# Linear, Square and Cubic Units Grade Five

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1 Ohio Standards Connection Measurement Benchmark F Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed. Indicator 4 Demonstrate understanding of the differences among linear units, square units and cubic units. Mathematical Processes Benchmarks J. Communicate mathematical thinking to others and analyze the mathematical thinking and strategies of others. K. Recognize and use mathematical language and symbols when reading, writing, and conversing with others. Lesson Summary: In this lesson, students demonstrate understanding of the differences among linear, square and cubic units. They investigate packages with measurements such as a box of aluminum foil, package of ribbon and bag of mulch. They determine the dimensional attributes of each measurement unit and the measurable attributes of a box. By matching the attributes of the units to the measurable attributes of the box, students understand and label measurements appropriately. Estimated Duration: One hour Commentary: A measurement is a number that compares the attribute of an object being measured to the same attribute of a unit of measure (Van de Walle, 1998). Students must understand the attributes of the units and the attribute being measured. For example, attributes of a square unit include length and width or it is described as twodimensional. When measuring the length and width attributes of an object, a square unit is used because the attributes of the unit and object being measured are the same. Encourage students to think of filling with cubes, covering with squares and matching the lines (Van de Walle, 1998). Pre-Assessment: Have each student individually complete the following instructions on a sheet of blank paper: 1. Draw a line that is two inches long and label the measurement of the line. 2. Draw a shape with an area of two square inches and label the area and the dimensions. 3. Sketch an object that is two cubic inches and label the object. (If sketching is difficult for the student, have them name an object that is two cubic inches.) Collect the papers to informally assess student understanding of linear, square and cubic measurements. Scoring Guidelines: Informally review the students pre-assessment papers. Use the following guidelines: a. Draws a line measuring two inches and labels as linear measurement b. Draws a rectangle of two square inches and labels measurement using square unit. 1

2 c. Sketches cubic object (two one-inch cubes placed next to each other or one on top of another) and labels measurement using cubic unit. Identify the level of student understanding of the concept of linear, area and volume and the labels used for each concept. Level of Understanding Adequate Understanding Partial Understanding Limited Understanding Performance Descriptor Provides pictures which are appropriately drawn and labeled. Measurements are accurate, dimensions are given and labeled with appropriate unit. A student who experiences difficulty drawing may use a ruler and/or build models with square-inch tiles and cubic-inch cubes to complete the task. Provides pictures for one or two of the measurements appropriately. Uses a rough sketch, not actual measurements. Continue to assess using manipulatives as explained in score-point two to determine understanding of the units. Provides little evidence of understanding units through drawing pictures or building models with tiles and cubes. Continue to assess by asking for description of the measurable attributes. For example: Which model is a square? a cube? Post Assessment: Have each student independently complete Post-Assessment Units, Squares or Cubes, Attachment A. Students pair and share their conclusions for each situation. Informally observe students. Collect the papers to evaluate student understanding of linear, square and cubic measurements. Scoring Guidelines: Use Post-Assessment Answer Key Units, Squares or Cubes, Attachment B, to evaluate student s understanding of identifying the appropriate unit of measurement and an adequate explanation of the choice. Instructional Procedures: Instructional Tip: Gather objects such as a box of aluminum foil, bucket, package of gift-wrap paper, bag used to sell mulch, plastic storage bin, spool of ribbon, package of a paper tablecloth, package of shoe laces, etc. Make sure the measurement of the object with unit label is on the object. 1. Show students an example of a linear unit such as a one-inch piece of ribbon, a square tile and a cube. Have small groups discuss and describe attributes of these units that can be 2

5 Extension: Invite professionals who measure in their careers to speak to the class. Speakers can discuss how important measurement skills are in their field and describe what could happen if measurements were not accurate. Home Connection: Ask students to make a list of situations or examples they find at home that require measuring in square units or cubic units in their journals. Have students share the examples with the class, having them verify the examples. Materials and Resources: The inclusion of a specific resource in any lesson formulated by the Ohio Department of Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, therefore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students. For the teacher: For the student: Packages of items with measurement labels (E.g., package of foil or wrapping paper, ribbon or string, buckets or plastic mulch bag), overhead projector, rulers, grid paper, square tiles, centimeter cubes, chart paper Boxes, paper, pencil, rulers, cubes, square tiles and grid paper (if needed) and chart paper for each group Vocabulary: area attribute cubic perimeter square volume width Research Connections: Marzano, Robert J., Jane E. Pollock and Debra Pickering. Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement, Alexandria, VA: Association for Supervision and Curriculum Development, Van de Walle, John A., Elementary and Middle School Mathematics: Teaching Developmentally, Addison Wesley Longman, Inc

6 General Tips: Have student create a chart the unit of measurement and attributes of the unit. Attachments: Attachment A, Units, Squares or Cubes Attachment B, Units, Squares or Cubes Answer Key 6

7 Attachment A Units, Squares or Cubes Name Date Directions: Read each situation and determine the attribute that is measured. Write the appropriate unit of measurement and explain your answer. 1. Tom is building a doghouse and kennel for his dogs. He wants to put a fence around the doghouse and kennel. What does Tom need to know for the fencing he needs? 2. Sarah is painting the walls in her room. What does Sarah need to know when buying the paint? 3. Sean wants to give his sister a sandbox. He needs to place the sandbox in the yard and buy sand to fill the sandbox. a. What does Sean need to know about the place for the sandbox? b. What does Sean need to know to fill the sandbox? 4. Anna needs to have water put in her swimming pool. What does Anna need to know about the amount of water she needs for the swimming pool? 5. Dennis is putting new carpet in his house. What does Dennis need to know when he buys the carpet? 6. Harry is putting a garden behind his house and needs to purchase topsoil to cover the garden to a specified depth. What does Harry need to know before he buys the topsoil? 7

8 Explanations may vary. Linear, Square and Cubic Units Grade Five Attachment B Units, Squares or Cubes Answer Key 1. Tom is building a doghouse for his dogs. He wants to put a fence around the doghouse. What does Tom need to know for the fencing he needs? The fence goes around the doghouse and kennel, Tom needs to find the length, which is measured in linear units. 2. Sarah is painting the walls in her room. What does Sarah need to know when buying the paint? To paint the walls of her room, Sarah needs to know the area of the walls. Area is measured in square units. 3. Sean wants to give his sister a sandbox. He needs to place the sandbox in the yard and buy sand to fill the sandbox. a. What does Sean need to know about the place for the sandbox? Sean needs to know the area of the place for the sandbox. Area is measured in square units. b. What does Sean need to know to fill the sandbox? Sean needs to know the volume of the sandbox to determine how much sand the sandbox will hold. Volume is measured in cubic units. 4. Anna needs to have water put in her swimming pool. What does Anna need to know about the amount of water she needs for the swimming pool? Anna is filling the swimming pool with water, which is volume. Volume is measured in cubic units. 5. Dennis is putting new carpet in his house. What does Dennis need to know when he buys the carpet? Carpeting is covering the floor, so Dennis needs to know the area of the floor. Area is measured in square units. 6. Harry is planting a garden behind his house and needs to purchase topsoil to cover the garden to a specified depth. What does Harry need to know before he buys the topsoil? Harry needs to know the volume of the topsoil that will cover the garden to the specified depth. 8

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