Lesson: Unit 6 Lesson 4: Dilations

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Lesson Objective

Students will be able to… 1. Describe a dilation in the coordinate plane 2. Draw the image of a figure under a dilation

Lesson Plan

Lesson Plan

Print Unit 6 Lesson 4 Dilations guided notes packet. Students follow along by writing notes. (Text from the notes is in italics). Students will need rulers during this lesson to connect the dots.

 
 Opening

1)     Show short clip of “Honey, I Shrunk the Kids!”

2)     Take a quick moment to discuss what students think the word “dilate” means and where they have heard or seen it (Example might be dilating pupils at the doctor’s office)

3)     Remember, in Math the word dilate means to expand or shrink a figure. When you expand or shrink something, the scale factor tells you by how much you need to expand or shrink it. When scale factors are greater than 1, your figure gets bigger. Examples: 1, 5, 10,000, 2.5, 50/2, etc. When scale factors are less than 1, your figure gets smaller. Examples: 0.5, 1/10, ¾, etc.

Vocabulary:

  1. Coordinate Grid/Coordinate Plane
  2. Point
  3. Image
  4. Transformation
  5. Dilation
  6. Scale Factor
  7. Quadrant
  8. Origin

Example 1: Dilate a figure with a scale factor > 1 (Expand)

  1. 1.     Identify and record the points (J, K, L) of the original figure.
  2. 2.     Have students identify the scale factor in the problem and predict whether it will expand or shrink given what they know about scale factors > or < 1.
  3. 3.     Show the multiplication by the scale factor in the space between J and J’, K and K’, and L and L’ and record the new points
  4. 4.     Have students plot the points and connect the dots
  5. 5.     Ask students if their dilation matches their prediction and if it makes sense.
  6. 6.     Have students complete You Try 1
    1. The second problem in you try 1 has a scale factor of 1.5. Students tend to have trouble multiplying by decimals, and this is a great opportunity for students to practice taking half of a number and adding it to the original
    2. Be aware that Z’ is in the negatives and that you have to take the 1.5 of the absolute value otherwise the negative will throw students off!

 

Common Student Mistakes:

  1. 1.     Students plot their points incorrectly, mixing up their x coordinates with their y coordinates
  2. 2.     Students multiply incorrectly
  3. 3.     Students commit transcription errors (get the answer but write it in the wrong place)
  4. 4.     Students plot a point incorrectly, resulting in a figure that is NOT similar. The first step of making a prediction and the last step of asking if their answer makes sense helps build the metacognitive piece.
  5. 5.     Students forget to label their points with appropriate letters and primes!

Example 2: Dilate a figure with a scale factor < 1 (Shrink)

Teacher’s Note:  Shrinking tends to be more difficult as students often have trouble with fraction operations. It’s a good idea to incorporate multiplying by fractions into a Do Now or previous homework.

  1. 1.      Identify and record the points (J, K, L) of the original figure.
  2. 2.     Have students identify the scale factor in the problem and predict whether it will expand or shrink given what they know about scale factors > or < 1.
  3. 3.     Show the multiplication by the scale factor in the space between J and J’, K and K’, and L and L’ and record the new points
  4. 4.     Have students plot the points and connect the dots
  5. 5.     Ask students if their dilation matches their prediction and if it makes sense.
  6. 6.     Have students complete You Try 2
    1. The first problem has a scale factor of 1/3. I recommend letting students struggle with the scale factor, and providing guiding questions that tie back to the 0.5 scale factor of Example 2.
    2. A question I found myself asking was, “When you get ½ of a pizza, how much do you have? How did you figure that out? So when you get 1/3 of a pizza, how much do you have? How did you figure that out? Interesting, so what conclusions can you draw about multiplying by 1/3 and dividing by 3?”

Example 3: Identify and Describe a Dilation

  1. 1.     Ask students how they can tell the difference between an original figure and a new image
  2. 2.     Have students describe the first dilation. Encourage them to find the coordinates of the points and figure it out the change like they did in examples 1 and 2. This skill leads perfectly into the table dilation problem
  3. 3.     Ask students how they can tell the difference between an original figure and a new image in a table
  4. 4.     Go through the other answer choices and discuss why each one would not work
    1. What would the answer choices have to look like for A, C and D to work?
  5. 5.     Have students complete You Try 3

Sample Test Questions

  1. 1.     Ask students what they notice about the answer choices?
  2. 2.     What kind of blunders were you making during the lesson?
  3. 3.     How can you avoid a similar fate?

Common Blunders:

Students should articulate mistakes they were making during their guided practice. Answers may vary but may include:

  1. Forgetting primes
  2. Multiplying the scale factor incorrectly
  3. Mixing up their x and y coordinates
  4. Students label the points wrong (A instead of B)
  5. Mixing dilations up with rotations, reflections, and/or translations.
  6. Students draw shapes that are not similar

Independent Practice

Have students work through questions 1 – 9 and continue onto the homework. The IP is more focused on describing dilations wherease the homework is more focused on actually drawing them.

Closing

Have students share out and summarize what they learned today.

Assessment

Have students complete the Exit Ticket


Reflection:

What works:

The coordinate method, multiplying by the scale factor really worked for my students. As students evolved in their understanding for dilations, I also challenged to them to dilate visually (by counting the number of grid boxes horizontally and vertically). There’s a decent mix of problems, and ample opportunity for students to make mistakes and learn from them.


What didn't work:
 I did not anticipate the difficult students would have multiplying by a scale factor smaller than one. Whether it was multiplying by ½ or 1/3 or 0.5, students had a lot of trouble applying what they know about the connection between multiplying fractions and dividing into pieces. I strongly recommend priming them on this idea through another structure like Do Now’s, home works, mental math, or cranium crunches leading up the lesson. I thought that teaching them the “half plus original” trick for 1.5 also worked will to address this. Lastly, students were not very reflective about their shape getting bigger or smaller and maintaining similarity. If a shape looked totally off, they did not stop and say, hey! This looks totally off! So, as you go through the lesson I strongly recommend reiterating that dilations result in similar figures and have students reflect if their answer makes sense given their predictions.

Lesson Resources

Unit 6 Lesson 4 Dilations HW.docx  
1,268
Unit 6 Lesson 4 Dilations.docx  
1,939
Memorable-Scene_-Honey,-I-Shrunk-the-Kids-The-Shrinking-Scene[www.savevid.com].mp4  
1,443

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