Translations (Day 1 of 2)

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SWBAT translate figures on the coordinate graph

Big Idea

Adding  fixed numbers to each of the coordinates of a  figure has the effect of sliding or translating the  figure.

Launch, Part 1

15 minutes

Once students settle down in class, I project the image resource Battleship Game. I ask the class if they've ever played this game. Some will say they have, others that they've never even heard of it. I tell the class the the version they are seeing is the version I had when I was a kid. In toy stores today, they have different versions of the game, but they are played pretty much in the same way. Each player has to sink all his/her opponent's ships by guessing the coordinates of where the opponent's ships may lie. There's no time to go further into the details of the game, but we will play a short version of it as a class, which pretty much exemplifies how it is played.

I project the resource Blank Ocean Plane and say, "I have 3 ships that I've previously placed in vertical and/or horizontal positions in this section of ocean." It takes two torpedoes to sink one of my ships, 3 torpedoes to sink the my second ship, and 4 torpedoes to sink my third ship." I tell the class that they will take shots at my ships by calling a pair of coordinates.

There is a lot of guesswork in the early stages of the game, but it eventually becomes more strategic. I like to give an example for those who have never played. Take  (A-4): I ask a student to come to the board and point out where the A-4 box is on the ocean plane. Students pick this up quite easily but I make sure everyone understands and start  pointing to any box and calling on students to give me the coordinates until I sense that students have it.  

I inform students that the map of where my ships are positioned is in my posession (see Map of Ships). I keep a paper copy at hand while students play.  Some students who aren't 100% sure of what's going on at this point will quickly "get it" once the game begins. 

I call on different students to take guesses (shots) at my ships. I ask each student I call on, to come up to the board and write a 0 in the box he called if it's a  MISS and an X, if I say I was a HIT.  We must try and make this part speedy, especially when there are too many misses on part of the students.  I continue playing until my ships have all been sunk. Then I show students the Map of Ships, so that all can verify that my ships were all sunk. 

Launch, Part 2

15 minutes

Once all my ships are sunk, I then pose the following situation for a second game: 

Let's say that you were behind me while I was playing against an opponent. Pretend you are a cheat. You have previously agreed to hand signal my opponent, so that he knows where to torpedo my ships.

Assume that from Game 1 to Game 2, I keep my ships heading in the same direction, in other words positioned in the same orientation. However, I slide them to other places on the "ocean" for the next game.

Your signals to my opponent start from the original positions of each ship. Each of you have a map of the first game. You also have agreed with your "acomplice" to sink the ships in order of ascending size and from front to back. This means the small ship will be sunk first and so on.

Now, I project Map of Ships Game 2 on the board. The thin outlined ships are where my previous ships were located in game 1.  I ask, "What hand signal would you use to hand signal my opponent (your accomplice) to start sinking all of my ships?" 

Samples of student responses:

  • I use my fingers for the numbers and my thumb for direction;left, right, up, or down
  • I use my fingers for numbers and move my head slightly to indicate direction
  • I have previously labeled tags which I raise for my accomplice to see

After allowing a few students to volunteer ideas, I ask students to write down how they would signal my opponent to hit my ships.

I think it's important to tell students from the start to begin with the horizontal shift first. This is because students will be sliding figures in the Cartesian plane. I ask students if they have to signal my opponent for each hit. The expected answer is that once my opponent hits the front of a ship, he/she should know where to send the rest of the torpedoes in order to sink it. So they would need to only signal 3 times.

Now, each pair of students in the class must observe game 2 on the board and write down the 3 instructions that they will give my opponent, behind my back. Once students are done, I ask different volunteers to share their answers with the entire class. After the three translations are given correctly, I would "milk" the task a bit by asking questions like: 

Compare the corresponding ship positions in Game 1 and Game 2.  What changed? Shape? Size? Orientation? 

New Info / Application

15 minutes

Once the game discussion is over I give students the vocabulary we will use in this lesson: Matching & Vector Resource. I ask them to try and match each vocabulary word to its meaning. I expect some students will be acquainted with a few of the terms.

Once students are done with the top of the worksheet, I go over each term and do my best to link back to when the term was used earlier in today's lesson. Then, I proceed to use the Vector Resource asking students to write how each pre-image of a ship was translated onto its image, this time on the Cartesian coordinate plane. The students should continue to work in pairs, yet each should have there own worksheet. 


10 minutes

As we prepare for the end of class, I hand out the Exit Slip to each student. The instructions ask students to draw the pre-image of the ships, given the description of the translation underwent. I encourage my students to use rulers to ensure neatness.

After they analyze the transformations, students complete the statement about translations:

Translations simply mean ____________, without ___________ of the pre-image.

Then, they answer Question 2, comparing translations to dilations, which were introduced in the the previous lessons.



Teaching Notes:

  1. Students should write that "Translations simply mean ("shifting", "moving", "sliding"), without (changing shape, changing size, or orientation ) of the pre-image.
  2. For question 2, students should state that different from translations, dilation images change size. But in neither of these transformations, does shape or orientation change.