##
* *Reflection: Diverse Entry Points
Translations (Day 2 of 2) - Section 2: New Info / Application

I've had different experiences with different groups of students when teaching to write the translation rule for a translated figure. It may be better off to begin with doing just horizontal shifts until students get acquainted, followed by vertical shifts only, before actually giving learners translations that involve both, simultaneously. It may be a good idea to introduce one at a time to students that struggle. What should definitely not be done, even with the more advanced learners is teaching that when the value added is positive, the figure will move right for x and up for y....or left for x and down for y, if the value is negative. This almost always creates confusion. The "positive right/ up, and negative left/down method, is a No No". In this lesson, having the students figure out the rule for the school building translation, themselves, after they shifted it graphically, worked ok for me.

*About teaching horizontal and vertical shifts*

*Diverse Entry Points: About teaching horizontal and vertical shifts*

# Translations (Day 2 of 2)

Lesson 4 of 16

## Objective: 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.

*55 minutes*

#### Launch

*15 min*

On Day 2 of this lesson on translations, I ask the students to continue with to work with their Day 1 partners. I first hand each pair of students the School Building Outline with corresponding instructions. I ask students to complete the task:

- Make a table
- Label the pre-image and the image correctly

I remind students:

- To always watch for the scale used in the diagram
- Not all points have to fall on the boundaries of the sheet of graph paper in front of them

I expect students to have a pretty good idea of how to interpret the diagram. I think that they will successfully slide each pre-image point the same number of units horizontally and vertically as they did with point A. As they work, I will walk around assessing students and stressing the correct labeling of the image points, making sure that my intuition about their understanding is correct.

The idea in the lesson is being able to describe the individual points by location and all points by a rule. Nonetheless, I encourage students to plot the image points and write their coordinates in their tables first. More advanced students will quickly "get the point" (no pun intended), and will eventually use arithmetic and avoid the entire graphing. Still, I allow time for all students to finish.

#### Resources

*expand content*

#### New Info / Application

*30 min*

Once students are done, I proceed to project my Building Outline Table on the board. I ask students to compare their table to mine and make appropriate adjustments. I like to ask students to inform the class of any difficulties that were encountered. Mistakes at this point are usually due to simple counting errors. I ask, "How can you immediately know when connecting your points of the image, that you've made a mistake?" Generally, one or more students will say that the image should be congruent to the pre-image, or simply say that they should have same shape and size.

I then introduce the class to translation notation by writing:

**T(x, y) >>>>>> (x + a, y +b)**

**Every point underwent this translation. What are the values of a and b for this particular task?**

I give the class a couple of minutes to come up with the values of a and b. Once they do, I write the rule on the board and ask students to copy it into their notebooks:

**T(x, y) >>>>>> (x + 16, y + 4)**

I like to ask, "How many matching points do we need to write the rule for a translation?"

I end the conversation by telling the class that in general, if you add "a" to each x-coordinate of the points of a pre-image you will get a slide image that is "a" units to the right when h is positive and "a" to the left if "a" is negative. If you add "b" to the second coordinate (y) of all the points, the image will slide "b" units up when "b" is positive and "b" units down if "b" is negative.

I then follow up by handing each student, the Four Translations Resource. I will give the students ample time to complete this worksheet. I make sure students have rulers and pencils, and I walk around again, assessing students.

*expand content*

#### Closure

*10 min*

In the Dominican Republic, students call a "cheat sheet" a "chivo", which literally means Goat. I don't know the history behind this, but "chivos" are those cheat sheets that a student takes out WITHOUT permission from the teacher, and they usually are very small. I'm sure every country in the world has a name for these little creations.

To close today's lesson, I will ask students to make a "Chivo" assuming that they were going to get a quiz or test the following day. I ask the students to write their "chivo" on the back of their Four Translations Worksheet in an appropriately small box, (about 1/4 or the sheet), and hand it in at the end of the class. I tell the students they can write anything they wish but thinking about what they may be asked on the quiz.

This provides a kind of quick review, reminding students of what they learned, or should have learned in today's lesson. Also, students will usually summarize main ideas, or write an idea or process that they are not sure about, which I think can be good formative assessment.

Here's an example of a "chivo" prepared for a Physics exam: cheat sheet.jpg

#### Resources

*expand content*

For homework I will give students the following problems: Translations Homework

Homework is great when content is pretty much learned in class and ready to practice at home. It is of little use if there is no feedback when corrected, pretty much like any formative assessment piece. Going over this piece in class after correcting is a good idea.

#### Resources

*expand content*

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- UNIT 1: Number Sense
- UNIT 2: Solving Linear Equations
- UNIT 3: Relationships between Quantities/Reasoning with Equations
- UNIT 4: Powers and Exponents
- UNIT 5: Congruence and Similarity
- UNIT 6: Systems of Linear Equations
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- UNIT 10: Volumes of Cylinders, Cones, and Spheres
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- LESSON 1: Exploring Dilations 1
- LESSON 2: Exploring Dilations 2
- LESSON 3: Translations (Day 1 of 2)
- LESSON 4: Translations (Day 2 of 2)
- LESSON 5: Exploring Reflections 1
- LESSON 6: Exploring Reflections 2
- LESSON 7: Exploring Rotations 1
- LESSON 8: Exploring Rotations 2: On the plane
- LESSON 9: Reflections over parallel or intersecting lines (Day 1)
- LESSON 10: Reflections over parallel or intersecting lines (Day 2 of 2)
- LESSON 11: Angles and Parallel Lines (Day 1 of 2)
- LESSON 12: Angles and Parallel Lines (Day 2 of 2)
- LESSON 13: Vertical angles and Linear Pairs
- LESSON 14: The Triangle Sum Setup
- LESSON 15: Kaleidoscope Eyes
- LESSON 16: Where's The Math? Analyzing our Kaleidoscope Images