Groups, Multiples and Factors

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Focus

Choose a mathematical focus Equal groupsReception–Year 1 · pre-formal language ArraysYears 1–3 · rows, columns and equal groups Multiples gridYears 2–6 · count in, then multiples Factor pairsYears 4–6 · systematic exact arrays Common factorsYears 5–6 · sort factors into two sets and their overlap Common multiplesYears 5–6 · sort multiples within a stated range Reason and proveYear 6 · completeness and justification

Explore Challenge

Example

Target Rows Columns First number Second number

Language Reviewed vocabulary Count-in language

Finite range 1–50 1–100

Test a row count

Number of rows

Arrays recorded

Using Groups, Multiples and Factors

Choose a Focus that matches the pupils’ current curriculum. Early focuses deliberately use group, repeat, row and column language before formal factor and multiple vocabulary.

Prepare a clean example

Focus, Explore and Challenge apply immediately. In the common-factors and common-multiples focuses, Explore shows a completed sort to discuss; Challenge puts every card in the tray for the pupil to sort and check. Open Example only to change the numbers or settings, then select Use this example to make those changes the Reset state.

Pupil actions

Array challenges test possible row counts and draw only exact registered arrays. On a multiples grid, choose a coloured Mark button, then tap numbers to shade them; keyboard users can focus a number and press Enter or Space. Use the matching Show all button to complete either pattern, or Show both to complete the whole grid. The finite positive domain begins at 1 and excludes zero.

Feedback and reset actions

In Equal groups Challenge, enter how many objects belong in each group. In Arrays, Factor pairs and Reason and prove, Challenge starts without an answer and pupils build exact arrays; Explore shows the completed example to inspect. Multiples grid begins unshaded in both activities so pupils can mark the two patterns themselves.

Hint gives one strategy step. Check diagnoses missing or extra work. Reveal completes and explains the representation. Clear preserves the teacher example and Reset restores its first state. New keeps the current mode: it gives another completed example in Explore or an unseen unsolved task in Challenge.

Common-set sorting

Common factors and common multiples use the shared two-set Venn. Drag a card, or tap it and choose left only, both, right only or outside. Keyboard users can select a card with Enter or Space, move through the named regions with the arrow keys, then place it with Enter or Space. Common-multiple tasks always use the stated finite range.

Print

Print produces the current display on one side of A4 landscape. Print Worksheet opens the protected teacher resource builder. Choose a lesson component or a complete lesson pack with teacher guidance, teaching models, guided practice, independent practice, reasoning and assessment, plus matching answers.