# Making 10

### Make 10

_ + _ = 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

### 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.