data:image/png;base64,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4.4

NOTE: The original version of GOSSIP 2 has only six inputs, not seven, because its "Oh, but... " ends with a space character. Students will notice that their first attempt doesn't have a space between the gossip response phrase and the WHO 2 subject of the sentence. They could fix that either by adding an input, as done here, or by putting spaces at the end of all the phrases in GOSSIP RESPONSE. It doesn't matter which solution they pick; what matters is that they notice the bug and figure out some way to fix it. Don't let them just ignore it. The solution used here, adding an input, is a little painful because the new input slot appears at the /end/ of the JOIN block. The easiest way to handle this, but still annoying, is to shift inputs over starting at the right end, moving WHO into the new empty slot, then typing a space into the slot that used to have WHO, and so on. It'll be important that students notice the white halo surrounding the slot into which Snap! thinks it should drop the block they're moving.

5.8

4.2

5.6

As noted in the problem statement, either or both calls to WHO can be replaced.

5.10 (ITIT)

The simplest solution, perfectly acceptable, is just to replace the call to WHO in GOSSIP 2 with MORE COMPLICATED WHO, because that takes advantage of code already written. If the student wants to replace WHO 2 instead, they need a MORE COMPLICATED WHO 2 that duplicated MORE COMPLICATED WHO but calling WHO 2 instead of WHO. That's a fine solution too.

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3.1 edits these blocks' definitions.3.3 Hannah listened to Hannah. (The sentences don't have to make sense!) Señora ran away from my cat. Not possible: Jake helped. (The structure of GOSSIP always puts an object in the sentence.) Señora and Ms. C helped. (Not only no object, but a subject that the code doesn't know how to make.)3.4 When I added the Sprite(2) costume I was surprised that it appeared upside down! The easiest way to fix this is to click the middle button of the three small round buttons up above the Sprite(2) scripting area, to the left of the small picture of the sprite. This constrains the costume not to turn, but does allow it to flip left-right depending on the direction the sprite is facing. NOTE: As of right now (Snap! 5.4), there are problems with editing vector costumes--the ones with "svg" in the corner of their pictures. Don't let students get hung up on this not-really-important issue; just have them pick a different costume. Maybe by the time you read this, the problem will be solved.5.4(a) A quarter of the time. The point for students to understand is that it doesn't matter which number between 1 and 4 appears in the = block. All four possibilities are equally likely, so 3 appears one out of four tries. (b) Change the 4 to 3. If we pick a random number out of three possibilities, we'll pick 3 a third of the time instead of a quarter of the time. Note, though, that changing it even further, to 2, will make the more complicated choice /never/ happen, because 3 (the 3 after the = sign) isn't in the range [1,2]. This is why, even though part (a) says it doesn't matter which number we look for, it's a better idea to use 1 after the = to allow for possible future changes. But don't get into this unless a student asks; it's a distraction from the purpose of this lab. 5.5(a) 2 * RANDOM(1, 5) Try to assess whether this problem needs discussion time. Students won't find it obvious, but with luck they can teach each other. That would teach a lesson about the power of collaborative learning! If you do have to teach about this, please try not to teach cookbook recipes. If students learn "for even numbers you say 2 * something" that won't help when they need numbers which give a remainder of 1 when divided by 7, or whatever. And this solution isn't a law of nature. You could imagine a random number generator that allowed PICK RANDOM 2 STEP 2 TO 10. So the starting point in analyzing the problem is to realize that /this/ random number generator was designed to provide consecutive integers (supposing it gets integer inputs). Then, think "How many possible answers should there be? Five. Okay, what function can we apply to numbers between 1 and 5 to get the result we want?" (b) RANDOM(1,6) + RANDOM(1.6) This really is a math problem, not a CS problem, but things like this may appear on the exam, so here it is in the curriculum. The mathematical part is understanding that this is not the same as RANDOM(2,12) because with two dice, not all results are equally likely. There's only one way to get 2 (one on both dice) but lots of ways to get 6 (one and five, two and four, etc.). The CS part of the problem, and there really is a deep idea here, is to understand that RANDOM is not a function -- that is, calling it repeatedly with the same inputs will not give the same answer each time. That's why 2*RANDOM(1,6) won't work, even though it's the first thing we all think of. That expression only gives six possible answers, not the eleven actual answers (2 to 12). Contrast this with, say, 2*max(1,6) or 2*average(1,6) or 2*(1 mod 6). Those really /are/ the same as max(1,6)+max(1,6) and so on. The rule of thumb that students should take away from this problem is that their code should reflect the actual situation they're modeling as closely as possible. If you roll two dice, you get two independent random numbers.TIF A. The condition tested in the IF has to be ((RANDOM FROM 1 TO 4) < 4). Here it does matter what number follows the < sign. Alternatively, to avoid changing the numbers, make it IF (NOT ((RANDOM FROM 1 TO 4) = 3)). B. You get really long sentences, because most of the time the "complicated" branch is chosen. Students may find this surprising. We are trying to lay a foundation so that the official introduction to recursion isn't quite so unexpected. "Explain why" questions are always hard for students, but look for "it calls itself" somewhere in what they say.