Each worksheet prints cleanly on A4 or Letter. Answer keys are on a separate page.

The Lumenary · K–2

Doing and undoing

Name: ______________________

Date: ______________________

You will learn to

Describe what an action does to an object, such as "turn the arrow a quarter turn"
Find the action that undoes a given action
Notice actions that cannot be undone, such as cracking an egg or wiping a board, and explain why
See that an action is not always undone by doing it again
Recognise "doing nothing" as an action that leaves everything as it was

1.
Mateo opens the door. Which action undoes that?
- A.Close the door
- B.Open the door again
- C.Open the window
2.
Rosa takes 4 steps forward. Which action undoes it?
- A.4 steps back
- B.4 steps forward
- C.3 steps back
3.
Which of these actions can be undone? Choose all of them.
- A.Put on a hat
- B.Switch the light on
- C.Put one more block on a tower
- D.Crack an egg
- E.Mix blue paint and yellow paint
4.
Which action is undone by doing exactly the same action again?
- A.Flip a card over
- B.Walk 2 steps forward
- C.Turn an arrow a quarter turn
- D.Add a block to a tower
5.
An arrow points up. You turn it a quarter turn, so it points right. How many more quarter turns, the same way, bring it back to pointing up?
6.
Gideon's game: true or false? "Doing nothing, and then putting on a hat, has the same effect as just putting on a hat."
- A.True
- B.False
7.
Gideon's game: true or false? "Every action can be undone."
- A.True
- B.False
8.
Why can't wiping the whiteboard be undone?
- A.A board with a cat and a board with a dog both become the same blank board, so nobody can tell which picture to bring back
- B.Because drawing a picture takes too long
- C.Because the pen has run out
9.
Margaret's tiny world: a lamp is on or off. She found exactly 4 actions: do nothing, press the switch (on becomes off, off becomes on), always make it on, and always make it off. How many of these 4 actions can be undone?

Answer key — Doing and undoing

1.
Before, the door was closed. After Mateo opens it, closing the door puts it back exactly as it was. So "close the door" undoes "open the door".
2.
To undo 4 steps forward, Rosa takes 4 steps back. Doing 4 steps forward again would take her 8 steps away, and 3 steps back would leave her 1 step short.
3.
Put on a hat (take it off), switch the light on (switch it off) and put one more block on a tower (take it off) can all be undone. Cracking an egg and mixing paints cannot.
4.
Flipping a card: face down → face up → face down again. For the others, doing the action again takes you further away, so the undo is a different action.
5.
From right: one quarter turn makes it point down, two make it point left, three make it point up. So 3 more quarter turns undo the first one. (A quarter turn back would also undo it.)
6.
True. Doing nothing leaves everything exactly as it was, so afterwards putting on the hat gives the same result as putting on the hat straight away. Doing nothing is an action that changes nothing.
7.
False. Cracking an egg or wiping a whiteboard cannot be undone. A single example like that — a counterexample — is enough to show the statement is false.
8.
The cat board and the dog board both turn into the same blank board. Looking at a blank board, there is no way to know whether to bring back the cat or the dog. An action that turns two different things into the same thing can never be undone.
9.
2 of them: do nothing (undone by doing nothing) and press the switch (undone by pressing it again). Always make it on turns both an on lamp and an off lamp into an on lamp, so nobody can tell what it was before — it cannot be undone, and the same goes for always make it off. Margaret's program finds the same answer: in a world of 2 things, 2 of the 4 actions can be undone.