Double Function Machine

Resources and Tools for Elementary Math Specialists and Teachers

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This Flash applet allows the user to explore the concept of a function using an input-output machine with two operations and options to set and hide or reveal all operations and numbers. A notepad is available for recording inputs and outputs, and a loop function takes the current output as the next input.

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Contributed by: Dan Bunker - Author, crickweb.co.uk - Publisher

Math TopicAlgebraic Thinking, Number Sense, Basic Operations, Number Concepts, Mathematical Practices, Mathematical Processes

Grade Level3, 4, 5, 6+

Resource TypeActivity, Interactive Media

Additional Information
- AudienceLearner
- LanguageEnglish (United Kingdom)
- Education Topic
- Interdisciplinary Connection
- Professional DevelopmentNo
- ContributorDan Bunker - Author, crickweb.co.uk - Publisher
- Publication Date2010
- RightsCopyright (c) 2010 v2vtraining.co.uk
  http://www.v2vtraining.co.uk/
- 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]
- Operations and Algebraic Thinking[K - 5]
- Understand properties of multiplication and the relationship between multiplication and division.[3]
- 5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)[3]
- 6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.[3]
- Multiply and divide within 100.[3]
- 7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.[3]
- Generate and analyze patterns.[4]
- 5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.[4]

Mathlanding is a project of Maryland Public Television in partnership with The Math Forum at Drexel University
and the International Society for Technology in Education. © 2012 Maryland Public Television

Double Function Machine

Common Core State Standards for Mathematics