Numbers Teach and Try Teacher Notes

Objective

The objective is to get the class to write a Go program to solve simple mathematical problems. The program will only use addition (typed +), subtraction (typed -), multiplication (typed * not ×) and division (typed / not \ or ÷). Creating this program will require the class to use the text editor (either Atom or LiteIDE) to create and save the source code file and the terminal/command line to run their program.

Each subsequent lesson will require the class to use both the text editor and the terminal.

Before you begin

We are aware that Computing has been added to the National Curriculum but that the majority of teachers have no background in Computing. These teacher notes are intended as an addition to any CPD you may have or will be undertaking through your school.

We strongly recommend that you read the lesson material and attempt the exercises for Numbers before you read these notes.

In doing so you may make the same mistakes as your class are likely to make. Solving these problems will provide you with both the confidence and knowledge to help your class with the material.

We will be taking a step by step approach that will build up your knowledge over time.

Learning outcome

The class should be able to:

• Start their text editor
• Create a source code file
• Save a source code file
• Build and run their program
• Understand how to type simple mathematics in Go
• Reason about the result of mathematics in Go.
• Understand that the program represents a sequence
• Understand that the sequence executes in order

Teaching prerequisites

The example program is sufficiently simple that little or no additional teaching should be required beforehand. However the class needs to have covered

• Basic keyboard/typing and mouse skills.
• The class needs to understand the four basic mathematics operators and how to use them.
• The class needs to understand numbers and how to read and write them, from units to thousands and ideally tens of thousands.
• The class need to understand that mathematics can be chained together. So example 1 + 2 + 3 + 4 + 5 = 15

Computing Links

Sequences. The program demonstrates a sequence of instructions that are executed in order to print the results to the terminal window.

Cross-Curricular links

There is a direct link to mathematics, both in terms of number theory and simple mathematics.

How Fast are You?

Notes for slide 2

How long the pupils take is not important in this case. The computer would be billions of times faster.

If each sum can be calculated in a single cycle then the total time for all 4 sums is

0.0000000005 * 4 = 0.000000002 seconds

0.0000000005 being the time in seconds for one cycle at 2Ghz.

Assuming there are no errors in the program, the computer will never make a mistake. If there is a mistake in the program that is the fault of the programmer not the computer.

This is why we use computers. They are faster and more reliable than people.

Everything is a Number

Notes for slide 4

Numbers are the most fundamental concept in computer science. Computers can only process numbers. So everything - numbers, letters, pictures, mp3 music files, word processor documents are lists of numbers.

Numbers also indicate the limit of a computer. A computer does not have an infinite range, as the set of natural numbers (ℤ) does. The range of a number is fixed. It depends how many bits are used to represent the number and if the number is also signed (or not). With 5 bits you can count to a maximum of 31. With 10 bits you can count to maximum of 1024. 16 bits gives 65,534.

This helps dispel the notion that computers can do anything. They can’t, there are limits.

The concept of a number range also leads to the concept of a type. Numbers with different ranges are of different types. Integer numbers are a distinct type from natural (or real) numbers. Types are fundamental to Go and all other computer languages at some level. Go makes the type explicit - it is a statically types language. Python by contrast hides or masks the type - it is a dynamically typed language. Both languages have types but they approach the problem differently.

Numbers also have a direct relationship to both the logical as well as the physical structure of a computer’s memory.

The concept of type and range and binary and the link to computer memory will be explored in later lessons.

The rainbow can be represented by numbers if a unique number is assigned to each colour. For example

• Red = 1
• Orange = 2
• Yellow = 3
• Green = 4
• Blue = 5
• Indigo = 6
• Violet = 7

The sequence

3, 2, 1, 4, 7, 6, 5

would therefore represent the colour sequence

Yellow, Orange, Red, Green, Violet, Indigo, Blue

Go Programs

Notes for Slide 4

Go is just one of about 400 computer languages - 99% of which are textual i.e. the programmer has to type the commands in before the program can be run. Scratch/Kudu/Alice etc are all graphical languages. The programmer connects blocks which represent the logical structure together to create the program. This is not typical.

Go programs are typed into a text editor. Once the commands have been typed in the file needs to be saved. A file that contains the Go instructions is called a source code file. Once the source code file has been saved an attempt can be made to run the program.

Numbers in Go

Notes for slide 5

The numbers are all whole numbers or more correctly integer numbers. There are no fractions or decimals in the list of numbers. For the avoidance of doubt, zero is considered to be in the set of whole numbers.

Go calls integer numbers int for short. The pupils will see this in subsequent lessons

Sums in Go

Notes for slide 6

Maths in Go is the same as maths anywhere else. The language of maths is universal. The normal rules of maths therefore apply.

The only unusual point is that × is replaced with * for multiplication and ÷ is replaced by / for division.

The answer is 7. 1 + 2 * 3 is 1 + 6 which is 7. Multiplication is done before addition as per normal algerbra.

How to Create a Go Program

Notes for slide 7

The pupils have to use a terminal window to make a new directory, and to run the Go program.

The pupils use a text editor to type in the program, and save it, before it can be run. The pupils are creating the source code file.

A Go source code file should be saved with a .go file extension.

How the pupils open a command prompt or terminal window varies with the operating system. See the Windows, MacOS X, Linux or Raspberry Pi install guides for the instructions

We are going to put each Go program in its own directory. This is the recommended practice for Go programs.

In your terminal you need to change to the location of your Go Workspace. To do this type

cd $GOPATH/src/

cd %GOPATH%\src\

Now you need to make a new directory. We need to call this numbers after the program we will write. Then we need to change directory into the new numbers directory.

mkdir numbers
cd numbers

Now you need to start you editor, either Atom or LiteIDE

atom numbers.go

liteide numbers.go

You must make sure that the source code file is saved as numbers.go in the numbers directory in the Go workspace.

To run the program the pupils need to use the terminal window and type:

go run numbers.go

Where numbers.go is the name of the source code file. The command must be run from the numbers directory.

The pupils will need to repeat this process in each lesson, so they will quickly become used to it.

The numbers.go Program

Notes for slide 8

Let’s look at the numbers.go program in more detail. Here it is again.

 1package main
 2
 3import "fmt"
 4
 5func main() {
 6	fmt.Println("The numbers program shows you how to add, subtract")
 7	fmt.Println("multiple and divide integer numbers.")
 8	fmt.Println("One plus one is typed: 1+1")
 9	fmt.Print("1+1=")
10	fmt.Println(1 + 1)
11
12	fmt.Println("Ten subtract three is typed: 10-3")
13	fmt.Print("10-3=")
14	fmt.Println(10 - 3)
15
16	fmt.Println("Three multiplied by four is typed: 3*4")
17	fmt.Print("3*4=")
18	fmt.Println(3 * 4)
19
20	fmt.Println("Six divided by two is typed: 6/2")
21	fmt.Print("6/2=")
22	fmt.Println(6 / 2)
23}

</div>

package main
....
func main() {

import "fmt"

fmt.Println("The numbers program shows you how to add, subtract")
fmt.Println("multiple and divide integer numbers.")
fmt.Println("One plus one is typed: 1+1")
fmt.Print("1+1=")

fmt.Println(1 + 1)

fmt.Println(2)

fmt.Println("2")