Update model.md

#259 (comment)

doc/model.md

@@ -6,10 +6,11 @@ This document is a high-level description of the model used in PhET's *Mean: Sha
 
 ## Overview
 
-The goal of this simulation is to provide users an understanding of mean as it relates to a data set. More specifically,
-how mean can be calculated and how individual data values impact the mean. The screens provide an experience of
-embodied math, allowing users to feel what the mean is in various qualitative scenarios, such as water
-leveling out among cups, evenly distributing candy bars across peers, or finding the balance point of a beam.
+The goal of this simulation is to provide users an opportunity to explore and develop a conceptual understanding of arithmetic mean
+within two standard paradigms: fair share and balance point. To illustrate fair share, the first three screens lean on context of water leveling out 
+between cups, evenly distributing discrete candy bars across stacks, and collecting and dividing apples across plates. To illustrate balance point, 
+the fourth screen has a beam, fulcrum, and stacks of soccer balls. These contexts provide an embodied math experience so users can "feel" the mean before 
+being instroduced to a standard algorithm. 
 
 ## Data Representations
 
@@ -19,11 +20,11 @@ a party table in the Distribute and Fair Share Screens, and a soccer field in th
 representations are the ground truth, determining the data set that users can interact with in the notepad
 representation.
 
-The notepad representation allows users to interact with the data set in order to gain a stronger understanding of the
-mean. In the "Level Out" screen users can add or remove cups and open or close pipes to level out the water. In the
+The notepad representation allows users to interact with the data in order to gain a stronger understanding of the
+mean. In the "Level Out" screen users can open or close pipes to level out the water. In the
 "Distribute" screen users can move candy bars from one plate to another. In the "Fair Share" screen users can collect
 and split apples into slices. In the "Balance Point" screen users can move the balance beam fulcrum to find the balance
-point across the data set.
+point of the dot plot.
 
 ## Level Out
 
@@ -44,16 +45,16 @@ physics of the simulation, data set integrity, and UX design.
   - When pipes are closed, the notepad cup set will sync to match their table representations.
 
 - **Adding and Removing Cups**
-  - When a cup is removed, the table cup is the "ground truth". That is the amount of water removed from the set's water total.
-  - When a cup is removed, notepad water levels reset to their corresponding table values. Pipe states remain the same, and water will level back out if the pipes remain open.
+  - When a cup is removed from the lab table, that cup's water is removed from the set's water total, which is reflected in the notepad water cups.
+  - When a cup is removed from the lab table, notepad cup water levels reset to their corresponding table values. Pipe states remain the same, and water will level back out if the pipes remain open.
 
 ## Distribute
 
 ### Candy Bars
 
 The candy bars in the notepad representation can be dragged from one plate to another, allowing users to evenly
-distribute candy bars across the plates. Since the candy bars cannot be broken into pieces, this screen allows users to
-interact with a remainder.
+distribute candy bars across the plates. Since the candy bars cannot be broken into pieces, this screen allows users to 
+approximate the mean as a whole number plus a remainder.
 
 As candy bars are added or removed from the table representations the notepad representation will update accordingly. If
 a notepad plate has reached max capacity the candy bar will be added to the plate with the least candy bars, while if a
@@ -63,7 +64,10 @@ notepad plate has no candy bars to remove the candy bar will be removed from the
 
 All the plates have the same maximum and minimum capacity. As plates are added and removed from the table representation
 the notepad representation will update accordingly so that the total number of candy bars is always equal between the
-two representations.
+two representations. 
+
+### Info Dialog
+The info dialog displays the calculation of the mean as a whole number plus a remainder.
 
 ## Fair Share
 
@@ -79,30 +83,36 @@ in the same arrangement as the table.
 
 **Collect:**
 All the apples are gathered into a central area in the notepad. This mode allows users to see all the apples as a total
-collection instead of on individual plates.
+collection.
 
 **Share:**
-The apples are evenly distributed across the plates in the notepad. The Fair Share screen explores the mean as a mixed
-fraction where we see Apples split into fractional pieces if needed. In share mode all the plates will have the exact
+The apples are evenly shared across the plates in the notepad, first by equally distributing the whole apples, 
+then evenly sharing frational pieces of apples. In share mode all the plates will have the exact
 same number of apples.
 
+### Info Dialog
+The info dialog displays the calculation of the mean as a mixed number. 
+
 ## Balance Point
 
-## Soccer Balls
+### Soccer Balls
 
-Each soccer ball represents a data point along a number line, with the distance the ball was kicked being the value of
-the data point. Soccer ball kick distance is measured in meters, and a soccer ball can only land or be dragged to an
-integer position. As soccer balls are dragged across the field, their notepad representations will adjust accordingly.
+Each soccer ball is kicked onto the field, and the distance the ball was kicked is represented by a data point on the dot plot on the notepad. 
+Soccer ball kick distance is measured in meters, and a soccer ball can only land or be dragged to an
+integer position. As soccer balls are dragged across the field, the notepad dot plot representation will adjust accordingly.
 
 Balls are removed in the reverse order they were added. 
 
-## Balance Beam
+### Balance Beam
 
 A balance beam is used to demonstrate the mean as a balance point. The beam's fulcrum can be moved along a number line
-to find the balance point across the data set. The beam will tilt as the fulcrum is adjusted, with it becoming
-completely level when the data set is evenly distributed across the beam. This screen does not accurately represent the
+to find the balance point of the dot plot. The beam will tilt as the fulcrum is adjusted, with it becoming
+completely level when the deviations are equal on both sides of the fulcrum. This screen does not accurately represent the
 physics of a balance beam, opting for an experience that provides more context for students aligned to the pedagogical
 goals of the sim.
 
-The balance beam fulcrum adjusts discretely along the number line, snapping to the nearest tenth. This allows users to
-explore the mean as a decimal, with mean values always rounding to the nearest tenth.
+The balance beam fulcrum is intended to feel continuous, but it is technically discrete as it snaps to the nearest tenth. This allows users to
+"feel" the mean as the balancing point, while ensuring that the balance point is always possible to locate.
+
+### Info Dialog
+The info dialog displays the calculation of the mean as a decimal rounded to the nearest tenth.