Braidedmath.com: Comprehending Math: Adapting Reading Strategies for Teaching Mathematics K-6
The Freight Trains Problem
Reference: (Chapter One, pages 20-29)
The mathematical structure of the Freight Trains problem is that of a typical combinations problem. We
are asked to find "different" arrangements of the 18 cars that fit the criteria .
We are trying to find:
• three addends that sum to 18
• all the different arrangements that would sum to 18
With the special conditions or constraints:
• the three addends are whole numbers
• each addend cannot be bigger the 10
• the trains must be different, but what does "different" mean?
• color (type of commodity) does not matter in this analysis
[example --- 3 livestock (red), 5 vegetables (green), and 10 lumber (yellow) is the same as --3 vegetables (green), 5 lumber (yellow) and 10 livestock (red)]
• Does the order of the trains matter? Is (3, 5, 10) different from (5, 3, 10) ?
• If not, then there are fifteen different trains. Each ordered triplet represents a "family" of
solutions.
1,
1,
2,
2,
2,
5,
5,
6,
7, 10
8, 9
6, 10
7, 9
8, 8
5, 8
6, 7
6, 6
4,
4,
4,
4,
3,
3,
3,
4, 10
5, 9
6, 8
7, 7
5, 10
6, 9
7, 8
Lynn Pittner has designed some recording sheets for this problem. The train cars may be colored with
crayons to find and/or record solutions.
Betty's second graders in the book needed Unifix cubes and recording sheets that were the same size.
Lynn's sheets are a little more abstract and more appropriate for fourth grade.
© Arthur Hyde • May be reproduced for classroom and professional development purposes.
Braidedmath.com: Comprehending Math: Adapting Reading Strategies for Teaching Mathematics K-6
The Freight Trains
At the train station there are many different freight trains.
They carry 3 kinds of freight across the United States:
lumber, livestock, and vegetables.
Each train has some lumber cars, some livestock cars, and some vegetables
cars.
Each train always has 18 freight cars.
There are never more than 10 cars of one kind.
Freight cars that are the same are always connected together.
How many different ways of making trains with 18 cars can you find?
© Arthur Hyde • May be reproduced for classroom and professional development purposes.
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At the train station there are many different freight trains.
They carry 3 kinds of freight across the United States: lumber, livestock, and vegetables.
Each train has some lumber cars, some livestock cars, and some vegetables cars.
Each train always has 18 freight cars.
There are never more than 10 cars of one kind.
Freight cars that are the same are always connected together.
How many different ways of making trains with 18 cars can you find?
The Freight Trains
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