Subnetting: Network, Broadcast and Usable Addresses

Lesson plan

Level

Beginner

Time

About 80 minutes; the steps below add up to 80

A street of 256 houses with two numbers kept back, split into blocks of 64, gives learners the subtract-two rule and the block-size method before any network address is calculated. Each method step then opens with a prediction (what AND with the mask does, what the broadcast address must be, which block 77 is in, what a longer prefix does), and checks use new addresses after each method is taught. The habit to build: find the shared octet and the block size first, then everything else follows.

Objectives

• Find a network address with a binary AND, and a broadcast address by setting the host bits to 1
• Count total and usable addresses from the number of host bits
• Use the block-size method when the boundary falls inside an octet
• Decide whether two devices share a subnet
• Explain why /31 and /32 do not follow the subtract-two rule

Before the lesson

• Open this page on your own screen and use “Open the lesson window” to open the lesson in a second window. Share only that second window.
• Learners need the Subnet Masks and CIDR and Number Systems lessons first.
• This is a long, practice-heavy lesson: consider two sessions, breaking after the octet-boundary step. Have spare addresses ready for extra practice.
• The lesson takes about 80 minutes. To teach it in two parts, stop after “When the boundary falls inside an octet”; the second part opens with “How changing the prefix moves the boundary”.
• In presentation mode every step is shown in turns: Next reveals one moment, part or answer at a time, and the instructor view names what is on screen and what comes next.

Steps

1. Introduction Opening

   On screen: the lesson’s title, module and number; Next adds its objectives and key terms, as the lesson page lists them; Next again begins the first step.

   Objectives on screen

   • Find a network address with a binary AND, and a broadcast address by setting the host bits to 1
   • Count total and usable addresses from the number of host bits
   • Use the block-size method when the boundary falls inside an octet
   • Decide whether two devices share a subnet
   • Explain why /31 and /32 do not follow the subtract-two rule

   Purpose: A street of 256 houses with two numbers kept back, split into blocks of 64, gives learners the subtract-two rule and the block-size method before any network address is calculated. Each method step then opens with a prediction (what AND with the mask does, what the broadcast address must be, which block 77 is in, what a longer prefix does), and checks use new addresses after each method is taught. The habit to build: find the shared octet and the block size first, then everything else follows.

2. 1. A street of 256 houses Think 5 min

   Purpose: Preview the subtract-two rule and the block-size method with a street.

   Ask

   • How many houses can be lived in?
   • Ask which block house 77 is in.

   Responses to expect

   • 256 is often miscounted as 255; count 0 to 255 together.
   • On screen in turns: the opening question, its answer; then the question on which block house 77 is in, and its answer.

   Discussion pause: Let learners work both answers out on paper before revealing them.

   In the lesson window

   • Think it through: A street has houses numbered 0 to 255. Number 0 is kept to name the street, and number 255 is kept for a noticeboard that reaches every house. How many houses can actually be lived in?
   • Think it through: The street is split into four equal blocks of 64 numbers. Which block is house 77 in?

3. 2. What we want to find Explain 3 min

   Purpose: Set out the five questions subnetting answers.

   Ask

   • Which of the five questions decides whether a router is needed?

   Responses to expect

   • Whether two devices share a subnet.
   • On screen in turns: the opening; then the five questions subnetting answers.

4. 3. Step 1: find the network address with binary AND Predict 7 min

   Purpose: Find the network address with a bitwise AND.

   Ask

   • What happens to the network bits and the host bits when ANDed with the mask?

   Responses to expect

   • Most see it once they read the four rows of the AND table aloud.
   • On screen in turns: the opening question, its answer; then why AND gives the network address, worked for 131.107.5.15.

   In the lesson window

   • Think it through: Look at the AND table. If you AND an address with a mask that has 1s for every network bit and 0s for every host bit, what happens to each part of the address?

5. 4. Step 2: find the broadcast address Predict 4 min

   Purpose: Find the broadcast address by setting host bits to 1.

   Ask

   • What must the broadcast address be?

   Responses to expect

   • The last address: all host bits 1.
   • On screen in turns: the opening question, its answer; then the broadcast address for 131.107.5.15/24.

   In the lesson window

   • Think it through: If the network address is the address with every host bit set to 0, what would you expect the broadcast address to be?

6. 5. Step 3: count the addresses Explain 6 min

   Purpose: Count total and usable addresses from the host bits.

   Ask

   • Five host bits: how many usable?

   Responses to expect

   • 32 is the common slip; ask which two are reserved.
   • On screen in turns: the opening; then the check question on five host bits, and its answer; 131.107.5.15/24 worked out.

   Misconceptions to challenge

   • A learner may believe: “A subnet with 6 host bits has 64 usable addresses.” Respond: It has 64 in total and 62 usable.

   In the lesson window

   • Check your understanding: A network has 5 host bits. Which statement is right, by the usual rule?

7. 6. Prefixes on octet boundaries: /8, /16 and /24 Explain 6 min

   Purpose: Read answers straight off for /8, /16 and /24.

   Ask

   • For 10.20.30.40/8, which octets become 0 for the network address?

   Responses to expect

   • The last three.
   • On screen in turns: the opening; then three octet-boundary examples, starting with /8; /16; /24; the /8 and /16 examples worked out.

8. 7. When the boundary falls inside an octet Experiment 16 min

   Purpose: Work out subnets whose boundary falls inside an octet, with the block-size method and the AND to confirm.

   Ask

   • For /26, what is the block size and which block holds 77?
   • Ask for the network address of 10.5.200.9/20.

   Responses to expect

   • The third-octet case (/20) is where most mistakes happen: the fourth octet becomes 0 and 255.
   • On screen in turns: the opening; then worked example: the question on 192.168.10.77/26, and its answer; 192.168.10.77/26 step by step, starting with the shared octet; the mask; the block size; placing the address; the network and broadcast addresses; the count; the blocks for 192.168.10.77/26; the binary AND that confirms it, and the result; 172.16.45.9/20 step by step, starting with the shared octet; the mask; the block size; placing the address; the network address; the broadcast address; the count; 172.16.45.9/20 worked out; the check question on 10.5.200.9/20, and its answer.

   Misconceptions to challenge

   • A learner may believe: “The network address always ends in .0 and the broadcast in .255.” Respond: Only where the boundary lies on an octet edge.

   Discussion pause: Reveal each step of the two worked examples one at a time; let the class do the step before it appears.

   If the explanation does not land: Write the block starts along the board (0, 16, 32 … 240) and have learners point to where the address falls.

   To go further

   • Work out the network and broadcast addresses of 172.31.77.200/19.

   In the lesson window

   • Think it through: Before the worked example: for 192.168.10.77/26 the fourth octet has 6 host bits. What is the block size, and which block is 77 in?
   • Check your understanding: What is the network address of 10.5.200.9/20?

9. 8. How changing the prefix moves the boundary Predict 6 min

   Purpose: Show how each extra network bit halves the network.

   Ask

   • /26 to /27: what happens to the size?

   Responses to expect

   • Doubling is a common first guess.
   • On screen in turns: the opening question, its answer; then the same address from /24 to /28, starting with /24; /25; /26; /27; /28.

   Discussion pause: Before each row of the prefix table appears, ask what the network, broadcast and counts will be.

   In the lesson window

   • Think it through: The prefix of 192.168.10.77 changes from /26 to /27. What happens to the size of its network?

10. 9. Do two devices share a subnet? Check 8 min

    Purpose: Decide whether two devices share a subnet by comparing network addresses.

    Ask

    • Ask whether 10.0.8.5/21 and 10.0.13.200/21 share a subnet.

    Responses to expect

    • Different third octets mislead; find the block first.
    • On screen in turns: the opening; then four pairs to compare, starting with .77 and .100; 192.168.10.77 and .130; 172.16.40.1 and 172.16.45.9; the two-PC example; the check question on 10.0.8.5 and 10.0.13.200, and its answer.

    If the explanation does not land: Two houses are neighbours if they are on the same street block; the house numbers can differ a lot and still share the block.

    In the lesson window

    • Check your understanding: Are 10.0.8.5/21 and 10.0.13.200/21 on the same subnet?

11. 10. Special cases: /31 and /32 Predict 6 min

    Purpose: Explain the /31 and /32 exceptions.

    Ask

    • Two addresses minus two: is that a problem?

    Responses to expect

    • Learners see the problem immediately.
    • On screen in turns: the opening question, its answer; then why /31 is an exception; /32, a single address; /31 and /32 worked out; a wrong mask and partial reachability.

    Misconceptions to challenge

    • A learner may believe: “A /31 has no usable addresses.” Respond: On a point-to-point link both are usable.

    In the lesson window

    • Think it through: A link joins exactly two routers, and its network has only 2 addresses. By the usual rule, how many usable addresses would it have, and is that a problem?

12. 11. Apply it in a new situation Apply 5 min

    Purpose: Set up independent application, ideally on a later day.

    Ask

    • Who will try these now, and who later in the week?

    Responses to expect

    • The wrong-mask question is a classic support fault; the /29 tests counting.
    • On screen in turns: the opening question, its answer; then the question on 203.0.113.0/29, and its answer.

    In the lesson window

    • Apply it: A device has 192.168.10.77 with /24, while its neighbours use /26. It can reach some devices but not others. Why?
    • Apply it: How many usable addresses does 203.0.113.0/29 have?

13. 12. Check your understanding Check 5 min

    Purpose: Check the lesson against the approved revision-bank questions.

    Ask

    • Answer individually, then compare before revealing.

    Responses to expect

    • The two-PC question links back to the same-subnet step.
    • On screen in turns: the opening; then the revision questions one at a time, each followed by its answer; where to practise next.

14. 13. What to remember Consolidate 3 min

    Purpose: Summarise the five points, the key terms and the misunderstandings.

    Ask

    • Without looking: the network and broadcast addresses of 192.168.10.77/26.

    Responses to expect

    • 192.168.10.64 and 192.168.10.127.
    • On screen in turns: the opening; then the summary; the key terms; the common misunderstandings.

15. Lesson recap Closing

    On screen: the lesson’s objectives again; Next adds the closing question, which asks the class to explain each one in their own words without looking back. It says nothing about what anyone has learnt: use the answers to decide what to revisit.

    Points to listen for

    • Network bits kept, host bits zeroed: the network address.
    • Host bits all set: the broadcast address.
    • Two to the power of the host bits, less two, are usable.
    • Find the shared octet, then the block it falls in.
    • Point-to-point /31 and single-host /32 break the subtract-two rule.

Consolidation

• Network bits kept, host bits zeroed: the network address.
• Host bits all set: the broadcast address.
• Two to the power of the host bits, less two, are usable.
• Find the shared octet, then the block it falls in.
• Point-to-point /31 and single-host /32 break the subtract-two rule.