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Mathematics Alignment Lesson Grade 5 Quarter 3 Day 129 Common Core State Standard(s) 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. Standards for Mathematical Practice Standard 3: Construct Viable Arguments and Critique the Reasoning of Others. Standard 4: Model with Mathematics. Standard 5: Use Appropriate Tools Strategically. Standard 6: Attend to Precision. Materials Needed: Chart paper Pop Cubes Transparency/Blackline Masters“Perspectives of Volume”,“Building Rectangular Prisms” Blackline Masters-“Questioning Volume”, “Volume-A Journal Prompt” Assessment Informal: During group work, listen and record discussions students are having as they build prisms. Transparency/Blackline “Perspectives of Volume” Alignment Lesson Exploring the Concept of Volume (Day 1 of 3) Content Note: This unit represents the first time that students begin exploring the concept of volume. In third grade, students begin working with area and covering spaces. The concept of volume should be extended from area with the idea that students are covering an area (the bottom of cube) with a layer of unit cubes and then adding layers of unit cubes on top of bottom layer. Students should have ample experiences with concrete manipulatives before moving to pictorial representations. This is a 3-day lesson. Please make sure you read all lessons prior to teaching. 1. Pose the question, “What is volume?” Ask students to write some their own ideas in the first column “I THINK volume is…” on Transparency/Blackline “Perspectives of Volume”. (on their own) 2. Elicit student responses and write different responses on chart paper, “I THINK volume is….” (Chart paper is best for this activity so you can keep displayed and make changes to the list as you spend time with the concept of volume). At this time, accept all responses. Let students know that this is not our final definition, but instead our ideas that we are allowed to make changes to as we work in the volume unit the next few weeks. Note: Students’ prior experiences with volume were restricted to liquid volume. 3. How can we determine the volume of a figure? With today’s activity, students will investigate what volume is. It is important that the traditional algorithm is not taught or given first. Students will spend the next few days exploring volume using models. In today’s lesson, students will build different prisms out of cubes and discuss that volume is measured by cubic units. Homework Bring in a rectangular prism box for use beginning in Alignment Lesson Day 132 and throughout the volume unit Blackline Master “Volume-A Journal Prompt” Vocabulary Rectangular Prism: a prism with six rectangular faces Dimension: length, width or height of a figure Volume: the amount of space, measured in cubic units that a 3-D object occupies Wake County Public School System, 2012 4. In small groups, students will use pop cubes to create as many rectangular prisms as they can with a given amount of cubes: 12, 20, 36, and 40. (You may need to review “rectangular prism” with students. Ask them to identify “rectangular prisms” around the room. Define “rectangular prism” as a class). Make sure that each group has plenty of pop cubes to experiment and build. You may want to assign each group 1 or 2 of the given amount of cubes (12, 20, 36, or 40) to focus their time on-this will ensure that each given amount of cubes has the time to be built and may also help with your pop cube supply. As students are building their prisms, monitor each group by circulating the room and posing questions as groups need assistance. Encourage all students to be a part of the building process. “Is there a different way you can build a rectangular prism with 36 cubes?” “Have you built all the possible prisms?” “How are you sure?” “How does orientation play a role in your construction or thinking?” CONTINUED NEXT PAGE Alignment Lesson Exploring the Concept of Volume (Day 1 of 3) continued 5. After students have built their prisms, have students record the class findings on Transparency/Blackline “Building Rectangular Prisms”. Discuss the meaning of dimensions (length, width, and height). Use one rectangular prism as an example. Ask each student group to share their prisms. As students share, have a student leader record on a class chart and while each student records on their own copy. Teacher Content Note/Background: We often get caught up on which is the length, width, and height – interchanging the three. When discussing with students, focus on the base of the prism to identify the length and width and the height is the remaining dimension (see picture below). This will eliminate misconceptions later when students are asked to find volume of other figures. In later grades, students will learn the mathematical formula for any prism is V=Bh, where B is the number of cubic units needed to cover the base and h is the number of layers. For a rectangular prism, the B represents the base of the prism which is a rectangle; therefore it is length x width. For a triangular prism, the B represents the base of the prism which is a triangle; therefore, the area of the base is ½bh. (see picture below) ….CONTINUED NEXT PAGE Wake County Public School System, 2012 Alignment Lesson Exploring the Concept of Volume (Day 1 of 3) continued 6. After the class chart is complete and the class has discussed all the possible prisms for 12, 20, 36, and 40 cubes, have partner groups discuss and answer the questions on Blackline Master “Questioning Volume”. (Answers; 1) 8, 2) No, see student response, 3) See student response) 7. Once students have worked with a partner and have had a partner discussion about their prisms, have the class come back together to have a Math Talk discussion about what they noticed about volume today. Facilitate class discussion by using Math Talk questions and probes such as: Can you repeat what _______just said in your own words? Would someone like to add on? Do you have another way to explain your thinking? Does anyone have the same answer but a different way to explain it? Do you agree or disagree with _______ and why? Does anyone else have comments or questions for __________? **At this time, students should be defining volume by the number of cubic units. For example: the prism built with 36 cubes has a volume of 36 cubic units or 36 u3. Students will work to derive the formula for volume of any prism during the next two days of alignment lessons. 8. Ask students to complete Transparency/Blackline “Perspectives of Volume” with any information they discussed today (during small group, partner, and/or whole group Math Talk). 9. As a class, revisit the chart paper from the beginning of class and make any changes needed. Have students complete Blackline Master “Volume – A Journal Prompt” for homework. In addition, ask students to bring in a rectangular prism box prior to the lesson on Day 132. Source: Teacher Created **Keep a few different rectangular prisms that students built for class models and for demonstration purposes of future lessons or review.** Note: This lesson is designed to facilitate the connections of volume and area as well as to determine the vocabulary associated with volume. This activity allows for students to come to their own conclusions about volume and allows them to explore dimensions. Source: Teacher Created Additional Resource: Classroom Discussions Seeing Math Discourse in Action, Faciliatior’s Guide with Two DVDs (Each School received a copy of this resource Summer 2012). Disc 2, Video Clips 8.3a, 8.3b, 8.3c, 8.3d. Wake County Public School System, 2012 Transparency/Blackline Master Grade 5 Day 129 Standard 5.MD.3 Perspectives of Volume I THINK volume is… Building rectangular prisms gave me the following ideas about volume…. Drawings/ diagrams of one of my rectangular prisms I made today with included dimensions I am taking away the following NEW information about volume from today Wake County Public School System, 2012 Transparency/Blackline Master Grade 5 Day 129 Standard 5.MD.3 Building Rectangular Prisms Directions: Use pop cubes to create rectangular prisms. How many different prisms can you make with these cubes: 12, 20, 36, and 40? Record the total number of cubes used and the dimension of each prism you made. Number of Cubes Used Wake County Public School System, 2012 Dimensions Blackline Master Grade 5 Day 129 Standard 5.MD.3 Questioning Volume How many different rectangular prisms can you make with 36 pop cubes? ______ Did each of the rectangular prisms you made with 36 cubes have the same dimensions? __________ Why do you think this is? ________________________________________________________ ________________________________________________________ ________________________________________________________. Make some observations about the different prisms you made. Think about the volume of these figures, the dimensions and anything else you noticed while building your rectangular prisms. Wake County Public School System, 2012 Blackline Master Grade 5 Day 129 Standard 5.MD.3 Volume- A Journal Prompt Thinking about your exploration and discussion today in class, how would you explain what volume is? Write your own thoughts using pictures, numbers, and/or words. (DO NOT WRITE A BOOK DEFINITION) Wake County Public School System, 2012 Answer Keys & Teacher Guide Grade 5 Day 129 Standard 5.MD.3 Answer Key-Building Rectangular Prisms Number of Cubes: 12 Number of Cubes: 20 1 x 1 x 12 1 x 1 x 20 1x2x6 1 x 2 x 10 1x3x4 1x4x5 2x2x3 2x2x5 Number of Cubes: 36 Number of Cubes: 40 1 x 1 x 36 1 x 1 x 40 1 x 2 x 18 1 x 2 x 20 1 x 3 x 12 1 x 4 x 10 1x4x9 1x5x8 1x6x6 2 x 2 x 10 2x2x9 2x4x5 2x3x6 3x3x4 Multiplication is commutative. The order of the numbers does not change the overall volume. See example below - this is the same rectangular prism rotated to different positions. Remember from the Teacher Note in the lesson that we identify the length and width of the prism by its base (or bottom layer) and the height is “how many total layers”. 2x3x6 2x6x3 3x6x2 3x2x6 Since all 6 of these combinations are the same prism (just different orientation), it only counts as 1 prism, not 6. As students are building their prisms, you may need to have discussions about the significance of the orientation of the prism. 6x3x2 6x2x3 Wake County Public School System, 2012