PARCC Grade 5 Mathematics Rationale Lesson 16: Performance-Based Assessment Measurement and Data Volume Goals Objectives Standards Materials The CCSS requires students to understand the concept of volume using concrete manipulatives. The concept of volume should be extended from area with the idea that students are covering an area (the bottom of a cube) with a layer of unit cubes and then adding layers of unit cubes on top of the bottom layer. Prior to grade 5, students worked on liquid volume. Students develop their understanding of volume by finding that a 1-unit by 1-unit by 1-unit cube is the standard unit for measurement of volume. To find volume of rectangular prisms by counting units To justify answers using precision Students will find volume of rectangular prisms by counting cubic units. Students will design a variety of rectangular prisms with a given volume. Students will justify answers with precision. 5.MD.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Performance-Based Tasks-There are two separate Type II tasks. Journal Class Folder Labeled: Lesson 16: Performance-Based Assessment Measurement and Data. (At the end of the lesson, place the class papers in the folder. If students used scratch paper, please have students attach the scratch paper to their Mathematics Items handout.) Lesson 16: PBA Measurement and Data Volume Page 1
Procedures Say, This year, you will be taking the math PARCC Assessment. It will test all of the things you have learned this year in math in order to find out if you have mastered the concepts or if you still need more practice. Today we will be learning about what you will need to know for the test. You will determine what is easy for you and what is challenging for you. We will then work on a plan for improving the areas which are difficult for you right now. Assign students to groups of 2 or 3. Give them the Performance-Based Assessment. Tell students that this is an example of what a Performance-Based Assessment may look like. Review the directions for the Tasks. Instruct students to record their answers on the assessment. Ask students to work in pairs and discuss each Task. Each student should complete their own assessment. Remind students to use clear explanations in their justification of their answers. While the students are working, circulate the room and monitor students approaches. Note patterns of difficulty and/or errors. When students have finished, ask them to share their answers to the questions. Have each student share one thing that they found easy or difficult about this Performance-Based Assessment. Assessment or Check for Understanding Follow-up Journal writing: in the last 2-3 minutes of class, students should record what they learned about themselves regarding test taking strategies and the content of the CCSS. During any Performance-Based Assessment mathematics lesson, engage students in a discussion of why one task was less challenging and another task more challenging. Technology Enhanced Problem This is an example of a machine scored and human scored Performance-Based Assessment. Students will be asked to type in answers and select all that are true with this type of problem.. They may be asked to type their justifications in the PARCC Open Response Equation Editor. The Open Response Equation Editor is for words and math. The box will expand; there is NO limit to the size of a student s response. PARCC Technology Tips PARCC Open Response Equation Editor is provided as the answer box for responses that require a written response and/or a mathematical answer that is created using a mathematical function. When a written response is indicated, it is possible to respond with a combination of words and mathematical expressions and equations. It is suggested that letters, numbers, and punctuation symbols from the standard keyboard be used. Any part of the response that indicates mathematical processes can be described using the function keys provided in the Open Response Equation Editor; the question mark function is used to represent the unknown in an equation. It is NOT possible to create diagrams, models and/or step-by-step solution processes (such as solving with an algorithm). Lesson 16: PBA Measurement and Data Volume Page 2
PARCC Grade 5 Mathematics Lesson 16: Performance-Based Assessment Number and Operations - Volume Task # 1 (PARCC 5.C.6) The Diamond Ring Company is packing their rings for shipment to stores in the area. Each ring is packaged in a box that measures one cubic inch. They want to pack them in boxes with no extra space. PART A How many ring boxes can be packed in Box A below? Explain how you arrived at your answer. = 1 cubic inch Lesson 16: PBA Measurement and Data Volume Page 3
PART B Would Box B hold more rings than Box A? Explain your answer. = 1 cubic inch Lesson 16: PBA Measurement and Data Volume Page 4
Task # 2 (PARCC 5.C.6) The Diamond Ring Company is packing their rings for shipment to stores in the area. Each ring is packaged in a box that measures one cubic inch. They want to pack them in boxes with no extra space. PART A Design two different packing boxes that will hold 24 rings without any extra space. The boxes must be in the shape of a rectangular prism. Record the dimensions of each of your boxes. Explain how you know your answers are correct. Lesson 16: PBA Measurement and Data Volume Page 5
PART B Jonathan thinks that the box below will hold 24 boxes without any extra space. Is he correct? Explain your reasoning. = 1 cubic inch Lesson 16: PBA Measurement and Data Volume Page 6
. PARCC Grade 5 Mathematics Lesson 16: Performance-Based Assessment Number and Operations - Volume Rubric Task # 1 Part A Score Description Student response includes each of the following 2 elements: Computation Component: 30 boxes Reasoning Component: Valid explanation of reasoning. Sample Student Response: I saw in the diagram that the bottom layer of boxes was 3 units long and 2 units wide. I found the 2 number of boxes in the bottom layer by multiplying 3 x 2 = 6. Next, I saw that the diagram had five layers. If each layer has 6 boxes then five layers is 30 boxes. 6 x 5 = 30 boxes. 1 Student Response includes 1 of the 2 elements. 0 Student Response is incorrect or irrelevant. Task # 1 Part B Score Description Student response includes each of the following 2 elements: Computation Component: Box B would not hold more than Box A. Reasoning Component: Valid explanation of reasoning. Sample Student Response: Box A holds 30 boxes. I know this because each layer has 6 boxes and there are five layers. 6 x 5 = 30 2 Box B holds 24 boxes. I know this because each layer has 4 boxes. Thee are two boxes in the length and two boxes in the width. 2 x 2 = 4. There are 6 layers of 4 boxes. 6 x 4 = 24 boxes The number of boxes in Box B is 24 and that is less than the number of boxes in Box A, which is 30. 24 < 30 1 Student Response includes 1 of the 2 elements. 0 Student Response is incorrect or irrelevant. Lesson 16: PBA Measurement and Data Volume Page 7
Task # _2 Part A Score Description Student response includes each of the following 2 elements: Computation Component: Two different designs in which the three dimensions equal a product of 24. Reasoning Component: Valid explanation of reasoning for each design. Sample Student Response: 2 For a box in the shape of a rectangular prism to hold 24-1 unit boxes, the area of the bottom layer multiplied to the number of layers equals the product of 24. Design Box 1 Area of bottom layer: 2 boxes by 3 boxes. 2 x 3 = 6 boxes Box 1 will hold 24 unit boxes if there are 4 layers. 6 x 4 = 24 boxes. Design Box 2 Area of bottom layer: 2 boxes by 6 boxes. 2 x 6 = 12 boxes Box 2 will hold 24 unit boxes if there are 2 layers. 2 x 12 = 24 boxes. 1 Student Response includes 1 of the 2 elements. 0 Student Response is incorrect or irrelevant. Task # _2 Part B Score Description Student response includes each of the following 2 elements: Computation Component: Jonathan is not correct. He designed a box that holds 36 unit boxes. Reasoning Component: Valid explanation for Jonathan s mistake and correct reasoning. Sample Student Response: Jonathan s design is not correct. His design holds 36 boxes. He should change his design; the bottom layer should only have 12 unit boxes, if he keeps two layers. He could remove one row of 6 2 boxes from the bottom layer. 6 x 2 = 12 unit boxes in the bottom layer. 2 x 12 = 24 unit boxes in the design. 1 Student Response includes 1 of the 2 elements. 0 Student Response is incorrect or irrelevant. Lesson 16: PBA Measurement and Data Volume Page 8