Elena

> Earlier in the unit, we showed that we can cover any two-dimensional shape with rectangles, so the property that area changes by k² when we dilate a figure by k applies to all shapes, not just rectangles.
>
> Elena, Geometry Unit 5, Lesson 6.3

**Elena** has many friends, who she is very supportive of. Similar to Diego, she appears with almost every other character, although she is missing two instead of one, those two being Priya and Mai. It is known that she likes science, pizza, track, and going on walks.

Elena is friends with Clare, Jada, Lin and Diego. Interestingly, she is the only character in the Illustrative Mathematics universe whose most common partner in math problems is of the same gender, as far as I'm aware, that being Clare. This may imply that she is the only gay representation in the lore.

Elena's favorite subject is science.

## Notable Appearances

**Geometry Unit 5**

* "Clare says, 'We know that if we dilate a cube by a factor of k, the cube's volume is multiplied by k^3. It seems like that must apply to all solids, but I'm not sure how to prove it.' Elena says, "Earlier in the unit, we showed that we can cover any two-dimensional shape with rectangles, so the property that area changes by k^2 when we dilate a figure by k applies to all shapes, not just rectangles. Can we do something similar here?'" (Lesson 6.3)

*Analysis: This shows that Elena is supportive of her friends.*

**Geometry Unit 7**

* "Elena was researching offers for the upcoming Pizza Palooza festival. She wants to get a good deal on a single slice of pizza." (Lesson 14.2)

*Analysis: This confirms that Elena likes pizza.*

**Algebra 2 Unit 4**

* "The distance from Elena's chin to the top of her head is 150 mm in an image." (Lesson 1.2)

*Analysis: This confirms that Elena has a chin and a head.*

**Algebra 2 Unit 5**

* "Every weekend, Elena takes a walk along the straight road in front of her house for 2 miles, then turns around and comes back home." (Lesson 9.1)

*Analysis: This confirms that Elena enjoys going on walks.*

**Algebra 2 Unit 6**

* "Jada, Noah, and Elena are riding a carousel. The carousel moves in a counterclockwise direction. When the ride begins, Jada is at position J, Noah is at position N, and Elena is at position E." (Lesson 18.2)

*Analysis: Confirms that Elena is friends with Jada and Noah, because they spend time together outside of school.*

**Algebra 2 Unit 7**

* "Elena is interested in whether music affects plant growth. For a science fair project, she will grow a plant in a room that is normally kept quiet. She will grow another plant in another room that has classical piano music playing all the time." (Lesson 1, Practice Problems)

*Analysis: Elena must be fond of science.*

* "When Elena throws a shot put during track and field practice, it travels an average of 26 feet with a standard deviation of 3 feet, and the distribution of lengths is approximately normal." (Lesson 8, Practice Problems)

*Analysis: Elena does track.*

## Miscellaneous Appearances

**Geometry Unit 1**

* "Elena found C' incorrectly. Elena is convinced that triangle C'D'E' 'looks fine'." (Lesson 11.3)

**Geometry Unit 2**

* "Elena needs to prove angles BED and BCA are congruent." (Lesson 2, Practice Problems)
* "Elena wonders whether she could play the Info Gap with area included as an extra piece of information from the data card. She draws a card with this information and asks Han to play." (Lesson 4.2)
* "Elena has another approach. 'I drew the line of reflection. If you reflect across C, then A and B will switch places, meaning A' coincides with B, and B' coincides with A. C will stay in place, so the triangles will be congruent." (Lesson 8.2)
* "Elena is thinking through a proof using a reflection to show that the base angles of an isosceles triangle are congruent." (Lesson 10, Practice Problems)

**Geometry Unit 3**

* "Elena thinks length BC is 16.5 units. Lin thinks the length of BC is 17.1 units." (Lesson 12, Practice Problems)
* "Elena is playing with the equivalent ratios she wrote in the warm-up. She rewrites a/x = c/a and a^2 = xc. Diego notices and comments, 'I got b^2 = yc. The a^2 and b^2 remind me of the Pythagorean Theorem.' Elena says, 'The Pythagorean Theorem says that a^2 + b^2 = c^2. I bet we could figure out how to show that.'" (Lesson 14.2)

**Geometry Unit 6**

* "Elena wants to find the center and radius of the circle." (Lesson 6.2)
* "Elena is writing an explanation on completing the square for circle equations for Diego because he missed class. Here is what Elena wrote: 'Suppose we want to rewrite an equation in the form (x - h)^2 + (y - k)^2 = r^2. First, move any numbers to the right side and group terms with the same variables together on the left. Second, figure out what must be added to the set of -terms and the set of -terms to create 2 perfect square trinomials. Add those numbers to both the left and right sides of the equation. Next, rewrite the perfect square trinomials as squared binomials, and rewrite the right side in the form r^2. The center and radius can now be read directly from the equation.' Diego is unsure how to determine what needs to be added in order to get 2 perfect square trinomials." (Lesson 14, Practice Problems)
* "A quadrilateral has vertices A=(0,0), B=(4,6), C=(0,12) and D=(-4,6). Mai thinks the quadrilateral is a rhombus and Elena thinks the quadrilateral is a square." (Lesson 17, Practice Problems)

**Geometry Unit 7**

* "Lin and Elena are trying to find the area of the shaded sector in the image. Lin says, 'We’ve found sector areas when the central angle is given in degrees, but here it’s in radians. Should I start by finding the area of the full circle?' Elena says, 'I saw someone using the formula 1/2r^2 0 where 0 is the measure of the angle in radians, and r is the radius. But I don’t know where that came from.'” (Lesson 13.2)
* "Elena is writing notes about central angles in circles." (Lesson 14, Practice Problems)

**Algebra 2 Unit 1**

* "Elena says that it's not possible to have a sequence of numbers that is both arithmetic and geometric." (Lesson 3.2)
* "Tyler has a piece of paper and is sharing it with Elena, Clare, and Andre. He cuts the paper to create four equal pieces, the hands one each to the others and keeps one for himself." (Lesson 11.2)

**Algebra 2 Unit 3**

* "Jada squared a number and got -4. Elena squared a different number and got -4." (Lesson 11, Practice Problems)
* "Elena and Han solved the equation x^2 - 6x + 7 = 0 in different ways." (Lesson 16.2)
* "Elena and Kiran were solving the equation 2x^2 - 4x + 3 = 0 and they got different answers. Elena wrote 1 ± i√0.5, and Kiran wrote 1 ± (i√8)/4." (Lesson 19, Practice Problems)

**Algebra 2 Unit 5**

* "Elena thinks that shifting up the graph of f up by 50 will match the data. Han thinks that shifting the graph of f up by 60 and then right by 1 will match the data." (Lesson 3, Practice Problems)

**Algebra 2 Unit 7**

* "Elena and Clare are working on a project about how high school students are having trouble finding jobs." (Lesson 11.2)