Welcome to SSDD problems!

SSDD Problems

587 sets of maths problems that look the same on the surface, but need different maths to solve them.

Browse by topicWhat are SSDD problems?New on mrbartonmaths.com

The Tips for Teachers Guide to Purposeful Practice and Problem Solving by Craig Barton
The book on SSDD problems

Purposeful Practice and Problem Solving

Everything I have learned about practice that makes students better problem solvers, including how to write and use SSDD problems in your classroom. A short, practical workbook from my Tips for Teachers series.

Buy on AmazonAll my books
Four questions about the same isosceles triangle: one on area, one on forming an equation from the perimeter, one on angles and one on Pythagoras.
Same triangle, four different ideas: area, equations, angles and Pythagoras.

What are SSDD problems?

SSDD stands for Same Surface, Different Deep structure. Each set has four problems that look alike, but each one needs a different mathematical idea.

Most practice is the other way round: lots of different-looking problems that all use the same idea, so students never have to decide which maths to use. SSDD problems make them stop, think about the deep structure, and choose.

Three ways I use them

  1. End of a topic, in place of a traditional applications lesson.
  2. Homework, instead of a homework on just one topic.
  3. Revision, especially for GCSE: four topics for the price of one.

Read more about SSDD problems →

Find a problem

Pick a topic, choose the kind of problem, or start with the favourites.

Number39 topics
High value skills4
Arithmetic
Mental addition12 Mental division6 Mental multiplication13 Mental subtraction5 Money calculations13 Order of operations2 Place value5 Using a calculator1 Written addition1 Written division3 Written multiplication10
Decimals
Operations with decimals6
Factors, multiples and primes
Factors4 Highest common factor4 Lowest common multiple5 Multiples3 Prime factors3 Prime numbers7
Fractions
Adding and subtracting fractions13 Dividing fractions8 Fraction of an amount42 Mixed and improper fractions1 Multiplying fractions13 Simplifying fractions6 Fraction, decimal, percentage equivalence13
Indices and surds
Laws of indices6 Standard form7 Surds12
Negative numbers
Adding and subtracting negatives4
Percentages
Compound interest16 Percentage decrease17 Percentage increase29 Percentage of an amount57 Reverse percentages22 Simple interest1
Rounding and estimation
Rounding to decimal places3 Bounds of error15 Estimation4
Algebra55 topics
Proof2
Algebraic fractions
Multiplying algebraic fractions3 Simplifying algebraic fractions3
Brackets
Completing the square10 Expanding double brackets8 Expanding single brackets2 Factorise cubic expressions1 Factorise quadratic expressions3 Factorise single brackets6
Equations
Finding roots1 Forming and solving equations41 Function machines1 Iteration2 Simultaneous equations5 Solving cubic equations1 Solving linear equations8 Solving quadratic equations17 Solving trigonometric equations2
Expressions
Dividing terms2 Multiplying terms3 Simplifying expressions3
Formula
Rearranging formula1 Substituting into formula17 Writing expressions4 Writing formula3
Functions
Composite functions4 Domain and range2 Function notation6 Inverse functions3 Solving functions2 Transformation of functions15
Graphs
Area under a curve1 Coordinates14 Cubic graphs4 Equation of a circle9 Equation of a normal1 Equation of a perpendicular line8 Equation of a quadratic curve6 Equation of a straight line32 Equation of a tangent6 Gradient21 Graphs of real life functions1 Graphs of trigonometric functions6 Midpoint of coordinates11 Roots of an equation10 Sketching quadratic functions15 Table of values3 Tangent to a circle4 Time series graphs1 Turning points9 y-intercept4
Inequalities
Quadratic inequalities1 Solving linear inequalities2
Sequences
Linear sequences14 nth term rule10
Ratio and proportion7 topics
Best buys7 Currency conversions3 Direct proportion18 Inverse proportion4 Scale drawing3 Sharing in a ratio49 Writing and simplifying ratio47
Geometry83 topics
Pythagoras98
Angles
Angles in a triangle7 Angles on parallel lines5 Basic angle facts12 Bearings11 Circle theorems10 Exterior angles of a polygon2 Interior angles of a polygon9
Circles
Arc length5 Area of a circle22 Circumference of a circle17 Parts of a circle2 Sector area15 Sector perimeter9
Construction and loci
Constructing polygons1 Constructing triangles1 General construction6 Loci5 Perpendicular bisector1
Measures
Acceleration2 Density14 Distance velocity time graphs1 Measures of capacity1 Pressure2 Reading scales2 Speed15 Temperature1 Time14 Units of capacity5 Units of length3 Units of mass6
Perimeter and area
Area of a kite2 Area of a parallelogram3 Area of a rectangle13 Area of a rhombus1 Area of a square3 Area of a trapezium7 Area of a triangle40 Compound area3 Measuring lengths3 Missing lengths1 Perimeter22
Ratio
Accurate drawing1
Shapes
Nets1 Plans and elevations2 Properties of 3D shapes6 Properties of polygons1 Properties of quadrilaterals12 Properties of triangles5 Symmetry11
Similarity and congruence
Area scale factor10 Congruency1 Similar shapes5 Volume scale factor4
Surface area and volume
Surface area11 Surface area of a cone3 Surface area of a cube1 Surface area of a cuboid4 Surface area of a cylinder6 Surface area of a frustum1 Surface area of a hemisphere1 Surface area of a prism4 Surface area of a sphere2 Volume of a cone7 Volume of a cube2 Volume of a cuboid13 Volume of a cylinder14 Volume of a frustum3 Volume of a hemisphere1 Volume of a prism15 Volume of a pyramid2 Volume of a sphere6
Transformations
Enlargement12 Reflection13 Rotation4 Tessellation1 Translation10 Vector geometry6
Trigonometry
Basic trigonometry (SOH CAH TOA)55 Further trigonometry8 Sine and cosine rules4 Area of a triangle (½ab sin C)1 3D trigonometry1
Probability8 topics
Conditional probability2 Estimated probability2 Expected probability5 Listing combinations8 Probability of a single event25 Probability of combined events15 Probability with Venn diagrams1 Tree diagrams1
Statistics25 topics
Averages and range
Estimate the mean8 Range from a list of data8 Interpreting a frequency table1 Mean from a frequency table5 Mean from a list of data25 Median from a frequency table2 Median from a list of data14 Median from grouped data5 Modal group1 Mode from a frequency table2 Mode from a list of data11
Diagrams
Bar chart8 Box and whisker plot3 Correlation1 Cumulative frequency diagram7 Frequency polygon5 Frequency tree2 Histogram7 Pictogram1 Pie chart15 Scatter diagram3 Stem and leaf diagram1 Time series1 Two way tables2 Venn diagrams2
A Level23 topics
Arithmetic sequences1 Binomial expansion1 Differentiation15 Factor and remainder theorem2 Fibonacci sequences1 Geometric sequences4 Integration11 Logs2 Mechanics3 Mid-ordinate rule1 Partial fractions1 Point of inflection1 Quadratic sequences2 Rational functions1 Vectors2
Solving equations
Solving exponential equations1 Solving logarithmic equations1 Solving trigonometry equations1
Statistics
Advanced probability2 Binomial distribution3 Geometric distribution1 Permutations and combinations3 Poisson distribution1

Three kinds of problem

276Based on a contextA real-life situation, like a shop, a journey or a recipe, with questions that need different maths. 146Based on a shapeOne shape, like the triangles on the left, with four questions that need different ideas. 164Based on an imageA picture or diagram that sparks questions from several topics.

Most popular

Similar rectangles The rectangle and its area Rectangular expressions 12cm, 15cm and 85°

New resources on mrbartonmaths.com

I’m creating loads of new, free resources on mrbartonmaths.com to help students think hard about maths. SSDD problems will join them there one day. In the meantime, here are some to try.

Visit mrbartonmaths.com →
Open Middle ProblemsPractice and problem solving at the same time, with many routes to an answer. Minimally Different Mega PracticeSequences where each question changes one thing, so students spot what matters. Venn DiagramsFind examples that fit each region, and think hard about properties. Probing QuestionsQuestions that check whether students really understand an idea. AtomsTopics broken into small steps, taught with examples and non-examples. Interactive Maths ToolsFree tools to explore and demonstrate ideas on the board.

Supporting this site

I don’t make any money from this website. If you would like to support my work, and learn more about the ideas behind it, here are some ways.

The four ingredients of problem solvingShort on-demand CPD course. Student practiceShort on-demand CPD course. Support me on PatreonHelp keep this site and mrbartonmaths.com free for everyone.

Made an SSDD problem of your own? Share it on the site. Thanks so much for visiting. Craig