5 · Ordering numbers
5
This session is designed to enable learners to:
앫 decide which of two numbers (up to 1 000) is the larger (or smaller);
앫 arrange numbers in order (up to 1 000);
앫 position numbers between two given numbers.
and to help learners to:
앫 develop confidence when comparing and ordering numbers.
앫 A set of 10 cards, at least 15 cm square, numbered from
0 to 9.
앫 12 cards, each with a different number between 1 and 1 000.
앫 Blank cards about 15 cm square (about 12, plus at least one per learner, plus some spares).
앫 String and pegs or clips (the same number as the number of cards, including blanks).
앫 Felt tip pens.
For each learner you will need:
앫 calculator;
앫 mini-whiteboard, marker and cloth.
For each pair or small group of learners you will need:
앫 Sheet 1 – Finding consecutive numbers (part one).
For learners who need more challenging or more straightforward examples you will also need copies of:
앫 Sheet 2 – Finding consecutive numbers (part two);
앫 Sheet 3 – Finding consecutive numbers (part three).

Ask each learner to draw three boxes, each about 5 cm square, in a row on a sheet of paper or on their mini-whiteboard.
Show learners your set of 10 cards, each with a digit from 0 to
9, and explain that you are going to draw a card at random from the set and show it to them. They have to write that digit in any one of their boxes. You will then draw a second card; they have to write that digit in another box. You will then draw a third card. They should write this digit in the third box, thus ending up with a three-digit number.
If necessary, carry out a ‘trial run’ to make sure everyone understands the procedure.
Next, explain that the object of the activity is to make as large a number as possible from the three cards/digits you draw from the set. However, once a digit has been written in a box, it cannot be moved. Explain that once you have chosen a digit from your pack, you will put it to one side so it cannot be selected again in that game, though you will start with the full pack for each game.
Carry out the activity.
Ask a learner for their three-digit number and write it on the board. Ask if anyone has a larger number.
Learners must read their number out in full and not digit by digit. (For example,
‘five hundred and sixty three’ not ‘five six three’.)
If a learner reads out what they think is a larger number, write it on the board and ask the group if they agree that it is larger and, if so, why
(or, if not, why not). This discussion should help to bring out some misconceptions about place value.
The activity can be repeated several times. It can be varied by asking learners to aim to make the smallest possible number.

It can be made more challenging by drawing four cards from the set. Learners still have only three boxes so they have to decide whether to write a given digit in a box or to reject it.
Another variation is for learners to aim to make a number that is nearest to a given one, for example 654.
Have a discussion about the strategy learners used when doing this activity. You could ask questions such as:
앫 If you have to place a large number, where’s the best place to put it?
앫 How do you deal with where to put mid-range numbers?
앫 How would the game change if the teacher put the cards back in the pack instead of discarding them?
앫 You could have a discussion about probabilities if appropriate. For example, is each number equally likely to come up? If I draw an 8, is it best to put it in the highest or second highest position? Are there any situations when there is only one place to put a number?
If learners are still unsure about ordering numbers, put up some string across the room and peg about 12 cards to it, each with a number between, say, 1 and 1 000, but not in numerical order. Ask learners to take it in turns to move one card, aiming to arrange the numbers in ascending order from left to right.
Each learner should explain to the group why they moved the card/number that they did.
It may be helpful to draw attention to the difference between the value of the numbers on the line, especially if the cards for, say, 10, 100 and 1 000 have been spaced equally.
Next, ask each learner to write on a piece of card a number that does not yet appear on the line. Ask learners to exchange cards with each other. Each learner should then peg their card/number in position on the line and explain why it goes in that position.
This can be repeated as many times as is needed until learners are confident.
The activity can be varied by arranging cards/numbers in descending order from left to right.

Explain ‘consecutive numbers’ by writing the following pairs of numbers on the board and asking learners to identify what they have in common.
1, 2 14, 15 27, 28 101, 102 456, 457
Ask learners to give examples of two consecutive numbers, three consecutive numbers, and so on, using their mini-whiteboards.
Ask learners to work in pairs. Give each pair a copy of
Sheet 1 – Finding consecutive numbers (part one) and a calculator. The Sheet can be cut into horizontal strips if you prefer. Explain that, in each case, two consecutive numbers multiply to produce the given answer. Using estimation and trial and error, learners have to find the two consecutive numbers. Emphasise that they must keep a record of each trial and its product on a mini-whiteboard or a piece of scrap paper.
This will give guidance for the next trial and avoid repetition.
In the process of finding the correct numbers, learners have to decide whether a number shown on their calculator display is bigger or smaller than the number on the Sheet, so they are also working on ordering numbers.
Learners who find the activity easy could be given Sheet 3 –
Finding consecutive numbers (part three), which is more challenging, or be given even more challenging answers such as 135 792.
Similarly, Sheet 2 – Finding consecutive numbers (part two) gives a selection of easier examples for learners who may need to start with these.
Write on the board the numbers 1, 2, 3, 4 and a single-digit number of your choice. Explain to learners that the task is to use their calculators to create a multiplication sum that produces the largest possible number. No number can be repeated and only one multiplication can be performed, for example (if the extra number is 7) 321 × 74 or 7 × 4 321.
As soon as a learner has a possible answer, write it in full on the board (or ask the learner to do so). If another learner thinks they can improve on it, write their answer on the board but without making any comment. When everyone has finished trying, review and discuss the answers that are on the board.
Learners should discuss which is the best answer and justify

their decision. Encourage learners to give their answers in the correct format, for example ‘seven hundred and forty-three’ not
‘seven, four, three’. Ask learners to explain how they decide which is the largest number.
To vary the activity, ask learners to make the smallest possible number, or to see who can get nearest to a given number, for example 450.
The activity can be made more challenging by using 1, 2, 3, 4, 5 and another number, and then 1, 2, 3, 4, 5, 6 and another number, and so on.
앫 Using mini-whiteboards, ask learners to give an example of a number that is less than, say, 500, or greater than 735, or between 675 and 680.
앫 Write four or five numbers on the board and ask learners to write on their mini-whiteboards which is the biggest, or the smallest, or the one nearest to, say, 650.
앫 Some of these ideas can be adapted for decimals or negative numbers.

×
×
×
×
×
= 462
= 870
= 992
= 702
= 272

×
×
×
×
×
= 20
= 72
= 110
= 6
= 42

×
×
×
×
×
= 1 482
= 3 906
= 3 422
= 8 372
= 2 070