Activity: TEKS: Holds More, Holds Less, Holds the Same (K.10). The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. The student is expected to: (C) compare two containers according to capacity (holds more, holds less, or holds the same); (K.13) Underlying processes and mathematical tools. The student applies mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (A) identify mathematics in everyday situations; (D) use tools such as real objects, manipulatives, and technology to solve problems. (K.14) Underlying processes and mathematical tools. The student communicates about mathematics using informal language. The student is expected to: (A) communicate mathematical ideas using objects, words, pictures, numbers, and technology; and (K.15) Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to justify his or her thinking using objects, words, pictures, numbers, and technology. Note: Portions of this lesson address TEKS at other grade levels as well; however, the intent of the lesson fits most appropriately at the grade level indicated. Overview: Materials: A strong foundation in the early grades is essential for students to progress to the desired level of understanding of capacity and volume by the end of Grade 5. This lesson begins with a focus on understanding the attribute to be measured, which is typically developed by direct comparisons (comparing and ordering). These concepts are addressed in the early grades so that students will have the opportunity to engage in several hands-on activities that deal with comparing and ordering to determine which container holds more, holds less, or holds the same. 3 bowls for demonstration (1 very small, 1 medium-sized, and 1 very large) Holds More, Holds Less, Holds the Same Page 1
More/Less/Same Signs Handouts/Transparencies 1a, 1b, and 1c 1 large plastic cup labeled X 1 small plastic cup labeled Y Variety of empty assorted containers (4 different pairs of containers, each container labeled with a different letter, A - H. Containers may be rotated among groups. Make an identical set to accommodate more students.) Ziploc bag of dried beans, peas, rice, sand, or other material (one per group) Funnel or 2-liter bottle with the end cut out (one per group) Dish pan or tray to catch spills (one per group) Craft stick or popsicle stick (one per group) Variety of scoops with no markings (one per group) More, Less, or the Same? Transparency 2 (one per class) I Think, I Discover Recording Sheet Handouts/Transparencies 3a and 3b (one per student) Which Holds More? Handout/Transparency 4 (one per student) Grouping: Time: Whole class and groups of 2 4 students, teacher discretion 2 or 3 class periods Lesson: Procedures 1. Ask: How many of you have ever heard the story, The Three Bears? Ask students to think about the 3 characters: Papa Bear, Mama Bear, and Baby Bear. Notes This introduction is to get the students to begin to think about the attribute of capacity. Show the students the 3 very different sized bowls and ask them to choose which of these bowls would make a good bowl for Papa Bear. What makes the largest bowl a good bowl for Papa Bear? Discuss which bowl would be best for Baby Bear. What makes the smallest bowl a good bowl for Baby Bear? Use Handouts/Transparencies 1a, 1b, and 1c More/Less/Same signs, to label bowls. 2. Define capacity as how much something will hold. When we talk about capacity, we use words like, holds more than, holds less One of the most critical aspects of teaching measurement in the early grades is to help students Holds More, Holds Less, Holds the Same Page 2
Procedures than, and holds the same amount. Hold up the very small bowl and the very large bowl and ask: Which of these bowls holds more? How do you know? How could we prove that this little bowl holds less than this big bowl? If a student does not suggest it, lead the class to the idea of directly comparing the capacity of the two bowls by filling one bowl and then pouring the contents of that bowl into the other bowl. Model this for the class using rice, beans, sand, peas or water. Use a dishpan to catch spills and a funnel to make pouring easier. Prove to the class by direct comparison which bowl holds more and which bowl holds less. Notes understand what it means to measure a given attribute. As stated by Van de Walle (2006), measurement involves comparing an attribute of an object with a unit that possesses that same attribute. After identifying the attribute to be measured, students need to choose an appropriate unit of measure, and then compare the unit to the object that is to be measured. The measure of the attribute is a count of how many units are needed to fill, cover, or match the attribute of the object being measured (Van de Walle, 2006, p. 224). Now demonstrate again using the mediumsized bowl and either one of the other two bowls. 3. Tell the class: Today we are going to be Detectives. We will investigate containers to see which container s capacity holds more. Show the class the assortment of containers and discuss how the containers are used in real life. Ask: Where have you seen these containers before? at school, at home, in the kitchen, at the store, or maybe in the kitchen center Notice that the TEKS statement says directly compares. students should have lots of opportunities to directly compare two containers according to capacity (holds more, holds less, or holds the same). (K.10C) Also note that the TEKS statement refers to comparative language: holds more, holds less, holds the same. How do we use these containers? To hold things, to store things like leftovers, etc. 4. Teachers may use More, Less, or the Same? Transparency 2, to introduce and model the recording sheet. Demonstrate the process by using a large Holds More, Holds Less, Holds the Same Page 3
Procedures plastic cup labeled X and a small plastic cup labeled Y. Notes First, students should predict: Does the large plastic cup hold more, hold less, or hold the same amount as the small plastic cup? Explain to students that they must record their predictions on the I think side of the recording sheet. For example, if the students predict that the container labeled X will hold more, write the letter X next to the word More on Transparency 2 to model for the students how to use the recording sheet. Then ask students where you should write the letter Y. Students should respond by telling you to record the letter Y next to the word Less on the recording sheet. The students are predicting at this point, and you are modeling for them a way to record their predictions. Next, demonstrate how students should investigate their predictions. Fill one of the cups with rice, beans, sand, peas, or water. Level the contents using the craft stick, and then pour the entire contents of the cup into the other cup. Ask: Do the cups hold the same amount? Did the contents of one cup not fill the other cup? Does one cup hold less? Did the contents of one cup spill over and out of the other cup? Does one cup hold more? Students must record their investigations on the I discovered side of the recording sheet. Write the letter X next to the word More because the large plastic cup holds more than the small plastic cup. Then they must record the letter Y next to the word Holds More, Holds Less, Holds the Same Page 4
Procedures Less because the small plastic cup holds less than the large plastic cup. 5. Provide a wide variety of assorted containers for this investigation. Each container should be labeled with a different letter A H so that students can identify and talk about the containers easily. Each group of 2-4 students should be given 2 containers. (Not all groups need to have the same two containers.) The group should predict which one of the containers will hold more, which one will hold less, or if they think the containers will hold the same amount. Predictions should be recorded on I Think, I Discover Recording Sheet Handouts/Transparencies 3a and 3b. Notes You can ask the students to bring a container or containers from home to donate to the class set. Containers need to be paired and labeled ahead of time. Examples may include, but should not be limited to: 2 containers with very different capacities but with similar shapes 2 containers with similar capacities but with different shapes such as one tall, skinny container and one short, wide container 2 containers with different capacities and with different shapes 6. After each group has made its prediction and recorded it on Handouts/Transparencies 3a and 3b, the group will verify its prediction using the following procedure. Give each group a dishpan (to catch any spills) and a Ziploc bag of dried beans, peas, rice, sand, or the like. Each group will also need a funnel and a craft stick or popsicle stick. Have the group members directly compare the capacities by filling one container, leveling the contents with the craft stick, and then pouring the contents into the other container. Tell the students to see if the container holds the same amount, holds less, or holds more. Students should record their investigations on Handouts/Transparencies 3a and 3b by writing the letter of the container next to the Make certain the funnel has a wide enough mouth for the material to flow freely. A funnel may be made out of an empty 2- liter bottle. Cut off and discard the bottom of the bottle. The open top of the bottle becomes the funnel. Craft sticks may be used to level the contents of the container. Make sure that students know how to interpret the results when they transfer the contents of one container into the other container. Asking the students for a verbal description of what happened and for their conclusion is a good way Holds More, Holds Less, Holds the Same Page 5
Procedures word More or Less or Same. Allow students to trade containers with other groups until each group of students has had opportunity to investigate all of the containers A H. Share the results of the investigation in a class discussion. Notes to assess this activity. The teacher can follow up with additional questions if needed. Additional questions might include: Which container holds more? Which container holds less? How do you know? Which container s contents will fit into another container? 7. Ask: What is another way of saying, Which object has the greater capacity? Which object holds more? Ask: Which has a greater capacity, a bathtub or a coffee cup? the bathtub How do you know? The bathtub can hold more. Which has a smaller capacity? the coffee cup How do you know? The coffee cup holds less. If I show you a picture of a bathtub and a picture of a coffee cup, and the pictures are both the same size, would the bathtub still have the greater capacity? Yes, it is just a picture. In real life, a bathtub is bigger than a coffee cup. It doesn t matter what size the picture is, a coffee cup holds less than a bathtub. Say: In the next part of the lesson, I am going to ask you to look at some pictures and decide which object has the greater capacity. As you look at these pictures and decide which container holds more, think about when you were a detective and investigated the capacity of the containers. Holds More, Holds Less, Holds the Same Page 6
Procedures 8. Show the Handout/Transparency 4, Which Holds More?, and read the directions aloud for the students. 9. When papers are completed, allow students to share their decisions in circle time. Students should discuss what they have learned about capacity. Notes See extensions for other ideas of capacity investigations. Homework: Assessment: Extensions: Have students tell their parents about the capacity investigation they did in class today. Encourage them to find two containers at home and determine which container holds more. Which Holds More? Handout/Transparency 4, and teacher observations. Repeat the activity using a variety of empty assorted sacks (4 different pairs of sacks, each sack labeled with a different letter A - H). Repeat the activity using a variety of empty assorted jars (4 different pairs of jars, each jar labeled with a different letter A - H). Repeat the activity using a variety of empty assorted boxes (4 different pairs of boxes, each box labeled with a different letter A - H). Resources: Van de Walle, J. A. (2006). Teaching student-centered mathematics: Grades K-3. Boston: Pearson Education, Inc. Modifications: This investigation should be done over the course of the year. Based on the developmental level of the students, you may want to change the containers to make the task easier. Some students may find it helpful to use the More/Less/Same Signs (Handouts/Transparencies 1a, 1b, and 1c) as they do their investigation. Holds More, Holds Less, Holds the Same Page 7
Handout/Transparency 1a Holds More, Holds Less, Holds the Same Page 8
Handout/Transparency 1b Holds More, Holds Less, Holds the Same Page 9
Handout/Transparency 1c Holds More, Holds Less, Holds the Same Page 10
More, Less, or the Same? X Y More Less Do you think container X or container Y holds more? Predict first; then investigate. Record your answer by writing the letter of the container next to the chosen word: More Less Same I think More Less Same Transparency 2 I discovered More Less Same Holds More, Holds Less, Holds the Same Page 11
I Think, I Discover Recording Sheet I think I discovered Handout/Transparency 3a Holds More, Holds Less, Holds the Same Page 12
I Think, I Discover Recording Sheet I think I discovered Handout/Transparency 3b Holds More, Holds Less, Holds the Same Page 13
Which Holds More? For each pair of objects, circle the object that has the greater capacity. or or or or Handout/Transparency 4 Holds More, Holds Less, Holds the Same Page 14