Making 10

dialogue:
- Gork, look at this earthling worksheet on finding missing numbers.
- There's no pattern to it. 
-Let's add a constraint to create a pattern.

Make 10

Start with the number sentence

_ + _ = 10

  • Roll a number cube (a six-sided die) to get the first number.
  • Calculate the second number, then use the two numbers to write a number pair. You can use a table like the one shown in the animation below.
  • Plot the ordered pairs on a grid. You can use this grid pdf file.
  • Continue until you exhaust all possible numbers.
They line up!
Math is so cool!

Make 8

Now try the steps above with the number sentence

_ + _ = 8

  • Plot the ordered pairs on the same grid.
  • What do you notice?

Changing direction

  • Which graphs match the equations below? Move your mouse over the purple dots to check your answers.
Blue
Green
Red
Yellow

Summary of ideas so far

Can we make the graph curve?

So far, we have explored linear equations. They have this structure X + Y = 10 and they make a straight line when graphed in a grid.

But what types of equations can make curves?

One type of curve is called a hyperbola:

  • When a table lamp casts a shadow against a wall, the line that separates the light from the shadow is a hyperbola.
  • The cooling towers of nuclear power plants are hyperbolic.
  • When two pebbles are thrown simultaneously into a pond, the interference pattern of the waves forms hyperbolic curves.

Look at the hyperbola graphs below:

Another type of curve is called a parabola:

  • Satellite dishes are parabolic in shape.
  • So are the mirrors used in headlights and flashlights.
  • A ball thrown travels a parabolic path.

Check the two parabola graphs below.

Can we make a circle?

How could we change _ + _ = 10 so that its graph becomes a circle?

Look at the graphs below.