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Basic 3 · Mathematics · Counting and Representation

Describing Numbers and Their Relationships

In this topic you will describe numbers using expanded form and say how numbers are related.

By the end of these notes you should be able to:

  • Write numbers in expanded form
  • Find numbers 10, 100 and 1000 more or less
  • Describe odd and even numbers up to 10,000

What you already know

  • Numbers up to 10,000

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

Strand
Number
Sub-strand
Counting and Representation
Indicator
B3.1.1.1.2 – Describe numbers and the relationship between numbers

Introduction

The number 3,562 can be broken into parts: 3,000 + 500 + 60 + 2. Breaking numbers into parts helps us understand them.

1. Expanded Form

Expanded form: A number written as the sum of the values of its digits.

Example

Write 3,562 in expanded form.

  1. 3 thousands = 3,000
  2. 5 hundreds = 500
  3. 6 tens = 60
  4. 2 ones = 2

Answer: 3,000 + 500 + 60 + 2

2. More and Less

Around 4,650
1000 less100 less10 lessNumber10 more100 more1000 more
3,6504,5504,6404,6504,6604,7505,650
The number 4,650 with arrows to 10, 100 and 1000 more and less
Figure 1: More and less than 4,650 Draw the arrows for 2,300.Illustration: Sirbus

3. Odd and Even

Look at the ones digit only. 7,384 is even (ends in 4). 5,219 is odd (ends in 9).

New words

expanded form
A number shown as a sum of place values.
relationship
How things are connected.
more
Bigger by an amount.
less
Smaller by an amount.

Summary

  • Expanded form shows the value of each digit.
  • Adding 10, 100 or 1000 changes only one place.
  • The ones digit tells if a number is odd or even.

Class activity: Number Neighbours

  1. Pick a number card.
  2. Write it in expanded form.
  3. Write the numbers 10, 100 and 1000 more and less.

You need: Bottle tops, Bundles of sticks, Locally made number cards

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. What is 100 more than 2,450?

    • A. 2,550
    • B. 2,460
    • C. 3,450
    • D. 2,350
    Show answer
    Answer: 2,550Only the hundreds digit goes up by 1.

  2. 2. Which is the expanded form of 6,041?

    • A. 6,000 + 40 + 1
    • B. 6,000 + 400 + 1
    • C. 600 + 40 + 1
    • D. 6 + 0 + 4 + 1
    Show answer
    Answer: 6,000 + 40 + 1There are no hundreds.

  3. 3. 1000 less than 5,000 is 4,000.

    • A. True
    • B. False
    Show answer
    Answer: True5,000 − 1,000 = 4,000.

  4. 4. 10 more than 3,995 is 4,095.

    • A. True
    • B. False
    Show answer
    Answer: False3,995 + 10 = 4,005.

  5. 5. 7,000 + 200 + 30 + 4 = ______

    Show answer
    Answer: 7,234Add the parts.

  6. 6. Write 9,308 in expanded form.

    Show answer
    Answer: 9,000 + 300 + 8No tens.

Homework

  1. Write your house number or a phone number part in expanded form.