Picture Matrices

Free puzzles to print

Each set: a Learn sheet with a worked example, 10 puzzles from easiest to hardest, and the answers.

• Level 1

  Ages 4–6 · Pre-K–K

  

  2 × 2 grids of objects with one change, then two features (one across, one down). Then 3 × 3 grids where something stays the same along a row, or steps up along it in number or size.

  On the sheet: “Which one fills the empty box? Check it.”

  Print Level 1 (Letter)Other paper size: A4

• Level 2

  Ages 6–8 · Grades 1–2

  

  3 × 3 grids of shapes. First one thing stays the same while another steps up. Then each row holds the same three shapes, fills or counts, on one feature and then two, then three rules at once.

  On the sheet: “Which one fills the empty box? Check it.”

  Print Level 2 (Letter)Other paper size: A4

• Level 3

  Ages 8–10 · Grades 3–4

  

  Six options, count rules that start higher each row, sums (third = first + second), and rows and columns with different rules.

  On the sheet: “Which one fills the empty box? Check it.”

  Print Level 3 (Letter)Other paper size: A4

The thinking it works on

• Pattern and rule finding

  Looks across a row and down a column for what stays the same and what changes.

  Rittle-Johnson and colleagues (2013) found that 4-year-olds could copy and continue repeating patterns, and some could make the same kind of pattern with new materials. Source

• Thinking about several features at once

  Holds shape, fill and count in mind when several rules run together.

  Stevenson and colleagues (2014) gave grid puzzles to 1,422 children aged 4½ to 12½. Rules about kind, color, number and size were easier than rules about direction and position. Source

• Switching attention between features

  Lets go of the first feature found and looks at the next.

  Zelazo (2006) found that most 3-year-olds keep sorting by the old feature when asked to switch (say, from color to shape), while most 5-year-olds can switch. Source

• Looking at the whole grid before the answers

  Says the rule before choosing, instead of picking by a glance.

  Starr, Vendetti and Bunge (2018) used eye tracking with 6-year-olds. Those who looked at the first pair of a picture analogy before the answer choices were the more successful reasoners. Source

• Resisting the look-alike option

  Checks the chosen picture against the whole row and the whole column.

  Thibaut, French and Vezneva (2010) found that how well 6- and 8-year-olds did on picture analogies depended heavily on what the wrong choices looked like. Source

• Saying the rule in words

  Puts the rule into words so it can be tested.

• Counting and adding inside a pattern

  Counts and adds inside the pattern when the rule is a sum.

  Gathercole and colleagues (2004) tested children aged 4 to 15 and found that every part of working memory kept growing through the school years. Source

Where is this thinking used?

• Schedules and charts: Rows and columns each mean something, and every row follows a rule.
• Sorting and labeling: Things are grouped by shape, color and size at the same time.
• Science: Several things vary at once and one rule must explain all of them.