Tower View

Free puzzles to print

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

• Level 2

  Ages 6–8 · Grades 1–2

  

  First 4 × 4 grids with every edge number and one or two towers filled in. Then a 4 × 4 with no towers and a few edge numbers missing. Then 5 × 5 with a few towers filled in; the hardest also hide a few edge numbers.

  On the sheet: “Each row and column has buildings 1, 2, 3, 4. An edge number says how many you can see.”

  On the sheet: “Each row and column has buildings 1, 2, 3, 4, 5. An edge number says how many you can see.”

  Print Level 2 (Letter)Other paper size: A4

• Level 3

  Ages 8–10 · Grades 3–4

  

  5 × 5 with no towers given and fewer edge numbers; children list the orders that fit a row.

  On the sheet: “Each row and column has buildings 1 to 5. An edge number says how many you can see.”

  Print Level 3 (Letter)Other paper size: A4

• Level 4

  Ages 10–12 · Grades 5–6

  

  6 × 6, from nearly all edge numbers down to only 7 to 9.

  On the sheet: “Each row and column has buildings 1 to 6. An edge number says how many you can see.”

  Print Level 4 (Letter)Other paper size: A4

The thinking it works on

• Picturing the view from an edge

  Stands at an edge number in the mind and counts only the towers that show.

  Frick, Möhring and Newcombe (2014) asked children what a scene looks like from someone else's spot. The 4-year-olds mostly guessed; from about 6 the skill grows, with big differences between children still at 8. Source

• Turning a clue into a sure fact

  Turns each edge number into something certain, like 'the tallest is first'.

  Barrouillet and Lecas (1999) studied third, sixth and ninth graders reading 'if… then' rules. Older students took more possible cases into account, in line with their working memory. Source

• Comparing and ordering numbers

  Keeps asking which tower is taller and what order fits a clue.

  Girelli, Lucangeli and Butterworth (2000) found that older schoolchildren, unlike first graders, could not help noticing which digit was bigger even when asked only which was printed larger. Source

• Picturing a skyline from numbers

  Turns a row of digits into a skyline and back again.

• Listing the orders that fit

  Writes out the few orders that fit a row's clues and crosses out what none allow.

  English (1991) found that some children as young as 7 found every combination by holding one item fixed while changing each of the others. Source

• Keeping track of what each row still needs

  Keeps a note of the heights each row and column still needs.

  Luciana and colleagues (2005) found that holding and rearranging several places in mind kept developing until 13 to 15, in a study of 9- to 20-year-olds. Source

Where is this thinking used?

• Displays: Arranging a class photo, a shop window or a bookshelf so everything can be seen.
• Floor plans and maps: Picturing the view from a spot on the plan.
• Engineering drawings: A whole part is rebuilt from a few side views.
• Science: A shadow or a cross-section tells you about the whole object.