Multiplication as repeated addition

For 5–6 year olds (roughly UK Y1, US K–Grade 1), introduce multiplication as repeated addition of EQUAL groups ('a groups of b'): 3 groups of 4 = 4+4+4. Build on the skip counting children are learning at this age (counting in 2s, 5s and 10s, e.g. 2, 4, 6 = one, two, three twos); when using groups of 4, introduce counting in fours alongside the groups (4, 8, 12 = one, two, three fours) rather than assuming it is already known. Keep the group structure visible from real objects → pictures/arrays → the repeated-addition sentence → later the × symbol. Stress that the groups must be equal (the defining feature children most often drop) and keep the two numbers distinct (how many groups vs how many in each). Repeated addition is the correct entry model at this age, but it is a model, not the whole meaning of multiplication.

• Adding groups that are not equal and still calling it multiplication — losing the 'equal groups' defining property.
• Reading 3 × 4 as 3 + 4 (confusing multiplication with a single addition).
• Counting the number of groups when asked for the total, or vice versa — muddling the two roles.
• Believing multiplication is ONLY repeated addition (a seed of later trouble with fractions/decimals/scaling) — at this age fine, but teachers should model equal-groups language, not 'times means add lots'.
• Miscounting the total by losing track of which groups have been counted (no systematic skip count).

• Equal groups of concrete objects ('3 groups of 4')
• Number line with equal jumps (linking to skip counting)
• Repeated-addition number sentence (4 + 4 + 4)
• Arrays (rows of equal size) as the bridge to the × symbol

• Introduce × as 'groups of' with equal groups the child physically makes, and always stress the groups must be EQUAL — the defining feature children most often drop.
• Bridge explicitly from the skip counting already mastered: counting 4, 8, 12 IS one four, two fours, three fours — so multiplication is met as something familiar (equal jumps) not brand new.
• Move along the concrete–pictorial–abstract path: real objects in groups → pictures/arrays → the repeated-addition sentence 4+4+4 → later the × symbol; keep the group structure visible at each step.
• Use the number line with equal jumps alongside grouped objects so repeated addition and skip counting are seen as the same thing in two representations.
• Distinguish the two numbers in 'a groups of b' (number of groups vs size of group) with consistent language, so children don't muddle 3 groups of 4 with 4 groups of 3 even before commutativity is formalised.