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```Science Math Masters
Current Standards:
MA.912.G.5.1 Prove and apply the Pythagorean
Theorem and its converse.
MA.912.G.5.4 Solve real-world problems
involving right triangles.
Typical Textbook Problem
(NGSSS – Current Standards)
Dan and Ben start at point A and want to get to
point B. Dan walks 1 mile north and 3 miles east
to reach point B. Ben takes a shortcut and walks
directly from point A to point B.
Who travels the greatest distance? By how much?
a b  c
2
2
12  32  c 2
1  9  c2
10  c 2
10  c
3 miles
2
1 mile
B
c  10  3.16 miles
A
Dan travels 4 miles and Ben travels 3.16 miles, so Dan
travels approximately 0.84 miles more than Ben.
Typical Textbook Problem
(NGSSS – Current Standards)
Dan and Ben start at point A and want to get to
point B. Dan walks 1 mile north and 3 miles east
to reach point B. Ben takes a shortcut and walks
directly from point A to point B.
Who travels the greatest distance? By how much?
3 miles
1 mile
B
c  10  3.16 miles
A
What geometric concepts are used in this problem?
Common Core…Taco Cart Problem
(Modified from Dan Meyers The Taco Cart: http://threeacts.mrmeyer.com/tacocart/)
Click picture for video.
Who will reach the taco cart first? Write down your
guess.
What information do you need to answer the question?
Taco Cart Problem: Who will reach the taco cart first?
Distances
Dan
Ben
Speeds:
Walking on the sidewalk:
5 ft./sec.
Walking in the sand: 2
ft./sec.
Taco Cart Problem: Who will reach the taco cart first?
Click picture for video.
How many seconds did Dan beat Ben by?
49.695 seconds
Taco Cart Problem: Who will reach the taco cart first?
d
d

rt
;
t

The work:
r
Dan
Ben
Dan travels 325.6 ft. at a rate of 2 ft./sec
and 562.6 ft. at a rate of 5 ft./sec.
325.6 ft. 562.6 ft.

2 ft./sec. 5 ft./sec.
162.8 sec. + 112.52 sec.  275.32 sec. 
4 minutes and 35.32 seconds
Ben travels approximately 650.03 ft. at a
rate of 2 ft./sec. (Pythagorean theorem)
650.03 ft.
 325.015 sec. 
2 ft./sec.
5 minutes and 25.015 seconds
Dan’s time: 275.32 seconds = 4 minutes 35.32 seconds (04:35:32)
Ben’s time: 325.015 seconds = 5 minutes 25.015 seconds (05:25:02)
Therefore, Dan beats Ben by 49.695 seconds.
Taco Cart Problem: Where would the taco cart
have to be so that both Dan and Ben will
reach it at the same time?
Click picture for video.
Taco Cart Problem: Where would the taco cart
have to be so that both Dan and Ben will
reach it at the same time?
310.095 ft.
Click picture for video.
Taco Cart Problem: Where would the taco cart
have to be so that both Dan and Ben will
reach it at the same time?
The work:
d  rt ; t 
325.6 ft.
Dan
x ft.
325.62  x 2
d
r
Dan’s two times
Ben’s time
325.6 ft.
x ft.
325.62  x 2 ft.


2 ft./sec. 5 ft./sec.
2 ft./sec.
 325.6 ft.
x ft.
325.62  x 2 ft. 
10 



 2 ft./sec. 5 ft./sec.

2
ft./sec.


1628 + 2 x  5 106015.36  x 2
325.6  0.4 x  106015.36  x 2
106015.36  260.48 x  0.16 x 2  106015.36  x 2
0  0.84 x 2  260.48 x
0  x  0.84 x  260.48 
x0
x0
0.84 x  260.48  0
x  310.095
Taco Cart Problem: Where do you think the taco
cart problem fits in the Common Core
curriculum?
The algebraic skills required for this problem are
covered by the following Algebra I Common Core
State Standard.
Group Activity
Choose a problem from the hand-out and
brainstorm ways to adapt the problem so that it
captures the spirit of the Common Core State
Standards by adding depth, multiple standards
and/or a new level of questioning.
Be prepared to share.
```