Lessons Used in This Pathway

Students look at opening questions, either at their desks or in a walk around the room. They select a question they are personally interested in, and think about the data required to answer that question. This process draws a direct line between answering questions they care about and the basics of data science.

Students may lean towards questions about individuals, instead of questions about what’s true for a group of individuals who vary from one to another. For example, instead of wondering what movie gets the highest rating, they should ask what’s the typical rating for movies in a list, or how much those ratings tend to vary.

Have students share back the different data they would gather to answer their questions. For each question, students would likely have to gather many different kinds of data. If we wanted to find out if small schools are better than big schools, for example, we might want to gather data on SAT scores, college acceptance, etc. Each of these is a variable in our dataset: any two schools we look at could vary by each of them.

What is the most popular movie of all time? Is Climate Change real? How long do quarterbacks tend to stay in the league? Is Stop-and-Frisk racially biased? We can’t survey every school in the world, get data on every movie ever made, or every police action - but we can do an analysis for a sample of them, and try to infer something about all of them as a whole. These questions quickly turn into a discussion about data — how you assess it, how you interpret the results, and what you can infer from those results. The process of learning from data is called Data Science. Data science techniques are used by scientists, business people, politicians, sports analysts, and hundreds of other different fields to ask and answer questions about data.

We’ll use a programming language to investigate these questions. Just like any human language, programming languages have their own vocabulary and grammar that you will need to learn. The language you’ll be learning for data science is called Pyret.

Students explore the Animals Dataset, sharing observations and familiarizing themselves with the idiosyncrasies and patterns in the data. In the process, they learn about Categorical and Quantitative data.

Have students open the Animals Spreadsheet in a browser tab, or turn to The Animals Dataset (Page 2) in their Student Workbooks.

This table contains data from an animal shelter, listing animals that have been adopted. We’ll be analyzing this table as an example throughout the course, but you’ll be applying what you learn to a dataset you choose as well.

Any two animals in our dataset may have different ages, weights, etc. Each of these is called a variable in the dataset.

Data Scientists work with two broad kinds of data: Categorical Data and Quantitative Data. Categorical Data is used to classify, not measure. Categories aren’t subject to the laws of arithmetic. For example, we couldn’t ask if “cat is more than lizard”, and it doesn’t make sense to "find the average ZIP code” in a list of addresses. “Species” is a categorical variable, because we can ask questions like “which species does Mittens belong to?"

Quantitative Data is used to measure an amount of something, or to compare two pieces of data to see which is less or more. If we want to ask “how much” or “which is most”, we’re talking about Quantitative Data. "Pounds" is a quantitative variable, because we can talk about whether one animal weighs more than another or ask what the average weight of animals in the shelter is.

Have students share back their noticings (statements) and wonderings (questions), and write them on the board.

Data Science is all about using a smaller sample of data to make educated guesses about a larger population. It’s important to remember that tables are only a sample of a larger population: this table describes some animals, but obviously it isn’t every animal in the world! Still, if we took the average age of the animals from this particular shelter, it might tell us something about the average age of animals from other shelters.

Students open up the Pyret environment (code.pyret.org, or "CPO") and see the Animals Dataset reflected there.

Let’s take a look at our programming environment, and see what the Animals Dataset looks like there.

The first few lines on the lefthand side of the screen tell Pyret to import files from elsewhere, which contain tools we’ll want to use for this course. We’re importing a file called Bootstrap:Data Science, as well as files for working with Google Sheets, tables, and images:

After that, we see a line of code that defines shelter-sheet to be a spreadsheet. This table is loaded from Google Drive, so now Pyret can see the same spreadsheet you do. (Notice the funny scramble of letters and numbers in that line of code? If you open up the Google Sheet, you’ll find that same scramble in the address bar! That scramble is how the Pyret editor knows which spreadsheet to load.) After that, we see the following code:

The first line (starting with #) is called a Comment. Comments are notes for humans, which the computer ignores. The next line defines a new table called animals-table, which is loaded from the shelter-sheet defined above. We also create names for the columns: name, species, sex, age, fixed, legs, pounds and weeks. We could use any names we want for these columns, but it’s always a good idea to pick names that make sense!

Every table is made of cells, which are arranged in a grid of rows and columns. The first row and first column are special. The first row is called the header row, which gives a unique name to each variable (or “column”) in the table. The first column in the table is the identifier column, which contains a unique ID for each row. Often, this will be the name of each individual in the table, or sometimes just an ID number.

Below is an example of a table with one header row and two data rows:

After the header, Pyret tables can have any number of data rows. Each data row has values for every column variable (nothing can be left empty!). A table can have any number of data rows, including zero, as in the table below:

Pyret lets us use many different kinds of data. In the animals table, for example, there are Numbers (the number of legs each animal has), Strings (the species of the animal), and Booleans (whether it is true or false that an animal is fixed).

Once you know how to program, you can do a lot with datasets:

In this course, you’ll be learning to do all three in Pyret: Display, Filter, and Build.

What are some other examples each?

Students experiment with the Editor, exploring the different kinds of numbers and strings and how they behave in this programming language.

Students should open code.pyret.org (CPO) in their browser, and click "Sign In". This will ask them to log in with a valid Google account (Gmail, Google Classroom, YouTube, etc.), and then show them the "Programs" page. This page is empty - they don’t have any programs yet! Have them click "Open Editor".

Our Editing Environment 🖼Show image This screen is called the Editor, and it looks something like the diagram you see here. There are a few buttons at the top, but most of the screen is taken up by two large boxes: the Definitions Area on the left and the Interactions Area on the right.

The Definitions Area is where programmers define values and functions that they want to keep, while the Interactions Area allows them to experiment with those values and functions. This is like writing function definitions on a blackboard, and having students use those functions to compute answers on scrap paper.

Math is a language, just like English, Spanish, or any other language. Languages have nouns (e.g. “ball”, “tomato”, etc.) and verbs, which are actions we can perform on these nouns (e.g. - I can “throw a ball”). Math and programming also have values, like the numbers 1, 2 and 3. And, instead of verbs, they have functions, which are actions we can perform on values (e.g. - “I can square a number”).

Languages also have rules for syntax. In English, for example, words don’t have ! and ? in the middle. In math and programming numbers don’t have & in them.

Languages also have rules for grammar. The cat sat. is a sentence, whereas The sat cat. is nonsense, even though all the words are valid syntax. The order of the words matters!

Keeping the importance of syntax and grammar in mind is helpful when learning to program!.

In Pyret, writing decimals as .5 (without the leading zero) results in a syntax error. Make sure students understand that Pyret needs decimals to start with a zero!

Our programming language knows about many types of numbers, and they behave pretty much the way they do in math. Discuss what students have learned:

Error messages are a way for Pyret to explain what went wrong, and are a really helpful way of finding mistakes. Emphasize how useful they can be, and why students should read those messages out loud before asking for help. Have students see the following errors:

This lesson introduces students to Booleans, a unique datatype with only two values: "true" and "false", and why they are useful in both the real world and the programming environment.

Boolean-producing expressions are yes-or-no questions and will always evaluate to either true (“yes”) or false (“no”). The ability to separate inputs into two categories is unique and quite useful!

For example, some rollercoasters with loops require passengers to be a minimum height to make sure that riders are safely held in place by the one-size-fits all harnesses. The gate keeper doesn’t care exactly how tall you are, they just check whether you are as tall as the mark on the pole. If you are, you can ride, but they don’t let people on the ride who are shorter than the mark because they can’t keep them safe. Similarly, when you log into your email, the computer asks for your password and checks whether it matches what’s on file. If the match is true it takes you to your messages, but, if what you enter doesn’t match, you get an error message instead.

Debrief student answers as a class.

Students learn how to apply functions in Pyret , reinforcing concepts from standard Algebra, and practice reading error messages to diagnose errors in code.

Students know about Numbers, Strings, Booleans and Operators -- all of which behave just like they do in math. But what about functions? Students may remember functions from algebra: fx = x + 4$\displaystyle f(x) = x + 4$.

Arguments (or "inputs") are the values passed into a function. This is different from variables, which are the placeholders that get replaced with input values! Pyret has lots of built-in functions, which we can use to write more interesting programs.

Have students log into code.pyret.org (CPO) , open the editor, type the words include image on Line 1 of the Definitions area (left side) and press "Run" to load the image library. Then type num-sqrt​(​16​) into the interactions area and hit Enter.

Have students type string-length​(​"rainbow"​) into the interactions area and hit Enter:

Have students complete Applying Functions (Page 9) to investigate the triangle function and a series of error messages. As students finish, have them try changing the expression triangle​(​50, "solid", "red"​) to use "outline" for the second argument. Then have them try changing colors and sizes!

Debrief the activity with the class.

This activity introduces the notion of Contracts, which are a simple notation for keeping track of the set of all possible inputs and outputs for a function. They are also closely related to the concept of a function machine, which is introduced as well. Note: Contracts are based on the same notation found in Algebra!

When students typed triangle​(​50, "solid", "red"​) into the editor, they created an example of a new data type, called an Image.

The triangle function can make lots of different triangles! The size, style and color are all determined by the specific inputs provided in the code, but, if we don’t provide the function with a number and two strings to define those parameters, we will get an error message instead of a triangle.

As you can imagine, there are many other functions for making images, each with a different set of arguments. For each of these functions, we need to keep track of three things:

The Name, Domain and Range are used to write a Contract.

Where else have you heard the word "contract"? How can you connect that meaning to contracts in programming?

An actor signs a contract agreeing to perform in a film in exchange for compensation, a contractor makes an agreement with a homeowner to build or repair something in a set amount of time for compensation, or a parent agrees to pizza for dinner in exchange for the child completing their chores. Similarly, a contract in programming is an agreement between what the function is given and what it produces.

Contracts tell us a lot about how to use a function. In fact, we can figure out how to use functions we’ve never seen before, just by looking at the contract! Most of the time, error messages occur when we’ve accidentally broken a contract.

Contracts don’t tell us specific inputs. They tell us the data type of input a function needs. For example, a Contract wouldn’t say that addition requires "3 and 4". Addition works on more than just those two inputs! Instead, it would tells us that addition requires "two Numbers". When we use a Contract, we plug specific numbers or strings into the expression we are coding.

Let’s take a look at the Name, Domain, and Range of the functions we’ve seen before:

Optional: Have students make a Domain and Range Frayer model (Page 10) and use the visual organizer to explain the concepts of Domain and Range in their own words.

Have students complete pages Practicing Contracts: Domain & Range (Page 11) and Matching Expressions and Contracts (Page 12) to get some practice working with Contracts.

This activity digs deeper into Contracts. Students explore image functions to take ownership of the concept and create an artifact they can refer back to. Making images is highly motivating, and encourages students to get better at both reading error messages and persisting in catching bugs.

(If needed, you can print a copy of these contracts pages for your students.)

Students are given contracts for some more interesting image functions and see how much more efficient it is to write code when starting with a contract.

You just investigated image functions by guessing and checking what the contract might be and responding to error messages until the images built. If you’d started with contracts, it would have been a lot easier!

Have students turn to Using Contracts (Page 13), Using Contracts (continued) (Page 14) and use their editors to experiment.

Once they’ve discovered how to build a version of each image function that satisfies them, have them record the example code in their contracts table. See if you can figure out what aspect of the image each of the inputs specifies. It may help you to jot down some notes about your discoveries. We will be sharing our findings later.

Have students turn to Triangle Contracts (Page 15) and use the contracts that are provided to write example expressions. If you are ready to dig into triangle-sas, you can also have students work through Triangle Contracts (SAS & ASA).

Sometimes it’s helpful to have a contract that tells us more information about the arguments, like what the 3 numbers in a contract stand for. This will not be a focal point of our work, but to give students a taste of it, have them turn to Radial Star (Page 16) and use the contract to help them match the images to the corresponding expressions. For more practice with detailed contracts you can have them turn to Star Polygon to work with the detailed contract for a star-polygon. Both of these functions can generate a wide range of interesting shapes!

Make sure that all students have completed the shape functions in their contracts pages with both contracts and example code so they have something to refer back to.

Students are very likely to randomly experiment, rather than to actually use the Contracts. You should plan to ask lots of direct questions to make sure students are making this connection, such as:

Students extend their understanding of Contracts and function application, learning new functions that consume Tables and produce displays and plots.

Have students ever seen any pictures created from tables of data? Can they think of a situation when they’d want to consume a Table, and use that to produce an image? The library included at the top of the file includes some helper functions that are useful for Data Science, which we will use throughout this course. Here is the Contract for a function that makes pie charts, and an example of using it:

🖼Show image

Hovering over a pie slice reveals the label, as well as the count and the percentage of the whole. In this example we see that there are 15 females, representing 46.9% of the population.

We can also resize the window by dragging its borders. This allows us to experiment with the data before closing the window and generating the final, non-interactive image.

The function pie-chart consumes a Table of data, along with the name of a categorical column you want to display. The computer goes through the column, counting the number of times that each value appears. Then it draws a pie slice for each value, with the size of the slice being the percentage of times it appears. In this example, we used our animals-table table as our dataset, and made a pie chart showing the distribution of sex across the shelter.

Here is the Contract for another function, which makes bar charts:

Pie charts and bar charts may show counts or percentages (in Pyret, pie charts show percentages and bar charts show counts). Bar charts look a lot like histograms, which are actually quite different because they display quantitative data, not categorical. Also, a pie chart can only display one categorical variable but a bar chart might be used to display two or more categorical variables.

Pie and Bar Charts display what portion of a sample belongs to each category. If they are based on sample data from a larger population, we use them to infer the proportion of a whole population that might belong to each category.

While bars in some bar charts should follow some logical order (alphabetical, small-medium-large, etc), the pie slices and bars can technically be placed in any order, without changing the meaning of the chart.

Students freely explore the Data Science display library. In doing so, they experiment with new charts, practice reading Contracts and error messages, and develop better intuition for the programming constructs they’ve seen before.

There are lots of other functions, for all different kinds of charts and plots. Even if you don’t know what these plots are for yet, see if you can use your knowledge of Contracts to figure out how to use them.

There are many possible misconceptions about displays that students may encounter here. But that’s ok! Understanding all those other plots is not a learning goal for this lesson. Rather, the goal is to have them develop some loose familiarity, and to get more practice reading Contracts.

Today you’ve added more functions to your toolbox. Functions like pie-chart and bar-chart can be used to visually display data, and even transform entire tables!

You will have many opportunities to use these concepts in this course, by writing programs to answer data science questions.

Students get some more practice applying the plotting functions and working with Contracts, and begin to shift the focus from programming to data visualization. This activity stresses a hard programming skill (reading Contracts) with formal reading comprehension (identifying key portions of the sentence).

The Contracts page in the back of students' workbooks contains contracts for many plotting functions.

Suppose we wanted to generate a display showing the ratio of fixed to un-fixed animals from the shelter? How do we go from a simple sentence to working code that makes a data display?

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Once we can answer these questions, all we need to do is find the Contract for that display and fill in the Domain!

To display the categorical data, we can choose between pie and bar charts. Which one of these two is best, and why?

Do you know what kind of data is used for each display?

Let’s get some practice going from questions to code, making visualizations.

Debrief the activity with students.

Optional: As an extension, have students break into teams and come up with additional Data Display challenges, then race to see which team can complete the other team’s challenges first!

Students learn how to define values in Pyret, and practice by defining Numbers, Strings, and Images. They also learn how to define an individual row from a table in Pyret, and how to access a particular column from that row.

Have students open their saved Animals Starter File (or make a new copy), and click “Run”.

Sometimes we have a value that we want to use again and again, and it makes sense to define a name for it. Every definition includes a name and a value. In the code below, we have definitions for a String, a Number and an Image.

We can even define Rows from our tables!

Tables have special functions associated with them, called Methods, which allow us to do all sorts of things with those tables. For example, we can get the first data row in a table by using the .row-n method:

What is the Domain of .row-n? What is the Range? Find the contract for this method in your contracts table. A table method is a special kind of function which always operates on a specific table. In our example, we always use .row-n with the animals table, so the number we pass in is always used to grab a particular row from animals-table.

The code below will define the first row from the animals table:

Pyret also has a way for us to get at individual columns of a Row, by using a Row Accessor. Row accessors start with a Row value, followed by square brackets and the name of the column where the value can be found. Here are three examples that use row accessors to get at different columns from the first row in the animals-table:

And of course, we can use our defined name, substituting it in place of all the redundant code:

Flip back to page 2 of your workbook and look at The Animals Dataset. Which row is animalA? Label it in the margin next to the dataset. Which row is animalB? Label it in the margin next to the dataset.

Now turn back to your screen. What happens when you evaluate animalA in the Interactions Area?

Have students share their answers, and see if there are any common questions that arise.

Students get some practice reading function definitions, and in the process they build knowledge that’s needed later on in the lesson.

Let’s see how much you remember about function definitions! Load the Table Methods Starter File, go to the File menu, and click "Save a Copy".

Can students explain what each function does?

Students learn to sort Rows of a Table in ascending or descending order, according to one column.

Have students find the contract for .order-by in their contracts pages. The .order-by method consumes a String (the name of the column by which we want to order) and a Boolean (true for ascending, false for descending). But what does it produce?

Students learn how to filter tables, by removing Rows.

Explain to students that you have "Function Cards", which describe the purpose statement of a function that consumes a Row from a table of students, and produces a Boolean (e.g. - "this student is wearing glasses"). Select a volunteer to be the "filter method", and have them randomly choose a Function Card, and make sure they read it without showing it to anyone else.

Have 6-8 students line up in front of the classroom, and have the filter method go to each student and say "stay" or "sit" depending on whether their function would return true or false for that student. If they say "sit", the student sits down. If they say true, the student stays standing.

Ask the class: based on who sat and who stayed, what function was on the card?

Suppose we want to get a table of only animals that have been fixed? Have students find the contract for .filter in their contracts pages. The .filter method is taking in a function. What is the contract for that function? Where have we seen functions-taking-functions before?

The .filter method walks through the table, applying whatever function it was given to each row, and producing a new table containing all the rows for which the function returned true. Notice that the Domain for .filter says that test must be a function (that’s the arrow), which consumes a Row and produces a Boolean. If it consumes anything besides a single Row, or if it produces anything else besides a Boolean, we’ll get an error.

Students often think that filtering a table changes the table. In Pyret, all table methods produce a brand new table. If we want to save that table, we need to define it. For example: cats = animals-table.filter(is-cat).

Debrief with students. Some guiding questions on filtering:

Students learn how to build columns, using the .build-column table method.

Suppose we want to transform our table, converting pounds to kilograms or weeks to days. Or perhaps we want to add a "cute" column that just identifies the puppies and kittens? Have students find the contract for .build-column in their contracts pages. The .build-column method is taking in a function and a string. What is the contract for that function?

The .build-column method walks through the table, applying whatever function it was given to each row. Whatever the function produces for that row becomes the value of our new column, which is named based on the string it was given. In the first example, we gave it the is-old function, so the new table had an extra Boolean column for every animal, indicating whether or not it was young. Notice that the Domain for .build-column says that the builder must be a function which consumes a Row and produces some other value. If it consumes anything besides a single Row, we’ll get an error.

Debrief with students. Ask them if they think of a situation where they would want to use this. Some ideas:

In this lesson, students will build their flexibiltiy of thinking by engaging with multiple representations. Students will search for structures that are dynamic, meaning they change in a predictable way. This is the foundation for defining functions.

Students should have their workbook, pencil, and be logged into code.pyret.org on their computer.

I Love Green Triangles 🖼Show image

I Love Green Triangles 🖼Show image

This is a fun lesson to make silly! Dramatically confess to your students, "I LOVE green triangles!" Challenge them to use the Definitions Area to code as many unique, solid, green triangles as they can in 2 minutes.

Walk around the room and give positive feedback on the green triangles. When the time is up, ask for some examples of green triangles that they wrote and copy them to the board. Be specific and attend to precision with the syntax such that students can visually spot the pattern between the different lines of code.

Select a student to act out gt. Make it clear to the class that their Name is "gt", they expect a Number, and they will produce an Image. Act out some examples before having the class add their own and record them on the board:

Thank your volunteer.

Have students turn to Matching Examples and Definitions (Math) (Page 30).

You may also want to have students complete Matching Examples & Function Definitions (Desmos)

Now that we’ve seen how this works in math, let’s go back to gt.

400 🖼Show image

400 🖼Show image

You may also want to have students complete Matching Examples & Function Definitions (Desmos) .

Have students turn to Matching Examples and Contracts (Page 32).

Confirm that everyone is on the same page before moving on. You may want to have students turn to a partner, compare their findings, and discuss their thinking about anything they didn’t agree on at first.

Have students open the gt starter file (Pyret) .

Have students turn to Contracts, Examples & Definitions (Page 33)

If you have time, have students complete

Primary: Students use different representations of functions to define Row-based functions.

Secondary: Students discover functions that consume other functions, and compose a scatter plot function with a function they’ve defined.

The shelter wants to print nametags for all the animals, with their names written in red letters. Turn to The Animals Table in your Student Workbook.

This would be pretty repetitive! Just like making green triangles in ../defining-functions/, there’s got to be a better way! In this lesson, we’ll learn a step-by-step process that helps us define functions, called the Design Recipe.

The Design Recipe uses multiple representations of functions in a specific order, to help us solve problems. Let’s look at an example to see how this works!

Make sure students have changed the 20 to 15, matching the Purpose Statement.

Those last two examples provide the pattern that allows us to write our definition. Everything stays the same except the Row itself. Just as we did for gt, we can circle and label the the Rows. In this case, r or animal would be a pretty good name for the Row that represents an animal in our table:

Have students try this function on some of the animals they defined, by typing nametag(unfixed-row), nametag(dog-row), etc. Then have them find find the contract for image-scatter-plot in their Contracts pages.

Note: the optional lesson If Expressions goes deeper into basic programming constructs, using image-scatter-plot to motivate more complex (and exciting!) plots.

Scatter plots allow us to display two dimensions of data: one on the x-axis and the other on the y-axis. This is useful if we want to explore a relationship between how much an animals weighs and how long it takes to be adopted! But what if we wanted to also see the impact of an animal’s age? We could make a different scatter plot, using age as our x-axis. But maybe we want to combine all three into a single plot, and see three dimensions?

Each step in the Design Recipe helps us write the next one.

These steps also help us check our work. If any two representations don’t match, it means there’s likely a bug somewhere.

Students use different representations of functions to write functions that produce true and false by asking questions of Rows.

Let’s try solving some other word problems using the Design Recipe, starting from scratch.

How could we describe this work to the computer, so that we can define a function and make it do the work for us? Complete the following sentence: For each Row, I…​

Since we’re asking if an animal is a cat, we’ll call our new function is-cat. What type of data is going in? What type is coming out?

The last two examples are what we want, because we can see the pattern! Just as with nametag, the only thing changing is the Row itself. Once we circle and label the Rows, we’re ready to define the function:

It’s extremely likely that students will struggle with this Boolean expression:

That’s because they are confusing false with wrong. It’s absolutely correct that this expression will produce false, because the species of the dog row isn’t "cat". But this doesn’t make the example wrong! Remember, the first example said that false is the answer we expect.

There are lots of Boolean-producing functions that would be handy to write. We might want functions that tell us if an animal is old, if it’s male, or if it was adopted in under a week.

What are some other Boolean-producing functions that would be useful?

Students use different representations of functions to define Lookup functions.

Have students share back their Purpose Statements, and discuss.

Since we’re looking up the fixed column, we’ll call our new function lookup-fixed. What type of data was going in? What type was coming out? This gives us the Contract:

Have students share back their examples.

Ironically, students are likely to struggle with lookup functions that don’t do nothing more than look up a column ("but it doesn’t do any work!"). This may come from a misunderstanding that a column lookup is doing work!

Students may ask "why would I need this, if I can already see all the values in the Row?"

The big idea here is that functions provide a standard way to compose computations. Every wall plug has a standard shape, which allows us to plug all sorts of appliances, lamps, etc into any room in the house. Having a standard like function-name(argument1, argument2, …​) allows us to stack functions together and do all kinds of sophisticated analysis.

Students practice more of what they learned in the previous lesson, applying the Design Recipe to simple table functions that operate on rows of the Animals Dataset. The functions they create - in addition to the ones they’ve already made - set up the method-chaining activity.

The Design Recipe is a powerful tool for solving problems by writing functions. It’s important for this to be like second nature, so let’s get some more practice using it!

Did students find themselves getting faster at using the Design Recipe? Can students share any patterns they noticed, or shortcuts they used?

Students learn how to perform multiple table operations (sorting, filtering, building) in the same line of code.

Now that we are doing more sophisticated analyses, we might find ourselves writing the following code:

That’s a lot of code, and it also requires us to come up with names for each intermediate step! Pyret allows table methods to be chained together, so that we can build, filter and order a Table in one shot. For example:

This code takes the animals-table, and builds a new column. According to our Contracts Page, .build-column produces a new Table, and that’s the Table whose .filter method we use. That method produces yet another Table, and we call that Table’s order-by method. The Table that comes back from that is our final result.

It can be difficult to read code that has lots of method calls chained together, so we can add a line-break before each “.” to make it more readable. Here’s the exact same code, written with each method on its own line:

Suppose we want to build a column and then use it to filter our table. If we use the methods in the wrong order (trying to filter by a column that doesn’t exist yet), we might wind up crashing the program. Even worse, the program might work, but produce results that are incorrect!

How well do you know your table methods? Complete Chaining Methods (Page 42) and Chaining Methods 2: Order Matters! (Page 43) in your Student Workbook to find out.

As our analysis gets more complex, method chaining is a great way to keep the code simple. But complex analysis also has more room for mistakes, so it’s critical to think carefully when we use it!

Students explore a program that makes use of an if-expression, develop their own understanding, and modify it.

So far, all of the functions we know how to write have had a single rule. The rule for gt was to take a number and make a solid, green triangle of that size. The rule for bc was to take a number and make a solid, blue circle of that size. The rule for nametag was to take a row and make an image of the animal’s name in purple letters.

What if we want to write functions that apply different rules, depending on the input? For example, what if we want to change the color of the nametag depending on the species of the animal?

Have the class share their own explanations for how if-expressions work.

Pyret allows us to write if-expressions, which contain:

We can chain them together to create multiple rules, with the last else: being our fallback in case every other condition is false.

Students discover how "dot appearance" can be used to show more data in a scatterplot, and why that would be valuable.

Suppose we want to make a scatter plot for the Animals Dataset, but with dots taking different colors depending on the species. This would make it possible to see if certain species are "clustered" in different parts of the plot.

Have students open Word Problem: species-color (Page 46). Make sure they all write the Contract and Purpose Statement first , and check in with their partner and the teacher before proceeding.

Once they’ve got the Contract and Purpose Statement, have them come up with examples: for each species. Once again, have them check with a partner and the teacher before finishing the page.

Age v. Weeks Scatterplot 🖼Show image

What does this new visualization tell us about the relationship between age and weeks? What other analysis would be helpful here?

Statistical inference involves looking at a sample and trying to infer something you don’t know about a larger population. This requires a sort of backwards reasoning, kind of like making a guess about a cause, based on the effect that we see. To better understand the process of going from the sample back to the population, it helps to understand the more straightforward process of going from the population to a sample. If the sample is random, we call this process Probability!

In real life we typically don’t know what’s true for an entire population. But this probability thought-experiment will start with a larger population with known properties (such as the fact that nearly half of the entire population are males). Then we’ll see what kind of behavior we tend to see in random samples taken from that population.

One of the most useful tasks in Data Science is using sample data to infer (guess) what’s true about the larger population from which the sample was taken. This process, called statistical inference, is used to gain information in practically every field of study you can imagine: medicine, business, politics, history; even art! Early on, statisticians discovered that random samples almost always work best.

Suppose we want to estimate what percentage of all Americans plan to vote for a certain candidate. We can’t ask everyone who they’re voting for, so pollsters instead take a sample of Americans, and generalize the opinion of the sample to estimate how Americans as a whole feel. But choosing a sample can be tricky…​

Sampling is a complicated issue. The main reason for doing inference is to guess about something that’s unknown for the whole population. But a useful step along the way is to practice with situations where we happen to know what’s true for the whole population. As an exercise, we can keep taking random samples from that population and see how close they tend to get us to the truth. Another discovery (besides the value of randomness) that statisticians made early on was something that’s perfectly consistent with common sense: Larger samples are better than smaller ones, because they tend to get us closer to the truth about the whole population.

Let’s see what happens if we switch from smaller to larger sample sizes, if we’re taking a random sample of shelter animals to infer what’s true about the larger population…​

The Animals Dataset we’ve been using is just one sample taken from a very large animal shelter. How much can we infer about the whole population of hundreds of animals, by looking at just this one sample?

Many people mistakenly believe that larger populations need to be represented by larger samples. In fact, the formulas that Data Scientists use to assess how good a job the sample does is only based on the sample size, not the population size.

Have students share how much better their larger samples are at guessing the truth about the whole population.

This activity is all about grouped samples: Students make a bunch of subsets from the Animals Dataset, and see how each subset might answer the same question differently.

🖼Show image When looking at a scatter plot of our animals, it looks like the amount an animal weighs may have something to do with how long it takes to be adopted.

But if we label the dots by animal (see the image on the right), we notice every data point after 25 pounds belongs to a dog from the shelter! The cats are all clumped together in the lower weight range, making it hard to see how weeks to adoption may relate to a cat’s weight.

Divide the class into groups of 3-4, with one student identified as the "reporter".

Have the reporters share their findings with the class.

Imagine that you’ve been handed a dataset from a country where half the people are wealthy and have access to amazing medical care, and the other half are poor and have no healthcare. If we took a random sample of the population as a whole, we might think that they are generally middle-income and have average health. But if we ask the same question about the two groups separately, we would discover inequality hiding in plain sight!

Ultimately, it might make more sense to ask certain questions about "just the cats" or "just the dogs". Averaging every animal together will give us an answer, but it may not be a useful answer.

Data Scientists define grouped samples of datasets, breaking them up into sub-groups that may be helpful in their analysis.

Earlier, you learned how to define values in Pyret. We can define Numbers, Strings, Images, and even rows:

Let’s use this skill to define Tables…​

We already know how to define values, and how to filter a dataset. So let’s put those skills together to define one of our subsets:

Debrief with students. Thoughtful question: how could we filter and sort a table? How can we combine methods?

Students revisit the data display activity, now using the samples they created.

Making grouped and random samples is a powerful skill to have, which allows us to dig deeper than just making charts or asking questions about a whole dataset. Now that we know how to make subsets, we can make much more sophisticated displays!

Were any of the students' displays interesting or surprising? Given a novel question, can students identify what helper functions they would need to write?

Students learn about the Data Cycle, which helps them get situated in the process of analyzing the datasets they will select in this lesson. They browse through the library of provided datasets, and choose one they want to work with. NOTE: the selection process can also be done as a homework assignment, if all students have internet access at home.

Zoom out a little and help students reflect on what they’ve done so far. Students began by exploring the Animals Dataset, formulating questions and exploring them with data displays. This led to further questions, making subsets, and asking more questions.

🖼Show image The Data Cycle[*] is a roadmap, which helps guide us in the process of data analysis.

(Step 1) We start by Asking Questions - statistical questions that can be answered with data.

(Step 2) Then we Consider Data. This could be done by conducting a survey, observing and recording data, or finding a dataset that meets our needs.

(Step 3) Then it’s on to Analyzing the Data, in which we produce data displays and new tables of filtered or transformed data in order to identify patterns and relationships.

(Step 4) Finally, we Interpret the Data, in which we answer our questions and summarize the results. As we’ve already seen from the Animals Dataset, these interpretations often lead to new questions…​.and the cycle begins again.

Explain to students that they will now select a dataset for them to work with for the remainder of the course. Make sure they understand that it genuinely has to be something they are interested in - their engagement with the data is critical to engaging with the class.

Students can also find their own dataset, and use this Blank Starter file. See this tutorial video for help importing your own data into Pyret.

Have students choose a dataset that is interesting to them! They should have at least two questions that the dataset can help them answer, and write them on What’s on your mind? (Page 57).

We have also compiled some , which we recommend for all teachers before having their students choose a dataset.

Have students share their datasets and their questions.

For the rest of this course, students will be learning new programming and Data Science skills, practicing them with the Animals Dataset and then applying them to their own data.

Students apply what they’ve learned about describing and making subsets from the Animals Dataset to their own dataset. Note: this activity can be done briefly as a homework assignment, but we recommend giving students an additional class period to work on this.

By now you’ve already learned what to do when you approach a new dataset. With the Animals Dataset, you first read the data itself, and wrote down your Notice and Wonders. You described the columns in the Animals Dataset, identifying which were categorical and which were quantitative, and whether they were Numbers, Strings, Booleans, etc. Finally, you used the Design Recipe and table methods to make random and logical subsets.

Now, you’re doing to do the same thing with your own dataset.

Have students share which subsets they created for their datasets.

[*] From the Mobilizing IDS project and GAISE

Students look at a bar chart and a histogram, compare/contrast them, and make observations about what they have in common and how they are different. Then they learn a more formal explanation of histograms.

The display on the left side of that page is a Bar chart.

The display on the right side is called a histogram.

To build a histogram, we start by sorting all of the numbers in our column from smallest to largest, marking our x-axis from the smallest value (or a bit below) to the largest value (or a bit above) and dividing into equally-sized intervals, or “bins”. For example, if our values ranged from 3 to 53 we might mark our x-axis from 0 to 60 and divide it into bins of width 10. If they range from 22 to 41 we might mark our x-axis from 20 to 45 and divide it into bins of width 5. Once we have our bins, we put each value in our dataset into the bin where it belongs, and then count how many values fall in each bin. This count determines the height of the bars on our y-axis.

Note that intervals on this display include the left endpoint but not the right. If we included the right endpoint and someone had 0 teeth, we’d have to add on a bar from -5 to 0, which would be awfully strange!

Review: How are histograms and bar charts different?

Students make histograms from the animals-dataset, and explore different bin sizes.

The size of the bins matters a lot! Bins that are too small will hide the shape of the data by breaking it into too many short bars. Bins that are too large will hide the shape by squeezing the data into just a few tall bars. In this workbook exercise, the bins were provided for you. But how do you choose a good bin-size?

A display of how long it takes animals to get adopted can make it easier to get an idea of what adoption times were most common, and if there were any unusually long or short times that it took for an animal to be adopted.

Some observations you can share with the class, to get them started:

If someone asked what was a typical adoption time, we could say: “Almost all of the animals were adopted in 10 weeks or less, but a couple of animals took an unusually long time to be adopted — even more than 20 or 30 weeks!” Without looking at the histogram’s shape, we could not have drawn this conclusion.

Have students talk about the bin sizes they tried. Encourage open discussion as much as possible here, so that students can make their own meaning about bin sizes before moving on to the next point.

Histograms are a powerful way to display a data set and assess its shape. Choosing the right bin size for a column has a lot to do with how data is distributed between the smallest and largest values in that column! With the right bin size, we can see the shape of a quantitative column. But how do we talk about or describe that shape, and what does the shape actually tell us? The next lesson addresses all of these.