Picturing Mathematics starters

The starters are free of cost and intended to be displayed for GCSE students to work on at the start of the lesson. Included within the answer files are teachers' notes which indicate which mathematical topics the starter connects to, and additional questions which could be asked.

Please use the links below to find a suitable starter document:

Mathematical Reasoning


All the starters need some mathematical reasoning. The ones in this section emphasise proof and associated reasoning.

ProvingPythagoras question
ProvingPythagoras answer

Cake question
Cake answer



Factors, multiples, primes

Powers, roots, standard form

Fractions, decimals, percentages

Proportional reasoning

Penny Question
Penny Answer

VAT Question
VAT Answer

Working with a calculator

Non-calculator methods

Rounding and estimating



Graphs - Straight line graphs

StraightLine Question
StraightLine Answer

Graphs - Quadratic graphs

PointsOnGraph Question
PointsOnGraph Answer

Graphs Question
Graphs Answer

Graphs - General graphs

Bacteria Question
Bacteria Answer

Graphs - Transforming graphs

Graphs Question
Graphs Answer

Equations - Linear equations

Scales Question
Scales Answer

Equations - Quadratic equations


Equations - Simultaneous equations

FourPortions Question
FourPortions Answer

Algebraic expressions and formulae - Factorising, multiplying out and simplifying

SquareDiff Question
SquareDiff Answer

Algebraic expressions and formulae - Forumulae

Mosaic Tiling Question
Mosiac Tiling Answer



Geometry and Measures


Scale drawing

BigBen Question
BigBen Answer


BigBen Question
BigBen Answer

Speed and other compound measures


Area and volume

HowManyCards Question
HowManyCards Answer

Cake Question
Cake Answer

Circumference and area of a circle

BigBen Question
BigBen Answer

Trigonometry and Pythagoras's theorem

ProvingPythagoras Question
ProvingPythagoras Answer

Symmetry, congruence, similarity

ScatterRectangle Question
ScatterRectangle Answer




StraightLine Question
StraightLine Answer

Properties of shapes - Angles in shapes

Triangles Question
Triangles Answer

Properties of shaped - 3D shapes

BuildIt Question
BuildIt Answer

Statistics and Probability



ScratchCard Question
ScratchCard Answer

Statistical diagrams

Gas Question
Gas Answer

Statistical measures

Gas Question
Gas Answer

Scatter diagrams

ScatterRectangle Question
ScatterRectangle Answer

Statistical problem solving

Gas Question
Gas Answer

If you have comments, suggestions or questions, contact Stella Dudzic.