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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?
Where we’re headed with the
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.
Work with your shoulder partner to answer the question.
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.
Work with your shoulder partner to answer the question.
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.

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