True, False or Can't Tell

Free puzzles to print

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

• Level 3

  Ages 8–10 · Grades 3–4

  

  One "all" rule and a fact about one fish or robot. Then can't-tell traps, where the rule is run backwards. Then "some" and "none" cards; the hardest chain two rule cards.

  On the sheet: “Read the rule and the fact. Check one box.”

  Print Level 3 (Letter)Other paper size: A4

• Level 4

  Ages 10–12 · Grades 5–6

  

  Two rules in words; then "if… then" cards, including when the "then" part is false. Next, two rules and a fact, with three sentences to judge (one True, one False, one Can't tell). The hardest ask which of three extra facts would make a Can't-tell sentence True.

  On the sheet: “Read the rule and the fact. Check one box.”

  Print Level 4 (Letter)Other paper size: A4

The thinking it works on

• Reasoning from a rule and a fact

  Uses a rule and a fact to reach a sure answer.

  Datsogianni and colleagues (2020) gave if-then problems to 102 children in grades 2, 4 and 6: even second graders drew some correct conclusions, and accuracy rose by grade. Source

• Recognizing when you can't tell

  Says Can't tell when the card doesn't settle it.

  Byrnes and Overton (1986) studied first, third and fifth graders. All handled sure cases alike, but seeing when a concrete situation was still undecided got better with grade. Only fifth graders showed it with if-then sentences. Source

• Avoiding the backwards trap

  Knows a rule doesn't run backwards.

  Janveau-Brennan and Markovits (1999) studied 512 children in grades 1 to 6. With age there was a steady rise in answering "can't tell" to the two forms that don't follow, such as reasoning backwards from an effect to its cause. Source

• Understanding all, some and none

  Keeps the quantity words apart.

  Noveck (2001) found that 8- and 10-year-olds usually read "some" as compatible with "all", as logic does, while adults were split. Source

• Chaining rules

  Joins two rule cards to reach a new fact.

  Andrews and Halford (2002) studied children aged 3 to 8. Linked problems with three parts, such as ordering from two clues, were solved later than two-part ones, around age 5. Source

Where is this thinking used?

• Reading the news: Asking whether a claim really follows from the facts given.
• Signs and rules: A rule for one area says nothing about the next.
• Science: Saying "we can't tell yet" until a test settles it.
• Computer code: If-then rules act only when their condition is met.