January/February 2018 – Vol. 31 No. 2

## 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.

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.

#### Written by 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

# LATEST POST

## California Science Test Academy for Educators

Posted: Thursday, February 15th, 2018

### California Science Test Academy for Educators

To support implementation of the California Science Test (CAST), the California Department of Education is partnering with Educational Testing Service and WestEd to offer a one-day CAST Academy for local educational agency (LEA) science educators, to be presented at three locations in California from 8:30 a.m. to 3:30 p.m. As an alternative to traveling, LEA teams can participate virtually via WebEx on one of the dates listed below.

The dates and locations for the CAST Academy are as follows:

• Monday, April 23, 2018—Sacramento
• Wednesday, April 25, 2018—Fresno
• Thursday, April 26, 2018—Irvine

The CAST Academy will help participants develop a deeper understanding of the assessment design and expectations of the CAST. The academy also will provide information and activities designed to assist educators in their implementation of the California Next Generation Science Standards and three-dimensional learning to help them gain an understanding of how these new science assessment item types can inform teaching and learning. The CAST Academy dates above are intended for school and district science instructional leaders, including teacher leaders, teacher trainers, and instructional coaches. Additional trainings will be offered at a later date specifically for county staff. In addition, curriculum, professional development, and assessment leaders would benefit from this training.

A \$100 registration fee will be charged for each person attending the in-person training. Each virtual team participating via WebEx will be charged \$100 for up to 10 participants through one access point. Each workshop will have the capacity to accommodate a maximum of 50 virtual teams. Each virtual team will need to designate a lead, who is responsible for organizing the group locally. Registration and payment must be completed online at http://www.cvent.com/d/6tqg8k.

#### Written by California Science Teachers Association

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

## Accelerating into NGSS – A Statewide Rollout Series Now Accepting Registrations

Posted: Friday, January 19th, 2018

Are you feeling behind on the implementation of NGSS? Then Accelerating into NGSS – the Statewide Rollout event – is right for you!

WHO SHOULD ATTEND
If you have not experienced Phases 1-4 of the Statewide Rollout, or are feeling behind with the implementation of NGSS, the Accelerating Into NGSS Statewide Rollout will provide you with the greatest hits from Phases 1-4!

OVERVIEW
Accelerating Into NGSS Statewide Rollout is a two-day training geared toward grade K-12 academic coaches, administrators, curriculum leads, and teacher leaders. Check-in for the two-day rollout begins at 7:30 a.m., followed by a continental breakfast. Sessions run from 8:00 a.m. to 4:15 p.m. on Day One and from 8:00 a.m. to 3:30 p.m. on Day Two.

Cost of training is \$250 per attendee. Fee includes all materials, continental breakfast, and lunch on both days. It is recommended that districts send teams of four to six, which include at least one administrator. Payment can be made by check or credit card. If paying by check, registration is NOT complete until payment has been received. All payments must be received prior to the Rollout location date you are attending. Paying by credit card secures your seat at time of registration. No purchase orders accepted. No participant cancellation refunds.

REGISTER

http://bit.ly/ACCELERATINGINTONGSS

DATES & LOCATIONS
MARCH 28-29, 2018
Host: San Mateo County Office of Education
Location: San Mateo County Office of Education, Redwood City

APRIL 10-11, 2018
Host: Orange County Office of Education
Location: Brandman University, Irvine

MAY 1-2, 2018
Host: Tulare County Office of Education
Location: Tulare County Office of Education, Visalia

MAY 3-4, 2018
Host: San Bernardino Superintendent of Schools
Location: West End Educational Service Center, Rancho Cucamonga

MAY 7-8, 2018
Host: Sacramento County Office of Education
Location: Sacramento County Office of Education Conference Center and David P. Meaney Education Center, Mather

JUNE 14-15, 2018
Host: Imperial County Office of Education
Location: Imperial Valley College, Imperial

Presented by the California Department of Education, California County Superintendents Educational Services Association/County Offices of Education, K-12 Alliance @WestEd, California Science Project, and the California Science Teachers Association.

#### Written by California Science Teachers Association

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

## The Teaching and Learning Collaborative, Reflections from an Administrator

Posted: Friday, January 19th, 2018

by Kelly Patchen

My name is Mrs. Kelly Patchen, and I am proud to be an elementary assistant principal working in the Tracy Unified School District (TUSD) at Louis Bohn and McKinley Elementary Schools. Each of the schools I support are Title I K-5 schools with about 450 students, a diverse student population, a high percentage of English Language Learners, and students living in poverty. We’re also lucky to be part of the CA NGSS K-8 Early Implementation Initiative with the K-12 Alliance. Learn More…

#### Written by NGSS Early Implementer

In 2015 CSTA began to publish a series of articles written by teachers participating in the California NGSS k-8 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.

## 2018 CSTA Conference Call for Proposals

Posted: Wednesday, January 17th, 2018

CSTA is pleased to announce that we are now accepting proposals for 90-minute workshops and three- and six-hour short courses for the 2018 California Science Education Conference. Workshops and short courses make up the bulk of the content and professional learning opportunities available at the conference. In recognition of their contribution, members who present a workshop or short course receive 50% off of their registration fees. Click for more information regarding proposals, or submit one today by following the links below.

Short Course Proposal

#### Written by California Science Teachers Association

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