**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.

**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.