MATHEMATICSOrdering Numbers

• The aim of this powerpoint is to teach you techniques for putting numbers in order as well as comparing numbers.

EITHER

• Take notes as you go along, include some examples and write down any questions and your answers (which you can mark as you go along)

OR

• At the end of the powerpoint, printout the notes called Calc1b

Key Terms

• Before we start ordering numbers you need to know the meanings of several key words and symbols as follows:

ASCENDING means going up

(from smallest to biggest)

DESCENDING means going down

(from biggest to smallest)

< means that the left is smaller than the right

> means that the left is greater than the right [HINT: Think of the symbol as a crocodile’s open mouth – the crocodile will want to eat the biggest number!]

Ordering Numbers

• Many students find it easier to order numbers by writing them in column format ensuring the correct digits line up in their correct column values.

• If you are finding things in ascending order, you then look for the value whose first digit appears in the smallest value column.

• If you are finding things in descending order, you look for the value whose first digit appears in the largest column.

Simple Example

• Put these values in ascending order:

173 59 1208 804 7.4 31 95

Writing them in column format we get … Th H T U . Tth

1 7 3 5 9

1 2 0 8 8 0 4

7 . 4 3 1 9 5

ANSWER: 7.4

This is the smallest value starting in the units column

These three are the next biggest as they all start in the tens column

1208

Of the three, the one starting with 3 tens is smaller than the one starting with 5 tens and then lastly the one starting with 9 tens

31 59 95

These two are the next biggest as they start in the hundreds column

Of the two, the one starting with 1 hundred is smaller than the one starting with 8 hundreds

173 804

This leaves this as the last (and biggest) value

Harder Example

• Put these in descending order:

3.14 4.013 0.0143 4.31 3.104 1.43

Write them in column format

They all start in the units column but

TWO values start with the biggest units

digit of 4 so look at THEIR next digit…

0 and 3, so the 4.3…. value is bigger

than the 4.0…. value.

U . Tth Hth Thth TThth

3 . 1 44 . 0 1 30 . 0 1 4 35 . 3 16 . 1 0 41 . 4 3

The next biggest are the TWO values starting with 3 units. BOTH of these have 1 as their next digit so look at the NEXT digit after that and we have… 4 and 0, so the 3.14…. value is bigger than the 3.10…. value.

The next biggest value starts with 1 unit

and

The smallest value starts with 0 units.

ANSWER: 4.31 4.013 3.14 3.104 1.43 0.0143

Practice 1

• On paper, have a go at writing these two sets of numbers in ascending order.

• When you have ALL your answers, click to check them.

Set 1: 759 83 12 3582 430 2995

Set 2: 5.92 2.95 9.5 2.059 5.002

ANSWERS:

Set 1: 12 83 430 759 2995 3582

Set 2: 2.059 2.95 5.002 5.92 9.5

Practice 2

• On paper, have a go at writing these two sets of numbers in descending order.

• When you have ALL your answers, click to check them.

Set 1: 6308 8603 3680 8306 6830 3086

Set 2: 12.5 5.012 2.15 51.02 15.02 5.12

ANSWERS:

Set 1: 8603 8306 6830 6308 3680 3086

Set 2: 51.02 15.02 12.5 5.12 5.012 2.15

Practice 3

• Put the correct symbol (< or >) between each pair of answers.

• When you have worked ALL of your answers out, click to check them

1) 59 76

2) 3276 3267

3) 835 853

4) 4.7 3.02

5) 1.25 1.052

6) 12.08 12.8<

<

<

>

> >

What next? (Page 1 of 2)

• If you haven’t made any notes or copied any examples, questions and answers out during this presentation, print out the notes called Calc1b. Read through them and make sure you answer any questions.

• Work through the MyMaths lesson (and then the online homework) called Ordering Whole Numbers found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=placevalue/orderingwhole&taskID=1217 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=placevalue/orderingwholeOH&taskID=1217

• Save and complete the worksheet called: OrderInt-S1.xlsx

• Continued on next slide…

What next? (Page 2 of 2)

• Work through the MyMaths lesson (and then the online homework) called Ordering Decimals found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=decimals/decimalOrdering&taskID=1072 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=decimals/decimalOrderingOH&taskID=1072

• Save and complete the worksheet called OrderDec-S1.xlsx

• Now move on to the Calc2a-Round powerpoint