Lesson 3: A Sophisticated Calculator¶

Authors:	Paul Xu, Marcus Penny
Date:	Jan 27, 2018
Time:	1 hour

Lesson Information¶

This lesson introduces the students to the basic mathematical and string operations in Python. Although we will not formally formulate the differences between data types, they will have first hand experience of the differences between numeric types and string types. They will also have basic concepts of variables and how to store values in variables. Using interactive programming, the students will use Python to solve mathematical problems in Python and print it out.

The purpose of the lesson is to:¶

Introduce students to Python programming using the interactive shell
Familiarize students with mathematical operations in Python
Informally introduce the concept of data types and variables
Use Python to solve mathematical problems

Driving Questions:¶

What does computation mean?
How can we use computation in Python?
What are the differences between numbers and strings?
How can we save the result of our computation?

Computer Science Concepts:¶

Mathematical operators, primitive data types (string and numbers), variables (storing values)

Materials Needed:¶

Raspberry Pi 3

Target Skills:¶

Students will be able to

SWBAT use mathematical operators to work on math problems in Python shell
SWBAT informally distinguish the differences between data types
SWBAT understand one reason why we need variables

Instructional Plan and Structure¶

Overview of the lesson (5 minutes)¶

Why do we call computers computers? What do we mean by computation? Begin the class by asking the students these questions, and engage them in a brief whole-class discussion. Then, introduce the students to the topic of this class: mathematical computations.

Let’s Code Together! (30 minutes)¶

Start a Python shell (either in Thonny Python or the terminal), and if possible, also start a Linux calculator on the side or use a real calculator, so students understand that Python can be used as a sophisticated calculator. Start typing in basic math operations, such as 5 + 10 and 1.2-1.0. Addition and subtraction might be easy, but some students might not be familiar with the multiplication * operator, the division / operator, and/or the exponentiation operator **. Make sure they locate these operators on the keyboard. The exponentiation operator can be used to obtain really large numbers, which Python handles well. Make sure the students have the chance to experience that.

Tip

Interesting result

The result of 1.2-1.0 might not be unexpected. It has something to do with the way Python represents floating numbers, and we will get back to that more formally later in this course.

Also, it does NOT matter if there are spaces between values and operators.

Here are the basic mathematical operators in Python:

Python operator Mathematical Operator

a + b \(a+b\)

a - b \(a-b\)

a * b \(a \times b\)

a / b \(a \div b\)

a ** b \(a^b\)

It is possible to carry out complicated operations. The order in which each operation is performed is exactly the same as what students are familiar in math. It is, of course, possible to change the precedence by using the parenthesis ().

With this knowledge, let’s do some math! The following two questions are taken from 6th Grade MCAS Math released problems.

At the beginning of the day, a water tank contained 526.8 gallons of water. During the day, some of the water was used to water a garden. At the end of the day, the water tank contained 318.05 gallons of water. What was the total amount of water used that day?
Which of the following expressions have the largest value?
1. \(2^3+2^3\)
2. \(2^3+7^1\)
3. \(3^2+3^2\)
4. \(3^2+7^1\)

Saving the results of our computation (10 minutes)¶

Just like we want to save the games that we have played for a while, sometimes we want to save the results of operations so that we can use them in the future. We can achieve this by using variables. For example:

>>> a = 2**5
>>> b = (3+10) * 8

The computer will associate these names with the values, and later when we use them, we can just use the name:

>>> a
32
>>> b
104
>>> c = a + b
>>> c
136

Caution

What happens if we write a = a + b?

Numbers and Strings (10 minutes)¶

What if we want to use texts in Python? Unfortunately, if we use texts directly like this:

>>> Hello, Python!
  File "<stdin>", line 1
    Hello, Python!
                 ^
SyntaxError: invalid syntax

As you can see we encountered an error called SyntaxError. This means Python does not understand what we just wrote. In Python (and most programming languages), texts are put in quotation marks. For example:

>>> "Hello, Python!"
'Hello, Python!'

Tip

Single quotation marks ' or double "?

It doesn’t matter as long as they match.

What if we put numbers in quotation marks?

>>> "123" + "456"
'123456'

We got unexpected results!!! And when we do this:

>>> "123" + 456
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: must be str, not int

We got a TypeError!!! We will discuss that in our next lesson.

Review and Assessment¶

Answer the following review questions:

What is computation?
What is one type of computation Python is really good at?
Why do we need variables?