Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Patterns and Functions: What Comes Next?Content Guide - Andee Rubin
Supplies Needed for Workshop #1:
About the WorkshopWhat is the theme of the workshop?
In a sense, doing mathematics requires looking for patterns everywhere and expecting to find them - believing that the world is often predictable. This workshop explores how the idea of predictability forms the basis of mathematics, and introduces some mathematical activities in which patterns are central.
Whom do we see? What happens in the videoclips?
What issues does this workshop address?
What teaching strategy does this workshop offer?
To which NCTM Standards does this workshop relate?
In addition, this workshop is related to the general standards: Mathematics as Problem Solving and Mathematics as Communication. The students are solving problems and communicating about them verbally, in pictures, in graphs, and even in song.
Suggested Classroom ActivitiesGuess My Rule
You may structure this activity as presented in the Workshop: have one student (or a group of students) make up a rule and give a three-number set that follows the rule, and have other students in class try to guess the rule by suggesting other three-number sets that they think follow the rule. Each guess must be accompanied by a reason. Other ways to play the game include:
This activity provides a strong basis for the concept of functions, as it captures one of the most important characteristics of a function: that it is defined by a rule that will always give one - but only one - answer for every number you put into it.
Patterns in Poems and Songs
Patterns in poems usually have to do with the rhyme scheme. Choose a poem and have students find others with the same rhyme scheme. Some verses of songs count as poems, too. See if all of the verses of a song follow the same rhyming pattern.
These activities are accessible to younger students and introduce them to the idea of predictability in an entertaining way.
These codes are actually functions - the rule specifies how a letter is transformed to another. The rule works in the same way for all letters, just as functions work in the same way for all numbers.
These kinds of patterns are especially interesting because they can be looked at both numerically and geometrically; different students are likely to approach the problem in different ways. There are many other problems of this general type, such as the Tiles problem from the Workshop.
Suggested StrategiesThe Guess My Ruleactivity puts students in both the "expert" role and the "guesser" role. This is an important shift away from students always trying to answer the teacher's questions. Try this strategy for some math activity - either the Guess My Ruleactivity or some other - and watch what students can learn in each role.
Pre-Workshop Assignment for Workshop #2
Please administer the "really quick" survey to your class. Copy enough for your class (e.g., seven if you have a class of 28) and cut them into individual forms.
Explain to your class that they are participating in a survey of students from around the country as a part of a workshop you will be attending. If you wish, you can explain that no one will know what they answer (it's anonymous), and that the purpose of the survey is to help the teachers in the workshop learn about different ways to display data.
Pass out the forms, asking students to fill them in. Collect the forms. This should take less than five minutes.
Important: If students should ask whether they can mark more than one box per question ("What if we like both dogs and cats?") or none ("I only like soccer. What if I hate both basketball and football?"), DO NOT answer the question directly. Instead, PLEASE say simply, "Follow the instructions on the survey as best as you can." If necessary, explain that your directions indicated that you can only tell them to follow the instructions on the form. In a pinch, show them these instructions!
Afterwards, you may, if you wish, share the data with the class and have them try to figure out a good way to display it.
If you have students who are non-readers or ESL students, you may adapt this questionnaire any way you think will give us the same data. The easiest way is to read it aloud or to make a new questionnaire with pictures.
If you are an administrator or do not have direct access to a classroom, we encourage you to submit your own data, or poll some students on your own.