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Session 3: Number Diagrams

Session Title

Number Diagrams 

Objective
  1. Understand different ways to represent numbers using diagrams and number sentences.
  2. Explore addition, subtraction, and multiplication patterns for small numbers.
  3. Strengthen visual learning and numerical flexibility using hands-on activities.

Concept

Number diagrams are visual representations that show the different ways to break down or build a number using operations like addition, subtraction, or multiplication.

Examples:


4 = 2 + 2


4 = 2 × 2


4 = 1 + 1 + 2


4 = 5 – 1


4 = 8 - 4


4 = 8 ÷ 2


4 = 16 ÷ 4

Materials Required

Board & Chalk, Number cards, Colored markers, Chart paper, Dice, Counters(Counters means small physical objects used to help students visualise and solve math problems.

They can be anything like:

Colored chips

Bottle caps

Beads

Pebbles

Coins

Buttons

Methodology

Activity-based Learning: Drawing diagrams, using counters. Exploratory Learning: Discovering patterns in numbers through multiple operations.

Session Duration 

120 MInutes

Introduction Activity (10 minutes):

NUMBER EXPLOSION: Write a number (e.g., 4 or 5) in the centre of a chart. Ask students to shout out all the ways they know to make that number using +, –, ×. Write each version as a diagram around the number like a web.

Main Activity:

Objective: Help students visualise number flexibility.

Hands-On Activity:

Counter Challenge (20 minutes)

  1. Give students counters and a number (e.g., 6).
  2. Ask them to use the counters to show different ways to make the number:
  3. Grouping (e.g., 3 + 3)
  4. Arrays (e.g., 2 rows of 3)
  5. Removal (e.g., start with 10 and take away 4)
  6. Students draw diagrams of each representation.

Diagram Race Game (30 minutes)

(Show one example of how to do it.)

  1. Write numbers 1–10 on the board.
  2. Divide the class into teams.
  3. Each team gets a number and 3 minutes to write or draw as many correct diagrams as possible (e.g., 6 = 3 + 3, 2 × 3, 7 – 1).
  4. Teams present and explain their diagrams.

Time to Solve (10 Minutes)

Individual worksheet:

  1. Match the number diagrams to their values.
  2. Complete number webs.
  3. Create 3 different diagrams for each of the given numbers: 5, 6, and 8.

Expected Learning  Outcome:

Knowledge building: Deeper understanding of number structure.

Flexible use of basic operations to express numbers.

Skill Building:

  • Visual reasoning
  • Creative problem-solving
  • Mathematical communication

Review Questions:

Ask:

    1. How many ways can you show the number 7?
    2. Is 2 × 3 the same as 3 + 3? Why or why not?
    3. What’s the smallest number you can show using both multiplication and subtraction?

Follow-up Tasks:

Homework:

  1. Choose a number between 5 and 10. Show 4 different ways to make that number using diagrams.
  2. Complete a number web for the number 6 using +, –, ×.
  3. Explain which representation you find easiest and why
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