# How Long ’till Brayden is 6′? -3Act Math

ACT 1:

Brayden celebrated his 6th birthday this May.  Every year we mark his height on the shed door frame.

What questions do you have when you look at this picture?

Ask students to write down their questions, I normally ask students to find at least 3.  When I observe that most students have questions written, I ask them to share those questions with their neighbor.  I then throw up a Microsoft Word document and start typing down questions students supply.  Students from my classroom came up with all sorts of different questions, some we can easily answer and others that we can’t.  I am looking for a key question or questions to start this lesson.  If students do not ask one of these questions, I tell them that I hope I can answer most of the questions provided, but that I need them to consider one of these questions first.

• How tall is Brayden?
• How much does he grow in a year?
• How tall will he be next year?
• How tall will he be as an adult?

Any of these type of questions will lead students down the inquiry I hope to explore with them.

My wife and I are fairly tall people, and Brayden wants to be at least as big as us so he can play basketball (he seems to think he needs to be tall to play).  How many years will it be before Brayden is 6′?

ACT 2:

Scatter Plots, Line of Best Fit and Estimation are the topics I wish to address with my students.  Students will need to think of ways to determine his height or growth between years.  There are many different combinations of ways to figure this number out, but here are the stats:

• At age 6, Brayden is actually 45″
• At age 5, Brayden is actually 42″
• At age 4, Brayden is actually 39.5″
• At age 3, Brayden is actually 36.5″
• At age 2, Brayden is actually 33″
• At age 1, Brayden is actually 29″

Students should construct a scatter plot similar to this:

And draw a line of best fit similar to this:

I also ask students to create an equation for the Brayden’s height growth per year (he was 22 inches when he was born).

Some students will work with average on this problem, so they will take the average height grown from 0-6, then use that growth average to complete a height table:

45-22 = 23

23/6=3.83333333…

Students will round that to 3.8 inches per year.

ACT 3:

Using Excel for drafting the line of best fit, it gave me this equation:

So, solving for y=72 gives me Brayden’s age of 13.  Using the average model, students will get the same answer.

Extensions:

After we decide the general equation for Brayden’s height, I will ask students to predict Brayden’s height at various points in his life (16, 18, 21, 30, 40, 70).  Some students will just blindly evaluate what his height will be without considering the fact that we do stop growing as adolescents.