Unit 1 Lab 4 Teacher Guide

Students begin a project—building a Tic Tac Toe game and other games that are played by placing marks (X or O, or a number) on a square array of tiles. This project will develop over the course of a few units. In this lab, students get as far as creating the grid, getting it automatically to fit the screen regardless of the number of tiles, and placing marks on the grid (but not yet with the computer checking to see if the moves are legal or if a player has won). In doing this, students continue to use ideas (and new levels) of abstraction, and learn also how to use a variety of math reporters—four basic operations (+, -, ×, ÷), and mod—to create new reporter blocks, functions to perform specialized calculations for them.

Pacing:

The 2 lab pages could take about 1-2 days (40-80 minutes). Expected times to complete follow:

Prepare

Students will:

Goals for the Lab:

As a Class:

Discussion/Writing Prompts

Assignments:

Encourage students to suggest their own ideas for programming projects based on the material they have learn so far. If a project idea is too advanced for this time, offer suggestions for elements of the larger goal that could be tackled now with a smaller project.
Assessment Ideas:
- Submit (through whatever mechanism your class utilizes) a URL for a program that implements the following procedures:
  1. Draw Triangle that takes side Length as input and uses iteration to make the sprite make a point-up equilateral triangle with the specified sideLength.
  2. Row of Triangles that takes triangles and sideLength as input and uses iteration to make a row of the specified number of triangles, as shown in the image below, with the specified sideLength. This procedure must use the Draw Triangle block.
  3. Pyramid of Triangles that takes triangles and sideLength as input and uses iteration with the for block to create a pyramid with the specified number of triangles (that each have the specified sideLength) along the base, as shown in the image below. You must use the Row of Triangles block.

Tips:

Page 1: Building Tic Tac Toe and Other Board Games.
- This is the most complicated project in Unit 1, but students are given enough subtasks to make it likely that, working together, they can succeed. Working together is key. Some will figure out how to solve certain parts, and others will figure out how to solve other parts. Sharing, they will learn from each other.
- What do I do when a student asks how to solve a problem? There will almost certainly be parts of some of these projects that you don't quickly see how to do. But even when you do know how to solve the problem, the most useful answer you can give is often one of these:
  - Show me what you've already figured out.
  - What are the parts of the problem that need to be built?
  - Is there a good starting place (or a thing to do next), something really simple that will get us a bit closer?
- To avoid overloading the text, the orange box about abstraction doesn't mention that even building the board out of boxes is an abstraction-based design decision. That's not how you draw a tic-tac-toe board by hand; you draw long intersecting lines. We could have done that here, too, but wanted a draw tile block that could be modified later.
- Mathematics Note: State invariance. Drawing a row of tiles requires that students build in instructions to move the sprite to "the next" position. That's because the typical routine for drawing a square, "repeat (4) [move (100), turn (90)]" puts the sprite back in its original position—the script is state invariant. Building state invariance into scripts and blocks is a good idea, because it makes "ending where you stated" makes it easier to problematically move the sprite to the next state.
Page 2: Expressions and Operations.
- Remind students that they can run scripts by clicking on them. Reporters that stand alone (not inside another block) report their result in a speech balloon next to the block.
- Discuss the new mathematics and create scripts to review what students are learning.
- Some vocabulary (for you to use in context, not to require of students):
  - A command is a single Lego-brick-shaped block, without its inputs.
  - A reporter is a single oval-shaped block, without its inputs.
  - A predicate is a single hexagonal block, without its inputs.
  - An instruction is a command block along with its input expressions.
  - An expression is a reporter block along with its input expressions.
  - A Boolean expression is a predicate block along with its input expressions.
  - A Boolean value is or . (Not the text strings "true" and "false"; not 0 and 1.)
  So a reporter or a predicate is a function; an expression is a function applied to arguments.
- Mathematics Note: Order of Operations. There's no need to teach "order of operations." Nesting the operations does the work for you—it's like automatic parenthesization. For example: $\frac{4}{7+(3\times2)}$
  is and
  $\frac{4}{7} + (3 \times 2)$
  is
- Mathematics Note: Rounding. The round block reports the closest integer to its input. If there's a tie (like with 3.5), it rounds up, so that round (3.5) reports 4.
- Mathematics Note: Mod. The mod block returns the remainder when the first input is divided by the second.
  
  For positive whole numbers, this is the same as the notion of remainder that students learn in elementary school when they learn to divide one whole number by another. So:
  
  because when 7 is divided by 5, the remainder is 2 (and the quotient is 1).
  
  The behavior of the mod block may seem mysterious when one or both of the inputs are negative integers. For example:
  
  The sign of the output of mod agrees with the sign of its second input. But why?
  
  Let's go back to positive whole numbers for a moment. The fact that mod (7, 5) = 2 comes from $7 \div 5 = 1 \text{ remainder } 2$ , which comes from $7 = 5 \times 1 + 2$ where 1 is the quotient and 2 is the remainder. The quotient is the key to the mystery.
  
  In Snap!, you can get the quotient by dividing 7 by 5 to get 1.4 and then rounding down. This operation of rounding down is called floor, and it's built into Snap! (you can find it as a drop-down option in the sqrt block in the Operators palette). For any real number, floor takes the closest integer to the left on the number line (hence the name "floor").
  
  So, given any two integers $a$ and $b$ (or real numbers, really) you can calculate the quotient $\frac{b}{a}$ and then the floor of their quotient $\text{floor}(\frac{b}{a})$ . Let's call this quotient $q$ . Then, $b$ will equal $aq$ plus the little left over that we lost by using floor (the remainder, which we'll call $r$ ). So now, $b = aq + r$ much like $7 = 5 \times 1 + 2$ .
  
  That remainder is what Snap! and most programming languages report for mod(b, a) and this explains the signs of the outputs when one or both inputs are negative.
  
  For example: , so
  and $-7=5\times(-2)+3$ , so .
  
  Another example: , so
  and $-7=-5\times(1)+-2$ , so .