Standard: Algebra
Read the NCTM Algebra Standard: Instructional programs from prekindergarten through grade 12 should enable all students to:
- Understand patterns, relations, and functions
- Represent and analyze mathematical situations and structures using algebraic symbols
- Use mathematical models to represent and understand quantitative relationships
- Analyze change in various contexts
Featured Topic: Investigating Growing Patterns
Introduce elementary students to the concept of functions by investigating growing patterns. Visual patterns formed with manipulatives are especially effective for elementary students and allow them to concretely build understanding as they first reproduce, then extend the pattern to the next couple of stages. Finally, students explain the pattern in words and try to write a rule that works for any stage.
See Investigating Growing Patterns for specific suggestions on using these patterns to help elementary students develop a concept of functions. The article includes activities with handouts that teachers can use to introduce this topic to elementary students. A Function Scrapbook of function ideas is included and examples of function problems created by elementary students will be added as they are completed. Literature connections and web links to relevant sites on the internet are also included in the article.
Patterns & Algebra
These activities support student development of the concept of patterns through concrete activities with manipulatives, The use of variables is developed as a mathematical way of recording the general rule.
- See Investigating Growing Patterns for specific suggestions on using these patterns to help elementary students develop a concept of functions. The article includes activities with handouts that teachers can use to introduce this topic to elementary students. A Function Scrapbook of function ideas is included and examples of function problems created by elementary students will be added as they are completed. Literature connections and web links to relevant sites on the internet are also included in the article.
- Guess My Rule: function machine game was created to give students practice in saying and writing the rule, given an input/output table. One student has the rule which the other student has to guess. The guesser records an input number in the table. The rule person must apply the rule and tell the output number. Student pairs repeat this until the guesser correctly identifies the rule by saying and writing it. Students then switch places and repeat the activity. Download three different levels of rules for play: simple addition & subtraction, multiplication or two-step rules.
- Magic Pot Workmat for students to use in sheet protectors as a follow-up to reading Two of Everything, a humorous introduction to functions and function machines. This mat is also used to record input and output numbers in the Guess My Rule game.
- Function Machine Template can be placed in a sheet protector so that students can use dry-erase markers to play the game by recording input/output numbers, then erasing when they switch places.
- Function: Table & Graph Template for student use in sleeve protectors to provide template for students to create a table of values and graph the values on the coordinate plane.
- Make a Path Template for student use in sleeve protectors. This model serves as a pictorial solution for equations, working forward with a word problem, then creating a backward path by doing the opposite. Look for Make a Path problems coming soon.
- Who Has? Algebra A Deck are pre-formatted to printeon 2x4 inch labels for easy application to index cards. This deck provides practice of variable expressions. See webpage Who Has? Activities for additional decks and classroom management ideas.
- Pascal's Pumpkins introduces students to the patterns found in Pascal's triangle.
- Twelve Days of Christmas problem solving activities that investigate the growing pattern found in this holiday song. Online links provide information on the current prices of the gifts so that students can calculate the total cost of the twelve day extravaganza.
- See more Patterning activities and problems in the Winter Math activities.
Additional Mathwire.com Resources
- See more Patterns & Algebra Math Templates: insert in sheet protectors for student use with dry erase markers or for teacher use as overhead transparencies.
- See Problem Solving Resources for open-ended assessments that involve patterns and algebra.
- See all Patterns & Algebra Games.
- See Literature Connections for patterns and algebra.
- See more Patterns & Algebra Links.
- See all Enrichment Activities for patterns and algebra.