Section 4.1 Using Equations to Model Patterns

SECTION 4.1 USING EQUATIONSTO MODEL PATTERNS

I) WRITING EQUATIONS

We can use equations to model situations in the real world

Using equations, we can solve complex problems easily

The first step to writing equations is to find a pattern!

Ex: The following diagram shows the number of triangles createdwith a number of toothpicks used. Write an equation to describethe number of triangles (T) vs number of toothpicks (P).

The number of toothpicks used to equal to the number oftriangles times “2” and then plus one

Practice: Tiles are placed around a rectangular garden asshown. Write an equation that shows the size of thegarden vs the number of tiles

S-1

Size 2

Size 3

The number of tiles used to equal to the size of thegarden times “2” and then plus six

II) FINDING PATTERNS IN A TOV

Check if the rows are increasing at a consistent ratio

If one column is increasing faster, multiply the othercolumn by that constant

Compare the new column with the right column to derivean equation

Since the right column

is increasing TWICE asfast, multiply the leftcolumn by 2

Therefore, the equation will be:

Practice: Find an equation for the following TOV’s

III) EVALUATING EQUATIONS:

When you have an equation, you can solve for valuesby simply plugging in numbers

Ex: Given the following pattern, How many toothpickswill you need to make 87 triangles?

Practice: Suppose you have 300 tiles to form a walkwayaround the garden as shown. What is the size of thelargest garden that you can create?

S-1

Size 2

Size 3

The largest garden size that youcan create will be 147.

Challenge: 4 Adults and 2 students are trying to cross a riverwith a raft. However, the raft can carry only 1 adult at a time, or2 students, or 1 student at a time. What is the minimum numberof trips we need to take to bring everyone across?

HOMEWORK: