Lesson Summary:The teacher will pre-assess the students’ knowledge of three-dimensional figure names and reteach the names, if s/he finds that it’s necessary. Students will learn the definitions of face, edge, and vertex and practice identifying these properties on 3D figures and/or pictures of 3D figures. Students will look at an attributes chart of several different 3D figures and build these figures using toothpicks and marshmallows. Students will identify the number of faces, edges, and vertices for each 3D object on the attributes chart. Advanced learners will read a set of clues that describe the attributes of a specific three-dimensional object and identify the correct figure. They will then write their own set of clues for 2 three-dimensional figures. Struggling learners will build the remaining figures from the attributes chart using nets. Students will use a marker to label each face on the figure with a number. They will use dot stickers to mark each vertex on the figure, and they will use a marker to trace along the edges of the built figures.
Lesson Understandings:
The students will know…
- The definitions of face, edge, and vertex.
- How to identify faces, edges, and vertices on three-dimensional figures.
- Identify faces, edges, and vertices on three-dimensional figures.
Learning Styles Targeted:
Visual / Auditory / Kinesthetic/Tactile
Pre-Assessment:Give each student a whiteboard, dry-erase marker, and a tissue. Tell students that you are going to quiz them on their knowledge of three-dimensional figures. Tell students that you are going to show them a picture, and they will choose the name of that figure from a list of names given and write it on the whiteboard. Project the first slide of the Pre-assessment PowerPoint*. Read aloud the statement and the possible answer choices. Have students write their answer (a, b, c, or d) on the whiteboard and hold it up at your request. If you see that many students are not choosing “cube” as the answer, review with them why the figure is a cube. (Every side is a square.)Go through the remaining slides, reteaching the figure names as needed.
Whole-Class Instruction
Materials Needed:1 copy of the graphic organizer* per student, writing utensils, colored pencils, assorted 3D objects for students to touch, a document camera, 1 copy of the 3D Attributes Chart* per student, toothpicks, mini-marshmallows
Procedure:
1)Prior to teaching the lesson, set out assorted 3D objects near students. During the lesson, you will want them to hold a 3D object and touch the parts of the object that represent the different vocabulary words they are learning.
2)Tell students that today they are going to learn 3 vocabulary words that describe certain properties of 3D objects. Give each study a copy of the graphic organizer. Tell students that they are going to learn about the word face. Have students get one of the 3D objects that you have set out for them. Ask them to touch one the flat surfaces of that object. Tell students that the flat surface that they are touching is called the face. Project a copy of the graphic organizer under a document camera and record “the flat surFACE of a 3D object” under the definition section on the graphic organizer. Ask students why you capitalized the last four letters in the word “surface.” Elicit responses until students say that the word “face” is part of the word “surface.” Have students record the definition on their own graphic organizers.
3)Tell students that you are going to show them a picture in order to help them remember what “face” means. Draw a smiley face on the cube in the box with the word “face” on the graphic organizer. See the teacher example of the graphic organizer, if necessary. Have students draw the same picture on their graphic organizers.
4)Now tell students that you are going to help them count the number of faces on the cube and square pyramid in the examples section. If you have enough cubes for each student (dice would work), give each student a die to hold. Have students start by holding one hand on the top face and one on the bottom face. Have students count out loud, “two.” Now have students move their hands to the two side faces. Have students count out loud, “four.” Have students move their hands to the front and back side faces. Have students count out loud, “six.” There are six total faces on the die, just like there are on a cube. Remind students that a die is a cube, and a die has 6 sides labeled 1-6. Have students record “6” beside the picture of the cube.
5)Have students look at the square pyramid. If you have enough square pyramids available, allow each student to hold one. If not, they can act it out in the air. Have students use their hands to form the two side faces that come together to a point. Have them count out loud, “two.” Have students move their hands to form the front and back faces that come together to a point. Have them count out loud, “four.” Ask students which face of the square pyramid hadn’t been counted yet. Elicit responses until students say the base, or bottom. Have students use one hand to represent the base of the pyramid. Have students count out loud, “five.” Have students record “5” beside the picture of the square pyramid.
6)Tell students they are now going to learn a new vocabulary word about 3D figures. Have students get one of the 3D objects that you had set out for them. Tell them to touch the corners of the object. Tell students that the corners of a 3D object are called the vertices. Tell students that the word “vertex” is used when talking about only one corner, and “vertices” is used when talking about more than one corner. Under a document camera, record “the corners of a 3D object” as the definition of vertex/vertices. Have students record the definition as well. Use a colored pencil or marker and model for students under a document camera how to circle each of the vertices in the rectangular pyramid in the examples section on the graphic organizer. Have students use a colored pencil and do the same. After students have circled each vertex, ask them to go back and count how many they circled. Elicit responses. Tell students that if they are having trouble counting, they can count the 4 vertices on top and then add it to the 4 vertices on the bottom. Students should record “8” next to the picture of the rectangular pyramid. Have students try to circle and count the vertices on the square pyramid in the examples section by themselves. When they have finished, elicit their answers. Model for students the correct way to circle each vertex, count, and record the answer of “5” beside the picture of the square pyramid.
7)Tell students that the last word they are going to learn is “edge.” Ask students what they normally think of when they hear that word. Elicit responses. Lead students to see that what they already know about the word isn’t very different from what it means for a 3D figure. If they think of “the edge of a cliff,” the edge is where the cliff stops. The edge of a 3D figure is where a face ends or stops. Have students get one of the 3D objects that you had set out for them. Tell them to run their fingers along the edges. Under the document camera, record the definition for edge as “where the faces of a 3D object come together.” Have students record the definition as well. Model for students how to use a colored pencil to trace the edges of the triangular prism in the examples section, and count as you trace. Have students do the same. Tell students that one way to check themselves is to count the edges around the top (3), count the edges around the bottom (3), then count the edges connecting the top to the bottom (3), and add them together to get a total of 9. Have students record 9 as the answer beside the picture of the triangular prism. Have students try to trace and count the edges of the square pyramid on their own. Once they are finished, elicit their answers. Model for students the correct way to trace each edge, count, and record the answer of “8” beside the picture.
8)Tell students that they are going to be working in pairs to build some 3D figures and identify the number of faces, edges, and vertices on each one. Give each student a copy of the 3D Figure Attributes Chart, and put students in to pairs. Tell students that they will build the figures together but will be responsible for recording answers individually on their own papers. Tell students that the first figure they will build is a cube. Give each pair 8 mini-marshmallows and 12 toothpicks and tell them that those will be their building materials. Model for students how to build the base of the cube by forming a square with 4 toothpicks and connecting the corners with marshmallows. Have students do the same. Model for students how to build the top of the cube by forming another square with 4 toothpicks and connecting the corners with marshmallows. Have students do the same. Students should now have two separate squares. Now show students to connect the base square with the top square by using a toothpick to connect each top marshmallow with its corresponding base marshmallow. The cube should now be formed. Have students finish their cubes.
9)Ask students which attribute is represented by the toothpicks. Elicit responses, prompting students to explain why they think the toothpicks represent the edges. Underneath the word “edges” on the attributes chart, have students write “toothpicks.” Have students count how many edges, or toothpicks, are in their cubes. Students should record 12 on the chart under “edges.” Now ask students which attribute is represented by the marshmallows. Elicit responses, prompting students to explain why they think the marshmallows represent the vertices. Underneath the word “vertices” on the attributes chart, have students write “marshmallows.” Ask students to count how many vertices, or marshmallows, are in their cubes. Students should record “8” on the chart under “vertices.” Tell students that the remaining attribute is faces. Have students place their hands on the top and bottom of their cubes and count, “two.” Have students place their hands on the front and back of their cubes and count, “four.” Have students place their hands on the sides of their cubes and count, “six.” Students should record “6” on the chart under “faces.”
10)Allow students to work in their pairs to build the remaining figures from the attributes chart unless you think they need more support. If you think they need more guidance, lead them through building another figure or two. Allow them to work independently when you feel they are ready to do so. Remind students that they should build the figures together, but each person is responsible for filling out their own chart.
Advanced Learner
Materials Needed:1 copy of the 3D Figure Pictures* per student, 2 large index cards per student, writing utensils, teacher’s riddle example*, a document camera
Procedure:
1)Give each advanced learner a copy of the 3D Figure Pictures. Tell them that you are going to read a set of clues that describes the attributes of a particular figure on the page. Their job is to correctly identify the figure described by the clues.
2)Project the teacher’s example riddle under a document camera, and read it aloud to students. Leave it projected for students as they try to figure out which figure has been described. When students have finished figuring it out, ask students for their answers. Prompt students by asking them which clues were the most helpful.
3)Project the second teacher’s example riddle under a document camera, and read it aloud to students. Leave it projected for students as they try to figure out which figure has been described. Ask students for their answers. Cross out the clue that says, “All six of my faces are squares.” Ask students what figure besides the cube could be described by the remaining clues. Students should answer with the rectangular prism. Point out that the clues must be specific enough to correctly describe just one figure.
4)Give each student 2 large index cards. Tell them they should choose two of the remaining figures from the 3D Figure Pictures and write a set of clues for each figure they chose. They should write one set of clues on one index card and another set of clues on the other index card. Students should write the name of the figure described on the back of each index card.
5)Allow students to work independently to write their two sets of clues. When students have finished, they can switch clues with a partner and try to figure out the shape described by the partner’s clues.
Note: The students’ riddles can be bound with a binder ring and put with a copy of the 3D Figure Pictures to make a math center.
Struggling Learner
Materials Needed:several sheets of dot stickers (or any kind of small circular stickers), markers, 1 set of 3D Figure nets* per student, several tape dispensers, 1 copy of the 3D Figures Attributes Chart per student*, 1 pair of scissors per student
Procedure:
1)Have struggling learners bring with them their 3D Figure Attributes Chart that they began filling out during the whole-class lesson. Tell students that they are going to build the figures, but they are going to build them in a different way.
2)If you have already built a couple of the figures from the chart together as a class, begin with the figure the students haven’t already built. If you’re starting with the rectangular prism, give each student a rectangular prism net. Model for students how to cut around the edges of the net, fold along the lines and tape or glue the edges together to create a rectangular prism. Allow students to build their own, helping those who are struggling.
3)When all students have built their rectangular prisms, tell them that you are going to help them identify the number of faces. Have students touch their own faces with their palms flat. Tell them their palms can touch their own faces, and they can touch the faces of the 3D object. Have students use their outstretched hands to touch each of the prism’s faces. Use a marker to model for students how to number each face of the rectangular prism from 1-6. Give each student a marker, and have them do the same. Have students record 6 for the number of faces on the attributes chart.
4)Now tell them they’re going to identify the number of vertices. Remind students that the vertices are the corners. Have them use one finger to touch each of the vertices. Tell them to notice how they feel; they’re sharp and pointy. Get dot stickers or another kind of small circular stickers, and show students how to stick one sticker on each of the vertices. Give students some stickers, and have them do the same. When they have finished, count together how many vertices have been marked. Have students record 8 for the number of vertices on the attributes chart.
5)Now tell students they’re going to identify the number of edges. Remind students that the edges are where the faces meet. Have students trace one finger along each edge. Ask them to imagine a tiny little person walking on the face. When he comes to the edge, he falls. Use a brightly colored marker to model for students how to trace each edge so that it shows over the black line where they folded it. Count the edges as you trace. Give each student a brightly colored marker, and have them do the same, reminding them to count the edges as they trace them. Have students record 12 for the number of edges on the attributes chart.
6)Continue this process for the remaining figures on the chart.
*see supplemental resources
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