Concrete, pictorial, abstract
A widely used approach moves pupils through three stages. First they handle physical objects such as counters, cubes or fraction strips. Then they draw representations such as bar models or number lines. Only then do they work with symbols alone.
The stages are not a ladder to climb once. Older pupils meeting a new idea, such as algebraic expressions, still benefit from a concrete or visual starting point before moving to notation.
Free activities to download
Find All the Ways
Primary · Ages 7–10
Foundation · 45 min
Pupils use counters to find every way to arrange 12 in equal rows, record them as multiplication facts and explain how they know they have found them all.
Fraction Walls
Primary · Ages 8–11
Developing · 45 min
Pupils fold and cut paper strips into halves, quarters and eighths, build a fraction wall and record every equivalence they find.
Growing Patterns
Middle School · Ages 11–14
Intermediate · 60 min
Students build growing patterns with cubes, describe how they grow, write an nth term rule and justify it using the structure of the pattern.
Fair Game?
Middle School · Ages 12–14
Intermediate · 60 min
Students play a two-dice game, decide whether it is fair, list all outcomes to find theoretical probabilities and compare them with experimental results.
Modelling Decay with Dice
High School · Ages 15–18
Advanced · 75 min
Students roll 100 dice, remove sixes each round, model the decline with an exponential function and compare their model with data and theory.
Liked the free activities? Go further with a 20-week programme.
Each free activity comes from a full EduTrend Contents programme: a Family Guide or Teacher's Guide with one-page session plans for 20 weeks, plus an Assessment Toolkit with rubrics, trackers and certificates. Choose the one for your child's age or your class below. Instant PDF download after checkout.
EDT-241 · 20 WEEKS · $29
Maths Talk at Home
Family · Ages 6–11 with a grown-up
Number games, shapes, kitchen maths and puzzles.
EDT-242 · 20 WEEKS · $39
Young Mathematicians
Primary · Ages 7–11
Arrays, fraction walls, area and conjectures.
EDT-243 · 20 WEEKS · $39
Mathematical Reasoning Lab
Middle school · Ages 11–14
Proportion, algebra tiles, proofs and probability.
EDT-244 · 20 WEEKS · $45
Mathematical Modelling and Proof Studio
High school · Ages 15–18
Models, rates, inference and proof.
Photos: Vitaly Gariev, Chris Liverani / Unsplash
Mathematics
Build mathematical reasoning with five free printable activities, from finding all the arrays and fraction walls to growing patterns, fair games and exponential models. For longer learning, choose a 20-week programme for families, primary, middle or high school.
Edutech
/
/
Mathematics
