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Alaska Department of Education & Early Development
Math and Sciences Frameworks

Chapter 7: Vignettes


Math - Primary Level: Fish Camp in the Classroom
Math - Intermediate Level: Dog Mushing
Math - Middle School Level: Shelter
Math - Middle School Level: Hands Across Alaska
Science - Primary Level: Earth and Rocks
Science - Intermediate Level: Solids and Liquids
Science - Middle School Level: Spruce Bark Beetle
Science - Middle School Level: Water Quality
Science - Middle School Level: Space Exploration Project
Math and Science - High School Level: Project Chariot

Introduction to the Vignettes

The eight vignettes presented in this chapter are glimpses into some Alaska classroom settings, real and imagined, while mathematics and science are being taught in ways to develop the Standards in this Framework. These vignettes are not complete lesson plans; they are meant to inspire teachers to design interdisciplinary instruction that is tailored to the region and the students' interests.

The right-hand column of each vignette identifies points in the lesson which address the Standards. It also includes annotations to help the readers recognize strategies that are suggested by the Framework. Other than this, the vignettes have not been standardized into a single format. Instead, each reflects the individuality of a specific classroom setting. In some instances, the voice of the teacher is included to explain the educational rationale behind various activities. These vignettes were written and contributed by Alaskan teachers.

We hope these examples will be helpful to educators throughout the state as they attempt to translate the Mathematics and Science Framework and the Alaska Content Standards into effective practice in the classroom.


Math - Primary Level: Fish Camp in the Classroom
The classroom has a tent, equipment, and supplies set up as a representation of a typical fish camp. Students have discussed the variety of activities and responsibilities everyone has in camp. An elder has come in and talked to the students about fish camp and told them stories. The language/culture teacher has begun to develop fish camp vocabulary and has played some typical games from the culture with the students. Math Standard:
C. Communication
D. Reasoning
E. Connections

The teacher is using questioning/inquiry techniques and making connections to real life by use of culturally relevant activities.

As the scene opens, the students are gathered around the front of the tent. They are discussing how to sort a tub full of authentic-looking paper fish into different groups. Size is the first focus for the students. As students compare the different fish, the teacher asks them to place the fish into separate tubs.

Children make a picture graph of the groups of fish, using a felt board and pictures. The students each make their own picture graphs.

The teacher then interviews the students asking them to explain their graphs. The teacher makes notes on the sample assessment rubric to document the students' responses.
Math Standards:
A. Content
D. Reasoning
E. Connections

Science Standards:
B. Inquiry

An open ended problem is presented to the children. Sorting requires logical reasoning and the classification and graphing of the fish are parts of the process skills of science. The children make a graphic organizer to document these thoughts. The teacher makes continuous progress assessments through interviews.
The teacher encourages the children to discuss another method for sorting the fish. As before, the fish are separated, but this time they are sorted according to the new criteria.

Children make changes to the graph as needed. Discussion follows as the teacher helps children identify all the different ways they found to sort the fish.
Math Standards:
B. Problem Solving
C. Communication
D. Reasoning
E. Connections

Science Standards:
B. Inquiry

The teacher uses a collaborative process to help students realize that there are numerous options for sorting. The teacher is building connections between math and science.
The teacher asks the students to create simple addition and subtraction number sentences for the following problems:

How many fish would we have if you caught all of the fish in the whitefish category and I caught all of the fish in the salmon category?

How many salmon would there be in the tub if you ate two of them?

Then the teacher asks the students to work in pairs to create a number sentence problem of their own.
Math Standards:
A. Content
B. Problem Solving

The teacher is encouraging collaboration during problem solving and building connections between math skills and real-life activities.
Extensions: This activity could be used at various grade levels. For example students might go to a local creek and survey fish, write letters to the Department of Fish and Game, or invite elders to come in and describe the life histories of these fish based upon their first-hand experience and oral traditions. Science Standards:
C. Nature of Science
D. Application

Sample Assessments

The first two assessments examples are holistic rubrics with space for the teacher to insert anecdotal information (observations) about each student. See the Assessment chapter for more information.

Stage 1. The student sorts successfully by one attribute.
Student
Emerging
Developing
Applying


Identifies characteristics only. Can identify only one way of grouping.

Identifies characteristics and is able to group.

Identifies characters, groups by characteristics, and explains reasons for classifications.
Johnnie


Wylie


Sarah


Stage 2. Student creates graph and interprets it correctly.
Student
Emerging
Developing
Applying


Can participate in graph-making process without interpreting the results.

Can place fish from each tub in appropriate column of graph, but may be confused about the concept of more (i.e., if there are more smaller fish, but the other fish are bigger., which is more?).

Correctly places fish on graph. Correctly interprets which is more. .May go on to rearrange the graph, as, for example, to show a linear arrangement between size and number.
Johnnie


Wylie


Sarah


The teacher is keeping an ongoing checklist of student's math content knowledge. (For more information see Assessment). The following are just a few that could be identified in this lesson:
Student's Names
Translates word problems into number sentences for simple addition.



Translates word problems into number sentences for simple subtraction.



Can complete addition fact number problems that add to 10.



Can complete subtraction fact number problems using numbers 1-10.




Math - Intermediate Level: Dog Mushing
It is 8:00 a.m., Mrs. Titus greets her students at the door. The students are studying dog mushing. Today they will be discussing how to find out how much it costs to raise a team of dogs.

Mrs. Titus: How many of you have a dog? (Show of hands.) What do you know about how much it costs for your family to keep a dog?

Student: I think we buy 50 lb. of dog food every two weeks.

Mrs. Titus: Are there other costs in caring for a dog?

Student: Every once in a while we have to take the dog to the vet.

Mrs. Titus: Do you know how much it costs to take your dog to the vet?

Student: No.

Mrs. Titus: Would it be possible for you to find out? If you were raising your dog to race in the XYZ dog race, do you think there would be other costs?

Student: I know a musher; I could ask.

The teacher makes a KWL chart during this discussion and fills out the "What We Know" section. She then solicits questions from the students for the "What We Want to Learn" section.
Math Standards:
E. Connections
A. Content

The teacher is using open-ended questioning strategies, making connections to real-life and to local culture, and using a graphic organizer (KWL Chart).
The student invited the musher to come into the classroom to answer questions about raising dogs. Math Standards:
A. Content
E. Connections

Science Standards:
A. Content
C. Nature of Science

The teacher is involving the community in the classroom.
Mrs. Titus: What did we find out? (The teacher completes the "What We Learned" Section of the KWL chart during this discussion.)

Student: I found out that there are lots more costs to raising a race dog than in caring for our pet dog.

Student: A race dog has to have special kinds of food, disease is a problem in kennels, the equipment for racing costs a lot of money, nice kennels have to be built, the musher has to work with his/her dogs everyday, and you have to buy special dogs.
Math Standards:
A. Content
E. Connections

Science Standards:
D. Application

The teacher conducts continuous progress assessment through a KWL Chart.
Mrs. Titus: Can a musher do this as a hobby, or is it a full time job?

Henry Oyoumiak has the land and kennels to raise 50 racing dogs. How much will it cost him to acquire 10 dogs and take care of them in preparation for the XYZ dog race in 10 months. He will also use 10 dogs from another kennel.

Decide what information you need and collect that information. Determine how much it will cost him to raise and rent dogs for the race.
Math Standards:
A. Content
B. Problem Solving
C. Reasoning

The teacher creates an application for the problem solving task.
Extensions:
The topic could be extended to focus on the optimum number of dogs to run in the XYZ dog race (within a certain budget) and the student's rationale for his/her choice.

This could require the use of a spreadsheet.
Math Standards:
A. Content
B. Problem Solving
D. Reasoning

The students are developing useful technology tools.

Sample Assessment

The following is an example of a Likert Scale For more information see Assessment.

Student Name:

No Evidence of Understanding
Some Evidence of Understanding
Effective Mastery
Distinguishes important from unimportant information.


Finds source of accurate estimates of costs per dog per month.


Recognizes whether or not answer is reasonable.


Writes out complete answer to the problem.


Appropriate use of multiplication and addition.



Math - Middle School Level: Shelter
A. The Lottery

Students will choose their building lot from a subdivided area that the teacher has obtained. (Maps of subdivisions can be obtained from the borough assessor's office or from the State Division of Lands). Potential lots could also be collected from previous state lotteries or remote parcel sites. To make the choosing more realistic a land lottery could be held (probability and statistics) or the lots could be purchase with mini-society money or community bucks. To make it fair and simple, students could draw numbers out of a hat and select their parcel based on their number.
Math Standards:
A. Content
E. Connections


The students are gaining information on how land is actually plotted and described in local agencies.
Students will then cut a scale model of their parcel from a piece of corrugated cardboard so that they can place a scale model building on the property. Any physical features that are indicated on the subdivision map should be transferred to this enlarged model (creeks, ponds, easements, etc.). If the parcels selected by the teacher are not simple rectangular shapes, this process of enlarging the scale will involve angle measurements as well as linear dimensions. Math Standards:
D. Reasoning
B. Designing the House

Students will select a building site on their property, making sure that they leave a 10 ft. easement on all property lines. They will design a home for a family of four that shows some consideration of site weather patterns, climate and materials. The design will be drawn to scale as a floor plan. If the home has more than one floor each floor should be drawn separately. Students will find it easier to draw floor plans on graph paper than on blank sheets. A collection of housing floor plans should be available for students to look at. These can be obtained from newspapers and magazines.
Math Standards:
D. Reasoning
E. Connections

Science Standards:
D. Application
C. Building the House

Students will make a 3-D scale model of the exterior of their house. Floor plans glued to poster board or corrugated cardboard could be used as floors within the structure. The exterior should have all the doors and windows appropriately placed and scaled for the design. This 3-D model will then be placed on the cardboard model of the lot for which it was designed. (Extra credit will be given for designing landscaping, outbuildings, garden plots, composting area, accommodations for the use of alternative energy, etc.)
Math Standards:
B. Problem Solving
E. Connections
D. Selling the Homestead

Students will create a sales brochure that fully describes their lot and structure. This brochure would describe all basic design features (square footage, lot size, location, etc.) and include a picture of the house with a name for the house plan. Examples of this type of writing are often found with house plans in magazines and newspapers. This sales brochure must also list an asking price for the homestead based on construction costs and local market conditions. Students could utilize a computer assisted drawing program for the picture of their house and desktop publishing for production of the text.
Math Standards:
A. Content
C. Communication
D. Reasoning

Science Standards:
D. Application
Spin-offs and Connections:
1) Cooperative Groups:
Use cooperative groups to design water, sewer, power systems for a community made up of several homes. They can also design community space, roads and walkways.
Math Standards:
E. Connections
2) Guest Speakers:
  • Talk to a builder or a developer to learn how they estimate building/selling costs.
  • Talk to a realtor to learn about market conditions and loan programs.
  • Have an engineer talk about site limitations regarding water, waste water and power systems.
  • Invite a borough planner to learn about permits, codes, surveys and recording requirements/costs.
  • Meet with an energy expert to learn about energy efficient building techniques and materials.
Math Standards:
E. Connections
2) Science:
  • Geology (soil permeability, ground water, soil type) and topography considerations are included in justifying designs.
  • Incorporate insulation materials in the model houses. Test houses for rate of heat loss. Manipulate environmental variables (like using a fan to simulate wind) and test for rate of heat loss.
  • Incorporate alternative energy designs and assess for application of knowledge of these technologies.
Math Standards:
E. Connections

Science Standards:
A. Content
B. Inquiry
D. Application

Sample Assessments:

Journaling
(For more information see Journals and Learning Logs).

Students will keep a daily record in a journal. This should include their calculations and problem solving activities as well as rough sketches and resources.

Checklist
(For more information see Scoring Guides/Checklist)
Floor Plans and Models
Self
Peer
Teacher
Used accurate measurements


Used appropriate scale


Construction is neat and accurate


Plans are realistic for a family home (all bedrooms have windows, stairways are included, doors can open, etc.)


Exterior walls fit with the floor plan.


Sales Brochure
Self
Peer
Teacher
Accurately computed square footage for the house and each room


Closely estimated the acreage of the lot (show work in journal)


Price their homestead and support their asking price based on construction costs and local market


Picture shows a flattering, but realistic, view of the house


Text accurately describes the positive features of the house and lot.



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Last modified on: Tue, Jun 11, 1996.