Unit 1: Negative Numbers and the Number Line
Where numbers below zero come from, how the number line orders them, and the four operations extended to negatives.
7 topics · 27 questions
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The Number Line and Negative Numbers
- How it worksHow does the number line put every negative number in a mirror position across from a positive one?
- Worked exampleFind which is farther from zero, negative 8 or positive 5, and plot both on a number line.
- Going furtherWhat happens to a point's position on the number line when you flip the sign of its number?
Your turn1 of 2
A diver is 28 metres below sea level. How far is the diver from sea level, which is 0?Comparing and Ordering Integers
- How it worksHow does moving farther left on the number line always mean a smaller number?
- Worked exampleFind the order from least to greatest of the numbers negative 3, 7, negative 9, and 0.
- Going furtherWhat happens to the order of two negative numbers when you compare their absolute values instead of the numbers themselves?
- Common mistakeWhy isn't negative 10 bigger than negative 1 just because 10 is bigger than 1?
Your turn1 of 2
One night the temperature was negative 15 degrees, and another night it was negative 14 degrees. Which temperature was greater?Absolute Value
- How it worksHow does absolute value measure a number's distance from zero instead of just stripping its sign?
- Common mistakeWhy doesn't absolute value just mean making a number positive by erasing a minus sign?
- Worked exampleFind the absolute value of negative 12 and the absolute value of 7.
Your turn1 of 2
An elevator is 35 floors below the lobby, at negative 35. How many floors is it from the lobby?Adding Integers on the Number Line
- How it worksHow do you add integers by walking steps left and right along the number line?
- Worked exampleFind negative 4 plus 9 by walking it out on the number line.
- Worked exampleFind negative 6 plus negative 3 using the number line.
- Common mistakeWhy can't combining two negative amounts ever land you on a positive total?
Your turn1 of 2
A submarine is at negative 14 metres, meaning 14 metres below the surface, then rises 13 metres. What is its new depth?Subtracting Integers
- How it worksHow does turning a subtraction into adding the opposite let you subtract integers with the same rules as adding?
- Worked exampleFind 5 minus negative 8 by turning it into an addition problem.
- Going furtherWhat happens to a subtraction problem when you swap which integer comes first?
- Common mistakeWhy doesn't subtracting a negative number make the answer smaller?
Your turn1 of 2
Today is 14 degrees. Yesterday was negative 13 degrees. How many degrees warmer is today, found as 14 minus negative 13?Multiplying Integers
- How it worksHow does continuing the pattern in a multiplication table down through zero force negative times negative to be positive?
- How it worksHow does thinking of multiplying by negative 1 as flipping direction explain why two flips point you back the same way?
- Worked exampleFind negative 6 times negative 7 and negative 6 times positive 7.
- Common mistakeWhy doesn't a negative times a negative just stay negative, the way negative plus negative does?
- Going furtherWhat happens to the sign of a product when you multiply three negative numbers together instead of two?
Your turn1 of 2
A game removes a penalty of 9 points from a player's score, and this happens 8 separate times (removing a penalty is like subtracting a negative). Find negative 9 times negative 8 to see how much the score rises.Dividing Integers
- How it worksHow does thinking of division as undoing multiplication explain why a negative divided by a negative is positive?
- Worked exampleFind negative 36 divided by 4 and negative 36 divided by negative 4.
- Common mistakeWhy doesn't dividing a negative number by a negative number leave you with a negative answer?
- Going furtherWhat happens when you divide a positive integer by a negative one instead of a negative by a negative?
Your turn1 of 2
A hot air balloon's altitude changed by negative 70 metres (it dropped 70 metres total) evenly over 8 equal stages of descent. What was the altitude change during each stage?