Birthday Cakes

Resources and Tools for Elementary Math Specialists and Teachers

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This problems is an opportunity to explore triangular numbers in the familiar context of decorating a birthday cake with a number of candles corresponding to a child's age. The problem lends itself to systematic strategies and multiple representations. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

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Contributed by: Millennium Mathematics Project, Publisher

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

Grade Level1, 2, 3

Resource TypeActivity

Additional Information
- AudienceLearner
- LanguageEnglish (United Kingdom)
- Education Topic
- Interdisciplinary Connection
- Professional DevelopmentNo
- ContributorMillennium Mathematics Project, Publisher
- Publication Date2003-05
- 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]
- Construct viable arguments and critique the reasoning of others.[K-12]
- Model with mathematics.[K-12]
- Look for and make use of structure.[K-12]
- Operations and Algebraic Thinking[K - 5]
- 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]
- Solve problems involving the four operations, and identify and explain patterns in arithmetic.[3]
- 8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.[3]

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Birthday Cakes

Common Core State Standards for Mathematics