How can we tell whether an algorithm is understood or memorised?
Ask for an estimate, explanation of each part and another method or inverse check. If the child can do this and apply it in a problem, the algorithm is connected to understanding.
Practical takeaways
- Partitioning explains long multiplication.
- Check division using multiplication and the remainder.
- Understand equivalent fractions through models before rules.
Multiplication by partitioning
Represent 2 406 × 7 as 2 000 × 7, 400 × 7 and 6 × 7, then connect the sum to the written algorithm.
Division and estimation
Estimate the quotient with a nearby multiple, then check: quotient × divisor + remainder = dividend.
Multiples and factors
Use organised tables or rows to distinguish multiples and factors and connect them to multiplication and division.
Equivalent fractions and fractions of quantities
Fold paper into halves then quarters to see 1/2 = 2/4. For 3/8 of a quantity, divide it into 8 equal parts and take 3.
Frequently asked questions
Should we memorise fraction rules straight away?
Start with models and a number line, then derive the rule from understood examples.
How can we check division?
Multiply quotient by divisor and add the remainder; the result must equal the dividend.
What is the difference between a factor and a multiple?
A factor divides a number without a remainder; a multiple results from multiplying by a whole number.