Making Trains

Resources and Tools for Elementary Math Specialists and Teachers

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This activity uses Cuisenaire Rods to develop flexibility and fluency with addition facts and to encourage systematic thinking. Several different challenges are posed, all involving making equivalent trains using a given number of rods of different colors. An interactive Flash Cuisenaire applet is provided as an alternative to using real rods. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a related activity, Cuisenaire Counting (cataloged separately).

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Contributed by: Millennium Mathematics Project, Publisher

Math TopicNumber Sense, Basic Operations, Number Concepts, Mathematical Practices, Mathematical Processes

Grade Level1, 2

Resource TypeActivity, Interactive Media

Additional Information
- AudienceLearner
- LanguageEnglish (United Kingdom), Chinese, Dutch, French, German, Italian, Spanish
- Education Topic
- Interdisciplinary Connection
- Professional DevelopmentNo
- ContributorMillennium Mathematics Project, Publisher
- Publication Date2005-10
- RightsCopyright (c) 2007 University of Cambridge
  http://nrich.maths.org/public/terms.php
- AccessFree access
Standards
- Common Core State Standards for Mathematics
  Select a standards document:
- Standards for Mathematical Practice[K-12]
- Make sense of problems and persevere in solving them.[K-12]
- Reason abstractly and quantitatively.[K-12]
- Model with mathematics.[K-12]
- Look for and make use of structure.[K-12]
- Operations and Algebraic Thinking[K - 5]
- Represent and solve problems involving addition and subtraction.[1 - 2]
- 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.[1]
- 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.[1]
- Understand and apply properties of operations and the relationship between addition and subtraction.[1]
- 3. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)[1]
- Add and subtract within 20.[1 - 2]
- 5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).[1]
- 6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 — 4 = 13 — 3 — 1 = 10 — 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 — 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).[1]
- 2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.[2]
Related Resources
- Cuisenaire Counting
User Comments
- Average
  5
  
  A Train of Many Colors
  By Uncle Bob on 05/23/2012 - 10:24
- The app is easy to use, provides good mouse or touchpad practice for younger students, and keeps a record of several trains for comparisons. As is often the case at nrich, the student solutions raise new questions, in this case, does the order of the rods make a difference? What is a combination?

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Making Trains

Common Core State Standards for Mathematics