Math // Multiplication & Division

Arrays for multiplication

Use arrays to represent multiplication and division situations

Ages
5 to 6
Type
Representation
Builds on
2 topics
Leads to
3 topics
Standards
1 code

Quick check

If the learner sees eggs arranged in 3 rows of 4 in a box, can they use that grid layout to work out both '3 × 4 = 12' and '12 ÷ 3 = 4'?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Build an array of 3 rows of 4 objects to show 3 × 4
  • Read an array and state the total
  • Use an array to solve a simple division problem (e.g. 12 objects in rows of 4 → 3 rows)

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics

You are here

Arrays for multiplication

Ages 5 to 6 // Representation

Leads to

3 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For ages 5–6 (roughly UK Year 1 into early Year 2; US Kindergarten–Grade 1, noting that US standards formally introduce arrays in Grade 2, ages 7–8), use rectangular arrays (equal rows and columns) as a central model for multiplication and division. Learners build arrays, read them two ways to see commutativity, read them as repeated addition, and cover part to reveal division — so one picture yields a whole fact family and seeds the later area model.

Common misconceptions

  • Confusing rows with columns and so mis-describing the array (though the total is the same, the language matters for later).
  • Counting every object one-by-one instead of using the row/column structure (missing the point of the array).
  • Not seeing that a rotated array has the same total — treating 3×4 and 4×3 as needing separate counts.
  • Building arrays with unequal rows (ragged rectangles) — breaking the equal-groups structure.
  • Not recognising the array as a division picture as well as a multiplication one.

Useful representations

  • The rectangular array of counters/dots (rows × columns)
  • The array rotated 90° to show commutativity
  • Fact-family link: one array → two × facts + two ÷ facts
  • The array as precursor to the area model / grid method for written multiplication

Teaching practices

  • Build arrays physically in equal rows and columns and describe them precisely as 'rows of' and 'columns of' before recording — the regular structure is what makes the total computable without counting every object.
  • Rotate the array a quarter turn to reveal commutativity concretely: 3 rows of 4 becomes 4 rows of 3, same total — the array makes 3×4=4×3 obvious rather than asserted.
  • Read the SAME array as repeated addition (row by row) and as multiplication, so the array ties the two together.
  • Use the array to introduce division as the inverse: cover the total and ask 'if 12 objects make 3 equal rows, how many in each row?' — one picture yields the whole fact family.
  • Treat the array as the seed of the area model — keep rows/columns aligned in a rectangle so the later transition to area and the grid/expanded written methods is continuous.

Activities to try

  1. 1

    Build and read an array

    Why it works: An array has a regular row/column structure, so you can find the total by using the rows rather than counting every object one by one.

    1. Lay out counters (or draw dots) in equal rows and columns to make an array, e.g. 3 rows of 4.
    2. Say aloud exactly what you made: '3 rows of 4' — then also read it as columns: '4 columns of 3'.
    3. Find the total WITHOUT counting every object: skip-count each row, '4, 8, 12'.
    4. Write the multiplication the array shows: 3 × 4 = 12.
    5. Try building another array to order as an extension, e.g. 'Show me 2 × 5 as an array', and state its total.
  2. 2

    Rotate the array to see commutativity

    Why it works: Rotating an array turns 3 rows of 4 into 4 rows of 3 while the total stays the same — so 3 × 4 = 4 × 3 is something you can see, not just a rule to remember.

    1. Build 3 rows of 4 and record the total (12).
    2. Turn the whole array a quarter turn so it becomes 4 rows of 3.
    3. Count or check the total again and notice it is still 12.
    4. Write both multiplications from the one array: 3 × 4 = 12 and 4 × 3 = 12.
  3. 3

    Find the division in the same array

    Why it works: One array is a division picture as well as a multiplication picture: the rows and columns are the two factors, and reading the total the other way reveals the inverse fact.

    1. Start from a total, e.g. 12 loose counters.
    2. Arrange them into an array with rows of 4; count how many rows you made.
    3. State the division the array shows: 12 ÷ 4 = 3 (12 grouped into rows of 4 makes 3 rows).
    4. Cover the array, tell a partner the total (12) and the number of rows (3), and ask how many are in each row (12 ÷ 3 = 4); then uncover to check.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y1/MD/1

Math // Multiplication & Division

More in Multiplication & Division

All 57 topics