March/April 2017 – Vol. 29 No. 6

Number Patterns

Posted: Wednesday, September 1st, 2010

by Judy Scotchmoor

Overview:
In this lesson, students are challenged to discover the relationship among six numbers. The objective of this activity is to engage students in a problem-solving situation in which they practice aspects of the process of science: observation, conversation, questioning, developing expectations/predictions, formulating explanations, testing their ideas; modifying their initial ideas, and sharing their results with others. Students are then asked to reflect on whether they were doing science. The activity can serve as an effective introduction to or reminder about the process of science, as well as provide an opportunity for students to reflect on the basic characteristics that help delimit the scientific enterprise.

Lesson concepts:

  • The process of science involves observation, exploration, discovery, testing, communication, and application.
  • Scientists try to come up with many different natural explanations (i.e., multiple hypotheses) for the patterns they observe.
  • Scientists test their ideas using multiple lines of evidence.
  • Test results sometimes cause scientists to revise their hypotheses.
  • Scientists are creative and curious.
  • Scientists work together and share their ideas.

Grade span: 6-12

Materials:

  • Scratch 8.5 x 11″ paper cut into sixths for displaying predictions
  • A surface upon which to write the numbers — e.g., chalk board

Time: 15-20 minutes

Grouping: Small groups of 2-4 students and whole group discussion

Teaching tips: Only one example of a number pattern is given below (a, b, c, c-a, c-b, c-c). You may wish to begin with a much simpler challenge for younger students and then build up to this one, or you may wish to raise the level of difficulty! Great rainy day activity!

Procedures:

  1. 1. Place 6 lines on the chalkboard and explain to students that you are going to fill in the first three blanks and their job is to fill in the last three, one at a time. There is a relationship among all six numbers. Their job is to figure out what that relationship is.
  2. ___ ___ ___ ___ ___ ___

  1. 2. Fill in the first three numbers as follows:
2 4 6
  1. 3. Ask students to predict what the next number is. They should talk with members of their team and decide what it should be, then write the number on the scratch paper and hold it up for you to see. Most students will suggest an 8. Once all groups have a paper raised, reveal the next number as follows:
2 4 6 4
  1. 4. After the groans have died down, ask the students: Based on what you see now, what do you think the 5th number will be? Proceed as above and when all groups have a paper raised, reveal the 5th number as follows:
2 4 6 4 2
  1. 5. Do not worry if there is some frustration at this point. And maybe some students will have guessed right! Just continue to be positive, and ask the students: Based on what you see now, what do you think the last number will be? Proceed as above and when all groups have a paper raised, reveal the 6th number as follows:
2 4 6 4 2 0
  1. 6. At this point, reassure the students that they will eventually figure this out and you will help them by giving them another set of three numbers. The same relationship will hold true. So just as before, you will give them the first three numbers and they are to figure out the 4th, then the 5th, then the 6th. You can go with any three numbers, but the following works well:
3 5 7
Followed by:
3 5 7 4
Followed by:
3 5 7 4 2
Followed by:
3 5 7 4 2 0
  1. 7. For the 3rd round, you can go with any three numbers, but something like the following works well:
5 8 11
Followed by:
5 8 11 6
Followed by:
5 8 11 6 3
Followed by:
5 8 11 6 3 0
  1. 8. Continue with any three numbers. As the rounds proceed, eventually a group or two will think they have the relationship—but don’t let them tell the whole class. At that point, ask one of those groups how they could test their idea. This encourages students to think about how ideas are tested. Students may need help here, but you can prompt them: Thus far, I have been giving the first three numbers, what would happen if you give the first three numbers? How could that act as a test? Let them know that they can give you any three whole numbers, but not to make it too hard on you! Ask the group to make a prediction at this point: what do they expect to happen based on their idea? Proceed exactly as above, using their three numbers and let the entire class participate. If they were correct or incorrect, find out if any other group thinks they know the relationship, and let them test their idea with three numbers. Eventually as more groups “get it,” ask a group to explain the relationship. Then ask another group to suggest three numbers that would provide a good test for that idea. And proceed as above.
  2. 9. Eventually the relationship will be revealed and you can express it as follows:
a b c c-a c-b c-c

Class discussion

  1. 10. Have students reflect on what they were doing that scientists do. This could be prompted by the questions: “Were you doing science? What were you doing that was like what scientists do?” Discussion should reflect the concepts listed above.

If this activity is used as an introduction to the nature and process of science, then it would be helpful to use students’ comments to initiate a list of what scientists do as they engage in scientific investigations. This list can them be referenced as they read about scientists and their work or as the students participate in future investigations. Their list can also be compared to those represented in the Science Flowchart.

Science Flowchart.

Written by California Science Teachers Association

California Science Teachers Association

CSTA represents science educators statewide—in every science discipline at every grade level, Kindergarten through University.

One Response

  1. Ms Scotchmoor illustrates the beauty of integrating math and science at levels deeper than superficial and which provides an opportunity to produce profound results amongst students. Of all ages! Though initially teacher-directed, this lesson also gives a lot of power to students who are working both individually and cooperatively. If I were still teaching, I would use a lesson like this very early in the school year. The only thing I might add would be for the teacher to keep a chart that records the different hypotheses along with explanations for how (or why) thinking changed. If appropriate, a student might be able to keep such a record. Bravo

Leave a Reply

LATEST POST

California Science Curriculum Framework Now Available

Posted: Tuesday, March 14th, 2017

The pre-publication version of the new California Science Curriculum Framework is now available for download. This publication incorporates all the edits that were approved by the State Board of Education in November 2016 and was many months in the making. Our sincere thanks to the dozens of CSTA members were involved in its development. Our appreciation is also extended to the California Department of Education, the State Board of Education, the Instructional Quality Commission, and the Science Curriculum Framework and Evaluation Criteria Committee and their staff for their hard work and dedication to produce this document and for their commitment to the public input process. To the many writers and contributors to the Framework CSTA thanks you for your many hours of work to produce a world-class document.

For tips on how to approach this document see our article from December 2016: California Has Adopted a New Science Curriculum Framework – Now What …? If you would like to learn more about the Framework, consider participating in one of the Framework Launch events (a.k.a. Rollout #4) scheduled throughout 2017.

The final publication version (formatted for printing) will be available in July 2017. This document will not be available in printed format, only electronically.

Written by California Science Teachers Association

California Science Teachers Association

CSTA represents science educators statewide—in every science discipline at every grade level, Kindergarten through University.

Call for CSTA Awards Nominations

Posted: Monday, March 13th, 2017

The 2017 Award Season is now open! One of the benefits of being a CSTA member is your eligibility for awards as well as your eligibility to nominate someone for an award. CSTA offers several awards and members may nominate individuals and organizations for the Future Science Teacher Award, the prestigious Margaret Nicholson Distinguished Service Award, and the CSTA Distinguished Contributions Award (organizational award). May 9, 2017 is the deadline for nominations for these awards. CSTA believes that the importance of science education cannot be overstated. Given the essential presence of the sciences in understanding the past and planning for the future, science education remains, and will increasingly be one of the most important disciplines in education. CSTA is committed to recognizing and encouraging excellence in science teaching through the presentation of awards to science educators and organizations who have made outstanding contributions in science education in the state and who are poised to continue the momentum of providing high quality, relevant science education into the future. Learn More…

Written by California Science Teachers Association

California Science Teachers Association

CSTA represents science educators statewide—in every science discipline at every grade level, Kindergarten through University.

Call for Volunteers – CSTA Committees

Posted: Monday, March 13th, 2017

Volunteer

CSTA is now accepting applications from regular, preservice, and retired members to serve on our volunteer committees! CSTA’s all-volunteer board of directors invites you to consider maximizing your member experience by volunteering for CSTA. CSTA committee service offers you the opportunity to share your expertise, learn a new skill, or do something you love to do but never have the opportunity to do in your regular day. CSTA committee volunteers do some pretty amazing things: Learn More…

Written by California Science Teachers Association

California Science Teachers Association

CSTA represents science educators statewide—in every science discipline at every grade level, Kindergarten through University.

A Friend in CA Science Education Now at CSTA Region 1 Science Center

Posted: Monday, March 13th, 2017

by Marian Murphy-Shaw

If you attended an NGSS Rollout phase 1-3 or CDE workshops at CSTA’s annual conference you may recall hearing from Chris Breazeale when he was working with the CDE. Chris has relocated professionally, with his passion for science education, and is now the Executive Director at the Explorit Science Center, a hands-on exploration museum featuring interactive STEM exhibits located at the beautiful Mace Ranch, 3141 5th St. in Davis, CA. Visitors can “think it, try it, and explorit” with a variety of displays that allow visitors to “do science.” To preview the museum, or schedule a classroom visit, see www.explorit.org. Learn More…

Written by Marian Murphy-Shaw

Marian Murphy-Shaw

Marian Murphy-Shaw is the student services director at Siskiyou County Office of Education and is CSTA’s Region 1 Director and chair of CSTA’s Policy Committee.

Learning to Teach in 3D

Posted: Monday, March 13th, 2017

by Joseph Calmer

Probably like you, NGSS has been at the forefront of many department meetings, lunch conversations, and solitary lesson planning sessions. Despite reading the original NRC Framework, the Ca Draft Frameworks, and many CSTA writings, I am still left with the question: “what does it actually mean for my classroom?”

I had an eye-opening experience that helped me with that question. It came out of a conversation that I had with a student teacher. It turns out that I’ve found the secret to learning how to teach with NGSS: I need to engage in dialogue about teaching with novice teachers. I’ve had the pleasure of teaching science in some capacity for 12 years. During that time pedagogy and student learning become sort of a “hidden curriculum.” It is difficult to plan a lesson for the hidden curriculum; the best way is to just have two or more professionals talk and see what emerges. I was surprised it took me so long to realize this epiphany. Learn More…

Written by Guest Contributor

From time to time CSTA receives contributions from guest contributors. The opinions and views expressed by these contributors are not necessarily those of CSTA. By publishing these articles CSTA does not make any endorsements or statements of support of the author or their contribution, either explicit or implicit. All links to outside sources are subject to CSTA’s Disclaimer Policy: http://www.classroomscience.org/disclaimer.