Rows & Columns in Rectangles

PROCEDURAL

Mathematics›Multiplication & Division|Ages 7—8|ID: mt_UTnDKQkVX5

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them

Mastery Evidence

Divide a rectangle into equal rows and columns of unit squares
Count the total number of squares using repeated addition or skip counting
Relate the rows-and-columns structure to a rectangular array

Assessment Prompt

“Can [child] draw lines to divide a rectangle into a neat grid of equal squares, then count all the squares to find the total?”

Curriculum Standards1 alignment

2.G.2Common Core State Standards for Mathematics

Partition a rectangle

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Geometry

Prerequisites1

Arrays for multiplication (age 7+)
hardAges 7—8

Show full prerequisite tree

Arrays for multiplication (age 7+) hard
Partitioning rectangles into unit squares builds on understanding rectangular arrays
- Arrays for multiplication hard
  Rectangular arrays with repeated addition extends array representation from Y2
  - Division as equal sharing hard
    Using arrays for division requires understanding division as grouping
    - Subtraction as taking away or separating hard
      Division as equal sharing/grouping requires understanding subtraction as taking away/separating
      - How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
  - Multiplication as repeated addition hard
    Using arrays requires understanding what multiplication means
    - Counting in 2s soft
      Skip counting supports understanding equal groups (2s, 5s, 10s)
      - Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        One-to-one counting hard
        One-to-one correspondence requires knowing the number name sequence
    - Addition as combining or putting together two hard
      Multiplication as repeated addition requires understanding addition as combining groups
      - How Many in Total? hard
        Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Multiplication as repeated addition hard
  Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
  - Counting in 2s soft
    Skip counting supports understanding equal groups (2s, 5s, 10s)
    - Rote counting to 100 hard
      Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
      - One-to-one counting hard
        One-to-one correspondence requires knowing the number name sequence
  - Addition as combining or putting together two hard
    Multiplication as repeated addition requires understanding addition as combining groups
    - How Many in Total? hard
      Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
      - One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

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