Math // Multiplication & Division

Arrays for multiplication (age 7+)

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and 5 columns; write an equation to express the total as a sum of equal addends

Ages
7 to 8
Type
Concept
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

If the learner sees 4 rows of 5 stickers on a sheet, can they use repeated addition — '5 + 5 + 5 + 5' — to find the total, and write it as an equation?

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.
  • Count objects in a 3×4 array and write 4 + 4 + 4 = 12
  • Explain that each row has the same number of objects so the total can be found by repeated addition
  • Draw a rectangular array to model a given repeated-addition equation

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
  • Multiplication as repeated additionRequired

    Multiplication & Division // Ages 5 to 6

    Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition

  • Arrays for multiplicationRequired

    Multiplication & Division // Ages 5 to 6

    Rectangular arrays with repeated addition extends array representation from Y2

You are here

Arrays for multiplication (age 7+)

Ages 7 to 8 // Concept

Leads to

2 topics
  • Rows & Columns in RectanglesRequired

    Multiplication & Division // Ages 7 to 8

    Partitioning rectangles into unit squares builds on understanding rectangular arrays

  • What Multiplication MeansRequired

    Multiplication & Division // Ages 8 to 9

    Extends array-based repeated addition to formal multiplication interpretation

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 7–8 (UK Y2–Y3, US Grade 2): use addition to find the total of objects in a rectangular array (up to 5×5) and write an equation expressing the total as a sum of EQUAL addends, then bridge to the multiplication fact. The core insight is that each row of the array contributes one equal addend, so reading an array row by row turns it into repeated addition (4+4+4=12) and then into 3×4. Equality of the rows is what makes it a multiplication situation, so a ragged (unequal-row) arrangement serves as the key non-example.

Common misconceptions

  • Adding UNEQUAL groups and still writing it as a single multiplication (missing the equal-addends requirement).
  • Counting every object individually rather than adding equal rows.
  • Confusing the number of rows with the number in each row when writing the equation.
  • Not connecting the repeated-addition equation to the multiplication (seeing them as separate).
  • Miscounting by losing track of which rows have been added (no systematic row-by-row approach).

Useful representations

  • Rectangular array read row-by-row (each row = one equal addend)
  • Repeated-addition equation (4 + 4 + 4 = 12)
  • Paired addition/multiplication (4+4+4 ↔ 3×4)
  • Ragged (unequal-row) non-example for contrast

Teaching practices

  • Read the array row by row so each row becomes one equal addend, then write the repeated-addition equation — making 'sum of equal addends' concrete before the × symbol.
  • Stress that the addends must be EQUAL: contrast an array (equal rows) with a ragged arrangement (unequal rows) that is NOT a multiplication situation.
  • Bridge to the × symbol by pairing the equal-addend equation with the multiplication (4+4+4 alongside 3×4), so children see multiplication as the shorthand.
  • Read the same array by columns too, foreshadowing commutativity (three 4s or four 3s).
  • Keep arrays within 5×5 and physically buildable, so the structure (rows/columns) is clear and countable.

Activities to try

  1. 1

    Sum the rows: build the equal-addend equation from an array

    Why it works: Each equal row of an array is one equal addend, so adding the rows gives the total; the multiplication fact is just the shorthand for adding equal rows, and this only works when the rows are equal.

    1. Look at a 3×4 array (3 rows, 4 dots in each row) and point to one row to establish that it holds 4 dots.
    2. Add the array one row at a time, saying and writing the running total: 4, then 4+4, then 4+4+4 = 12 — one addend per row.
    3. After writing 4+4+4=12, write the matching multiplication 3×4=12 and say which number tells how many rows and which tells how many are in each row.
    4. Read the same array by columns instead and write it as 3+3+3+3 (four 3s), noticing you get 12 again.
    5. Now try a ragged arrangement where one row has 4 and another has 5; attempt to write a single equal-addend equation and explain why it will not form.
  2. 2

    Draw an array for a given equation

    Why it works: Children can move in both directions — from array to equation and from equation to array — which shows they understand the equal-groups structure rather than just reading one off the other.

    1. Given the equation 5+5+5+5, draw a rectangular array that matches it (four rows of five, or equivalently five columns of four).
    2. Say aloud which part of the equation is the number of rows and which is the amount in each row.
    3. Write the multiplication fact for your array (4×5 or 5×4) and check the total matches 20.
    4. Explain why your drawing shows equal rows and how that connects back to the repeated addition.
  3. 3

    Match and complete: array ↔ equal-addend equation ↔ multiplication

    Why it works: Recognising and completing the correct equal-addend equation (and rejecting an unequal-addend distractor) confirms the array-to-repeated-addition bridge and the equal-addends requirement.

    1. For a shown array, fill in the blanks of the equal-addend equation (__ + __ + __ = __).
    2. Write the matching multiplication fact for the same array.
    3. From a set of candidate equations, choose the one that matches a given equal-rows array; include a distractor that uses unequal addends (e.g., 3+4+5), which would correspond to a ragged arrangement and does not match.
    4. Explain why the unequal-addend distractor cannot represent the equal-rows array as a single equal-addend equation.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
2.OA.4

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