8th Grade: Patterns Practice

We have been looking at using patterns to write equations.

Below is the pattern we used last week. (All patterns from visualpatterns.org)

We start by thinking about what the next pattern will look like. 

Several students noticed each time it added 4 new blocks.

We then filled out the table like the one below.

You are then asked: What do you notice? What do you wonder?

On this table, you should notice you are adding 4 each stage.

You may wonder could my equation be y = n + 4

If you are wondering that, test out the equation. ALWAYS test out your equation.

Step 1:  y = 1 + 4  

             y = 5   (Correct amount of blocks for step 1)

Step 2: y = 2 + 4

            y = 6  (Not correct amount of blocks)

You should notice at step 2, this equation does not work.

Remember: We talked about the constant change being 4. Another way to think of adding 4 over and over again is to multiply by 4. 

Now I am wondering, could the equation be y = 4n. Let's test it out.

Step 1:  y = 4(1) 

             y = 4       (Not the correct amount of blocks)

Back to the drawing board.... or can we add on to this equation???

I would stop and think about how can I get the above equation to work for stage 1.

If I added a 1 to 4, that would give me the 5 I need.

y = 4n + 1   Lets, test it out............

Step 1: y = 4(1) + 1

            y = 5   (correct amount of blocks)

Step 2: y = 4(2) + 1

            y = 9 (correct amount of blocks)

Step 3: y = 4(3) + 1

            y = 13  (correct amount of blocks)

Now, we can find step 27.

Step 27: y = 4(27) + 1

              y = 109 blocks

Is this pattern proportional? How do we know? What would the graph look like?

Have a Great Night,

Mrs. Gilliam