Ladybug Patterns introduces students to the algebraic concept of growing patterns or functions. In this case, the dots on the ladybug change with age. Students may use the picture and a function table to analyze the pattern's growth and write a rule in words and/or variables/numbers.
- Download the Ladybug Patterns student handout.
- Download a blank Ladybug Patterns handout so that students can create their own original patterns to challenge their classmates.
- NOTE: teachers may use an overhead of the blank pattern handout to create additional patterns for students to analyze (e.g. double the age, 2 more than age, etc. )
This 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.
Differentiation: This game is easily differentiated by varying the rule cards provided to students. Use simple one-step addition and/or subtraction for basic skills students and challenge better students by graduating them to 2-step rules. Consider printing the different level rules on different color paper so that students may easily select the proper level from the math center.
Enrichment: Provide blank cards for students to create their own rules to challenge their peers. Be sure that students try their rule on at least 3 other students to be sure that they have written it correctly.
Use the book Two of Everything to 
introduce students to the doubling pattern. Students will enjoy the story and predict what will happen each time something is put into the magic pot.
Make the math connection even more concrete by using a pot and linking cubes to illustrate the story. Students may use a Magic Pot Workmat to record the input and output, then write a rule.
Extension: Extend the activity by using the magic pot and simple rules to create data sets. Students should guess the rule by giving an input number and telling the output that would result. By not stating the rule, students provide more time for other class members to generalize the rule. Each guess simply provides another data set for students to enter in their table.
Enrichment: After reading Two of Everything, challenge students to solve NCTM's 5 Coins problem: Would you rather have 1000 coins or 5 coins and a Magic Doubling Pot that works 10 times? Students might work in pairs and use in/out charts to record their solutions.
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.
