May/June 2017 – Vol. 29 No. 7

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

Participate in Chemistry Education Research Study, Earn $500-800 Dollars!

Posted: Tuesday, May 9th, 2017

WestEd, a non-profit educational research agency, has been funded by the US Department of Education to test a new molecular modeling kit, Happy Atoms. Happy Atoms is an interactive chemistry learning experience that consists of a set of physical atoms that connect magnetically to form molecules, and an app that uses image recognition to identify the molecules that you create with the set. WestEd is conducting a study around the effectiveness of using Happy Atoms in the classroom, and we are looking for high school chemistry teachers in California to participate.

As part of the study, teachers will be randomly assigned to either the treatment group (who uses Happy Atoms) or the control group (who uses Happy Atoms at a later date). Teachers in the treatment group will be asked to use the Happy Atoms set in their classrooms for 5 lessons over the course of the fall 2017 semester. Students will complete pre- and post-assessments and surveys around their chemistry content knowledge and beliefs about learning chemistry. WestEd will provide access to all teacher materials, teacher training, and student materials needed to participate.

Participating teachers will receive a stipend of $500-800. You can read more information about the study here: https://www.surveymonkey.com/r/HappyAtoms

Please contact Rosanne Luu at rluu@wested.org or 650.381.6432 if you are interested in participating in this opportunity, or if you have any questions!

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.

2018 Science Instructional Materials Adoption Reviewer Application

Posted: Monday, May 8th, 2017

The California Department of Education and State Board of Education are now accepting applications for reviewers for the 2018 Science Instructional Materials Adoption. The application deadline is 3:00 pm, July 21, 2017. The application is comprehensive, so don’t wait until the last minute to apply.

On Tuesday, May 9, 2017, State Superintendent Tom Torlakson forwarded this recruitment letter to county and district superintendents and charter school administrators.

Review panel members will evaluate instructional materials for use in kindergarten through grade eight, inclusive, that are aligned with the California Next Generation Science Content Standards for California Public Schools (CA NGSS). 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.

Lessons Learned from the NGSS Early Implementer Districts

Posted: Monday, May 8th, 2017

On March 31, 2017, Achieve released two documents examining some lessons learned from the California K-8 Early Implementation Initiative. The initiative began in August 2014 and was developed by the K-12 Alliance at WestEd, with close collaborative input on its design and objectives from the State Board of Education, the California Department of Education, and Achieve.

Eight (8) traditional school districts and two (2) charter management organizations were selected to participate in the initiative, becoming the first districts in California to implement the Next Generation Science Standards (NGSS). Those districts included Galt Joint Union Elementary, Kings Canyon Joint Unified, Lakeside Union, Oakland Unified, Palm Springs Unified, San Diego Unified, Tracy Joint Unified, Vista Unified, Aspire, and High Tech High.

To more closely examine some of the early successes and challenges experienced by the Early Implementer LEAs, Achieve interviewed nine of the ten participating districts and compiled that information into two resources, focusing primarily on professional learning and instructional materials. 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.

Using Online Simulations to Support the NGSS in Middle School Classrooms

Posted: Monday, May 8th, 2017

by Lesley Gates, Loren Nikkel, and Kambria Eastham

Middle school teachers in Kings Canyon Unified School District (KCUSD), a CA NGSS K-8 Early Implementation Initiative district, have been diligently working on transitioning to the Next Generation Science Standards (NGSS) integrated model for middle school. This year, the teachers focused on building their own knowledge of the Science and Engineering Practices (SEPs). They have been gathering and sharing ideas at monthly collaborative meetings as to how to make sure their students are not just learning about science but that they are actually doing science in their classrooms. Students should be planning and carrying out investigations to gather data for analysis in order to construct explanations. This is best done through hands-on lab experiments. Experimental work is such an important part of the learning of science and education research shows that students learn better and retain more when they are active through inquiry, investigation, and application. A Framework for K-12 Science Education (2011) notes, “…learning about science and engineering involves integration of the knowledge of scientific explanations (i.e., content knowledge) and the practices needed to engage in scientific inquiry and engineering design. Thus the framework seeks to illustrate how knowledge and practice must be intertwined in designing learning experiences in K-12 Science Education” (pg. 11).

Many middle school teachers in KCUSD are facing challenges as they begin implementing these student-driven, inquiry-based NGSS science experiences in their classrooms. First, many of the middle school classrooms at our K-8 school sites are not designed as science labs. Learn More…

Powered By DT Author Box

Written by NGSS Early Implementer

NGSS Early Implementer

In 2015 CSTA began to publish a series of articles written by teachers participating in the NGSS Early Implementation Initiative. This article was written by an educator(s) participating in the initiative. CSTA thanks them for their contributions and for sharing their experience with the science teaching community.

Celestial Highlights: May – July 2017

Posted: Monday, May 8th, 2017

May Through July 2017 with Web Resources for the Solar Eclipse of August 21, 2017

by Robert C. Victor. Twilight sky maps by Robert D. Miller. Graphs of planet rising and setting times by Jeffrey L. Hunt.

In spring and summer 2017, Jupiter is the most prominent “star” in the evening sky, and Venus, even brighter, rules the morning. By mid-June, Saturn rises at a convenient evening hour, allowing both giant planets to be viewed well in early evening until Jupiter sinks low in late September. The Moon is always a crescent in its monthly encounters with Venus, but is full whenever it appears near Jupiter or Saturn in the eastern evening sky opposite the Sun. (In 2017, Full Moon is near Jupiter in April, Saturn in June.) At intervals of 27-28 days thereafter, the Moon appears at a progressively earlier phase at each pairing with the outer planet until its final conjunction, with Moon a thin crescent, low in the west at dusk. You’ll see many beautiful events by just following the Moon’s wanderings at dusk and dawn in the three months leading up to the solar eclipse. Learn More…

Powered By DT Author Box

Written by Robert Victor

Robert Victor

Robert C. Victor was Staff Astronomer at Abrams Planetarium, Michigan State University. He is now retired and enjoys providing skywatching opportunities for school children in and around Palm Springs, CA. Robert is a member of CSTA.