Fifth Grade – November. Grant Purpose and Background Partnerships Purpose of this Training Target:...

Fifth Grade – November

• Grant Purpose and Background• Partnerships• Purpose of this Training

Target: Increase content knowledge of identified Tennessee Education Standards for Math as measured through a STEM challenge or a Math & Science integrated activity.

Introductions and Training Purpose

Agenda• Math Standards-Vertical Alignment• MICA and Writing of Assessment Items• Scaffolding Activities with Manipulatives • Lunch – 11:00-12:15• Digital/Electronic Resource• Math Task (Instructional)• Math and Science Integrated Activity leading

into a STEM Challenge • Closing

• Teams• Bathrooms/Breaks/Cell

Phones• Agenda• STEM• Materials

Training Teams and Logistics

NormsBe an active participant

Be mindful of air time

Be mindful of sidebar conversations

Use technology at appropriate times

• http://msptennessee.wikispaces.com

• Please take the time to visit the site later

• Contact us if you have any questions or need help.

MSP Wikispace – Your Source for All Resources

http://msptennessee.wikispaces.com/

http://msptennessee.wikispaces.com/

Challenge: Every year, our school has field day, but no one wants to drink warm Gatorade. Design a rectangular prism to freeze water in to create the longest lasting ice cube. This ice cube must last a minimum of three hours in the hot sun, even when the lunch box is opened and closed several times during field day. Your rectangular prism cannot have a volume greater than 300 cubic centimeters. Make it from graph paper and include the volume of your rectangular prism using a formula for volume. The class will vote to determine the best two designs and justify why. The best 2 designs will be tested under the heat lamp (sun) to see which lasts the longest.

Targeted StandardsMath

• 5.MD.C.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

• 5.MD.C.5b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

• 5.MD.C.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

• 5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

Science• GLE 0507.9.2 Design and

conduct an experiment to demonstrate how various types of matter freeze, melt, or evaporate.

• GLE 0507.9.3 Investigate factors that affect the rate at which various materials freeze, melt, or evaporate.

• SPI 0507.9.2 Describe the differences among freezing, melting, and evaporation.

• SPI 0507.9.3 Describe factors that influence the rate at which different types of material freeze, melt, or evaporate.

Integrated Math and Science Lesson

Clear Target:

I can determine factors

that influence the rate

of ice melting.

Clear Target:

I can measure liquid volume of ice after allowing time for melting.

.

• Introduce 4 sets of frozen water –Two investigations will be ongoing throughout the day.

–Each investigation will have a rectangular prism containing 150 ml of water that has been frozen overnight.

–Every 10 minutes measure the amount of melting that has occurred.

–Data will be compiled and analyzed at the end of the day.

Integrated Lesson

• Set A - Ice melting at room temperature

• Every 10 minutes, a group will:

–pour the melted water into the graduated cylinder and use the marker to mark each measurement.

–fill out the data sheet.–remove centimeter cubes from rectangular prism to match each melted milliliter of water.

Integrated Lesson

• Set B - Ice melting under the sun (simulated by heat lamp)

• Every 10 minutes, a group will:

-pour the melted water into the graduated cylinder and use the marker to mark each measurement.-fill out the data sheet.-remove centimeter cubes from rectangular prism to match each melted milliliter of water.

Integrated Lesson

Standards for Mathematical Practice

• Make sense of problems and preserve in solving them.• Reason abstractly and quantitatively.• Construct viable arguments and critique the reasoning of

others.• Model with mathematics.• Use appropriate tools strategically.• Attend to precision.• Look for and make use of structure.• Look for and express regularity in repeated reasoning.

Mathematical Practice Standards


Students who are math literate

demonstrate these

practices.

Mathematics Teaching Practices

• Establish mathematics goals to focus learning.

• Implement tasks that promote reasoning and problem solving.

• Use and connect mathematical representations.

• Facilitate meaningful mathematical discourse.

• Pose purposeful questions.• Build procedural fluency from conceptual

understanding.• Support productive struggle in learning

mathematics.• Elicit and use evidence of student thinking.

Mathematical Practice Standards Connections to Mathematical Teaching

Practices• Each table will receive a

mathematical teaching practice. Read and determine how it relates to the student math practices.

• Tables will share out.

Mathematical Teaching Practices

1. Establish mathematics goals to focus learning.

2. Implement tasks that promote reasoning and problem solving.

3. Use and connect mathematical representations.

4. Facilitate meaningful mathematical discourse.

5. Pose purposeful questions.6. Build procedural fluency

from conceptual understanding.

7. Support productive struggle in learning mathematics.

8. Elicit and use evidence of student thinking.


• Make sense of problems and persevere in solving them

• Attend to precision• Reason abstractly and

quantitatively • Construct viable arguments

and critique the reasoning of others

• Model with mathematics• Use appropriate tools

strategically• Look for and make use of

structure• Look for and express

regularity in repeated reasoning

Vertical Alignment• Using the Completed Vertical Progression

Guide– identify the vertical alignment of the targeted standards.

• Identify the implications across the grade levels.

• Each table will be given a standard to deconstruct and describe implications.

• Identify common student misconceptions.

Deconstruction of Standards


What does this standard mean?What will the students need to be able to do?

Think Time

• Why is it important to deconstruct standards?

Assessment Questions

It is important to know how these standards will be assessed. Viewing the items on MICA will give us the end in mind.

5.MD.C.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the bas

e. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

A box in the shape of a right rectangular prism is filled with 72 unit cubes. There are 9 layers of cubes in the box.

Use the grid to create a rectangle that shows a possible length and width of the base of the prism.

5.MD.C.5b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Leo packs 24 cubes into a box. Each cube has a volume of 1 cubic inch. Leo does not leave any gaps between the cubes, and the cubes completely fill the box. Click on all of the possible boxes that Leo could be using.


Kara and Will have two different boxes that are each right rectangular prisms. They have the same volume.

What is the height, in inches, of Will’s box?


A company makes toy cars.● Each toy car comes in a package that is 3

inches long, 3 inches wide, and 3 inches tall.

● The packages of toy cars are shipped in boxes that are 12 inches long, 12 inches wide, and 12 inches tall. How many cars fit inside a shipping box?

5.MD.C.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

A figure is made by joining two rectangular prisms, as shown.● All side lengths shown are in

inches.● The total volume of the

figure is 120 cubic inches.What is the difference, in cubic inches, between the volumes of the two rectangular prisms?A 0B 2C 18D 60

Centimeter Cube Activity

Clear Target: I can use unit cubes to determine the volume of a rectangular prism.


Clear Target: I can use unit cubes to determine the volume of a rectangular prism.Mathematical Practices: 5. Use appropriate tools strategically.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Centimeter Cube Activity• Count out 18 centimeter cubes.• Connect the nine cubes into one column.• Repeat process so you have two columns of

9.• Discuss with a partner what you know

about the model you have created.– What math vocabulary can you use to describe

this model?

Centimeter Cube Activity• Now with a partner, build three more

models of exactly like the first one.

Centimeter Cube ActivityVolume – space occupied by a three dimensional object

4 Layers

1 Layer

3 Layers2 Layers


18 cubes

18 cubes

18 cubes18 cubes

18 + 18 + 18 +18 = 72 cubic units

Volume – space occupied by a three dimensional object

Width Leng

th

Height


18 cubes

18 cubes

18 cubes18 cubes

18 + 18 + 18 +18 = 72 cubes

How is volume similar to area? How is it different?

Width Leng

th

Height

Centimeter Cube Activity• With your partner keep one model and

take the other set of 72 cubes to create a new base of three rows of eight.

• How many cubes are in this layer?

Centimeter Cube Activity• How many cubes are in the base layer?

24 cubes

Centimeter Cube Activity• Continue to build equal layers.• How many more layers can you add?


24 cubes

24 cubes24 cubes

24 + 24 + 24 = 72 cubic units

Width Leng

th

Height

Centimeter Cube ActivityQuickwrite - How can both rectangular prisms have a volume of 72 cubic units? How they similar? How are they different?

Using 72 more cubes, create a third model that is different from the other two.

Centimeter Cube Assessment

Jackie and Ron both have 12 centimeter cubes. Jackie builds a tower 6 cubes high and 2 cubes wide. Ron builds one 6 cubes long and 2 cubes wide.

Jackie says her structure has the greater volume because it is taller. Ron says that structures have the same volume.

Who is correct? Draw a picture to explain how you know. Use grid paper or isometric dot paper if you wish.

Brownie Bites

Clear Target: • I can determine the volume of a container using inch

cubes.

Mathematical Practices: 2. Reason abstractly and quantitatively.

5. Use appropriate tools strategically.6. Look for and make use of structure.7. Look for and express regularity in repeated reasoning.

Brownie BitesMaterials

Pans or containers of various sizes inch cubes

Brownie BitesYou are making 1 cubic inch brownie bites for your class party. You are planning for every person in your class to eat two brownie bites. You need 50 brownie cubes total. Which pan would be the best pan to use, an 8 x 8 x 1 or a 9 x 9 x 1, with the least amount of extras?

Brownie Bites1. Build with the inch cubes what the

volume would be based on the 8 x 8 x 1 pan measurements. Transfer to the pan.

2. Use a ruler to measure the sides across the top from edge to edge and record.

3. Measure the inside of the pan from inner edge to inner edge and record.

4. Have groups turn their pan over and measure the sides of the bottom and record.

Brownie BitesTable Talk: • What do you notice? • What influences the

measurements of the different areas?

• How many actual brownie cubes would we get from an 8 x 8 x 1 pan?

• Is it enough for your class party?

Brownie BitesMeasure the 9 x 9 x 1 pan in the same way (top edge to edge, top inner edge to inner edge, bottom edge to edge) and record. Calculate the number of brownie cubes you would get from this pan. Record your equation used.

Brownie BitesClosure: Why is it important to think about exact measurements like the baking pans?

Brownie BitesAssessment: You are given a container that is 3 x 4 x 6 to take cheese cubes with your lunch. Determine how many cheese cubes you should be able to fit into the container. Then measure the inside part of the container to the nearest inch and calculate how many you can actually fit.

NormsBe an active participant

Be mindful of air time

Be mindful of sidebar conversations

Use technology at appropriate times

Using Technology to Model Area

Using Technology to Model Area

https://www.buildwithchrome.com/

https://www.buildwithchrome.com/

Placing Cubes in Partially Filled Boxes

https://www.msu.edu/~stemproj/HTML5%20files/03-Volume/volume_filling_BlockConfig.html

Rectangular Prism Nets

http://illuminations.nctm.org/Activity.aspx?id=4095

Postal PackagesClear Targets: • I can determine the volume of a

rectangular prism by using a formula. • I can determine the volume of a figure

made of two rectangular prisms by adding their volumes.

Mathematical Practices: 2. Reason abstractly and quantitatively.

5. Use appropriate tools strategically.6. Look for and make use of structure.7. Look for and express regularity in repeated reasoning.

Postal PackagesMaterials:

inch grid chart paper

scissors

tape

cardboard boxfor each group

inch cubes

Postal PackagesYou are planning to send materials to an area that was affected by an earthquake caused by a transform boundary. You will be helping to send supplies to a school that was ruined and is being rebuilt. As part of your contribution, you would like to send new school supplies and other materials that will be needed to get the school running again. You know that you can send packages through the postal service using flat rate boxes. You can pack as much as you want into the box and pay a flat price, no matter how heavy. Your goal is to pack 3 smaller boxes full of pencils, crayons, and glue sticks inside of your large flat rate box.

Postal Packages

For your large box:• Draw and label the dimensions of

your box on your paper. • Calculate the volume and record the

equation used.

Postal PackagesWith your partners:• Determine the dimensions of your 3

smaller boxes. *They must all be different sizes.*

• Record their dimensions on your paper.

• Calculate the volume of each and record the equation you used.

• Build each box with your cubes to help you draw the nets. Put the nets together to create your boxes.

Postal PackagesQuestions to think about and share out:

1. How did you approach this problem? Why did you choose this method?

2. What were the volumes of the 3 smaller boxes? How could you check to make sure the combined volumes of these boxes filled your flat rate box?

3. Did another team with the same box end up with the same dimensions for the smaller boxes? If not, what were the differences?

4. What did you notice about the volumes of the 3 smaller boxes as they relate to the dimensions?

Postal PackagesWritten Response/Assessment:

The flat rate boxes come in the following sizes:

– 13 x 10 x 4– 12 x 10 x 6– 9 x 9 x 9

Which box would you choose if you wanted to mail the most school supplies in and why?

Planning Process for Instructional Task

• Why did I decide to find an instructional task for this lesson and these standards?

• How did I adapt this lesson to fit my instructional needs and the needs of my students?

• How did I adequately plan my assessing and advancing questions?

• What am I planning for the next lesson?

Differences in Tasks

• Similar to discovery learning or inquiry-based learning

• Used to teach new concepts/build on prior knowledge

• Must have multiple entry points/solution paths

• Involves students in math practices

• Uncovers students’ misconceptions

VS

• Often referred to PBA or CRA

• Used to assess what students know

• Should be objective with fewer solution paths

• Correct solutions will require one or more math practices

• Uncovers students’ misconceptions

INSTRUCTIONAL TASKS ASSESSMENT TASKS

Math Task

• Model Task• Discuss possible solution paths• Write Assessing and Advancing

Questions– Student that can’t get started– Student that finishes early

• Identify Misconceptions

Postal PackagesMath Task:

Your flat rate box has the dimensions 13 x 6 x 4. You are given a picture of a box of crayons and a box ofglue sticks.

• All side lengths shown are in inches.

• The total volume of the figures is 240 cubic inches.

Postal Packages1. What is the volume

of each box? 2. How much space is

left over for your box of scissors to fill your flat rate box entirely?

3. Explain how you calculated the space that is left over.

4. What are the dimensions of the box of scissors?

• Your flat rate box is 13 x 6 x 4.

• All side lengths shown are in inches.

• The total volume of the figures is 240 cubic inches.

Cari’s AquariumCari is the lead architect for the city’s new aquarium. All of the tanks in the aquarium will be rectangular prisms where the side lengths are whole numbers.A. Cari’s first tank is 4 feet wide, 8 feet long and 5 feet

high. How many cubic feet of water can her tank hold?

B. Cari knows that a certain species of fish needs at least 240 cubic feet of water in their tank. Create 3 separate tanks that hold exactly 240 cubic feet of water. (Ex: She could design a tank that is 10 feet wide, 4 feet long and 6 feet in height.)

C. In the back of the aquarium, Cari realizes that the ceiling is only 10 feet high. She needs to create a tank that can hold exactly 100 cubic feet of water. Name one way that she could build a tank that is not taller than 10 feet.

Challenge: Every year, our school has field day, but no one wants to drink warm Gatorade. Design a rectangular prism to freeze water in to create the longest lasting ice cube. This ice cube must last a minimum of three hours in the hot sun, even when the lunch box is opened and closed several times during field day. Your rectangular prism cannot have a volume greater than 300 cubic centimeters. Make it from graph paper and include the volume of your rectangular prism using a formula for volume. The class will vote to determine the best two designs and justify why. The best 2 designs will be tested under the heat lamp (sun) to see which lasts the longest.

Targeted StandardsMath

• 5.MD.C.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

• 5.MD.C.5b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

• 5.MD.C.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.


Science• GLE 0507.9.2 Design and

conduct an experiment to demonstrate how various types of matter freeze, melt, or evaporate.

• GLE 0507.9.3 Investigate factors that affect the rate at which various materials freeze, melt, or evaporate.

• SPI 0507.9.2 Describe the differences among freezing, melting, and evaporation.

• SPI 0507.9.3 Describe factors that influence the rate at which different types of material freeze, melt, or evaporate.

Integrated Math and Science Lesson

Clear Target:

I can determine factors

that influence the rate

of ice melting.

Clear Target:

I can measure liquid volume of ice after time for melting.

.

What can affect the rate of evaporation?

6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

https://www.youtube.com/watch?v=BHmUx0ylg-A

• Introduce 4 sets of frozen water –Two investigations will be ongoing throughout the day.

–Each investigation will have a rectangular prism containing 150 ml of water that has been frozen overnight.

–Every 10 minutes we will measure the amount of melting that has occurred.

–Data will be compiled and analyzed at the end of the day.

What factors influence the rate of melting?

Materials

Water

Graduated Cylinder

Heat Lamp

2 containers

with different

dimensions

Lunch Box

Liquid Volume vs. Solid Volume

• Liquid volume conversion to solid volume

• Set A - Ice melting at room temperature

•Record the data and your observations on your student recording sheet


• Set B - Ice melting under the sun (simulated by heat lamp)

•Record the data and your observations on your student recording sheet


Lesson Integration Reflection

• Discuss in your groups:

–What would be the perfect scenario for this lesson? (containers made of same material and same volume, with different dimensions)–How could this integrated lesson be extended to deepen/review math and science concepts?–Other ideas for using volume in relation to freezing, melting and evaporating?

Think About It

How can you use this integrated lessonin your classroom?

What is the purpose of applying math to science content?

Reflection

•How do I plan to share with others my learning of today?

•What support do I need to use the instructional resources shared today?

Take with you:

1 baggie cm. cubes

1 tub of in. cubes

1 cardboard box

graduated cylinder

CD Tin

Prism Tin

Lunchbox

Closure

Target: Increase content knowledge of identified Tennessee Education Standards for Math as measured through a STEM challenge.• Remember to check out the Wiki• Remember to share information with

rest of team (Math and Science)• Remember to bring back the

notebook and vertical progression book for future trainings

Fifth Grade – November. Grant Purpose and Background Partnerships Purpose of this Training Target:...

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