Math/Science Vignettes 2 of 4

Alaska Department of Education & Early Development

Math - Middle School Level: Hands Across Alaska

The setting is a tenth grade math class that is beginning its study of linear functions. Rather than diving right into various forms of equations to represent data, Mr. Rix engages his students with an activity. Mr. Rix: Way back when, when I was in school, I was taught that electrons flow through wires like water. I always tried to imagine an electron zipping down a wire, through the toaster, and back to the wall...something didn't seem right. Later it was explained to me that these electrons just sort of nudge each other like this (Mat makes a nudging motion with his arm). I need four volunteers to try to simulate this action.		Math Standards: E. Connections The teacher is engaging the students by using an advanced organizer that includes kinesthetic involvement.
Four volunteers come to the front of the classroom. Mr. Rix: Please face the class and hold hands. Now, to simulate a pulse I will squeeze Fred's left hand, at the same time starting my stop watch. When Fred feels my squeeze he will squeeze Dot's hand and so on down the line until we get to Angie. When Angie feels the pulse she will raise her free hand, and I will stop the watch.
After trying the activity the class decides that it would be better if the participants closed their eyes so they could not anticipate the pulse as easy. Also it is decided to generate the pulse both directions and use the average of both these times.		Math Standards: B. Problem solving C. Communication E. Reasoning Science Standards: B. Inquiry The students are collaboratively reflecting upon the experiences and proposing their own modifications.
Mr. Rix: Well, it took 1.7 seconds for the pulse to go through four people. How long would it take if we had eight people instead of just four? Student: It would take twice as long. (For eight people it took 2.8 seconds)		Science Standards: B. Inquiry The teacher has established the activity and would now like the class to make a prediction based on the student-generated data.
After the time has been recorded for four people, the process is continued for 8, 12, 16, 20, 24, and 28 people. The data is recorded as a graph on the chalkboard for all the class to see.		Math Standards: A. Content D. Reasoning Science Standards: B. Inquiry Embedded in this is the concept of slope. This kind of activity helps the students build an operational definition of what a slope is ("the increase of time as we add more people").
Mr. Rix: How long would it take if we continued this exercise to include all the student body in our school (154)? Let's hear how each of you came up with your numbers.		Math Standards: A. Content C. Communication D. Reasoning This requires some more thought from the students and some are quicker than others to begin to solve the problem posed. Most are using ratios to help to come to a conclusion.
After students have worked on the problem and had a chance to express their answer, Mr. Rix explains what he would like them to do: Use the data we generated to do three things: 1. Create a graphic representation of the data. 2. Formulate an equation that explains the relationship between the number of people and the time it takes the pulse. 3. Answer the following question: "Can you run as fast as the 'squeeze pulse'". Give your rationale for your answer, and make use of your work from Question #1 and #2.		Math Standards: A. Content B. Connections Science Standards: D: Application The activity allows for expansion of questions and applications. Question #3 requires students to estimate the distance between them so they can figure out the velocity of the pulse. The also have to estimate their own speed.
Extensions: Students could figure out the slope for productivity at a certain job over long periods of time.

Sample Assessment

For more information on creating checklists see Assessment.

Student Ramona Robbie Zan Wassalie Allan Sean

Creates appropriate labels for graph axes

Correctly interprets graphic information

Creates linear formula

Determines running speed in a manner that can be applied to this problem.

Science - Primary Level: Earth and Rocks

Lesson Concept : Rocks are products of the changing earth and are found everywhere. They are different from one another in many identifiable ways.

Day 1
After recess, Beau brings in a rock he found while playing.
Beau: Look at my rock! It has gold in it
Mr. Rix: What a treasure, Beau! Would you like to show it to the others?
Beau: Yes!
The kids gather around as Beau talks about his rock.
Mr. Rix: Where can we find rocks?
Beau: On our playground.
Jane: At my house.
Caity: On the nature trail.
Justin: At the beach.
The teacher writes ideas on chart paper in a KWL Chart under What we know about rocks. (See Assessment for a sample of a KWL Chart.)
Mr. Rix: Sounds like you know a lot of places to find rocks. I would like each person to bring one or two rocks to school tomorrow.
Science Standards:
A. Content

Math Standards:
B. Communication

The teacher is activating prior knowledge, using open-ended questions to stimulate involvement, and keeping the students in the middle of the instruction.

Note that this is emergent curriculum: the study of rocks is developed from student interest It allows flexible unit planning and it is developmentally appropriate.
Students experience discovery of a rock.
This entire unit is based upon a learning cycle model which follows the sequence engagement (gearing up), exploring, explaining, and extending (applying).

Day 2
Students put their rocks on a designated table and label them with their names. Give students time to look at and examine rocks. In a group, students and teacher discuss rocks and where they were found.
Mr. Rix: Tell me where you found your rock and I will write down all the places.
Science Standards:
B. Inquiry
The students are identifying the attributes of their rocks, preparing to sort and classify.

Joe and Rainbow found their rocks at the beach and the stream. These were the only smooth rocks.

Mr. Rix: Let's look at Joe's rock and Rainbow's rock. How are they different from the other rocks?
Mary: They are smaller.
Nelson: They aren't sharp. Mine is real sharp.
Mr. Rix: Joe and Rainbow said they found their rocks at the beach and the stream.

Field trip (Explore) :
Take students on a 'rock hunt'. Give each student a plastic bag or some sort of container. As a group walk around the school grounds, on the nature trail, to the park, etc. Look for and collect some rocks--any kind that students find interesting or beautiful or any they wish to keep. On the way back from the collection trip ask children to look for ways rocks are used: in buildings, bridges, walls, foundations statues. Chat about the different ways rocks are used. Science Standards:
D. Application

The teacher is using field studies to provide hands-on experience. The students are discovering connections to geology, architecture, engineering, and math.

Explore:
After returning to class, give students an opportunity to examine and freely explore their rocks.

Add information to the W section of the KWL chart (what we want to learn about rocks).
After returning:
To integrate math, ask students to help each other count rocks. Group rocks into tens. Add groups of ten, etc. Measure and weigh the rocks.
Mr. Rix: How many ways can you discover to sort your rocks?
The students sort rocks in many ways and compare their ideas and results
Rainbow: Look how many big rocks we found.
Mr. Rix: I see you have sorted your big rocks from your smaller rocks. You have sorted by size. Is there another way you can sort your rocks?
Johnnie: I put all my dark rocks over here and my light colored rocks over here.
Mr. Rix: It looks like you have sorted your rocks by color. Can you sort them in another way?
Science Standards:
B. Inquiry

Math Standards:
A. Content
E. Connections
Teacher lets students discover their own classification systems. Discourse is encouraged.

Day 3
Explore:
Give students a box and challenge them to look for the largest rock they can find that will fit inside the box. (This leads students to look at rocks more closely)
As they search, the teacher might ask questions like:
Why doesn't that rock fit in the box? (The rock fits in the box but it could be wider, or I'm looking for a slightly smaller rock). Will it fit if you turn it a different way?
Add information to the L section of the KWL Chart (what we Learned).
Science Standards:
B. Inquiry
E. Reasoning

Math Standards:
A. Content

Detailed observations are called for. Students are asked to reason about measurement and geometry.

Explore:
Classify Rocks: Comparing shape, size texture.
Set out lots of pie plates or egg cartons and ask kids to sort rocks on the plates. Put together the rocks that are alike in some way: color, size, shape, texture (smooth or not smooth) hard - not hard, shiny - dull. Let kids examine the variety of groupings, trying to figure out how peers sorted.
Mr. Rix: How are the rocks in this pie plate alike?
Pat: Smooth and round.
Mr. Rix: Can anyone remember where we found the smooth rocks?
Science Standards:
A. Content
B. Inquiry

The students are comparing and contrasting, possibly graphing their results. The teacher helps the students to discover that water motion can erode and change the shape of rocks.

Gertrude: I know. I found my smooth rock by the stream on the trail.
Johnnie: I found mine by the stream, too.
Mr. Rix: Hmmm. So we found the smooth rocks by the stream. Joe, didn't you find your smooth rock by the beach the other day?
Joe: Yep, there were lots of smooth rocks there.
Mr. Rix: And, Rainbow, didn't you find your rock by the water?
Rainbow: Yeah, but not at the beach. It was at the stream.
Mr. Rix: Can we say that most of our smooth rocks were found by water?
Add information to the L section of the KWL Chart (what we Learned).
Science Standards:
A. Content
B. Inquiry

The students are comparing and contrasting, possibly graphing their results. The teacher helps the students to discover that water motion can erode and change the shape of rocks.

Conduct various lessons where kids will be involved in guided actions: sorting according to texture, exploring color, testing for hardness, comparing weight, finding rocks that write. Conduct a guided exploration for kids to find out that differences may be related to location.

Add information to the L section of the KWL Chart (What weLearned).
Science Standards:
A. Content
B. Inquiry

Application:
Ask the students to discuss and decide what kind of structure they should build with their rocks. Divide into construction teams and build the structure. Science Standards:
A. Application

Extensions:

Read: Byrd Baylor's Everyone Needs a Rock.

Select your favorite rock from your collection. Put it with the other favorite rocks. Let kids find their own rocks. Science Standards:
B. Inquiry

Math Standards:
E. Connections

Lesson Concept: Rocks have internal structures. (Even though the earth is composed of distinct layers and not quite like the cookie, this activity enables kids to consider things that can't be seen directly.)

Day 4
Students analyze the ingredients of a chocolate chip cookie. Compare the idea of the 'internal structure' of a cookie to the internal structure of rocks. Buy or make cookies with lots of visible ingredients - choco chip with nuts, oatmeal, etc. Have available rocks with observable mineral components (or composites). Rocks and cookies can be distinguished from other rocks and cookies by observing, comparing, and identifying their components.
Science Standards:
B. Inquiry

This lesson provides a familiar framework (cookie composition and structure) for knowledge (rock composition and structure). The concrete exploration with the cookie is an appropriate model for the abstract inferences about rocks.

Explore:
Distribute hand lens and encourage kids to examine rocks with a hand lens. Discuss observations. Did you notice anything different using a hand lens?
Rocks are made of many materials, but it is hard to break a rock open to see what's inside. Scientists often use models of things that are difficult to investigate. We are going to examine choco cookies because, like rocks, they are made of many ingredients which sometimes can not be seen unless you break them open. Using a hand lens and toothpicks we are going to examine the ingredients of a cookie.
Distribute a cookie to pairs of kids, along with hand lens and toothpicks. (The cookies look yummy but don't eat them yet!). Encourage the students to dissect and discover the components of the cookie.
Science Standards:
A. Content
B. Inquiry

The teacher is providing models/analogies for the students and open-ended questioning techniques.

The students are discovering the concept that rocks are made of minerals (Structure and Matter).

Ask: What did you use to discover the different materials in the cookie? Were certain ingredients found in one part of the cookie or scattered? Were any ingredients harder to find than others? Do you think there are other ingredients in the cookie that you still cannot see? How does the inside differ from the inside? Do it again use cookies with different ingredients.
Repeat the activity using a rock that kids could break and see particles, such as sandstone or limestone. How does the inside differ from the outside? Discuss and compare findings.
At a center or in small groups, place a rock in a pillow case. Hit it with a hammer. Examine the broken parts. How does the inside differ form the outside?

Sample Assessment:

KWL or Discovered Principles Chart
(See Graphic Organizers.)

Use the KWL Chart to document the learning process for the whole class or a group. Collect anecdotes and documentation from each of the students when they demonstrate that they know. You can compare the first column helps the teacher to know where to begin. Comparing the first and last column gives an indication of how much was learned.

What We Already Know
What We Want to Know
What We Learned

Rocks are found everywhere
etc.

Why is my rock spotted?
Why did my rock break flat?
How are some rocks different from others?
etc.
Rocks are made out of more than one kind of material.
Smooth rocks are found by the stream.
etc.

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Student	Ramona	Robbie	Zan	Wassalie	Allan	Sean
Creates appropriate labels for graph axes
Correctly interprets graphic information
Creates linear formula
Determines running speed in a manner that can be applied to this problem.

Day 1 After recess, Beau brings in a rock he found while playing. Beau: Look at my rock! It has gold in it Mr. Rix: What a treasure, Beau! Would you like to show it to the others? Beau: Yes! The kids gather around as Beau talks about his rock. Mr. Rix: Where can we find rocks? Beau: On our playground. Jane: At my house. Caity: On the nature trail. Justin: At the beach. The teacher writes ideas on chart paper in a KWL Chart under What we know about rocks. (See Assessment for a sample of a KWL Chart.) Mr. Rix: Sounds like you know a lot of places to find rocks. I would like each person to bring one or two rocks to school tomorrow.		Science Standards: A. Content Math Standards: B. Communication The teacher is activating prior knowledge, using open-ended questions to stimulate involvement, and keeping the students in the middle of the instruction. Note that this is emergent curriculum: the study of rocks is developed from student interest It allows flexible unit planning and it is developmentally appropriate. Students experience discovery of a rock. This entire unit is based upon a learning cycle model which follows the sequence engagement (gearing up), exploring, explaining, and extending (applying).
Day 2 Students put their rocks on a designated table and label them with their names. Give students time to look at and examine rocks. In a group, students and teacher discuss rocks and where they were found. Mr. Rix: Tell me where you found your rock and I will write down all the places.		Science Standards: B. Inquiry The students are identifying the attributes of their rocks, preparing to sort and classify.
Joe and Rainbow found their rocks at the beach and the stream. These were the only smooth rocks. Mr. Rix: Let's look at Joe's rock and Rainbow's rock. How are they different from the other rocks? Mary: They are smaller. Nelson: They aren't sharp. Mine is real sharp. Mr. Rix: Joe and Rainbow said they found their rocks at the beach and the stream.
Field trip (Explore) : Take students on a 'rock hunt'. Give each student a plastic bag or some sort of container. As a group walk around the school grounds, on the nature trail, to the park, etc. Look for and collect some rocks--any kind that students find interesting or beautiful or any they wish to keep. On the way back from the collection trip ask children to look for ways rocks are used: in buildings, bridges, walls, foundations statues. Chat about the different ways rocks are used.		Science Standards: D. Application The teacher is using field studies to provide hands-on experience. The students are discovering connections to geology, architecture, engineering, and math.
Explore: After returning to class, give students an opportunity to examine and freely explore their rocks. Add information to the W section of the KWL chart (what we want to learn about rocks). After returning: To integrate math, ask students to help each other count rocks. Group rocks into tens. Add groups of ten, etc. Measure and weigh the rocks. Mr. Rix: How many ways can you discover to sort your rocks? The students sort rocks in many ways and compare their ideas and results Rainbow: Look how many big rocks we found. Mr. Rix: I see you have sorted your big rocks from your smaller rocks. You have sorted by size. Is there another way you can sort your rocks? Johnnie: I put all my dark rocks over here and my light colored rocks over here. Mr. Rix: It looks like you have sorted your rocks by color. Can you sort them in another way?		Science Standards: B. Inquiry Math Standards: A. Content E. Connections Teacher lets students discover their own classification systems. Discourse is encouraged.
Day 3 Explore: Give students a box and challenge them to look for the largest rock they can find that will fit inside the box. (This leads students to look at rocks more closely) As they search, the teacher might ask questions like: Why doesn't that rock fit in the box? (The rock fits in the box but it could be wider, or I'm looking for a slightly smaller rock). Will it fit if you turn it a different way? Add information to the L section of the KWL Chart (what we Learned).		Science Standards: B. Inquiry E. Reasoning Math Standards: A. Content Detailed observations are called for. Students are asked to reason about measurement and geometry.
Explore: Classify Rocks: Comparing shape, size texture. Set out lots of pie plates or egg cartons and ask kids to sort rocks on the plates. Put together the rocks that are alike in some way: color, size, shape, texture (smooth or not smooth) hard - not hard, shiny - dull. Let kids examine the variety of groupings, trying to figure out how peers sorted. Mr. Rix: How are the rocks in this pie plate alike? Pat: Smooth and round. Mr. Rix: Can anyone remember where we found the smooth rocks?		Science Standards: A. Content B. Inquiry The students are comparing and contrasting, possibly graphing their results. The teacher helps the students to discover that water motion can erode and change the shape of rocks.
Gertrude: I know. I found my smooth rock by the stream on the trail. Johnnie: I found mine by the stream, too. Mr. Rix: Hmmm. So we found the smooth rocks by the stream. Joe, didn't you find your smooth rock by the beach the other day? Joe: Yep, there were lots of smooth rocks there. Mr. Rix: And, Rainbow, didn't you find your rock by the water? Rainbow: Yeah, but not at the beach. It was at the stream. Mr. Rix: Can we say that most of our smooth rocks were found by water? Add information to the L section of the KWL Chart (what we Learned).		Science Standards: A. Content B. Inquiry The students are comparing and contrasting, possibly graphing their results. The teacher helps the students to discover that water motion can erode and change the shape of rocks.
Conduct various lessons where kids will be involved in guided actions: sorting according to texture, exploring color, testing for hardness, comparing weight, finding rocks that write. Conduct a guided exploration for kids to find out that differences may be related to location. Add information to the L section of the KWL Chart (What weLearned).		Science Standards: A. Content B. Inquiry
Application: Ask the students to discuss and decide what kind of structure they should build with their rocks. Divide into construction teams and build the structure.		Science Standards: A. Application
Extensions: Read: Byrd Baylor's Everyone Needs a Rock. Select your favorite rock from your collection. Put it with the other favorite rocks. Let kids find their own rocks.		Science Standards: B. Inquiry Math Standards: E. Connections
Lesson Concept: Rocks have internal structures. (Even though the earth is composed of distinct layers and not quite like the cookie, this activity enables kids to consider things that can't be seen directly.)
Day 4 Students analyze the ingredients of a chocolate chip cookie. Compare the idea of the 'internal structure' of a cookie to the internal structure of rocks. Buy or make cookies with lots of visible ingredients - choco chip with nuts, oatmeal, etc. Have available rocks with observable mineral components (or composites). Rocks and cookies can be distinguished from other rocks and cookies by observing, comparing, and identifying their components.		Science Standards: B. Inquiry This lesson provides a familiar framework (cookie composition and structure) for knowledge (rock composition and structure). The concrete exploration with the cookie is an appropriate model for the abstract inferences about rocks.
Explore: Distribute hand lens and encourage kids to examine rocks with a hand lens. Discuss observations. Did you notice anything different using a hand lens? Rocks are made of many materials, but it is hard to break a rock open to see what's inside. Scientists often use models of things that are difficult to investigate. We are going to examine choco cookies because, like rocks, they are made of many ingredients which sometimes can not be seen unless you break them open. Using a hand lens and toothpicks we are going to examine the ingredients of a cookie. Distribute a cookie to pairs of kids, along with hand lens and toothpicks. (The cookies look yummy but don't eat them yet!). Encourage the students to dissect and discover the components of the cookie.		Science Standards: A. Content B. Inquiry The teacher is providing models/analogies for the students and open-ended questioning techniques. The students are discovering the concept that rocks are made of minerals (Structure and Matter).
Ask: What did you use to discover the different materials in the cookie? Were certain ingredients found in one part of the cookie or scattered? Were any ingredients harder to find than others? Do you think there are other ingredients in the cookie that you still cannot see? How does the inside differ from the inside? Do it again use cookies with different ingredients. Repeat the activity using a rock that kids could break and see particles, such as sandstone or limestone. How does the inside differ from the outside? Discuss and compare findings. At a center or in small groups, place a rock in a pillow case. Hit it with a hammer. Examine the broken parts. How does the inside differ form the outside?