Mult-e-Maths



Comparing numbers 4NUM5

National curriculum objective

Pupils should be taught to:

• order and compare numbers beyond 1000.

Prior knowledge and skills

• Read and writing 4-digit numbers.

• Know what each digit represents in a 4-digit number.

• Compare numbers with less than 4 digits.

Vocabulary

symbol, >, greater than, more than, . Explain that they mean ‘is less than’ and ‘is greater than’. They can be used to show which of two numbers is greater because the smaller end or the ‘point’ of the sign always points to the smaller number. Demonstrate by creating two simple number sentences by dragging cards from the screen onto the orange boxes, e.g.

4 < 7 and 3 > 1

Drag the place value cards into the bin. Click on the ‘Image library’ icon [pic] in the vertical toolbar and then select ‘Place Value Chart’ from the dropdown menu. Insert appropriate cards from the place value chart by clicking on their icons, and combine them to create a 3-digit number in one of the orange boxes. (Scroll down to see more cards.) Invite pupils to show on their whiteboards a number that could be used to complete the number sentence.

Q How do you know that your number is smaller (greater) than mine?

Model and discuss answers using the place value cards. Establish that to decide which of two 3-digit numbers is smaller you need to compare their hundreds digits, then their tens and ones digits if appropriate.

Repeat for a few more examples. As pupils get more confident remove the ‘is less than’ and ‘is greater than’ text labels from the board by dragging them to the bin.

Main teaching activity

Whole class

(Screen 2: Activity 2, Question 1)

Click on a dice and then on the ‘Roll’ button [pic] on the bottom toolbar to roll all four of the dice on the screen. Explain that you can use the four numbers generated by the dice to produce a 4-digit number. Demonstrate making a number in this way using the place value cards in the Image library, e.g. if the dice numbers are 3, 5, 2 and 1 combine cards for 3000, 500, 20 and 1 to create the number 3521.

Q What number have I made? How do you know?

Refer to the two yellow boxes on the screen. Explain or establish that < means ‘is less than’ and > means ‘is greater than’ so ‘< 3500’ means ‘less than 3500’ and ‘> 3500’ means ‘greater than 3500’.

Q Which box does my number belong in? Why?

Invite a pupil to write your number, using the ‘Pen’ tool [pic], into the appropriate box. Establish that any number with more than 3 as its thousands digit is greater than 3500, as is any number with 3 as its thousands digit and more than 5 as its hundreds digit.

Ask pupils to think of a different 4-digit number that can be created using the dice numbers. They show their suggestions on their small whiteboards.

Invite some pupils to make their numbers on the board using place value cards. The rest of the class read the numbers and decide which yellow box they belong in.

Q What is the smallest 4-digit number you can make using the dice numbers? What the largest number? How do you know?

Establish that the smallest number will have its digits arranged in ascending order, and the largest number will have its digits arranged in descending order.

Pairs

Give each pair a dice. They roll the dice 4 times, each time recording the number thrown. They then use the 4 dice numbers to create 4-digit numbers and write each one under the appropriate heading: ‘< 3500’ or ‘> 3500’.

Encourage pupils to read their numbers and to explain how they decided which box to record them in.

Q What is the smallest 4-digit number you can make? What is the largest number?

Support: Pupils carry out a similar activity but roll the dice 3 times and write 3-digit numbers they can create under the heading ‘< 350’ or ‘> 350’.

Extension: Challenge pupils to try to find and record all the 4-digit numbers they can create using the 4 digits. Encourage them to work systematically, e.g. finding the numbers in order.

Whole class

(Screen 3: Activity 3, Question 1)

Refer to the numbers in the large green panels. Explain that someone has carried out the pupils’ activity, but they have made a mistake.

Q Which number is in the wrong box? How do you know?

Establish that 3562 is actually greater than 3500, because as well as having 3 thousands and 5 hundreds it also has 6 tens and 2 ones. Drag 3562 into the correct box.

Refer to the ( < ( inequality on the board. Ask pupils to show on their small whiteboards the inequality complete with two numbers from the first large green panel.

Q How did you decide which side of the symbol to put each number?

Establish that the smaller number needs to go on the left-side of the < sign. Use one pupil’s inequality to discuss how to find the smaller of a pair of numbers by comparing the digits of the numbers starting with the thousands digit.

Repeat for the ( > ( inequality.

Drag 3256 and 3265 into the end boxes of the first number sentence to create:

Q How would you describe a number that would complete the number sentence? (e.g. It must be more than 3256 and less than 3265.)

Ask pupils to show on their whiteboards any number that could complete the number sentence. Encourage them to explain their reasoning. Establish that the number must have 3 thousands and 2 hundreds. It can have 5 tens and more than 6 ones or 6 tens and fewer than 5 ones.

Repeat the activity for other numbers from the large yellow panel in the end boxes.

Pairs

Pupils use the numbers created in their previous activity to write inequalities of the kind shown on the board.

Q What does this symbol mean?

How do you know that this number is smaller than this one?

What other number could go between these numbers? Why?

Other tasks

You could ask pupils to:

• investigate and compare the lengths of two rivers or the heights of two mountains, in metres and display the results using the symbols < and >.

Review

Play ‘What’s my number?’. Secretly write a 4-digit number on a small whiteboard. Pupils try to identify your number by asking comparison questions that require ‘yes’ or ‘no’ answers, e.g. ‘Is your number greater than 3000?’, ‘Is your number less than 3500?’, ‘Is your number between 3200 and 3300?’.

When pupils have identified your number, repeat the activity for other numbers written on different small whiteboards.

Once you have 3 or 4 different numbers, ask pupils to order them from the smallest to the largest.

Key idea and assessment

To compare 4-digit numbers, start by comparing the thousands digits.

Can pupils:

• say which of two 4-digit numbers is greater or smaller?

• use < and > symbols?

• give a number that lies between two given 4-digit numbers?

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3256

3265

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