Ohio Standards Connection Measurement Standard Benchmark D Apply measurement techniques to measure length, weight and volume (capacity). Indicator 6 Measure length and volume (capacity) using non-standard units of measure (e.g., how many paper clips long is a pencil, how many small containers it takes to fill one big container using sand, rice, or beans). Mathematical Processes Benchmark D Evaluate the reasonableness of predictions, estimations and solutions. Lesson Summary: This lesson introduces children to the concept of the measures, length and volume. Story reading and children s play set meaningful contexts for young learners to explore the process of measuring volume and length using everyday items such as crayons, blocks and cups. Estimated Duration: 30 minutes - Lesson takes place during several short sessions, over several days. Commentary: The NCTM Principles and Standards for School Mathematics states, Measurement is one of the most widely used applications of mathematics. Young children develop their foundation of measurement understanding to be formalized and expanded in later years. Children compare length and volume while developing measuring skills. Asking children questions helps them focus on various aspects of measurement and helps them develop vocabulary used to compare and describe the objects being measured. By communicating verbally and in writing, children demonstrate their understanding of the procedural and conceptual aspects of measurement. Pre-Assessment: Informally assess children s understandings of size and use of a measurement tool by observing and posing questions during daily activities and play. For example, as children construct a long road made of wooden blocks, pose questions and comments such as the following to reveal the child s thinking about linear measurement: a. Which block is longer? Shorter? b. How long is your road? c. How do you know it is this long? d. How can you find out? Show me. Gather data on children s current understanding about measuring volume when children gather at the sand and water table to practice measuring. As children play with containers of various sizes, pose questions such as: 1. How many scoops of sand will it take to fill this bucket? 2. How can we find out? 3. How will we know when it is full? 1
Scoring Guidelines: Observe, listen and record anecdotal notes as children demonstrate and express their understanding. Note individual children s ease or difficulty. Post-Assessment: Post-Assessment occurs within the learning center context (e.g., block area, sand/water table) and embedded within lesson activities and play such as Observing children during and following the lesson as they use non-standard units of choice (e.g., hands, feet, paperclips, chain links, one-inch tiles, scoops, cups and buckets) to measure length of items or volume of material found within indoor and outdoor settings. Listen to children as they estimate. Talk about the process used to measure and respond to questions about linear and volume measurement. Compare individual children s understanding and skill to prior documentation to indicate growth and effectiveness of the activities. Scoring Guidelines: Assess children s ability to measure length and volume using non-standard units. Make note of the following: Did the child line up the non-standard units end to end? Did the child start at one edge of the item being measured and continue to the other end of the item? When filling a larger container using a cup as the measuring tool, did the student fill the cup to the top? How did the child determine the length or number of units (e.g., number of paperclips or number of cups of beans)? Did the child use 1. Global estimation? 2. Counting with random one-to-one correspondence? 3. Counting with organized one-to-one correspondence? Use Attachment A, Post-Assessment Checklist, to record observations made while the student performs the tasks. Instructional Procedures: Instructional Tips: Pre-select a children s book to stimulate discussion and interest in the concept of measurement. A big book version of the literature selection provides opportunities for all children within the group to view and to have access. Collect the following materials to use for exploration in small groups: set of 5-10 manipulatives of the same size for each child (e.g., worms, bugs, or other items the same size as the measurement unit depicted in the children s book); blocks longer in length than the manipulative for each member of the group to measure; other non-standard units of measurement, such as paperclips, crayons, markers, toothpicks, etc. 2
Part One - Measuring Lengths 1. Establish a context for children to explore, discuss and solve problems using linear measurement. Gather children in appropriately-sized groups to listen to a story about a child, animal or insect that explores linear measurement. 2. Conduct a picture walk before reading the story. Show children the pages and elicit conversations about the pictures to pique their interest in the story. Direct attention to the character that is curious about the size, width or depth of something in the story. Use questions and comments such as: Look at this picture. What do you see? What is the character doing? What do you think might happen next? 3. Read the story, stopping periodically to discuss the illustrations, story events and confirm predictions and ideas from the walk-through. Use questions or comments to introduce children to the concept of estimating length and focus children s attention on the need for and use of measurement as depicted in the story. 4. Provide a set of manipulatives to use as units of measurement (e.g., same size worms, blocks, flower stems) for manipulation and measuring. Lay the book on the floor or table for easy access by the children. Make manipulatives that are replicas of and the same length as the measuring unit in the storybook. 5. Model the process of measuring by placing the manipulatives end-to-end, from one edge of the measured part of the illustration to the other showing the path traveled to measure an object or animal in the story. Have children take turns using the manipulatives to measure the object or animals depicted in the book illustrations. 6. Continue reading the story, recording and discussing ideas and estimations offered by the children. Use the story text and manipulation of measurement units to talk about the measuring process and confirm their ideas. 7. After reading the story, discuss with children the use of the unit or tool to measure items (e.g., objects, animals, distance) in the story. Pose the following, What did you notice about how the character determine how long the is or how big the is? Revisit the action of placing the measuring tool end to end and counting as it measures and moves from one edge of the item measured to the other. Part Two 8. Revisit the story about measurement and the character s action of placing the measuring unit end-to-end and counting. Invite children to explore the use of linear measurement further by asking questions such as: The character in our story used to measure. Can you think of other things to use to measure the size or lengths of objects? How can we use to measure? What do you notice about these different measuring tools? 9. Make a list of children s ideas (e.g., blocks, crayons, straws, child s shoe or hand, pieces of yarn or string). Post the list for future reference. 10. Setup the following investigation and discussion using one item included in the list of responses (i.e., blocks): a. Show children a set of small blocks all of equal size (e.g., one-inch blocks) and set of 3
long blocks all of equal size (at least three times longer than the small block). b. Engage children in discussion, describing and comparing the size of the two sets of blocks (e.g., long, short). c. Place one long block on the floor or table for children to view. Point to the set of small blocks and pose a problem for children to solve. Elicit children s ideas and estimation of block length by commenting and asking questions such as: I want to measure and find the size of this (long) block. How can I use these small blocks to find out? How many small blocks does it take to reach from one end of the long block to the other? Can you help me line them up to find out? d. Accept and record children s estimations on the number of small blocks needed (length). Use the small blocks to measure the long block and have the children assist in counting the number of small blocks used. Check the children s predictions. 11. Provide several sets of small blocks all of equal size. Have children work in pairs as they manipulate blocks to estimate and measure an object/item in the learning setting (e.g., rug). 12. Gather children together to discuss their findings and processes used to measure. Build oral language and children s use of mathematical terms as they engage in conversations, with probing questions such as: What did you find out? How many blocks did it take to measure? Did you guess (estimate) the same number? How did you use the blocks to measure the rug? Tell us or show how you worked together. Instructional Tip: As children manipulate blocks and other non-standard units to measure length, point out the importance of placing the measuring unit at one end/edge of the object and placing the additional units end-to-end with no gaps between them. Provide assistance as needed. Part Three 13. Create a list on chart paper of objects/items in the room for children to measure and then compare sizes and lengths (e.g., a book, table, rug, big book, doll, puppet theatre, dollhouse, bookshelf, toy animals, play food, length of strung beads, etc.). Provide pictures or icons of the items listed and post the chart for easy reference. 14. Provide clipboards, markers and pencils for each child. Provide small bags or containers of non-standard units of measure for the children to select and use to measure objects, furniture, etc. in a learning setting. Provide sets of items listed by children during discussion in Part One of the lesson (e.g., large paperclips, wooden pegs, toothpicks, ribbon, yarn, string or linking cubes). 15. During free play, encourage children to choose an object(s) from the list displayed, and bag of measuring tools. Instruct children to estimate, measure and record their findings on Attachment B, How Many Did You Use? Encourage children to represent the number of units used with tally marks, stickers or numbers, number stamp or numerals. Use a measurement sheet for each investigation. 4
Instructional Tip: Throughout the lesson and over the course of the year, use daily routines, activities and play to pose problems asking children to think about, predict/estimate, explore, talk about and use nonstandard measurement tools and record linear measurement (e.g., height of block structures, length of ramps made for toy cars, road construction of blocks, length of fabric or clothing, size of feet or shoes, how far a wind up toy will go, etc.). 16. Gather the children together to discuss their findings and representations of the measurement experience. Collect completed measurement sheets and bind them in a class book for children to revisit the experience. Invite children to add pages to the book throughout the year. Part Four - Measuring Volume Instructional Tip: Collect these materials in advance: same-size cups, bowls or large containers, sand or water. The sensory (sand/water) table provides this context to small groups of children at play. (If no sensory table is available, use a large container, such as a dishpan or bucket, to hold the sand/water.) 17. Facilitate a discussion while children are busy exploring with the containers provided. Ask children the following questions: Which is larger, the bowl or the cup? Which would hold more sand? Why? How far do we need to fill the cup before pouring it? Show me. How many cups of sand does it take to fill the bowl? When do we need to stop pouring sand in the bowl? How do we know when the cup or bowl is full? 18. Have the children predict the number of cups of sand needed to fill the bowl. Ask each child to take a cup. Have the children take turns pouring a full cup of sand into the bowl. Remind them to fill the cup to the top. As children take turns filling and pouring, have the remaining group of children count the number of cups used to fill the bowl. Compare the estimates to the actual count. 19. During the next few days, provide different size cups and different size bowls/containers for the children to use when experimenting. Use different substances for filling, such as water, rice or beans. Scaffold children s understanding of volume measurement and build vocabulary through probing questions and conversations during their explorations. Reinforce the concepts and use of terms such as full, empty, how many. Differentiated Instructional Support: Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s). Encourage children who understand the concepts to compare the number of cups needed to fill two same size large containers with different substances, such as rice compared to beans. Intentionally pair children having difficulty with the concepts together during measuring experiences or provide individual assistance or hand-over-hand assistance. 5
It may be helpful, when teaching the process of measuring volume, to use a piece of colored tape or an other tangible medium to mark the fill line on the outside of the cup used for measuring. This gives children a tactile as well as a visual marker. Extensions: Children compare volumes of related substances such as snow versus water; wet sand versus dry sand. Use opportunities during outdoor play for children to measure distance (e.g., using blocks to measure and compare length or size of jumps). Children measure and compare their growth from birth to present. Ask families to provide length of children at birth. Have children string pieces of macaroni to match this length. Have children work in pairs to find current height. Place a long piece of butcher paper on the floor and lay the macaroni-measuring ruler or stick along one side, while each child lies down alongside the stick. Make a class height chart. Children work in pairs to estimate and then use paperclip rulers to determine how tall they are. Create a graph comparing the length of objects measured. Ask children to use the same nonstandard unit of measure. Have children work with partners or independently measure objects listed on class chart. Represent measurement by shading the appropriate number of spaces on a bar graph. Converse with children introducing and reinforcing terms of comparison while recording measurements on the chart (e.g., long, longer, short, shorter, more than, less than). Children practice measuring skills while making salt-dough, pudding or gelatin from simple recipes. Show children how to create a measuring stick by hooking large paperclips together or by stringing long macaroni. Children can work in teams or with partners as they use the chain to answer questions such as: a. How many paperclips high is the table? b. What is the distance from the rug to the door? Create a class book of How Many Did You Use? depicting non-standard units of measure and lengths of everyday objects/items found in the classroom. Children select and use measuring units to find the length of items found during a nature walk or while exploring the outdoor play area. Home Connections: Give children a non-standard measurement tool and have them measure the length of one shoe of each person who lives in their home. Children trace a shoe for each family member and determine the length of each person s shoe according to the non-standard measurement tool used. (Mom s shoe is six large paperclips long.) Children bring the shoe tracings to school. Arrange these by size and use for further practice in measuring length. Suggest that children measure different items around the home or yard, using pieces of string, yarn or long blocks. Ask families to chart their child s increasing height on a growth chart mounted on a door or refrigerator. 6
Ask that families allow children to assist in measuring ingredients used in preparing food for mealtime. Use measurement units required in the recipe. Interdisciplinary Connections: Standard: Physical Sciences Benchmark: A. Nature of Matter Indicator: 2. Explore and compare materials that provide many different sensory experiences (e.g., sand, water, wood). 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: chart paper, marker, objects of differing lengths (e.g., blocks, pencils, crayons, paintbrushes), children s book about linear measurement, replica of measuring unit in storybook, small blocks all the same length, paperclips, chain links, one-inch tiles, markers, toothpicks, wooden pegs, linking cubes, several pairs of large and small clear containers, water beans, sand, cups For the student: objects of differing lengths (e.g., blocks, pencils, crayons, paintbrushes),5-10 replicas of measuring unit depicted in storybook, small blocks all the same length, paperclips, chain links, one-inch tiles, markers, toothpicks, number stamps, wooden pegs, linking cubes, several pairs of large and small clear containers, water, beans, sand, rice, cups Vocabulary: big count estimate less long longer measure more one-half short shorter volume 7
Research Connections: Copley, Juanita. 2000. The Young Child and Mathematics. Washington, DC: National Association for the Education of Young Children. Attachments: Attachment A, Post-Assessment Checklist Attachment B, How Many Did You Use? 8
Attachment A Post-Assessment Checklist Student Lined up nonstandard units end to end Started at the edge of the item being measured, continued all the way to the end Filled up larger container all the way to top Counted number of non-standard units used to measure length/volume (i.e., number of paperclips, number of cups of beans) Comments 9
Attachment B How Many Did You Use? Draw a picture of the item you measured. Draw a picture of how you measured it. 10