 3.MD.D.83.G.A.1 · adapt
Triangle side equals sum of two radii 3.MD.D.83.G.A.1 · adapt
Bouncing ball rises a fraction of its fall 3.NF.A.13.OA.A.2 · take
Match fraction forms to compare sizes 3.NF.A.3 · take
Recover the whole from a fractional part 3.NF.A.13.OA.A.4 · take
Fraction of a number: divide then multiply 3.NF.A.13.OA.A.2 · take
Find the rule in a fraction sequence 3.OA.D.93.NF.A.1 · take
Split a whole into proper-fraction portions 3.NF.A.13.OA.A.2 · take
Same numerator: smaller denominator is larger 3.NF.A.3 · take
Smaller error means a better weight estimate 3.MD.A.2 · adapt
Find container weight after adding or removing 3.MD.A.2 · adapt
Net fill rate is inflow minus outflow 3.MD.A.23.OA.A.3 · adapt
Round the quotient up to carry the remainder 3.OA.A.33.MD.A.2 · adapt
Set up one-unknown equation for capacities 3.MD.A.23.OA.D.8 · adapt
Add poured water to find total capacity 3.MD.A.2 · adapt
Find the per-unit-weight rate first 3.OA.A.33.MD.A.2 · adapt
Combine sum and difference of two weights 3.MD.A.23.OA.D.8 · adapt
Translate between table and pictograph 3.MD.B.3 · take
Solve missing data from ratio or sum clues 3.MD.B.33.NF.A.1 · take
Determine the value each picture symbol stands for 3.MD.B.3 · take
Convert a pictograph into a frequency table 3.MD.B.3 · take
Fill the table by solving knowns first 3.MD.B.33.OA.D.8 · take
Total all categories from a pictograph 3.MD.B.3 · take
Build a number from digit conditions in order 4.NBT.A.2 · adapt
Compare place by place to bound an unknown digit 4.NBT.A.2 · adapt
Find one tick interval, then read the value 4.NBT.A.2 · adapt
Locate and compare numbers on a number line 4.NBT.A.2 · adapt
Ten of a unit carries to the next place 4.NBT.A.14.NBT.A.2 · adapt
Skip-count by the changing place value 4.NBT.A.24.OA.C.5 · adapt
Times ten adds one place 4.NBT.A.1 · adapt
A clock face is twelve equal 30-degree parts 4.MD.C.64.MD.C.7 · adapt
Small angles combine into larger angles 4.MD.C.74.MD.C.5 · take
Use the 180-degree line to find figure angles 4.MD.C.7 · take
Split a polygon into triangles to sum angles 4.MD.C.7 · take
Quadrilateral angles sum to 360 degrees 4.MD.C.7 · take
Set up an equation with one unknown angle 4.MD.C.7 · take
A straight line is 180 degrees 4.MD.C.7 · take
Triangle angles sum to 180 degrees 4.MD.C.7 · take
Smaller divisor makes a bigger quotient 4.NBT.B.6 · take
Deduce hidden digits from the ones place up 4.NBT.B.5 · take
A new symbol can define a custom operation 4.OA.A.35.OA.A.1 · take
A number divides by its factor pieces 4.OA.B.44.NBT.B.6 · take
The remainder is always less than the divisor 4.NBT.B.6 · take
How many times the unit quantity 4.OA.A.24.NBT.B.5 · take
Intervals differ on open paths versus closed loops 4.OA.A.34.MD.A.2 · adapt
Bigger units express numbers more simply 4.MD.A.14.MD.A.2 · adapt
Find the value of one unit 4.NBT.B.64.OA.A.2 · adapt
Even number of flips returns original 4.G.A.3 · take
Flip across a line creates symmetry 4.G.A.3 · take
Flipping or turning digits forms new digits 4.G.A.3 · adapt
Four 90-degree turns return original 4.MD.C.5 · take
Reverse the moves to recover original 4.G.A.3 · take
Center of rotation stays fixed 4.MD.C.5 · take
Read and compare multiple bars 3.MD.B.3 · take
Combine two graphs to find totals 3.MD.B.34.OA.A.3 · adapt
Choose a scale that fits the largest value 3.MD.B.3 · take
Use total and clues to fill missing bars 3.MD.B.34.OA.A.3 · adapt
Convert a table into a bar graph 3.MD.B.3 · adapt
Read a double bar graph 3.MD.B.3 · take
Find the value of one grid square 3.MD.B.3 · take
Sum-and-difference rules in a number grid 4.OA.C.53.OA.D.9 · take
Pair consecutive numbers with constant sum 4.OA.C.53.OA.D.9 · take
Express counts of dots, lines, faces 4.OA.C.5 · take
Use neighbor differences to find rule 4.OA.C.5 · take
Pattern in equations predicts the answer 4.OA.C.53.OA.D.9 · take
Find shape and number rule together 4.OA.C.5 · take
Add per-day work fractions to find combined output 4.NF.B.3 · take
Apply a defined symbol to compute with fractions 4.NF.B.3 · take
Find patterns in mixed-number sequences and sum 4.NF.B.34.OA.C.5 · take
Build largest and smallest mixed numbers from cards 4.NF.B.3 · take
Subtract the overlap when joining fraction lengths 4.NF.B.3 · take
Find a missing side, then sum sides as fractions 4.NF.B.34.MD.A.3 · take
Use submerged and exposed parts to find bar length 4.NF.B.3 · take
Undo a wrong fraction operation to recover the start 4.NF.B.3 · take
Systematically count all triangles in a composite 4.G.A.2 · take
Use equilateral 60-degree angles and equal sides 4.G.A.24.MD.C.7 · take
Folded angles are equal; chain to the unknown 4.MD.C.7 · take
Chain isosceles base angles to find unknown angles 4.MD.C.74.G.A.2 · take
Two radii form an isosceles triangle; find angles 4.MD.C.74.G.A.2 · take
Spot equal sides to build isosceles triangles 4.MD.C.74.G.A.2 · take
Rotation preserves side lengths and angle measures 4.MD.C.7 · take
Build the decimal closest to a target from cards 5.NBT.B.74.NF.C.7 · take
Place consecutive whole numbers to sum decimals 5.NBT.B.7 · take
Use weight differences to find the empty container 5.NBT.B.74.MD.A.2 · adapt
Compare the next digit to fill a blank in decimals 4.NF.C.7 · take
Find the extreme decimal satisfying an inequality 5.NBT.B.74.NF.C.7 · take
Reverse decimal operations to recover the start 5.NBT.B.7 · take
Eliminate to find two decimals from sum and difference 5.NBT.B.7 · take
Undo a wrong decimal operation to recover the start 5.NBT.B.7 · take
Perimeter as decimal side sums minus overlaps 5.NBT.B.74.MD.A.3 · adapt
Draw an auxiliary parallel line to find a bent angle 4.G.A.1 · adapt
Perimeter of overlapped squares and rectangles 4.MD.A.34.G.A.2 · adapt
Corresponding and alternate angles are equal 4.G.A.1 · adapt
Count all the rhombuses in a figure of small triangles 4.G.A.2 · take
Folding makes congruent corresponding angles 4.G.A.1 · adapt
Adjacent angles of a parallelogram sum to 180 4.G.A.2 · adapt
Perpendicular is half of a straight angle 4.G.A.14.MD.C.7 · take
Distance between parallel sides equals the side length 4.G.A.14.MD.A.3 · adapt
Compare line graphs that use different gridline scales 5.MD.B.2 · adapt
Largest vertical gap between two line graphs 5.MD.B.2 · adapt
Fill a table and complete a line graph from clues 5.MD.B.2 · adapt
Estimate an unmeasured midpoint value on a line graph 5.MD.B.2 · adapt
Read max, min, and gridline scale from a line graph 5.MD.B.23.MD.B.3 · adapt
Sum all data values read from a line graph 5.MD.B.2 · adapt
Slope of a time-distance line graph is speed 4.MD.A.25.MD.B.2 · adapt
Exterior angle sum of a regular polygon is 360 4.G.A.24.MD.C.7 · adapt
Isosceles triangle from a rectangle diagonal 4.G.A.24.MD.C.7 · adapt
Diagonals of a parallelogram bisect each other 4.G.A.2 · adapt
Polygon angle sum via triangulation from a vertex 4.G.A.2 · adapt
Square diagonals are equal and perpendicular bisectors 4.G.A.24.MD.A.3 · adapt
Count distinct shapes built by adding congruent tiles 4.G.A.2 · take
Identify tiling pieces and total area 4.G.A.24.MD.A.3 · adapt