☰ Year plan · Mathematics

Negative numbers and rational numbers

Week 3 Β· Negative numbers, opposites, comparing, and the families of numbers Β· 3 lessons
2

Comparing numbers with the number line and symbols

Discover Mathematics P6: Term 1, Unit 2, Lessons 1–3
GoalCompare two numbers, including negative numbers, with the symbols <, > and =.
New words
greater than ( > ) Β· further to the right on the number lineless than ( < ) Β· further to the left on the number lineorder Β· put numbers in a line from least to greatest
Explanation

On a number line the numbers get bigger as you go to the right. So of two numbers, the one further to the right is greater and the one further to the left is less. Every positive number is greater than 0, and 0 is greater than every negative number. When both numbers are negative, the one closer to 0 is greater: βˆ’2 is greater than βˆ’7, so βˆ’7 < βˆ’2. Be careful: 7 is greater than 2, but βˆ’7 is less than βˆ’2. In real life, βˆ’7 Β°C is colder than βˆ’2 Β°C, and owing 70 LE is worse than owing 20 LE. The symbols < and > open towards the greater number: 3 > βˆ’5 and βˆ’5 < 3.

β˜…Remember
Further right = greater. Further left = less. For two negatives, the one closer to 0 is greater.
Worked examples
βˆ’8βˆ’7βˆ’6βˆ’5βˆ’4βˆ’3βˆ’2βˆ’101234βˆ’7βˆ’2
Compare βˆ’7 and βˆ’2. On the number line βˆ’7 is further left than βˆ’2, so βˆ’7 < βˆ’2. We can also write βˆ’2 > βˆ’7.
βˆ’8βˆ’7βˆ’6βˆ’5βˆ’4βˆ’3βˆ’2βˆ’10123456βˆ’35βˆ’802
Order βˆ’3, 5, βˆ’8, 0 and 2 from least to greatest. Mark them on the line and read from left to right: βˆ’8, βˆ’3, 0, 2, 5.
ChildBalance (LE)
Minaβˆ’60
Karimβˆ’25
Salma40
Money balances. Salma has 40 LE, Karim owes 25 LE and Mina owes 60 LE. From least to greatest: βˆ’60, βˆ’25, 40. So Mina is in the worst position and Salma in the best.
Class activity

Number line on the floor. Use chalk or a long string with paper cards from βˆ’10 to 10. A grown-up calls two numbers, such as βˆ’4 and βˆ’9. The child stands on the greater one and says the symbol sentence: βˆ’9 < βˆ’4. Try ten pairs, then make a line of five children holding cards and order them.

Practice
1
Write <, > or = : βˆ’6 ___ βˆ’1.
2
Write <, > or = : 4 ___ βˆ’9.
3
Order from least to greatest: 7, βˆ’2, βˆ’10, 0, 3.
4
Which is colder, βˆ’5 Β°C or βˆ’9 Β°C?
5
Hana says βˆ’8 > βˆ’3 because 8 > 3. What is her mistake?