Unit 12: Negative Numbers and the Coordinate Plane
Negative numbers as a walk along a number line, and the grid where two number lines cross to locate any point.
7 topics · 27 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What a Negative Number Actually Means
- Worked exampleFind the temperature after it drops 12 degrees from a starting temperature of 4 degrees.
- Common mistakeWhy isn't the negative sign in front of a number just decoration that doesn't change its value?
- Going furtherWhat happens to your position on a number line if you start at negative 4 and move down 6 more?
Your turn1 of 2
The temperature starts at 11 degrees and drops 21 degrees overnight. What is the new temperature?Comparing and Ordering Negative Numbers
- How it worksHow do you tell which of two negative numbers is bigger by seeing which is further right on a number line?
- Common mistakeWhy isn't negative 5 bigger than negative 2, even though 5 is bigger than 2?
- Worked exampleFind which is greater, negative 8 degrees or negative 3 degrees, on a cold winter day.
- Going furtherWhat happens to the order of a list of temperatures if every single one goes up by 10 degrees?
- Ties togetherHow does ordering negative numbers on a number line connect to ordering fractions by their size?
Your turn1 of 2
One winter morning was negative 14 degrees and another was negative 13 degrees. Which temperature was greater?Adding and Subtracting on a Number Line
- How it worksHow do you add 3 and negative 5 by starting at 3 and walking 5 steps to the left?
- How it worksHow do you subtract 4 from negative 2 by starting at negative 2 and walking 4 steps left?
- Worked exampleFind the answer to negative 3 plus 7 using a number line that starts at negative 3.
- Common mistakeWhy doesn't adding a negative number always make the answer come out negative?
Your turn1 of 2
A submarine is at negative 14 metres, meaning 14 metres below sea level, and rises 20 metres. What is its new depth?Subtracting a Negative Number
- How it worksHow does turning around twice on a number line walk show why subtracting negative 3 is the same as adding 3?
- Worked exampleFind the answer to 5 minus negative 4 by turning around twice on a number line.
- Ties togetherHow does subtracting a negative number connect to finding the opposite of a number you already know?
Your turn1 of 2
Today's temperature is 21 degrees. Yesterday's was negative 13 degrees. How many degrees warmer is today, found by computing 21 minus negative 13?Multiplying and Dividing with Negative Numbers
- How it worksHow do you find the sign of an answer by counting how many negative numbers you multiplied together?
- Common mistakeWhy doesn't negative 2 times negative 3 equal negative 6?
- Common mistakeWhy doesn't negative 8 divided by negative 2 come out negative?
- Worked exampleFind the answer to negative 4 times 6.
- Going furtherWhat happens to the sign of the answer if you multiply three negative numbers together instead of two?
Your turn1 of 2
A hiker loses 9 metres of elevation every hour for 8 hours. What is the total change in elevation?Plotting Points on the Coordinate Plane
- How it worksHow do you plot the point (3, 5) by moving right 3 and up 5 from the center of the grid?
- Worked exampleFind the coordinates of a point that sits 4 to the left and 2 up from the center of a grid.
- Common mistakeWhy isn't the point (2, 5) the same location as the point (5, 2) on a coordinate grid?
- Going furtherWhat happens to a point's location if you move it 10 spaces to the right of where it started?
Your turn1 of 2
On a treasure map grid, a chest sits 7 steps to the left and 7 steps up from the center. What is the x-coordinate of the chest?The Four Quadrants
- How it worksHow do you tell which quadrant a point is in just by looking at the signs of its two coordinates?
- Worked exampleFind which quadrant contains the point (negative 3, 4).
- Common mistakeWhy isn't the point (negative 2, negative 2) in the same quadrant as the point (2, 2)?
Your turn1 of 2
Which quadrant contains the point (negative 7, 7)?