2012-2013 Enhanced Instructional Transition Guide Mathematics
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Unit 13: Geometry: Two- and Three-Dimensional Figures (7 days) Possible Lesson 01 (7days) POSSIBLE LESSON 01 (7 days) Lesson Synopsis: Students investigate relationships among two- and three-dimensional figures and describe distinctive attributes of a circle, triangle, rectangle, square, rectangular prism (including cube), sphere, cylinder, and cone using formal geometric language. TEKS: 1.6 1.6B 1.6C
Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. The student is expected to: Describe and identify three-dimensional geometric figures, including spheres, rectangular prisms (including cubes), cylinders, and cones. Describe and identify two- and three- dimensional geometric figures in order to sort them according to a given attribute using informal and formal language.
Underlying Processes and Mathematical Tools TEKS: 1.11 1.11A 1.12 1.12A 1.12B
Underlying processes and mathematical tools. The student applies Grade 1 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: Identify mathematics in everyday situations. Underlying processes and mathematical tools. The student communicates about Grade 1 mathematics using informal language. The student is expected to: Explain and record observations using objects, words, pictures, numbers, and technology. Relate informal language to mathematical language and symbols.
1.13
Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to:
1.13
Justify his or her thinking using objects, words, pictures, numbers, and technology.
Performance Indicator(s): Sort a variety of two- and three-dimensional geometric figures by their defining attributes. Orally explain the sorting process. Identify and describe orally five teacher-selected figures using formal geometric vocabulary. (1.6B, 1.6C; 1.11A; 1.12A, 1.12B; 1.13) 3H Key Understanding(s): • Objects and geometric figures can be identified and described by attributes. • Informal and formal geometric vocabulary is used to identify and describe the attributes of two- and three-dimensional geometric figures. • Attributes of two- and three-dimensional geometric figures are used to distinguish and justify one figure from another. • A collection of two- and three-dimensional figures can be sorted by various attributes. • Manipulatives and computers are tools that can assist in comparing and contrasting of two- and three-dimensional images of shapes and objects. • Two- and three-dimensional objects or figures can be identified in everyday settings. ©2012, TESCCC
04/30/13
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Misconception(s): • Some students may lack the ability to distinguish similarities and differences between two and three-dimensional figures (e.g., A student might refer to a sphere as a circle because they are both round.). Vocabulary of Instruction: • attribute • circle • cone • cube • curve • curved surface • cylinder • edge
Suggested Day
• • • • • • • •
• • • • • •
face opposite (sides) rectangle rectangular prism round side sphere square
square corner straight line three-dimensional figure triangle two-dimensional figure vertex (vertices)
Suggested Instructional Procedures
Notes for Teacher
1
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are present using the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Facilitate a class discussion to review standard form and expanded form. Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary 3. Instruct students to chorally count backward from 45 with you. 4. Using the displayed Wall Calendar, facilitate a class discussion about the components of the calendar. • What was the date two weeks ago? Answers may vary. • How did you find that answer? Answers may vary.
©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created in Unit 01 Lesson 01 Explore/Explain 5) • Wall Calendar (1 per teacher) (previously created in Unit 01 Lesson 01 Engage 1)
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures Topics: • Two-dimensional figures • Attributes • Formal geometric language
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher SPIRALING REVIEW MATERIALS • chart paper (2 sheets per teacher) • chart marker (1 per teacher)
Engage 1 Students compare and contrast all geometric attributes of a rectangle and square. Students describe their findings using formal geometric language. Instructional Procedures: 1. Prior to instruction, draw 3 different sizes of rectangles on a sheet of chart paper, and 3 different sizes of squares on another sheet of chart paper. 2. Display the chart paper with 3 sizes of rectangles for the class to see. Ask: • What are these two-dimensional figures called? (rectangles) • Who can describe the attributes of a rectangle? (4 sides, opposite sides same length, 4 vertices) 3. Display the chart paper with 3 sizes of squares for the class to see. Ask: • What are these two-dimensional figures called? (squares) • Who can describe the attributes of a square? (4 sides, all sides the same length, 4 vertices) 4. Display both sheets of chart paper side-by-side. Ask: • How are these two groups of figures alike? Answers may vary. Both sets of figures have 4 sides, with at least 2 sides the same length, and 4 vertices; etc. • How are these two groups of figures different? Answers may vary. The length of sides are not all the same; squares have all 4 sides same length; rectangles have opposite sides the same length; etc. • Do the attributes of size or color help us determine whether a figure is a rectangle or a square? (No, size and color do not help us define squares and rectangles.) • What makes a square different from a rectangle? (All sides of a square are the same length, not just opposite sides.) • How could I change a rectangle to make it a square? (make all sides the same length) Topics: • Three-dimensional figures • Attributes ©2012, TESCCC
MATERIALS • geometric solids (cube, rectangular prism, cylinder, 04/30/13
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures • Informal geometric language
Explore/Explain 1 Students sort a variety of three-dimensional solids based on one geometric attribute and describe the sort using informal geometric language. Instructional Procedures: 1. Place students into groups of 4. 2. Explain to students that when objects are sorted, they are grouped with other objects that have a common attribute. Groups of objects can be labeled according to the rule or attribute used for sorting. To determine common attributes for sorting objects, think about how they are like each other and how they are different from each other. Explain to students that they will sort a collection of objects and then explain their sort by describing how objects in one group are different from objects in the other group. 3. Distribute a set of geometric solids and a sheet of construction paper, to be used as a sorting mat, to each group of students. Instruct students to look at the geometric figures and identify an attribute that describes some of the figures. Then, place the figures with that attribute on the mat, leaving the other figures off of the mat. 4. Allow time for students to complete the sorting activity. Monitor and assess students to check for understanding. Note the variety of sorts and the language being used to describe the sorted figures. Facilitate a class discussion allowing student groups to share their sort. Ask: • What is the rule or attribute you used to sort your figures? Answer may vary. • How are the figures on the mat alike? Answer may vary. • How are the figures on the mat different? Answer may vary. 5. Allow students to describe and compare their sorted figures using informal language and two-dimensional formal language (e.g., figures that roll, figures that look like boxes or have faces that are rectangles, figures that have a triangle, figures that have a point, figures that have a circle, etc.). Formal vocabulary will be introduced later in this unit. The focus of this activity is on sorting by attributes. 6. Distribute 2 index cards and a marker to each group of students. Instruct students to use the index cards and marker to create a label listing the main attributes of each group. Allow time for students to create their labels. 7. Instruct students to take a gallery walk around the room. Each group of students will move together to each of the other displays of sorted figures. Instruct students to discuss as a group the way other students sorted the figures. Allow time for students to observe each of the other displays of sorted figures. 8. Facilitate a class discussion to review the gallery walk. Ask: • Did anyone notice if another group sorted their figures like your group? Answers may vary. ©2012, TESCCC
04/30/13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher cone, sphere) (1 set per 4 students, 1 set per teacher) • construction paper (1 sheet per 4 students) • index card (2 per 4 students) • marker (1 per 4 students)
INSTRUCTIONAL NOTE If the set of geometric figures being used are not all the same color, emphasize to students that color is not an attribute that should be used to sort or identify geometric figures.
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures •
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
Did anyone notice if another group sorted their figures differently from your group? Answers may vary.
2
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are absent using the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. Ask: • How many tens are in the number of children present today? Answers may vary. 2. Using the displayed Wall Calendar, facilitate a class discussion about upcoming events and, if applicable, post new events to the calendar. Ask: • What is the date of the next posted event? Answers may vary. • How many weeks until ______? Answers may vary. • Are there any entries listed next week? Answers may vary. • What are they? Answers may vary. • If today is Tuesday, what date would be a week from today? Answers may vary. Topics: • Three-dimensional figures • Attributes • Formal geometric language
SPIRALING REVIEW
Explore/Explain 2 Students explore the geometric attributes of a collection of boxes by investigating the faces of the solids. Instructional Procedures: 1. Prior to instruction, prepare a Box Collection by gathering various real-world rectangular prism and cube shaped boxes. Create sets of boxes with 1 box per student and 1 additional box per group of 4 students. The additional box per group will be used on Day 5. 2. Display the Box Collection for the class to see. Facilitate a class discussion to review the attributes of the three-dimensional objects. Allow students to use informal language to describe the attributes of the boxes. ©2012, TESCCC
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) (previously created)
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MATERIALS • boxes (real-world, various, rectangular prism, cube shaped) (1 box per student, 1 additional box per 4 students) • paper (Manila, 12” x 18”) (1 sheet per student, 1 sheet per teacher) • sticky note (small) (6 per 4 students) • color dot (different color per 4 students) (1 per student) page 5 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
3. Explain to students that today they will explore the formal name for the attribute often described as “flat surfaces.” Write the vocabulary word, face, for the class to see. 4. Display a box from the Box Collection. Touch a flat surface of the box to illustrate the meaning of the word, face. Explain to students that a face of a geometric solid is a flat surface in the shape of a twodimensional figure. Turn the box to show each face. Explain to students that they can tell when the surface is flat because the figure can sit on a face and not roll. Explain to students that faces can be different shapes. 5. Facilitate a class discussion to demonstrate the following activity. Display a sheet of Manila paper for the class to see. Explain to students that they will be tracing each face of a box on Manila paper. Demonstrate placing one face of the displayed box in the upper left corner of the Manila paper. Trace around the edge of the box. 6. Explain to students that they will use sticky notes to keep track of each face that has been traced. Demonstrate lifting the box and placing a sticky note on the face you just traced. 7. Explain to students that they will need to fit all 6 faces of the box on one sheet of Manila paper. Demonstrate tracing each of the remaining faces on the Manila paper, spacing the faces so that they all fit on the displayed Manila paper. After tracing each face, place a sticky note on the face to demonstrate tracking the faces already traced. 8. Remove the box. Facilitate a class discussion to identify the traced faces of the box. Ask: • What two-dimensional figures have been traced on the recording sheet? Answer may vary. • How many two-dimensional figures have been traced on the recording sheet? (6 twodimensional figures) • If there were 6 two-dimensional figures traced, how many faces make the three-dimensional box? (6 faces) 9. Distribute a large sheet of Manila paper and a box to each student. Instruct students to begin tracing the faces of their boxes, marking the faces with a sticky note as they trace them. Remind students to place their box faces so that all 6 faces will fit on the Manila paper. 10. Allow time for students to complete the activity. Monitor and assess students to check for understanding. 11. Place a colored dot sticker on the back of each box and box recording sheet. Use a different color dot for each group of 4 students. Collect the boxes and box recording sheets for use on Day 3 and Day 5. 3
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to observe the displayed Arithmetic Rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Facilitate a class discussion to review standard form and expanded form. ©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) page 6 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary. 3. Instruct students to pretend that 5 new students were added to the class today. Ask: • How many students would be present today if 5 new students were added? Answers may vary. 4. Using the displayed Wall Calendar, facilitate a class discussion about various past events. Encourage the use of time order words: yesterday, earlier, day before, last week, etc. Topics: • Two- and Three-dimensional figures • Attributes • Formal geometric language
Notes for Teacher (previously created)
SPIRALING REVIEW
Elaborate 1 Students study the recording sheets created by their peers in order to identify like figures. Students connect two-dimensional drawings with a three-dimensional model and justify their conclusions. Instructional Procedure: 1. Redistribute the box recordings created on day 2, ensuring each student does not have their own recording sheet. 2. Facilitate a discussion about the number of faces on the recording sheet and the shape of each face. Ask: • What two-dimensional figures have been traced on the recording sheet? Answer may vary. • How many two-dimensional figures have been traced on the recording sheet? (6 twodimensional figures) • If there are 6 two-dimensional figures traced, how many faces make the three-dimensional box? (6 faces) 3. Instruct students to bring their recording sheet and form a circle on the floor. Place 3 sheets of chart paper in the center of the circle to be used as sorting mats. Explain to the students that they will sort their recording sheets into 3 groups. Allow students to discover what the 3 groups represent throughout the activity. Do not tell students the categories at this time. 4. Instruct one student to place their recording on any of the 3 chart paper sorting mats. Instruct the student to describe the shape of each face and the number of faces. Ask: ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
MATERIALS • Box Collection (1 per teacher) (previously created) • chart paper (3 sheets per teacher)
TEACHER NOTE The 3 categories that will emerge are: a) figures that have faces that are all squares, b) figures that have faces that are all rectangles that are not squares, and c) figures that have rectangular and square faces. TEACHER NOTE If a student describes their figures as all the same size, facilitate a page 7 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures •
5. 6.
7.
8.
©2012, TESCCC
How could you describe the shape of each face and the number of faces in your recording? Answers may vary. My box has six faces—two faces are squares and four faces are rectangles; my box has six faces—two faces are rectangles and four faces are squares; my box has six faces—all six faces are rectangles; my box has six faces—all six faces are squares; etc. Invite a second student to decide whether his/her recording is like the first student’s recording or if it is different. Instruct the student to put their recording on the same mat as the first student if it is like the student’s recording or on the next mat if it is different. Instruct the second student to describe the shape of each face and the number of faces. Ask: • How could you describe the shape of each face and the number of faces in your recording? Answers may vary. My box has six faces—two faces are squares and four faces are rectangles; my box has six faces—two faces are rectangles and four faces are squares; my box has six faces—all six faces are rectangles; my box has six faces—all six faces are squares; etc. Repeat the process until all students have placed their recording sheet on a mat. Facilitate a class discussion regarding the sorted recording sheets. Ask: • What is the definition of a rectangle? (a two-dimensional figure with 4 vertices and opposite sides the same length) • What is the definition of a square? (a two-dimensional figure with 4 vertices and all sides the same length; a special rectangle because opposite sides are the same length) Direct students’ attention to the two sorting mats of rectangular prisms. Ask: • How are all of the recordings on this sorting mat alike? Answers may vary. The boxes have faces that are all rectangles (no squares); etc. • How are all of the recordings on this sorting mat alike? Answers may vary. The boxes have some faces that are rectangles and some faces that are squares; etc. Explain to students that boxes, or three-dimensional solids, that have faces that are all rectangles (and special rectangles, or squares) are called rectangular prisms. Display a few of the boxes from the Box Collection that are rectangular prisms (faces with all rectangles and faces that have both rectangles and squares). Direct the students to look at the sorting mat of cubes. Ask: • How are all of the recordings on this sorting mat alike? Answers may vary. The boxes have faces that are all squares; etc. Explain to students that boxes, or three-dimensional solids, that have faces that are all squares are called cubes. Display a few of the boxes from the Box Collection that are cubes.
04/30/13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher brief discussion allowing the student to justify how to prove that the figures are all the same size.
TEACHER NOTE Rectangular Prism – a geometric solid with 6 rectangular faces (Some of the rectangular faces may be squares.) Cube – a geometric solid with 6 square faces
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
4
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are present with the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Facilitate a class discussion to review standard form and expanded form. Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary. 3. Instruct students to chorally count backward from 42 with you. 4. Using the displayed Wall Calendar, facilitate a class discussion about the components of the calendar. Ask: • What is this month? Answers may vary. • How many days are in this month? Answers may vary. • What day of the week did this month end on? Answers may vary. • When will next month begin? Answers may vary. Topics: • Three-dimensional figures • Attributes • Formal and informal geometric language
SPIRALING REVIEW
Explore/Explain 3 Students explore the geometric attributes of a collection of three-dimensional solids (rectangular prisms and cubes) by investigating the vertices and edges of the solids, and curved-surface three-dimensional solids (cylinders, cones, and spheres) by investigating curved and flat surfaces of the solids. Instructional Procedures: 1. Prior to instruction, create 2 sets of geometric solids for each group of 4 students. Set 1 should include a rectangular prism or cube for each student in the group. Set 2 should include a sphere, cone, or cylinder for each student in the group. 2. Place students in groups of 4. Distribute Set 1 of the geometric solids to each group of students. 3. Facilitate a class discussion to review the definition of the term vertex and its plural, vertices. Instruct students to point to an example of a vertex on one of the models at their table. ©2012, TESCCC
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) (previously created)
04/30/13
ATTACHMENTS • Teacher Resource: Attribute Chart 1 (1 per teacher) • Handout: Attribute Chart 1 (1 per 4 students) • Teacher Resource: Attribute Chart 2 (1 per teacher) MATERIALS • geometric solids (rectangular prism, cube, cylinder, cone, sphere) (1 set per 4 students, 1 set per teacher) TEACHER NOTE page 9 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Notes for Teacher
4. Display a rectangular prism. Point to an edge on the prism. Explain to students that on three-dimensional figures this is called an edge. Instruct students to run their finger along an edge to a vertex on one of the models at their table. Facilitate a discussion comparing an edge of a three-dimensional solid to the side of a two-dimensional figure. 5. Facilitate a class discussion to compare the attributes of the geometric solids and to introduce the formal vocabulary associated with the cube and rectangular prism. Ask: • What attributes are used to describe a rectangular prism or cube? (vertices, edges, faces) 6. Distribute one handout: Attribute Chart 1 to each group of students. Explain to students that they will work as a group to complete the table. Instruct students to write “yes” if the figure has the attribute, and “no” if the figure does not have the attribute. As each attribute is discussed, instruct students to use the geometric solids at their table to justify their answer. Allow time for students to complete the chart. Monitor and assess students to check for understanding. 7. Display teacher resource: Attribute Chart 1 for the class to see. Facilitate a class discussion inviting students to share how they completed the chart and to justify their answers using a geometric solid. Record correct responses for the class to see.
TEA defines the attributes of cylinders, cones, and spheres as curved surfaces and flat surfaces (later to be defined as bases in Grade 3). sphere – a figure with one curved surface cone – a figure with one curved surface and one flat surface in the shape of a circle cylinder – a figure with one curved surface and two flat surfaces in the shape of a circle vertex (vertices) for twodimensional figures – the point where two lines meet vertex for three-dimensional figures – the point where three or more edges meet edge – a line segment where two faces meet
Face Prisms:
Attributes Edges Vertices
Rectangular Prism
yes
yes
yes
Cube
yes
yes
yes
8. Collect Set 1 of geometric solids and distribute Set 2 of the geometric solids to each group of students. 9. Display teacher resource: Attribute Chart 2 for the class to see. Explain to students that the class will complete the new Attribute Chart together. Facilitate a class discussion to compare the attributes of the geometric solids and to introduce the formal vocabulary associated with the spheres, cylinders, and cones. Ask: • What attributes are used to describe a rectangular prism or cube? (vertices, edges, faces) 10. Display a sphere for the class to see. Instruct student groups to find a sphere in the geometric solids at their table and pass it around to allow each student to hold it. Record students’ answers on teacher resource: Attribute Chart 2 as each attribute is discussed. Ask: • Does the sphere have a flat surface? (no) • Does the sphere have a curved surface? (yes) Explain to students the formal vocabulary curved surface. ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
TEA does not use the term vertex as an attribute for the cone in the elementary grades. So the top of the cone can be referenced as a vertex, an apex, or a point. In middle school mathematics, the term vertex is further defined to include the cone. State Resources:
Mathematics TEKS Toolkit: TEKS Clarifying Activity/Lesson page 10 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Sphere
Attributes Flat Surface (If yes, how many and what shape?) no
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
Curved Surface yes
•
Using attributes, how could a sphere be described? (A sphere is a curved surface with no flat surfaces.) • How are the surfaces of the sphere and the rectangular prism different? (A sphere has a curved surface, and a rectangular prism has flat surfaces.) • How are the surfaces of the sphere and the cube different? (A sphere has a curved surface, and a cube has flat surfaces.) 11. Display a cylinder for the class to see. Instruct student groups to find a cylinder in the geometric solids at their table and pass it around to allow each student to hold it. Record students’ answers on teacher resource: Attribute Chart 2 as each attribute is discussed. Ask: • Does the cylinder have a flat surface? (yes) • How many flat surfaces are on a cylinder? (2 flat surfaces) • What is the shape of the flat surface? (circle) • Does the cylinder have a curved surface? (yes)
Sphere Cylinder
Attributes Flat Surface (If yes, how many and what shape?) no yes, 2 circles
Curved Surface yes yes
•
Using attributes, how could a cylinder be described? (A cylinder is a curved surface with 2 flat surfaces in the shape of a circle.) • How are the surfaces of the cylinder and the sphere different? Alike? (A cylinder has 1 curved surface and 2 flat surfaces in the shape of a circle, whereas a sphere has only 1 curved surface.) • How are the surfaces of the cylinder and the rectangular prism or cube different? (A cylinder has 1 curved surface and 2 flat surfaces in the shape of a circle, and a rectangular prism or cube has all flat surfaces in the shape of rectangles or squares.) 12. Display a cone for the class to see. Instruct student groups to find a cone in the geometric solids at their ©2012, TESCCC
04/30/13
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
table and pass it around to allow each student to hold it. Record students’ answers on teacher resource: Attribute Chart 2 as each attribute is discussed. Ask: • Does the cone have a flat surface? (yes) • How many flat surfaces are on a cone? (1 flat surface) • What is the shape of the flat surface? (circle) • Does the cone have a curved surface? (yes)
Sphere Cylinder Cone • • • •
Attributes Flat Surface (If yes, how many and what shape?) no yes, 2 circles yes, 1 circle
Curved Surface yes yes yes
Using attributes, how could a cone be described? (A cone is a curved surface with 1 flat surface in the shape of a circle.) How are the surfaces of the cone and the sphere different? Alike? (A cone has 1 curved surface and 1 flat surface in the shape of a circle, whereas as a sphere has only 1 curved surface.) How are the surfaces of the cone and the cylinder different? Alike? (A cone has 1 curved surface and 1 flat surface in the shape of a circle, whereas as a cylinder has 1 curved surface and 2 flat surfaces in the shape of a circle.) How are the surfaces of the cone and the rectangular prism or cube different? (A cone has 1 curved surface and 1 flat surface in the shape of a circle, and a rectangular prism or cube has all flat surfaces in the shape of rectangles or squares.)
5
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to construct a pattern as they post their figures on the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion about if creating a pattern was helpful in determining the total. ©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) page 12 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures 2. Facilitate a class discussion to review standard form and expanded form. Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary. 3. Instruct students to chorally count backward from 28 with you. 4. Use the displayed Wall Calendar, facilitate a class discussion about the posted events and, if applicable, post new events to the calendar. Ask: • What events do we have posted for next week? Answers may vary. • What day of the week is it on? Answers may vary. • Does anyone have an event that we need to post? Answers may vary. • What date should I record it on? Answers may vary. Topics: • Two- and three-dimensional figures • Attributes • Formal geometric language
Notes for Teacher (previously created)
SPIRALING REVIEW
Elaborate 2 Students identify a two- or three-dimensional figure that matches the geometric attributes described by the teacher and description cards. Instructional Procedures: 1. Prior to instruction, create a set of cards for every 4 students and each teacher by copying card set and teacher resource: Two- and Three-Dimensional Figure Descriptions on cardstock, cutting apart, and placing in a plastic zip bag. 2. Prior to instruction, create a Two- and Three-Dimensional Figure Collection for each group of 4 students and each teacher. In each collection, include at least one cube, rectangular prism, cylinder, cone, sphere, square, circle, triangle, and rectangle. Three-dimensional objects in the collections may include commercial geometric solids and real-life objects. Two-dimensional figures may include real objects, pattern blocks, attribute blocks, die-cuts, and other objects that have been used in previous lessons. Add other shapes such as pyramids, polygons (pentagon, hexagon, trapezoid), ovals, and representations of shapes that are not regular (ex., triangles that are not equilateral). 3. Place students in groups of 4. Distribute a Two- and Three-Dimensional Figure Collection to each group. 4. Explain to students that you will read some descriptions of figures. For each description, student groups will discuss the description and find the figure from their collection that matches the figure you have ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
ATTACHMENTS • Teacher Resource: Two- and Three-Dimensional Figure Descriptions (1 per teacher) • Card Set: Two- and ThreeDimensional Figure Descriptions (1 set per 4 students) MATERIALS • two-dimensional figures (various, square, circle, triangle, rectangle) (1 set per 4 students, 1 set per teacher) • three-dimensional objects (various, cube, rectangular prism, cylinder, cone, sphere) (1 set per 4 students, 1 set per teacher) • cardstock (1 sheet per 4 students, 1 sheet per teacher) page 13 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
5. 6. 7.
8. 9.
described. One student from each group will hold up the figure. Instruct students to alternate holding up each figure described. Ask: • Who can find and name a figure that has more than 3 faces? (cube, rectangular prism) • Who can find and name a figure that has 3 or more sides? (triangle, square, rectangle) Instruct students to compare the last two figures described. • How are the figures with sides different than the figures with faces? (Figures with sides are twodimensional, and figures with faces are three-dimensional.) • Who can find and name a figure that has 3 or more vertices? (cube, square, rectangle, rectangular prism, triangle) • Are these figures two-dimensional, three-dimensional, or both? (both) • Who can find and name a figure that has a rectangular face? (rectangular prism, cube (special rectangular prism)) • How are rectangular prisms and cubes alike? Answers may vary. They have 6 faces that are rectangles; they have 8 vertices; they have 12 edges; etc. • How are rectangular prisms and cubes different? Answers may vary. All of the faces of a cube are the same size squares; etc. • Who can find and name figures with curved surfaces? (cone, cylinders, and spheres) • How are these figures the same? Answers may vary. They are all three-dimensional; they all have curved surfaces; they all roll; etc. Distribute card set: Two- and Three-Dimensional Figure Descriptions to each group. Instruct students to place all of the figures from their collection in the middle of the table. Explain to students that they will work as a group to match figures to the description cards. Instruct students to take turns selecting a description card, finding a figure that matches the description, and placing the figure on top of the description card. The other students in the group will confirm whether the figure matches the description, or not. Once all of the cards have been matched with a figure, students may take turns trying to find another figure that matches each description card. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief the activity and allow students to share their matches.
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher • scissors (1 per teacher) • plastic zip bag (sandwich sized) (1 per 4 students, 1 per teacher)
6
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to observe the displayed Arithmetic Rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Instruct students to pretend that 5 new students were added to the class today. ©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) page 14 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures Ask: • How many students would be present today if 5 new students were added? Answers may vary. • How many tens are in the number of students present if 5 new students were added? Answers may vary. 3. Using the displayed Wall Calendar, facilitate a class discussion about the school calendar. Ask: • How many weeks are there in this month? Answers may vary. • How many weeks have you been in school? Answers may vary. Topics: • Three-dimensional figures • Attributes • Formal geometric language
Notes for Teacher • Wall Calendar (1 per teacher) (previously created)
SPIRALING REVIEW ATTACHMENTS • Card Set: Shapes (1 set per 4 students)
Explore/Explain 4 Students sort pictures of three-dimensional figures to match a geometric attribute of a solid or to identify the solid pictured on a card. Students justify their groups using formal geometric language. Instructional Resources: 1. Prior to instruction, create card set: Shapes for every 4 students by copying on cardstock, cutting apart, and placing in a plastic zip bag. 2. Place students into groups of 4. Distribute card set: Shapes, 3 – 4 index cards, and a Two- and ThreeDimensional Figure Collection to each group. 3. Instruct student groups to match each shape card with a three-dimensional figure in their collection. 4. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate individual discussions, as necessary, to help students identify three-dimensional figures pictorially. 5. Instruct students to move the figure collection to the side of the table. Explain to students that they will work as a group to sort pictures of figures. Instruct students to decide as a group how to sort their shape cards into two or more groups. Students will use an index card to label each group in their sort. 6. Allow time for students to complete the activity. Monitor and assess students to check for understanding. 7. Facilitate a class discussion allowing student groups to share their sort. Invite one group to display the shapes in 1 of their groups for the class to see without displaying their index card label. Ask: • Who can guess the rule for this set of shapes? Answers may vary. Allow the presenting group to share their index card label when the class has given the correct answer. ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
MATERIALS • Two- and Three-Dimensional Figure Collection (1 per 4 students) (previously created) • cardstock (4 sheets per 4 students) • scissors (1 per teacher) • plastic zip bag (sandwich sized) (1 bag per 4 students) • index card (3 – 4 per 4 students)
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
• Is there another shape card that could be included in this group? Answers may vary. 8. Repeat the process, inviting each student group to display the shapes in 1 of their groups. Allow the class to guess the rule for the sort and to determine if additional shape cards could be added to the group. 9. If time allows, instruct student groups to sort their shape cards in different ways. 10. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate small group discussions, emphasizing the use of formal vocabulary as students describe and explain their sorts. 7
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are present with the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. Ask: • How many tens are in the number of students present? Answers may vary. • How many ones are in the number of students present? Answers may vary. 2. Using the displayed Wall Calendar, facilitate a class discussion about the calendar. Ask: • How many days are in one week? (7 days) • How many days are in two weeks? (14 days) • How many days are in three weeks? (21 days) • How many days are in four weeks? (28 days) • Is there the same number of days in a month as there are in four weeks? (no) Explain. Answers may vary. Except for February, there are more than 28 days in each month; etc.
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) (previously created)
Evaluate 1
MATERIALS • Two- and Three-Dimensional Figure Collection (1 per student) (previously created)
Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. Performance Indicator: Sort a variety of two- and three-dimensional geometric figures by their defining attributes. Orally explain the sorting process. Identify and describe orally five teacher-selected figures using formal geometric vocabulary. (1.6B, 1.6C; 1.11A; 1.12A, 1.12B; 1.13) 3H ©2012, TESCCC
04/30/13
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
©2012, TESCCC
Suggested Instructional Procedures
04/30/13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
page 17 of 17
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Unit 13: Geometry: Two- and Three-Dimensional Figures (7 days) Possible Lesson 01 (7days) POSSIBLE LESSON 01 (7 days) Lesson Synopsis: Students investigate relationships among two- and three-dimensional figures and describe distinctive attributes of a circle, triangle, rectangle, square, rectangular prism (including cube), sphere, cylinder, and cone using formal geometric language. TEKS: 1.6 1.6B 1.6C
Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both. The student is expected to: Describe and identify three-dimensional geometric figures, including spheres, rectangular prisms (including cubes), cylinders, and cones. Describe and identify two- and three- dimensional geometric figures in order to sort them according to a given attribute using informal and formal language.
Underlying Processes and Mathematical Tools TEKS: 1.11 1.11A 1.12 1.12A 1.12B
Underlying processes and mathematical tools. The student applies Grade 1 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: Identify mathematics in everyday situations. Underlying processes and mathematical tools. The student communicates about Grade 1 mathematics using informal language. The student is expected to: Explain and record observations using objects, words, pictures, numbers, and technology. Relate informal language to mathematical language and symbols.
1.13
Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to:
1.13
Justify his or her thinking using objects, words, pictures, numbers, and technology.
Performance Indicator(s): Sort a variety of two- and three-dimensional geometric figures by their defining attributes. Orally explain the sorting process. Identify and describe orally five teacher-selected figures using formal geometric vocabulary. (1.6B, 1.6C; 1.11A; 1.12A, 1.12B; 1.13) 3H Key Understanding(s): • Objects and geometric figures can be identified and described by attributes. • Informal and formal geometric vocabulary is used to identify and describe the attributes of two- and three-dimensional geometric figures. • Attributes of two- and three-dimensional geometric figures are used to distinguish and justify one figure from another. • A collection of two- and three-dimensional figures can be sorted by various attributes. • Manipulatives and computers are tools that can assist in comparing and contrasting of two- and three-dimensional images of shapes and objects. • Two- and three-dimensional objects or figures can be identified in everyday settings. ©2012, TESCCC
04/30/13
page 1 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Misconception(s): • Some students may lack the ability to distinguish similarities and differences between two and three-dimensional figures (e.g., A student might refer to a sphere as a circle because they are both round.). Vocabulary of Instruction: • attribute • circle • cone • cube • curve • curved surface • cylinder • edge
Suggested Day
• • • • • • • •
• • • • • •
face opposite (sides) rectangle rectangular prism round side sphere square
square corner straight line three-dimensional figure triangle two-dimensional figure vertex (vertices)
Suggested Instructional Procedures
Notes for Teacher
1
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are present using the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Facilitate a class discussion to review standard form and expanded form. Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary 3. Instruct students to chorally count backward from 45 with you. 4. Using the displayed Wall Calendar, facilitate a class discussion about the components of the calendar. • What was the date two weeks ago? Answers may vary. • How did you find that answer? Answers may vary.
©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created in Unit 01 Lesson 01 Explore/Explain 5) • Wall Calendar (1 per teacher) (previously created in Unit 01 Lesson 01 Engage 1)
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures Topics: • Two-dimensional figures • Attributes • Formal geometric language
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher SPIRALING REVIEW MATERIALS • chart paper (2 sheets per teacher) • chart marker (1 per teacher)
Engage 1 Students compare and contrast all geometric attributes of a rectangle and square. Students describe their findings using formal geometric language. Instructional Procedures: 1. Prior to instruction, draw 3 different sizes of rectangles on a sheet of chart paper, and 3 different sizes of squares on another sheet of chart paper. 2. Display the chart paper with 3 sizes of rectangles for the class to see. Ask: • What are these two-dimensional figures called? (rectangles) • Who can describe the attributes of a rectangle? (4 sides, opposite sides same length, 4 vertices) 3. Display the chart paper with 3 sizes of squares for the class to see. Ask: • What are these two-dimensional figures called? (squares) • Who can describe the attributes of a square? (4 sides, all sides the same length, 4 vertices) 4. Display both sheets of chart paper side-by-side. Ask: • How are these two groups of figures alike? Answers may vary. Both sets of figures have 4 sides, with at least 2 sides the same length, and 4 vertices; etc. • How are these two groups of figures different? Answers may vary. The length of sides are not all the same; squares have all 4 sides same length; rectangles have opposite sides the same length; etc. • Do the attributes of size or color help us determine whether a figure is a rectangle or a square? (No, size and color do not help us define squares and rectangles.) • What makes a square different from a rectangle? (All sides of a square are the same length, not just opposite sides.) • How could I change a rectangle to make it a square? (make all sides the same length) Topics: • Three-dimensional figures • Attributes ©2012, TESCCC
MATERIALS • geometric solids (cube, rectangular prism, cylinder, 04/30/13
page 3 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures • Informal geometric language
Explore/Explain 1 Students sort a variety of three-dimensional solids based on one geometric attribute and describe the sort using informal geometric language. Instructional Procedures: 1. Place students into groups of 4. 2. Explain to students that when objects are sorted, they are grouped with other objects that have a common attribute. Groups of objects can be labeled according to the rule or attribute used for sorting. To determine common attributes for sorting objects, think about how they are like each other and how they are different from each other. Explain to students that they will sort a collection of objects and then explain their sort by describing how objects in one group are different from objects in the other group. 3. Distribute a set of geometric solids and a sheet of construction paper, to be used as a sorting mat, to each group of students. Instruct students to look at the geometric figures and identify an attribute that describes some of the figures. Then, place the figures with that attribute on the mat, leaving the other figures off of the mat. 4. Allow time for students to complete the sorting activity. Monitor and assess students to check for understanding. Note the variety of sorts and the language being used to describe the sorted figures. Facilitate a class discussion allowing student groups to share their sort. Ask: • What is the rule or attribute you used to sort your figures? Answer may vary. • How are the figures on the mat alike? Answer may vary. • How are the figures on the mat different? Answer may vary. 5. Allow students to describe and compare their sorted figures using informal language and two-dimensional formal language (e.g., figures that roll, figures that look like boxes or have faces that are rectangles, figures that have a triangle, figures that have a point, figures that have a circle, etc.). Formal vocabulary will be introduced later in this unit. The focus of this activity is on sorting by attributes. 6. Distribute 2 index cards and a marker to each group of students. Instruct students to use the index cards and marker to create a label listing the main attributes of each group. Allow time for students to create their labels. 7. Instruct students to take a gallery walk around the room. Each group of students will move together to each of the other displays of sorted figures. Instruct students to discuss as a group the way other students sorted the figures. Allow time for students to observe each of the other displays of sorted figures. 8. Facilitate a class discussion to review the gallery walk. Ask: • Did anyone notice if another group sorted their figures like your group? Answers may vary. ©2012, TESCCC
04/30/13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher cone, sphere) (1 set per 4 students, 1 set per teacher) • construction paper (1 sheet per 4 students) • index card (2 per 4 students) • marker (1 per 4 students)
INSTRUCTIONAL NOTE If the set of geometric figures being used are not all the same color, emphasize to students that color is not an attribute that should be used to sort or identify geometric figures.
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures •
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
Did anyone notice if another group sorted their figures differently from your group? Answers may vary.
2
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are absent using the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. Ask: • How many tens are in the number of children present today? Answers may vary. 2. Using the displayed Wall Calendar, facilitate a class discussion about upcoming events and, if applicable, post new events to the calendar. Ask: • What is the date of the next posted event? Answers may vary. • How many weeks until ______? Answers may vary. • Are there any entries listed next week? Answers may vary. • What are they? Answers may vary. • If today is Tuesday, what date would be a week from today? Answers may vary. Topics: • Three-dimensional figures • Attributes • Formal geometric language
SPIRALING REVIEW
Explore/Explain 2 Students explore the geometric attributes of a collection of boxes by investigating the faces of the solids. Instructional Procedures: 1. Prior to instruction, prepare a Box Collection by gathering various real-world rectangular prism and cube shaped boxes. Create sets of boxes with 1 box per student and 1 additional box per group of 4 students. The additional box per group will be used on Day 5. 2. Display the Box Collection for the class to see. Facilitate a class discussion to review the attributes of the three-dimensional objects. Allow students to use informal language to describe the attributes of the boxes. ©2012, TESCCC
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) (previously created)
04/30/13
MATERIALS • boxes (real-world, various, rectangular prism, cube shaped) (1 box per student, 1 additional box per 4 students) • paper (Manila, 12” x 18”) (1 sheet per student, 1 sheet per teacher) • sticky note (small) (6 per 4 students) • color dot (different color per 4 students) (1 per student) page 5 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
3. Explain to students that today they will explore the formal name for the attribute often described as “flat surfaces.” Write the vocabulary word, face, for the class to see. 4. Display a box from the Box Collection. Touch a flat surface of the box to illustrate the meaning of the word, face. Explain to students that a face of a geometric solid is a flat surface in the shape of a twodimensional figure. Turn the box to show each face. Explain to students that they can tell when the surface is flat because the figure can sit on a face and not roll. Explain to students that faces can be different shapes. 5. Facilitate a class discussion to demonstrate the following activity. Display a sheet of Manila paper for the class to see. Explain to students that they will be tracing each face of a box on Manila paper. Demonstrate placing one face of the displayed box in the upper left corner of the Manila paper. Trace around the edge of the box. 6. Explain to students that they will use sticky notes to keep track of each face that has been traced. Demonstrate lifting the box and placing a sticky note on the face you just traced. 7. Explain to students that they will need to fit all 6 faces of the box on one sheet of Manila paper. Demonstrate tracing each of the remaining faces on the Manila paper, spacing the faces so that they all fit on the displayed Manila paper. After tracing each face, place a sticky note on the face to demonstrate tracking the faces already traced. 8. Remove the box. Facilitate a class discussion to identify the traced faces of the box. Ask: • What two-dimensional figures have been traced on the recording sheet? Answer may vary. • How many two-dimensional figures have been traced on the recording sheet? (6 twodimensional figures) • If there were 6 two-dimensional figures traced, how many faces make the three-dimensional box? (6 faces) 9. Distribute a large sheet of Manila paper and a box to each student. Instruct students to begin tracing the faces of their boxes, marking the faces with a sticky note as they trace them. Remind students to place their box faces so that all 6 faces will fit on the Manila paper. 10. Allow time for students to complete the activity. Monitor and assess students to check for understanding. 11. Place a colored dot sticker on the back of each box and box recording sheet. Use a different color dot for each group of 4 students. Collect the boxes and box recording sheets for use on Day 3 and Day 5. 3
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to observe the displayed Arithmetic Rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Facilitate a class discussion to review standard form and expanded form. ©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) page 6 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary. 3. Instruct students to pretend that 5 new students were added to the class today. Ask: • How many students would be present today if 5 new students were added? Answers may vary. 4. Using the displayed Wall Calendar, facilitate a class discussion about various past events. Encourage the use of time order words: yesterday, earlier, day before, last week, etc. Topics: • Two- and Three-dimensional figures • Attributes • Formal geometric language
Notes for Teacher (previously created)
SPIRALING REVIEW
Elaborate 1 Students study the recording sheets created by their peers in order to identify like figures. Students connect two-dimensional drawings with a three-dimensional model and justify their conclusions. Instructional Procedure: 1. Redistribute the box recordings created on day 2, ensuring each student does not have their own recording sheet. 2. Facilitate a discussion about the number of faces on the recording sheet and the shape of each face. Ask: • What two-dimensional figures have been traced on the recording sheet? Answer may vary. • How many two-dimensional figures have been traced on the recording sheet? (6 twodimensional figures) • If there are 6 two-dimensional figures traced, how many faces make the three-dimensional box? (6 faces) 3. Instruct students to bring their recording sheet and form a circle on the floor. Place 3 sheets of chart paper in the center of the circle to be used as sorting mats. Explain to the students that they will sort their recording sheets into 3 groups. Allow students to discover what the 3 groups represent throughout the activity. Do not tell students the categories at this time. 4. Instruct one student to place their recording on any of the 3 chart paper sorting mats. Instruct the student to describe the shape of each face and the number of faces. Ask: ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
MATERIALS • Box Collection (1 per teacher) (previously created) • chart paper (3 sheets per teacher)
TEACHER NOTE The 3 categories that will emerge are: a) figures that have faces that are all squares, b) figures that have faces that are all rectangles that are not squares, and c) figures that have rectangular and square faces. TEACHER NOTE If a student describes their figures as all the same size, facilitate a page 7 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures •
5. 6.
7.
8.
©2012, TESCCC
How could you describe the shape of each face and the number of faces in your recording? Answers may vary. My box has six faces—two faces are squares and four faces are rectangles; my box has six faces—two faces are rectangles and four faces are squares; my box has six faces—all six faces are rectangles; my box has six faces—all six faces are squares; etc. Invite a second student to decide whether his/her recording is like the first student’s recording or if it is different. Instruct the student to put their recording on the same mat as the first student if it is like the student’s recording or on the next mat if it is different. Instruct the second student to describe the shape of each face and the number of faces. Ask: • How could you describe the shape of each face and the number of faces in your recording? Answers may vary. My box has six faces—two faces are squares and four faces are rectangles; my box has six faces—two faces are rectangles and four faces are squares; my box has six faces—all six faces are rectangles; my box has six faces—all six faces are squares; etc. Repeat the process until all students have placed their recording sheet on a mat. Facilitate a class discussion regarding the sorted recording sheets. Ask: • What is the definition of a rectangle? (a two-dimensional figure with 4 vertices and opposite sides the same length) • What is the definition of a square? (a two-dimensional figure with 4 vertices and all sides the same length; a special rectangle because opposite sides are the same length) Direct students’ attention to the two sorting mats of rectangular prisms. Ask: • How are all of the recordings on this sorting mat alike? Answers may vary. The boxes have faces that are all rectangles (no squares); etc. • How are all of the recordings on this sorting mat alike? Answers may vary. The boxes have some faces that are rectangles and some faces that are squares; etc. Explain to students that boxes, or three-dimensional solids, that have faces that are all rectangles (and special rectangles, or squares) are called rectangular prisms. Display a few of the boxes from the Box Collection that are rectangular prisms (faces with all rectangles and faces that have both rectangles and squares). Direct the students to look at the sorting mat of cubes. Ask: • How are all of the recordings on this sorting mat alike? Answers may vary. The boxes have faces that are all squares; etc. Explain to students that boxes, or three-dimensional solids, that have faces that are all squares are called cubes. Display a few of the boxes from the Box Collection that are cubes.
04/30/13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher brief discussion allowing the student to justify how to prove that the figures are all the same size.
TEACHER NOTE Rectangular Prism – a geometric solid with 6 rectangular faces (Some of the rectangular faces may be squares.) Cube – a geometric solid with 6 square faces
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
4
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are present with the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Facilitate a class discussion to review standard form and expanded form. Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary. 3. Instruct students to chorally count backward from 42 with you. 4. Using the displayed Wall Calendar, facilitate a class discussion about the components of the calendar. Ask: • What is this month? Answers may vary. • How many days are in this month? Answers may vary. • What day of the week did this month end on? Answers may vary. • When will next month begin? Answers may vary. Topics: • Three-dimensional figures • Attributes • Formal and informal geometric language
SPIRALING REVIEW
Explore/Explain 3 Students explore the geometric attributes of a collection of three-dimensional solids (rectangular prisms and cubes) by investigating the vertices and edges of the solids, and curved-surface three-dimensional solids (cylinders, cones, and spheres) by investigating curved and flat surfaces of the solids. Instructional Procedures: 1. Prior to instruction, create 2 sets of geometric solids for each group of 4 students. Set 1 should include a rectangular prism or cube for each student in the group. Set 2 should include a sphere, cone, or cylinder for each student in the group. 2. Place students in groups of 4. Distribute Set 1 of the geometric solids to each group of students. 3. Facilitate a class discussion to review the definition of the term vertex and its plural, vertices. Instruct students to point to an example of a vertex on one of the models at their table. ©2012, TESCCC
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) (previously created)
04/30/13
ATTACHMENTS • Teacher Resource: Attribute Chart 1 (1 per teacher) • Handout: Attribute Chart 1 (1 per 4 students) • Teacher Resource: Attribute Chart 2 (1 per teacher) MATERIALS • geometric solids (rectangular prism, cube, cylinder, cone, sphere) (1 set per 4 students, 1 set per teacher) TEACHER NOTE page 9 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Notes for Teacher
4. Display a rectangular prism. Point to an edge on the prism. Explain to students that on three-dimensional figures this is called an edge. Instruct students to run their finger along an edge to a vertex on one of the models at their table. Facilitate a discussion comparing an edge of a three-dimensional solid to the side of a two-dimensional figure. 5. Facilitate a class discussion to compare the attributes of the geometric solids and to introduce the formal vocabulary associated with the cube and rectangular prism. Ask: • What attributes are used to describe a rectangular prism or cube? (vertices, edges, faces) 6. Distribute one handout: Attribute Chart 1 to each group of students. Explain to students that they will work as a group to complete the table. Instruct students to write “yes” if the figure has the attribute, and “no” if the figure does not have the attribute. As each attribute is discussed, instruct students to use the geometric solids at their table to justify their answer. Allow time for students to complete the chart. Monitor and assess students to check for understanding. 7. Display teacher resource: Attribute Chart 1 for the class to see. Facilitate a class discussion inviting students to share how they completed the chart and to justify their answers using a geometric solid. Record correct responses for the class to see.
TEA defines the attributes of cylinders, cones, and spheres as curved surfaces and flat surfaces (later to be defined as bases in Grade 3). sphere – a figure with one curved surface cone – a figure with one curved surface and one flat surface in the shape of a circle cylinder – a figure with one curved surface and two flat surfaces in the shape of a circle vertex (vertices) for twodimensional figures – the point where two lines meet vertex for three-dimensional figures – the point where three or more edges meet edge – a line segment where two faces meet
Face Prisms:
Attributes Edges Vertices
Rectangular Prism
yes
yes
yes
Cube
yes
yes
yes
8. Collect Set 1 of geometric solids and distribute Set 2 of the geometric solids to each group of students. 9. Display teacher resource: Attribute Chart 2 for the class to see. Explain to students that the class will complete the new Attribute Chart together. Facilitate a class discussion to compare the attributes of the geometric solids and to introduce the formal vocabulary associated with the spheres, cylinders, and cones. Ask: • What attributes are used to describe a rectangular prism or cube? (vertices, edges, faces) 10. Display a sphere for the class to see. Instruct student groups to find a sphere in the geometric solids at their table and pass it around to allow each student to hold it. Record students’ answers on teacher resource: Attribute Chart 2 as each attribute is discussed. Ask: • Does the sphere have a flat surface? (no) • Does the sphere have a curved surface? (yes) Explain to students the formal vocabulary curved surface. ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
TEA does not use the term vertex as an attribute for the cone in the elementary grades. So the top of the cone can be referenced as a vertex, an apex, or a point. In middle school mathematics, the term vertex is further defined to include the cone. State Resources:
Mathematics TEKS Toolkit: TEKS Clarifying Activity/Lesson page 10 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Sphere
Attributes Flat Surface (If yes, how many and what shape?) no
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
Curved Surface yes
•
Using attributes, how could a sphere be described? (A sphere is a curved surface with no flat surfaces.) • How are the surfaces of the sphere and the rectangular prism different? (A sphere has a curved surface, and a rectangular prism has flat surfaces.) • How are the surfaces of the sphere and the cube different? (A sphere has a curved surface, and a cube has flat surfaces.) 11. Display a cylinder for the class to see. Instruct student groups to find a cylinder in the geometric solids at their table and pass it around to allow each student to hold it. Record students’ answers on teacher resource: Attribute Chart 2 as each attribute is discussed. Ask: • Does the cylinder have a flat surface? (yes) • How many flat surfaces are on a cylinder? (2 flat surfaces) • What is the shape of the flat surface? (circle) • Does the cylinder have a curved surface? (yes)
Sphere Cylinder
Attributes Flat Surface (If yes, how many and what shape?) no yes, 2 circles
Curved Surface yes yes
•
Using attributes, how could a cylinder be described? (A cylinder is a curved surface with 2 flat surfaces in the shape of a circle.) • How are the surfaces of the cylinder and the sphere different? Alike? (A cylinder has 1 curved surface and 2 flat surfaces in the shape of a circle, whereas a sphere has only 1 curved surface.) • How are the surfaces of the cylinder and the rectangular prism or cube different? (A cylinder has 1 curved surface and 2 flat surfaces in the shape of a circle, and a rectangular prism or cube has all flat surfaces in the shape of rectangles or squares.) 12. Display a cone for the class to see. Instruct student groups to find a cone in the geometric solids at their ©2012, TESCCC
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
table and pass it around to allow each student to hold it. Record students’ answers on teacher resource: Attribute Chart 2 as each attribute is discussed. Ask: • Does the cone have a flat surface? (yes) • How many flat surfaces are on a cone? (1 flat surface) • What is the shape of the flat surface? (circle) • Does the cone have a curved surface? (yes)
Sphere Cylinder Cone • • • •
Attributes Flat Surface (If yes, how many and what shape?) no yes, 2 circles yes, 1 circle
Curved Surface yes yes yes
Using attributes, how could a cone be described? (A cone is a curved surface with 1 flat surface in the shape of a circle.) How are the surfaces of the cone and the sphere different? Alike? (A cone has 1 curved surface and 1 flat surface in the shape of a circle, whereas as a sphere has only 1 curved surface.) How are the surfaces of the cone and the cylinder different? Alike? (A cone has 1 curved surface and 1 flat surface in the shape of a circle, whereas as a cylinder has 1 curved surface and 2 flat surfaces in the shape of a circle.) How are the surfaces of the cone and the rectangular prism or cube different? (A cone has 1 curved surface and 1 flat surface in the shape of a circle, and a rectangular prism or cube has all flat surfaces in the shape of rectangles or squares.)
5
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to construct a pattern as they post their figures on the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion about if creating a pattern was helpful in determining the total. ©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) page 12 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures 2. Facilitate a class discussion to review standard form and expanded form. Ask: • How many students are present today? Answers may vary. • How could the number be recorded in standard form? Answers may vary. • How could the number be recorded in expanded form? Answers may vary. 3. Instruct students to chorally count backward from 28 with you. 4. Use the displayed Wall Calendar, facilitate a class discussion about the posted events and, if applicable, post new events to the calendar. Ask: • What events do we have posted for next week? Answers may vary. • What day of the week is it on? Answers may vary. • Does anyone have an event that we need to post? Answers may vary. • What date should I record it on? Answers may vary. Topics: • Two- and three-dimensional figures • Attributes • Formal geometric language
Notes for Teacher (previously created)
SPIRALING REVIEW
Elaborate 2 Students identify a two- or three-dimensional figure that matches the geometric attributes described by the teacher and description cards. Instructional Procedures: 1. Prior to instruction, create a set of cards for every 4 students and each teacher by copying card set and teacher resource: Two- and Three-Dimensional Figure Descriptions on cardstock, cutting apart, and placing in a plastic zip bag. 2. Prior to instruction, create a Two- and Three-Dimensional Figure Collection for each group of 4 students and each teacher. In each collection, include at least one cube, rectangular prism, cylinder, cone, sphere, square, circle, triangle, and rectangle. Three-dimensional objects in the collections may include commercial geometric solids and real-life objects. Two-dimensional figures may include real objects, pattern blocks, attribute blocks, die-cuts, and other objects that have been used in previous lessons. Add other shapes such as pyramids, polygons (pentagon, hexagon, trapezoid), ovals, and representations of shapes that are not regular (ex., triangles that are not equilateral). 3. Place students in groups of 4. Distribute a Two- and Three-Dimensional Figure Collection to each group. 4. Explain to students that you will read some descriptions of figures. For each description, student groups will discuss the description and find the figure from their collection that matches the figure you have ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
ATTACHMENTS • Teacher Resource: Two- and Three-Dimensional Figure Descriptions (1 per teacher) • Card Set: Two- and ThreeDimensional Figure Descriptions (1 set per 4 students) MATERIALS • two-dimensional figures (various, square, circle, triangle, rectangle) (1 set per 4 students, 1 set per teacher) • three-dimensional objects (various, cube, rectangular prism, cylinder, cone, sphere) (1 set per 4 students, 1 set per teacher) • cardstock (1 sheet per 4 students, 1 sheet per teacher) page 13 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
5. 6. 7.
8. 9.
described. One student from each group will hold up the figure. Instruct students to alternate holding up each figure described. Ask: • Who can find and name a figure that has more than 3 faces? (cube, rectangular prism) • Who can find and name a figure that has 3 or more sides? (triangle, square, rectangle) Instruct students to compare the last two figures described. • How are the figures with sides different than the figures with faces? (Figures with sides are twodimensional, and figures with faces are three-dimensional.) • Who can find and name a figure that has 3 or more vertices? (cube, square, rectangle, rectangular prism, triangle) • Are these figures two-dimensional, three-dimensional, or both? (both) • Who can find and name a figure that has a rectangular face? (rectangular prism, cube (special rectangular prism)) • How are rectangular prisms and cubes alike? Answers may vary. They have 6 faces that are rectangles; they have 8 vertices; they have 12 edges; etc. • How are rectangular prisms and cubes different? Answers may vary. All of the faces of a cube are the same size squares; etc. • Who can find and name figures with curved surfaces? (cone, cylinders, and spheres) • How are these figures the same? Answers may vary. They are all three-dimensional; they all have curved surfaces; they all roll; etc. Distribute card set: Two- and Three-Dimensional Figure Descriptions to each group. Instruct students to place all of the figures from their collection in the middle of the table. Explain to students that they will work as a group to match figures to the description cards. Instruct students to take turns selecting a description card, finding a figure that matches the description, and placing the figure on top of the description card. The other students in the group will confirm whether the figure matches the description, or not. Once all of the cards have been matched with a figure, students may take turns trying to find another figure that matches each description card. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief the activity and allow students to share their matches.
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher • scissors (1 per teacher) • plastic zip bag (sandwich sized) (1 per 4 students, 1 per teacher)
6
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to observe the displayed Arithmetic Rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. 2. Instruct students to pretend that 5 new students were added to the class today. ©2012, TESCCC
04/30/13
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) page 14 of 17
2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures Ask: • How many students would be present today if 5 new students were added? Answers may vary. • How many tens are in the number of students present if 5 new students were added? Answers may vary. 3. Using the displayed Wall Calendar, facilitate a class discussion about the school calendar. Ask: • How many weeks are there in this month? Answers may vary. • How many weeks have you been in school? Answers may vary. Topics: • Three-dimensional figures • Attributes • Formal geometric language
Notes for Teacher • Wall Calendar (1 per teacher) (previously created)
SPIRALING REVIEW ATTACHMENTS • Card Set: Shapes (1 set per 4 students)
Explore/Explain 4 Students sort pictures of three-dimensional figures to match a geometric attribute of a solid or to identify the solid pictured on a card. Students justify their groups using formal geometric language. Instructional Resources: 1. Prior to instruction, create card set: Shapes for every 4 students by copying on cardstock, cutting apart, and placing in a plastic zip bag. 2. Place students into groups of 4. Distribute card set: Shapes, 3 – 4 index cards, and a Two- and ThreeDimensional Figure Collection to each group. 3. Instruct student groups to match each shape card with a three-dimensional figure in their collection. 4. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate individual discussions, as necessary, to help students identify three-dimensional figures pictorially. 5. Instruct students to move the figure collection to the side of the table. Explain to students that they will work as a group to sort pictures of figures. Instruct students to decide as a group how to sort their shape cards into two or more groups. Students will use an index card to label each group in their sort. 6. Allow time for students to complete the activity. Monitor and assess students to check for understanding. 7. Facilitate a class discussion allowing student groups to share their sort. Invite one group to display the shapes in 1 of their groups for the class to see without displaying their index card label. Ask: • Who can guess the rule for this set of shapes? Answers may vary. Allow the presenting group to share their index card label when the class has given the correct answer. ©2012, TESCCC
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
04/30/13
MATERIALS • Two- and Three-Dimensional Figure Collection (1 per 4 students) (previously created) • cardstock (4 sheets per 4 students) • scissors (1 per teacher) • plastic zip bag (sandwich sized) (1 bag per 4 students) • index card (3 – 4 per 4 students)
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
Suggested Instructional Procedures
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
• Is there another shape card that could be included in this group? Answers may vary. 8. Repeat the process, inviting each student group to display the shapes in 1 of their groups. Allow the class to guess the rule for the sort and to determine if additional shape cards could be added to the group. 9. If time allows, instruct student groups to sort their shape cards in different ways. 10. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate small group discussions, emphasizing the use of formal vocabulary as students describe and explain their sorts. 7
Daily Routines
Daily Routines
Instructional Procedures: 1. Instruct students to determine how many children are present with the displayed Arithmetic Rack. Allow students to observe the rack and determine the attendance count. Facilitate a class discussion for students to share their total and explain the strategy they used to find the total. Ask: • How many tens are in the number of students present? Answers may vary. • How many ones are in the number of students present? Answers may vary. 2. Using the displayed Wall Calendar, facilitate a class discussion about the calendar. Ask: • How many days are in one week? (7 days) • How many days are in two weeks? (14 days) • How many days are in three weeks? (21 days) • How many days are in four weeks? (28 days) • Is there the same number of days in a month as there are in four weeks? (no) Explain. Answers may vary. Except for February, there are more than 28 days in each month; etc.
MATERIALS • Arithmetic Rack (1 per teacher) (previously created) • Wall Calendar (1 per teacher) (previously created)
Evaluate 1
MATERIALS • Two- and Three-Dimensional Figure Collection (1 per student) (previously created)
Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. Performance Indicator: Sort a variety of two- and three-dimensional geometric figures by their defining attributes. Orally explain the sorting process. Identify and describe orally five teacher-selected figures using formal geometric vocabulary. (1.6B, 1.6C; 1.11A; 1.12A, 1.12B; 1.13) 3H ©2012, TESCCC
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2012-2013 Enhanced Instructional Transition Guide Mathematics Grade 01 Unit 13 Suggested Day
©2012, TESCCC
Suggested Instructional Procedures
04/30/13
Grade 1/Mathematics Unit 13: Possible Lesson 01 Suggested Duration: 7 days
Notes for Teacher
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