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MATH UNIT CURRICULUM MAP OVERVIEW

Unit Title: __ Geometry Grade Level: _Second____________ Implementation Time Frame: _3 weeks and 2 days___________Brief Description of Unit: Students will be introduced to geometry through exploring different polygonal shapes, both 2-D and 3-D.

Theme, Enduring Understandings, Inquiry Questions and MisconceptionsTheme: Geometry Enduring Understandings:

Students will investigate characteristics and properties of two- and three- dimensional geometric shapes.

Students will use geometry to help describe, represent, and make sense of their environment.

Students will understand spatial reasoning and geometric modeling used to solve problems.

Students will develop an understanding of the relationship between solid or hollow figures and plane figures.

Essential Questions: What is a shape? What are the properties of shapes? How is the world of geometry

connected to the world of numbers?

Misconceptions: A larger space means a larger angle. Common shapes are not recognized

unless they are upright or in their usual orientation.

A regular shape is one that is common.

The tallest shape always has the greatest area.

Standards-based Essential Skills & Concepts to be Targeted Throughout the Unit

Common Core Critical Area to be Addressed: 2. G. Geometry- Reason with shapes and their attributes: Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation from understanding area, volume congruence, similarity, and symmetry in later grades.

Students will know …Common Core State Standards for Mathematics:1. Recognize and draw shapes having specified attributes, such as a given

Students will be able to …….Common Core State Standards Mathematical Practices:1. Make sense of problems and persevered in solving them.

Maniace (2012) Page- 1

number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.

How Students Will Demonstrate Their UnderstandingAssessment Evidence

Diagnostic Assessment Description (at the beginning of the unit):Pre-assessment of the geometry unit. The pre-assessment contain 5 questions which should help diagnose the class’s prior knowledge on geometry.

Summative Assessment Description (at the end of the unit):Post-assessment of the geometry unit. The post-assessment will be the same as the pre-assessment, except in different order. It will assess the knowledge that students gain throughout the unit. It can be used to compare to the pre-assessment. This comparison can show how the students’ understandings have grown though out the course of the unit.

Formative Assessments (brief description of assessments throughout the unit, i.e. Observation Checklists, Journal Entries, Discussions, etc.):Students will be assessed daily on an observation checklist. Each lesson has certain objectives the teacher will be checking to see if students are achieving. If there are students who are constantly not grasping a concept, or many students are not grasping the concept, the teacher should adjust the lessons.Students will also be creating various geometric objects and completing homework assignments which will demonstrate their understanding and how successful instruction is going.Students will also have the following formative assessment activities: Sorting Shapes by Number of Sides, Is it a Rectangle?, Faces of a Geoblock.

Unit PlanPacing Guide

SUNDAY MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY

Pre-Assessment and Glogster introduction on Geometry-40 minutes

Geoblock Faces-35 minutes(BrainPopJr. Quiz)

Geoblock Faces-45 mintues(Homework Assigned)

Working with Geoblocks-55 minutes

Sorting Geoblocks-50 minutes

Addition Combining Assessment: Sorting Sorting


Ways to Fill-45 minutes

Shapes-65 minutes

Sorting Shapes by Number of Sides-60 minutes(Homework Assigned)

Quadrilaterals-55 minutes

Quadrilaterals pt 2-35 minutes(Homework Assigned)

Ordering Rectangles-60 minutes

Building Rectangles-60 minutes

How Many Rectangles?-60 minutes(Homework Assigned)

Assessment: Is it a Rectangle?-60 minutes

Making Boxes from Rectangles-60 minutes

Assessment: Faces of a Geoblock-55 minutes

Post-Assessment- 40 minutes

Note: All lesson plans are derived from Investigation in Number, Data, and Space which Stadium Drive Elementary school has an license for. I have made a few adjustments and additions, but the lessons follow the basic structure of Investigations. All worksheets, Geoblocks, task cards, and plane shapes come from Investigations.

TERC. (2012). Investigations in Numbers, Data, and Space. Cambridge: National Science Foundation.


Unit: GeometryTitle: Pre-AssessmentMain Focus Points: Students will demonstrate their background knowledge of geometry.Resources needed for the lesson: Pre-Assessment worksheet for each student, document camera,

Glogster poster, privacy shield, Glogster websiteVocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, rectangle,

rectangular prismTime Required: 40 minutesEnvironment: Students sitting individually sitting at desks, students gathered in front of

document cameraProcedures:

1. Pre-Assessment: Geometrya. Say: “Today we are going to start a new math unit. We will be learning geometry.

Before we start our new unit each of you will be doing a pre-assessment. Please do not stress too much about this assessment. The only purpose of it is to see what each of you know about geometry. I will use this information to determine how I will teach you all.”

b. Make sure each student has a privacy shield and distribute the pre-assessment test.c. To grade the pre-assessment, use the answer key which shows how much each

correct answer is worth. Use the information provided by the pre-assessment to plan instruction for your students.

2. Activity: Glogster Poster Presentationa. After collecting the pre-assessment worksheets. Gather all the students together in

front of the document camera. Explain how the pre-assessment showed a preview of what to expect for this unit.

b. To help prepare the students for the unit, prepare a Glogster poster which can be used throughout the unit. The Glogster poster should include videos used to explain the unit further. It should include practice problems, and websites which students and parents can reference for additional help.


c. While having students together, go over the different features of Glogster and explain how you will be using this poster throughout the unit. Explain to students that you will be emailing the Glogster to each of their parents and will be including it on the class website.

Pre-Assessment: Geometry Name:

Number:

Score: /10 points Date:

1. Draw a line to match the 3D object to their 2D look alike:


2. Circle the polygon?

3. Circle the rectangles?


4. Explain two attributes which makes a shape a rectangle:

5. How is a rectangular prism different from a rectangle?

Pre-Assessment: Geometry Name: Answer Key


Number:


1. Draw a line to match the 3D object to their 2D look alike ( each correct match is 1 point):

2. Circle the polygon (1 point)?


3. Circle the rectangles (each rectangle is a point)?

4. Explain two attributes which makes a shape a rectangle (2 points- one for each correct attribute):

-Each angle is 90 degrees

-The sides parallel to each other are equal

-Has two pairs of parallel lines

6. How is a rectangular prism different from a rectangle (1 point, bonus points for extra reasons)?

-A rectangular prism is a 3-D solid of a rectangle.

-A rectangle is a plane shape.


Unit: GeometryTitle: Geoblock FacesMain Focus Points:

Students will identify names and attributes of 2-D and 3-D shapes.Students will attend to features of 3-D shapes, particularly the number of shape of faces.Students will draw 3-D shapes.

Resources needed for the lesson: Document camera, BrainPop Jr. Video: http://www.brainpopjr.com/math/geometry/planeshapes/preview.weml, Prism Geoblocks, drawing paper for each student, Student Math Homework “Shape of a Face,” glogster poster.

Vocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, face.Time Required: 2 Days (1-35 min session, 1-45 min session)Environment: Students sitting individually sitting at desks

Procedures:1. Motivation: BrainPop Jr. Video (15 minutes)

a. Turn on the projector to display the computer screen on the white board. Click on your BrainPopJr.link for plane shapes found in your Glogster poster. Play the video.

b. After the video do the interactive quiz with the students. Observe student’s understandings by having them vote on answers. Make notes of students who may not have an understanding of the content.

2. Activity: Introducing Quick Images: Shapes (15 minutes)a. Say: “Today we are going to look at some Quick Images, but instead of looking at

dot patterns and Ten-frames like we did in our last unit, we are going to look at some shapes. I’d like you to watch carefully because I’m going to show you a shape for just a few seconds. Then I’ll hide it and you will try to draw the shape you just saw.”

b. Show a square about for five seconds on the document camera and then remove the shape. Ask students to quickly sketch what they saw. After students have put their pencils down, show them the shape for another five seconds and ask them to look carefully again. They can then revise their shapes based on their second look. Finally, keep the shape on the document camera and leave the image visible while students make any final revisions.

c. Ask the students to describe the shape, ask them about its number of sides. Ask them about the angles.

d. Repeat the same procedure with a triangle. When students have finished drawing, ask the same questions again.

e. Next, try a somewhat more difficult shape, perhaps the trapezoid or a right triangle. Then ask some more detailed questions.

i. What did you notice the first time you saw the shape? Could you remember the whole shape? What happened when you saw the shape the second time? Did that help you add anything or change anything?

f. Say, “All of the shapes we have been looking at are closed shapes with straight sides, and they all have corners or angles. Mathematicians have a name for these


http://www.brainpopjr.com/math/geometry/planeshapes/preview.weml

types of shapes. They are called polygons. Polygon means a shape with many sides.”

3. Activity: Looking Closely at Geoblocks (45 minutes)a. Draw a rectangle on the white board.b. Say: “For the next few weeks, we are going to be working on geometry. Does

anyone have an idea about what geometry is? What types of activities might we be doing? What kind of materials do you think we might use?” (discuss)

c. Point to the rectangle that you just drew and hold up a large rectangular prism Geoblock.

d. Say, “I have drawn a rectangle on the board. This block that I’m holding is called a prism. How are the rectangle and the prism different?” (discuss)

e. “Sometimes we will be working with flat shapes like the rectangle. They are called two-dimensional shapes. Other times we will be using solid objects like the Geoblocks. They are called three dimensional shapes.”

f. Pass around a set of Geoblocks and have each student take out one block and examine it carefully. Ask students to describe one attribute of their block. List these on the white board. Discuss their findings.

g. Have students get white paper to draw on and a pencil to draw with out.h. Have students to draw a picture of their Geoblock, ask them to share their work

and say what was easy or hard form them while drawing the block. Ask them to describe what it means to make something look three-dimensional on paper means that it pops out at you, it doesn’t look flat, or it looks like something you can hold.

i. Encourage them to describe what it is like to draw something that is three-dimensional on a flat surface and what they did to try to make it look three dimensional. What did you notice about your block that helped you draw it?

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Does student participate in BrainPop Jr. video quiz?-Do students’ drawings contain the two-dimensional shapes of each of the faces of the block?-Are you able to identify the block by looking at the drawing?

Homework: Students find and record objects in their surroundings that have a face that matches one of the shapes on “Shapes of a Face” worksheet.


Unit: GeometryTitle: Working with GeoblocksMain Focus Points:

Students will attend to features of 3-D shapes, particularly the number and shape of faces.Students will draw 3-D shapes.

Resources needed for the lesson: The Greedy Triangle by Marilyn Burns, Geoblocks, “Double Arrays” Worksheet, document camera, Geoblock task cards, cards containing primary numbers.

Vocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, face.Time Required: 55 minutesEnvironment: Students sitting on carpet, students sitting individually sitting at desks, students

going to 3 math stations in groups.

Procedures:1. Motivation: Read Aloud- The Greedy Triangle by Marilyn Burns (10 minutes)

a. Gather the students on the carpet for a read aloud. Read The Greedy Triangle by Marilyn Burns. Students will see how different polygons differ from each other and where polygons are found in real life.

2. Activity: Introducing Find the Block (10 minutes)a. Return students back to their seats and turn on the document camera.b. Say “Yesterday we looked very closely at the faces of the Geoblocks. Take a look

at this card. This card shows all the faces of one Geoblock, and was made by tracing around each face. Can you figure out by looking at this card how many faces or sides the Geoblock had?”

c. In addition to noticing the number of sides, ask students to describe the shape of the faces on the block. Then, using this information, ask them to select the Geoblock that the task card represents.

d. Once the correct block has been chosen, show students how every face of the block can be matched to one of the outlines on the card. Show students some of the task cards for this activity. Clarify for students that each card represents only one block.

e. Say “This activity is called Find the Block. In Math Workshop, you will work with a partner to find the block. Each station has Geoblocks and multiple decks of task cards. Each pair of students will work with a deck of task cards. Decide with your partner which card to work on and try to find the block that matches that card. Once you have each found a block. Compare them and then prove to each other that yours is the correct block by showing how each side matches the outlines on the card.”

3. Math Workshop: Blocks and Doubles (30 minutes)a. Find the Block: Students work in pairs to match a Geoblock to the face outlines

on a task card. Follow the same lesson as in the Find the Block activity above.b. Drawing Geoblocks: Students build small constructions with two-three Geoblocks

and then draw what they have built as accurately as they can on drawing paper. Encourage students to draw their construction form more than one angle.

c. Double Arrays: Students draw a primary number card from the pile and color in that number of squares in one row on the “Double Arrays” worksheet grid. They


then double that number and color in the same number of squares in a second row directly underneath. They record an equation that illustrates the double.

4. Checking for understanding (5 minutes)a. Gather students together to discuss what they have learned. Ask students to share

what skills they demonstrated while working at the different math stations.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Can students identify one block that has faces that match the outlines on the card?-Do students’ drawings contain the two-dimensional shapes of each block face they used?-Are students able to accurately draw an array with doubles the number or squares that are on the card?-How do students calculate the double of a number?-Can students write an equation that represents the array they have drawn?

Differentiated Instruction (Find the Block):Some students may need help in understanding that each card represents one block. Initially, some students may benefit from working with an even smaller subset of blocks.

If students are having difficulty understanding the task, consider selecting the blocks that match the task cards and seeing whether the student can match the correct block to each card.

Some students may be adept at “seeing” the block by just looking at tis two-dimensional image. Show these students a task card and see whether they can describe what features the block will have.

Differentiated Instruction (Blocks and Doubles)If some students are having difficulty drawing in 3-D, you might want to ask them about the shapes of the faces and where they see them. For instance, does the student see that there is a triangle in front and a rectangle on the side?

Differentiated Instruction (Double Arrays)Some students will need larger-sized grids. Others will benefit from building the doubles with cubes or tiles, rather than coloring them.

Challenge students who are ready to name the double after they pick the card, but before they color the grid paper.


Unit: GeometryTitle: Sorting GeoblocksMain Focus Points:

Students will describe attributes of and sorting 3-D shapes.Students will identify a 3-D shape by touch.

Resources needed for the lesson: Geoblocks, 8.5” x 11” sheet of paper, two 11” x 17” sheet of paper, markers, paper bags (enough students to partner up with), drawing paper, student computers, Glogster posters.

Vocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, face.Time Required: 50 minutesEnvironment: Students sitting in a circle on the carpet, students working in partners, students

working at math stations and student computers.

Procedures:1. Activity: Sorting Geoblocks (20 minutes)

a. Call the class together in a circle on the carpet. Pass a set of Geoblocks around and have each student take one block.

b. Say “Look at your block. Describe your block to the person sitting next to you, and then listen while your partner tells you about his or her block. How are your blocks alike? How they are they different?”

c. Provide time for students to describe their blocks and then call the class together. Ask one student to stand, hold up his or her block, and describe one of its attributes. Other students should hold up their blocks if the statement is also true for theirs. Students may describe their blocks in imprecise ways.

d. Place one 8 ½” x 11” sheet of paper and two 11” x 17” sheets in the center of the circle. Label one 11” x 17” sheet, “match” and the other, “Don’t Match.”

e. Say, “I would like a volunteer to put his or her block on the small paper and then tell us one thing that you notice about your block.” If necessary, ask the students to clarify the descriptions.

f. The rest of the students determine whether the statement also applies to their block. They then place their blocks on either the “Match” or “Don’t Match” sheet. Students examine both sets to see whether the blocks are correctly placed and then take back their blocks.

g. Have different students try this several more times. Notice the attributes students suggest and know that there will be times when everyone’s block will match the attribute.

2. Activity: Introducing Mystery Block (5 minutes)a. Introduce this activity by asking two volunteers to demonstrate.b. While one partner’s back is turned, the other chooses a block and puts it in a bag.

The first partner then reaches in the bag without looking, feels the block, and describes at least three of its attributes. Then he or she finds an identical block in the set.

c. Break the students into partners and have them practice identifying the mystery block.

3. Math Workshop: Blocks and Doubles (25 minutes)a. Mystery Block: follow instructions from activity two from today’s lessons.


b. Find the Block: follow instructions from “Working with Geoblocks” lesson.c. Drawing Geoblocks: follow instructions from “Working with Geoblocks” lessond. (Use Glogster poster to access)National Library of Virtual Manipulatives:

http://nlvm.usu.edu/en/nav/frames_asid_270_g_1_t_3.html?open=instructions&from=topic_t_3.html - students use the computer and explore shape attributes.

e. (Use Glogster poster to access) NCTM Illuminations: http://illuminations.nctm.org/ActivityDetail.aspx?ID=70- students use the computer to learn about geometric solids and their properties.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Do students suggest geometric attributes, such as the number or shape of faces?-Are students able to find a matching block without looking at the block in the bag?-Do they need to confirm their match by looking at the blocks?


http://illuminations.nctm.org/ActivityDetail.aspx?ID=70-

http://nlvm.usu.edu/en/nav/frames_asid_270_g_1_t_3.html?open=instructions&from=topic_t_3.html%20

http://nlvm.usu.edu/en/nav/frames_asid_270_g_1_t_3.html?open=instructions&from=topic_t_3.html%20

Unit: GeometryTitle: Ways to FillMain Focus Points:

Students will cover a region, without gaps or overlaps, using different shapes.Students will combine shapes to make new shapes.

Resources needed for the lesson: Pattern blocks, document camera, “Ways to Fill: Pattern 1” worksheet, Glogster poster,

Vocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, face.Time Required: 45 minutesEnvironment: Students sitting individually at their desks.

Procedures:1. Activity: National Library of Virtual Manipulatives- Tangrams (5 minutes)

a. Use the projector to display your computer screen. Open up your Glogster poster for the unit and click on the National Library of Virtual Manipulatives link for Tangrams (http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities&from=topic_t_3.html) .

b. Demonstrate how Tangrams work and how they are like puzzle pieces. Call up some students to help you with the puzzle.

2. Activity: Ways to Fill (25 minutes)a. Distribute a set of pattern blocks to each table or group. Give each student a copy

of “Ways to Fill: Pattern 1” and place one copy on the document camera. b. Say, “Look at the outline at the top of the page. How many sides does this shape

have?” Do not spend a long time on this question, but see whether students are able to count the number of sides of this shape.

c. Try to fill in this shape using one type of pattern-block shape. Then try filling the block with multiple types of pattern blocks.

d. Have the students fill in the outline several ways- using only one type of pattern block at a time- and record the ways that work. Then move on to using two shapes to fill the outline and again record the number and type of shapes they use. They will continue to work on this and another similar sheet during the next session. After most students have finished filling the outline with one shape, call the class together for a discussion.

3. Discussion: Combining Shapes (15 minutes)a. Begin the discussion by asking students to share the ways that they filled Pattern 1

with only one type of pattern block. Record these on the board using the names of the shapes, such as two hexagons, four trapezoids, etc.

b. Once students think that they have shared all the ways, ask them to explain why they think these combinations are possible.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Do students notice relationships among the various?


http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities&from=topic_t_3.html


-Do students see that some shapes (the square and thin rhombus) will not fit on the patterns no matter how they are arrange?-Do students have a recording method that is accurate and easy to understand?

Differentiated Instruction (Ways to Fill):Some students may need clarification about what it means to “use two types of blocks” to fill the specified outline. Demonstrate by selecting two shapes- a triangle and rhombus. Ask students to fill the outline using only those shapes.


Unit: GeometryTitle: Combining ShapesMain Focus Points:

Students will combine 3-D shapes to make a 3-D whole.Students will identify a 3-D shape by touch.Students will cover a region, without gaps or overlaps, with a single shape or multiple shapes.Students will develop fluency with the doubles combinations

Resources needed for the lesson: Geoblocks, document camera, “Build the Geoblock” worksheets, “Ways to Fill: Pattern 2” worksheet, SmartBoard, student computers, Glogster poster.

Vocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, face.Time Required: 65 minutesEnvironment: Students sitting individually at their desks, students working in groups at math

stations.

Procedures:1. Activity: Using the Smart Board (5 minutes)

a. Using the SmartBoard, draw two solid squares and place them side by side. The shape you now have is a rectangle. Ask students what would happen if you split the rectangle in half? Demonstrate how “cutting” the rectangle in half will make either two smaller rectangles, or a square. Demonstrate how this can be done with other shapes.

2. Activity: Introducing Build the Geoblock (10 minutes)a. Say, “Yesterday, when we worked on “Ways to Fill,” you combined pattern

blocks to fill a region. Many of you found that you could combine certain shapes to make other shapes, such as combining two red trapezoids to make a hexagon shape. In the Math Workshop today, you will continue with that activity, but you will also work on combining shapes to make other shapes. This activity is called Build the Geoblock.”

b. Hold up, or place on a table where everyone can see, the rectangular prism. c. Say, “If I could glue Geoblocks together, how could I build a block that is the

same size and shape as this one? One way would be to glue these two blocks together.”

d. Hold up two 4 cm cubes to show that they could be glued together to make a block the same size and shape as the rectangular prism.

e. Use “Build the Geoblock” worksheets to demonstrate how to find the Geoblocks that match the ones shown on the sheets. Explain that students should find the Geoblock that fits each of the three illustrated blocks. They should then determine how many different ways they can combine other Geoblocks to make a block of the same size and shape.

f. Encourage students to use their experience from the “Drawing Geoblocks” activity to record their work.

3. Math Workshop: Combining and Covering (50 minutes)a. Build a Geoblockb. Ways to Fill: follow “Ways to Fill” lesson, use “Ways to Fill: Pattern 2.”


c. Mystery Block: follow “Sorting Geoblocks” lesson.d. (Use Glogster poster to access)National Library of Virtual Manipulatives:

http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities&from=topic_t_3.html- students use the computer and explore building shapes.

e. (Use Glogster poster to access) NCTM Illuminations: http://illuminations.nctm.org/ActivityDetail.aspx?ID=70- students use the computer to learn about geometric solids and their properties.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Do students randomly choose smaller blocks and try to build a larger one?-Do they seem to “see” blocks that are half of a block, and put two of them together?-Are students comfortable with their attempts to draw the blocks they used?-Do student notice relationships among the various blocks-Do students have a recording method that is easy to understand?

Differentiated Instruction (Combining and Covering):If students are finding it difficult to draw their block combinations, suggest that they put together as many combinations as possible and then show you their work. For some students, drawing the block may be such a difficult task that they may be less willing to work on the task of combining them.


http://illuminations.nctm.org/ActivityDetail.aspx?ID=70-



Unit: GeometryTitle: Assessment: Sorting Shapes by Number of SidesMain Focus Points:

Students will describe attributes of and sorting 2-D shapes.Students will identify categories for 2-D shapes.Students will sort polygons by the number of sides.

Resources needed for the lesson: If You Were a Polygon by Maric Aboff, set of Shape Cards, envelope of shape card (enough for each group of students), Assessment checklist, “Shapes at Home” worksheet.

Vocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, face.Time Required: 60 minutesEnvironment: Students sitting in circle on the carpet, students sitting with groups, students sitting

with partners

Procedures:1. Motivation: Read aloud- If You Were A Polygon by Marci Aboff. (10 minutes)

a. During this read aloud students will reinforce the definition of a regular polygon and show the meaning of an irregular polygon, the parts of a polygon and different shapes of a polygon.

2. Activity: Sorting Shape Cards (20 minutes)a. Gather students in a circle so that they can all see your set of Shape Cards.b. Say, “The cards in this envelope have different shapes. As I come around, I would

like you to reach in, take out one card, and place it in front of you. Look at your shape and think about how you can describe it.”

c. When all students have a card, ask a volunteer to place his or her Shape Card in the center of the circle and share one thing about it.

d. Write the sorting rule on the board or on a large sheet of paper. Students with shapes that match this rule should pace their cards in the center of the circle. Students with shapes that do not match should place their cards in front of them so that everyone can see.

e. Say, “Look at all the shapes in the center. Do they all have the attribute of the sorting rule? Look at all the shapes that are not in the center, do they all not have the attribute.”

f. Based on the discussion, students may want to adjust where they placed their shapes. When everyone agrees that the shapes of sorted correctly, students retrieve their Shape Cards and place them in front of them. Repeat this activity two more times.

g. Collect the demonstration set of Shape Cards to use later. Have students get in groups of 4-6 and distribute a set of shape cards to each group.

h. Say, “Sort your Shape Cards in at least two different ways. Each time, sort them into two, three, or four groups so that every card has a place. Pick one of the ways you sorted the Shape Cards and write down the labels of your groups. Later we will have a discussion about how you sorted your shapes.”

i. Walk around and observe students while they work. Encourage students to place all the cards in the set into categories. Some students may choose to sort into two


groups as in the previous activity, with one group following a rule and the other not. Others will make several categories.

3. Assessment Activity: Sorting Shapes by Number of Sides (20 minutes)a. During this activity you can observe students as they sort a set of Shape Cards by

the number of sides each shape has. You can record your observations on Assessment Checklist: Sorting Shapes by Number of Sides.

b. Introduce the activity by following up on the previous discussion. c. Say, “Did anybody count the number of sides to sort the shapes? Let’s look at this

shape (a triangle). How many sides does it have? Do all the shapes have three sides? What shape doesn’t have three sides? Now you will sort shapes by the number of their sides. With your partners, you will make three groups: sides with three sides, shapes with four sides, and shapes with more than four sides.”

d. As students are working, check in with each small group to see whether they are in agreement about the category that each shape belongs in.

Homework: Students look around at home to find at least five examples of different shapes. On “Shapes at Home” worksheet they draw a picture of what they found and write the name of the shape.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Do students’ categories allow them to sort all of the shapes?-Do students’ categories allow each shape to be placed unambiguously?-Are students able to come up with different ways to sort the shapes?

Differentiated Instruction (Sorting Shape Cards):If students have difficulty organizing their shapes into groups, suggest that they begin with two or three shapes that they think are the same in some way. Ask them to explain how they are the same. You may need to verbalize the rule for them at first. Once they have placed all of the relevant shape cards, have them focus on the remaining set of cards. Ask questions, such as:

-Which shapes seem to go together? If you’re sorting this way, where does this shape go? What do you call this group of shapes? Why did you place this shape in their group instead of that one?


Unit: GeometryTitle: Sorting QuadrilateralsMain Focus Points:

Students will sort quadrilaterals by angle.Students will identify quadrilaterals as shapes with 4 sides.Students will identify rectangles as 4-sided shapes with 4 right angles.

Resources needed for the lesson: If You Were a Quadrilateral by Molly Blaisdell, Shape cards, chart paper, markers, color tiles one for each student, “Identifying Different Types of Quadrilaterals” worksheet

Vocabulary: angle, right angle, rectangle, quadrilateralTime Required: 55 minutesEnvironment: Students sitting in in groups, students divided into two groups.

Procedures:1. Motivation: Read Aloud- If You Were a Quadrilateral by Molly Blaisdell. (10

minutes)a. In this read aloud students will learn about the quadrilateral and the different

types of shapes that fit the quadrilateral rules.2. Discussion: Looking at Angles (15 minutes)

a. Distribute a set of Shape Cards and one color tile per student to each small group. Ask students to make a group of shapes that have four sides.

b. Say, “Look at your shapes with four sides. What do you notice about these shapes?”

c. Once students have offered their observations, draw their attention to the angles of the shapes.

d. Say, “Look at the rectangle shape card. I’d like you to point to the place where two sides of this polygon come together. Does anyone know what this is called? (Pause for answers) Mathematicians call this an angle. Sometimes students, and even adults, call this a corner. How many angles does this shape have?”

e. Ask students what they notice about the angles of a rectangle. Students may say that all the corners are the same. They may describe them as shaped like an L or a square.

f. Say, “This kind of corner is very special and so it has a special name. Does anyone know what its name is?” (Right angles).

g. Say, “Let’s look at the square titles that I gave to each of you. Pick your tile up and feel the corners. What do you notice about the angles, or corners, of the square tile?” (discuss)

h. Say, “Now let’s look the rhombus shape card. Does this shape have right angles? How can we tell?” (discuss)

i. Say, “Now let’s look at the diamond shape card. Does this shape have right angles? How can we tell?” (discuss)

3. Activity: Creating a Quadrilateral Chart (30 minutes)a. Place the students into two groups. Say, “Now we’re going to sort all the shapes

with four sides. One group will be “4 sides and 4 right angles.” The second group will be “4sides, but not 4 right angles.”


b. When groups are done sorting their shapes, bring the whole class together. Show students the chart that you have prepared. (A table with one column heading: 4 Sides and 4 Right Angles and another column heading: 4 Sides, but not 4 Right Angles.)

c. Tape an example of each group in the corresponding sides of the chart.d. Say, “We are going to make a class chart of these two categories of shapes with

four sides. We already discussed a rectangle and decided it has four sides and four right angles, and we decided a rhombus has four sides, but not for right angles.”

e. Ask a student to choose a four-sided shape and say which category it belongs in.f. If students agree, add that shape to the chart accordingly. Where there is a

disagreement, have students explain how they determine whether an angle is right or not and show how they measured the angles of the shape.

g. Ask a different student to choose another four-sided shape and to say which category it belongs in. Continue until all four-side shapes appear on the chart.


Unit: GeometryTitle: Sorting Quadrilaterals pt. 2Main Focus Points:

Students will sort quadrilaterals by angle.Students will identify quadrilaterals as shapes with 4 sides.Students will identify rectangles as 4-sided shapes with 4 right angles.

Resources needed for the lesson: If You Were a Quadrilateral by Molly Blaisdell, Shape cards, chart paper, markers, color tiles one for each student, “Identifying Different Types of Quadrilaterals” worksheet, Glogster poster, BrainPop video: http://www.brainpop.com/math/geometryandmeasurement/angles/ , the Geometry Rap (Math Song 2 nd Grade : http://www.youtube.com/watch?v=15HvFEANERA

Vocabulary: angle, right angle, rectangle, quadrilateralTime Required: 35 minutesEnvironment: Students sitting in in groups, students divided into two groups.

Procedures:1. Motivation: The Geometry Rap (Math Song 2 nd Grade) (5 minutes)

a. Use your Glogster poster to access the YouTube video of The Geometry Rap (Math Song 2 nd Grade).

b. Students will get a review of some of the Geometry facts they have already learned in this unit.

2. Discussion: What’s a Rectangle? (15 minutes)a. Say, “We’re going to talk about the names mathematicians use for the shapes on

our chart. You might be surprised by some of them. Does anyone know the names for all the shapes in our category, “4 Sides and 4 Right Angles?”

b. Ask whether there is a name for all the shapes in this category. If some students say that all the shapes are called rectangles, let them explain why this is so. Allow students to debate this question for several minutes.

c. Say, “I know this might be surprising to many of you, but mathematicians say that rectangles are shapes with four sides and four right angles. All of the shapes in our first category have four sides and four right angles, so they are all rectangles.

d. Write “rectangle” under the label, “4 Sides and 4 Right Angles.” Then allow students to respond. The chart will remain on the wall for the rest of the unit so students can ponder this.

e. Say, “The word that mathematicians use for all four-sided shapes is quadrilateral. Has anyone heard the word quadrilateral before?

f. Write “quadrilateral” at the top of the chart. Then write “Other Quadrilaterals under the label, “4 Sides, but not 4 Right Angles.” Ask students whether they know any other names of shapes on the chart. They might offer trapezoid, parallelograms, or rhombus. Hang the chart in a place in the room where students will be able to see it for the rest of the unit.

g. Ask students to put away their four-sided shape cards and to take out the remaining cards- the ones with three sides and more than four sides.

h. Say, “What do you notice about the angles, or corners, of these shapes? Do any of these shapes have right angles?

3. Activity: BrainPop Video on angles (15 minutes)


http://www.youtube.com/watch?v=15HvFEANERA

http://www.brainpop.com/math/geometryandmeasurement/angles/

a. Turn on the projector to display the computer screen on the white board. Click on your BrainPopJr. link on angles found in your Glogster poster. Play the video.

b. After the video do the interactive quiz with the students. Observe student’s understanding by having them vote on answers. Make notes of students who may not have an understanding of the content.

Homework: Students identify and color specific types of quadrilaterals red or blue on “Identifying Different Types of Quadrilaterals” worksheet.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Can students identify the shapes that have right angles?-Do student recognize right angles that are not oriented with horizontal and vertical sides?-Can students recognize a right angle even if the sides of the shape are shorter than the sides of the square tile?


Unit: GeometryTitle: Ordering RectanglesMain Focus Points:

Students will define biggest in different waysStudents will order rectangles from biggest to smallestStudents will cover rectangles with arrays of tiles

Resources needed for the lesson: “Which is Biggest” worksheets, color tiles for each student, document camera, scissors, blank paper.

Vocabulary: angle, right angle, rectangle, quadrilateral, biggest, smallestTime Required: 60 minutesEnvironment: Students working in pairs

Procedures:a. Activity: Ordering Rectangles (30 minutes)

a. Distribute scissors and have students work in pairs to cut apart the rectangles on “Which is Biggest?” worksheet. Provide each student with blank paper.

b. Ask students about the name of the shapes on these pages and ask how they know that these are rectangles. If they do not mention that a rectangle has four sides and four right angles, point to the chart that you made in the previous session and remind them.

c. Say, “When you are finished cutting out your rectangles, work with your partners to decided how to put your rectangles in order. Start with the rectangle that you think is biggest, and then order them from the next biggest to the smallest. Then, on your paper, write the order. When everyone has finished, we’ll discuss what you’ve done.”

d. Hold a discussion with all the students to see how students organize their rectangles.

e. A few students may have arranged the rectangles differently, for example, “lying down,” or by area. Emphasize that there are different ways to define biggest.

b. Activity: Covering Rectangles (30 minutes)a. Each pair of students will need access to a set of color tiles. With rectangles still

visible from the previous activity, pose the following question: “Suppose these rectangles are chocolate bars. Which one would have the most chocolate? Which would have the least? How could you find out?”

b. Demonstrate, finding out the area of the rectangle, by having one student cover a rectangle with tiles. Record the total on the board. Even if area was one of the attributes used to order the rectangles in the previous area, it is important that all students practice covering the rectangles with square tiles.

c. Discuss with the class the number of rows and the size of the rows of a rectangle. Place the rectangle on the document camera and fill in the first row so that everyone can see how many tiles it has.

d. Say, “How many tiles are in the second row?”e. Keep adding rows and counting the tiles in each row. Then count the number of

rows.f. Say, “Do you think the other rectangles also have the same number of tiles in each

row? Let’s try it with another rectangle.”


g. Put another rectangle on the document camera and fill the first row and the second row. After filling the whole rectangle, ask the student which rectangle would have more chocolate.

h. Encourage students to discuss whether they think these two shapes are the same size or different sizes. The meaning of biggest depends on the attribute that is being compared and the context of the situation.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Do pairs of students agree on the attribute they are using to compare rectangles?-Do students consistently apply the same attribute to order the set of rectangles?-Do students recognize that, when considering a different attribute, the rectangles may be ordered differently?


Unit: GeometryTitle: Building RectanglesMain Focus Points:

Students will arrange squares tiles in rectangular arrays.Students will describe rectangular arrays of tiles.

Resources needed for the lesson: BrainPop Jr. video on area: http://www.brainpopjr.com/math/measurement/area/preview.weml , Glogster poster, color tiles, two sheets of blank paper to each student, “Inch Grid Paper” worksheet, student computers, document camera.

Vocabulary: angle, right angle, rectangle, quadrilateral, biggest, smallest, column, congruent.Time Required: 60 minutesEnvironment: Students sitting individually at their desks, students in groups working at math

workshop stations.

Procedures:1. Motivation: BrainPop Jr. Video (15 minutes)

a. Turn on the projector to display the computer screen on the white board. Click on your BrainPopJr. Link for area found in your Glogster poster. Play the video.

b. After the video do the interactive quiz with the students. Observe student’s understanding by having them vote on answers. Make notes of students who may not have an understanding of the content.

2. Activity: Describing Rectangles (15 minutes)a. Distribute color tiles and two sheets of blank paper to each student.b. Say, “We are going to put color tiles together to make our own rectangles. Take

six tiles and make a rectangle with them. Then cover the rectangle with a sheet of paper.”

c. Have every student build a rectangle and then cover it with a blank sheet of paper. Take a quick peek at your rectangle and cover it up again. Then draw a picture of it on the other sheet of paper. Show all six tiles in your drawing. Have students follow your lead.

d. Say, “Now take the cover off your tiles. Compare your drawing to the titles. If you need to make changes, draw a new picture beside your first one. This time, you don’t need to cover your tiles. Who can describe the rectangle they made so others can tell whether they made the same one?”

e. As a volunteer describes a rectangle, build it on the overhead projector or draw it on the board. If the description is not clear, encourage the student to tell you more about the rectangle. Ask the class if they think that is the rectangle that the student made and if anyone else made the same rectangle. Ask students if they can describe the rectangle in different ways. Record what they say on a chart paper to leave up during math workshop.

f. Use this opportunity to introduce the word column.g. Repeat this activity with a different student’s rectangle.h. It is common for students to see two rectangles with the same dimensions as

different, if one of them is rotated 90 degrees. Introduce the term congruent.


http://www.brainpopjr.com/math/measurement/area/preview.weml

i. Say, “When two shapes are the same size and shape, we say they are congruent. It doesn’t matter whether they are turned in different directions. They are congruent to one shape could fit exactly on top of the other one.

3. Math Workshop: Rectangles (30 Minutes)a. Describing Rectangles: Students use color tiles to make several rectangles. They

choose one and draw it on the bottom half of Inch Grid Paper, staying on the dotted lines. They fold the of half of the paper over their drawing and write a description of their rectangle on the top flap so that someone else can reproduce it without looking at the drawing. Point out to students if they need help describing their rectangles, they can use the chart they made in the first activity.

b. Rectangle Riddles: Students use color tiles to make a rectangle for each riddle on “Rectangle Riddles” worksheet. They draw the rectangular array below the riddle. When they have finished, they write their own rectangle riddles.

c. (Use Glogster poster to access) IXL: http://www.ixl.com/math/grade- Students can explore geometry sections T.1, T.2, T.3, and T.9.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Do students recognize that a rectangle arrangement of tiles must have equal rows lined up to make equal columns?-Do students recognize that rectangles may have the same dimensions but different orientations?-Are students able to make rectangular arrays (arrangements with equal rows and columns)?-Are students able to reproduce their rectangles on grid paper?-Do students give enough information in their descriptions to allow someone else to reproduce their rectangles?

Differentiated Instruction (Describing Rectangles):If students have difficulty copying their rectangles, suggest that they place the tile on the graph paper and trace around them. If students have trouble writing descriptions, suggest that they first tell you how to build their rectangles. If they still have difficulty, structure the writing for them. For example, “My rectangle has rows. There are tiles in each row.”


http://www.ixl.com/math/grade-

Unit: GeometryTitle: Drawing RectanglesMain Focus Points:

Students will draw rectangles by attending to the lengths of the sides.Students will make different rectangular arrays using the same number of tiles.Students will describe rectangular arrays of tiles.

Resources needed for the lesson: Geoboards, rubber bands, “Geoboard Dot Paper” worksheet, “Inch Grid Paper” worksheet, student computers, Glogster poster, “Rectangle Riddles” worksheets, document camera.

Vocabulary: angle, right angle, rectangle, quadrilateral, biggest, smallest, column, congruent.Time Required: 60 minutesEnvironment: Students sitting individually at their desks, students in pairs at their seats, students

working at Math Stations.

Procedures:1. Activity: Rectangles on the Geoboard (20 minute)

a. Put students in pairs. Give each a Geoboard and each student a sheet of “Geoboard Dot Paper.” Give students time to explore their Geoboards. Encourage them to make rectangles.

b. After about five minutes, bring the class together. Place “Geoboard Dot Paper” up on the document camera and draw a 2 x 4 rectangle.

c. Say, “Yesterday we built rectangles from square and drew rectangles by paying attention to the rows of squares. Today, we are going to draw just the outlines of rectangles. To start, let’s look at the rectangle I’ve drawn on my dot paper. To figure out how long a side is, I count the number of spaces between dots. Build the same rectangle on your Geoboards. Make it so that two opposite sides are four spaces and the other two sides are two spaces.”

d. After students have built the rectangle on Geoborads, ask them about the angles of their rectangles. Create a parallelogram that is not a rectangle on a Geoboard and show the class.

e. Say, “Nobody created a shape like this. What’s the difference between your shapes and this one?”

f. After the brief discussion, ask the students to reproduce their rectangles on “Geoboard Dot Paper.” Have students count the spaces on each side and write that number next to the side. Lead the class through two more examples. Then have students work in pair to create their own rectangles.

g. After removing the “Geoboard Dot Paper,” place a cleaned version of the “Geoboard Dot Paper” and say, “Now, I want directs to draw a rectangle on dot paper.”

h. Mark the spot where you will start drawing. Select one pair of students, and have them give each step of the drawing. For each side, make sure they tell you where to start, in what direction to draw the line, and how far to draw the line. Label the length of each side, and point out that the sides make right angles. Once you have drawn the rectangle, have the other pairs take a new rubber band and represent that rectangle on their


Geoboards. Then have students draw the same rectangles on their own sheet of dot paper. Have another pair of students to give you directions for drawing their rectangle on the doc cam.

2. Math Workshop: Making Rectangles (40 minutes)a. Rectangles on the Geoboard: Students make a rectangle of the Geoboard,

draw the rectangle on “Geoboard Dot Paper” worksheet and identify the length of each of its sides.

b. Describing Rectangles: See Building Rectangles lesson.c. Rectangle Riddles: See Building Rectangles lessond. (Use Glogster poster to access) IXL: http://www.ixl.com/math/grade-

Students can explore geometry sections T.1, T.2, T.3, and T.9.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Are students able to create rectangles on Geoboards?-Are they able to reproduce rectangles on dot paper?-Do students recognize that opposite sides of rectangles have equal lengths?-Do students identify the angles of a rectangle as right angles?



Unit: GeometryTitle: How Many Rectangles?Main Focus Points:

Students will draw rectangles by attending to the lengths of the sides.Students will make different rectangular arrays using the same number of tiles.Students will describe rectangular arrays of tiles.

Resources needed for the lesson: Document camera, colored tiles (12 of the same color for each student), construction paper, “Inch Grid Paper” worksheet, “Only One Rectangle” worksheets, Geoboards, rubber bands, Glogster poster, student computers, “Rectangle Riddles” worksheet.

Vocabulary: angle, right angle, rectangle, quadrilateral, biggest, smallest, column, congruent.Time Required: 60 minutesEnvironment: Students sitting individually at their desks, students working at math stations.

Procedures:1. Activity: How Many Rectangles? (10 minutes)

a. Each student takes 12 tiles of the same color.b. Say, “How many different rectangles do you think can be made from 12

tiles? Make as many rectangles as you can. When you make one, see whether you can make another.”

c. After a few minutes, have the class discuss the rectangles that everyone has made. As students describe a rectangle, draw the array on the doc cam. Next to each one, record students’ descriptions.

d. If students do not suggest a 1 x 12 rectangle, ask them whether they can make a rectangle that uses 12 tiles and is only one tile wide.

2. Math Workshop: Rectangles (50 minutes)a. How Many Rectangles?: Students investigate the number of rectangles

they can make for one or two of the following numbers of color tiles: 16, 18, 24, 36. When they draw or trace around them on “Inch Grid Paper” cut them out and past them on construction paper.

b. Rectangles on the Geoboard: See Drawing Rectangles lesson.c. Describing Rectangles: See Building Rectangles lesson.d. Rectangle Riddles: See Building Rectangles lesson.e. Use Glogster poster to access) IXL: http://www.ixl.com/math/grade-

Students can explore geometry sections T.1, T.2, T.3, and T.9.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Do students create rectangular arrangements of tiles: equal rows and equal columns?-Do students recognize that rectangles can be made of one row of tiles are rectangles?-Do students see that different rectangles can be made from the same number of tiles?-Are students able to make rectangular arrays?-Do students have a strategy for finding different rectangles of the same number?



Homework: Students cut out the paper squares on “Only One Rectangle” and use them to create rectangles for specific numbers of tiles. They can draw the rectangles on the “Only One Rectangle” activity pages.

Differentiated Instruction (How Many Rectangles):If students have difficulty building an array for these numbers, give them a smaller number of tiles to investigate first.If students have made rectangles for one or two of the larger numbers, they can choose a number of their own- from 8 to 36- to see how many different rectangles they can make. Challenge them to think about whether they have found all the possible arrays for a number and how they know when they have them.


Unit: GeometryTitle: Assessment: Is it a Rectangle?Main Focus Points:

Students will construct and describe rectangular arrays of tiles.Students will draw rectangles by attending to the lengths of the sides.Students will identify important features of a rectangle.

Resources needed for the lesson: Colored tiles for each student, “Assessment Activity: Is it a Rectangle” worksheet.

Vocabulary: angle, right angle, rectangle, quadrilateral, biggest, smallest, column, congruent.Time Required: 60 minutesEnvironment: Students sitting individually at their desks.

Procedures:1. Activity: Describing Rectangles? (40 minutes)

a. Say, “Today we are going to think about what makes a good description of a rectangle. We want to know whether the descriptions you wrote are clear enough so that someone else can build the rectangle. Some of you will read the descriptions you wrote to the class without showing the picture. Then everyone will try to build your rectangle with color tiles. We’ll compare the ones we’ve made with one another’s and then with your original drawing.”

b. Choose several students to read their descriptions. Students should compare their rectangles with one another before the reader shows his or her drawing. If students have made different rectangles then the reader, encourage them to share why they think the rectangle they have made is the one that was described. Do this several times and then gather as a class for a discussion.

2. Assessment Activity: Is it a Rectangle? (20 minutes)a. Distribute Assessment: Is it a Rectangle? worksheet. Explain to students that you are

interested in learning more about how they are thinking about rectangles and other polygon shapes. For each shape on the sheet, explain to students that they should say whether it is a rectangle and explain why or why not. Remind students to write as complete an answer as possible.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:-Are students able to reproduce the rectangle when given a clear description?-Are students able to identify what makes a clear description?-Are students able to identify shapes that are rectangles?-Do their written explanations indicate their understanding that a rectangle has four straight sides and four right angles?


Unit: GeometryTitle: Making Boxes from Rectangles?Main Focus Points:

Students will recognize that rectangular prisms have rectangular faces.Students will recognize which faces of a rectangular prism are the same size and shape.Students will construct a rectangular prism from rectangles.Students will compare rectangular prisms.

Resources needed for the lesson: 9”x5”x3” box, box of Geoblocks, tape, “Making Boxes” envelope.

Vocabulary: angle, right angle, rectangle, quadrilateral, biggest, smallest, column, congruent, rectangular prism.

Time Required: 60 minutesEnvironment: Students sitting individually at their desks, students in pairs at their seats.

Procedures:1. Activity: Examining Rectangular Prisms (10 minutes)

a. Show a box that is approximately 9”x5”x3”, such as a shoe box, a cereal box, or another box without square faces. Hold it up or place it where all can see.

b. Say, “Take a look at this box. In some ways it resembles some of the Geoblocks we examined in the beginning of this unit.”

c. Ask a student to go to the box of Geoblocks and find a block that resembles the box.

d. Say, “Let’s compare our box to the Geoblock. In what ways are they the same and in what ways are they different?” (discuss- bring up that both the box and the block have six rectangular faces.) “Let’s just look at this box. What can you say about the sizes of the faces? Are they all the same? Are some bigger than others?” (discuss)

2. Activity: Making Boxes (50 minutes)a. Say, “You’re going to make your own box with rectangles and tape. (holding up

the “Making Boxes” envelope) Here is what the flat rectangles look like. You’re going to figure out how to put them together.”

b. Each pair of students works with one envelope of box pieces. This gives students the pieces they need to make two different boxes: one that is 3”x5”x8” and another that is 3”x5”x2.”

c. Say, “You and your partner will get a set of rectangles of different sizes. These pieces won’t all fit together. It’s like puzzle. You have to figure out which pieces you can put together to make a box. The box should have sides, a bottom, and a top.”

d. Before they start taping, encourage students to do some planning by holding pieces next to each other to see how they want to put them together. If they want to separate pieces that they have already taped, they can just cut through the tape.

On-going Assessment: Observing Students at WorkUsing an excel sheet with students’ names, check to see if students are doing these characteristics:


-Can students count the six faces of a rectangular prism?-Do students make use of the information that opposite faces of a rectangle prism are the same size and shape?-Do students lay out the pieces on the table and see how they can “fold” them into a box?

Differentiated Instruction (Making Boxes):If some students complete the two boxes, ask them to open the top of the larger box- by cutting through the tape on the top face- and figure out how many smaller boxes could fit inside without going over the top.


Unit: GeometryTitle: Assessment: Faces of a GeoblockMain Focus Points:

Students will recognize that rectangular prisms have rectangular faces.Students will recognize which faces of a rectangular prism are the same size and shape.Students will construct a rectangular prism from rectangles.Students will compare rectangular prisms.

Resources needed for the lesson: 9”x5”x3” box, box of Geoblocks, tape, “Making Boxes” envelope, set of Geoblocks, “Assessment: Faces of a Geoblock”

Vocabulary: angle, right angle, rectangle, quadrilateral, biggest, smallest, column, congruent, rectangular prism.

Time Required: 60 minutesEnvironment: Students in pairs at their seats, whole class on the carpet, students sitting

individually at seats.

Procedures:1. Activity: Making Boxes (25 minutes)

a. Students continue their work making boxes.b. Use Making Boxes Rubric to assess student’s boxes. Use the discussion activity

that follows to help fill out the Rubric. If all students do not participate in discussion, hold individual conferences to discuss the box and fill out the rubric.

2. Discussion: Comparing Boxes (20 minutes)a. Gather students together to discuss the boxes they have made. Ask pairs to sit

together with their boxes. Begin by taking a box from one pair of students. Ask everyone who has made the same box to hold it up. Once the class agrees that everyone is holding up the same box, pair put that box aside. Now hold up another box form a different pair of students. Again ask students who made the same box to hold it up and then put it aside. If students have used new cards to make different boxes, have them share their boxes, too. In this way, create a collection that includes one example of the two different boxes that students have made using the box pieces along with any boxes made from other pieces.

b. Say, “What were some of the things that you needed to pay attention to as you began to make a box out of the pieces?” (Discuss)

c. “So you are giving some important hints about how to make a box, but you are also giving us some important information about what makes a box be a box or as mathematicians call it, a rectangular prism.”

d. Reiterate some of the important features of boxes that students mention. For example, the opposite sides of a box are the same and there need to be six sides.

3. Assessment Activity: Faces of a Geoblock (15 minutes)a. Distribute to each student one rectangular prism from the set of Geoblocks and

“Assessment: Faces of a Geoblock.” Explain that you are interested in how they each are thinking about rectangular prisms and what they think is important about them. Review the question with students and explain that they are to use the Geoblock to answer it.


Differentiated Instruction (Making Boxes):Some students may complete their boxes while others are still working. Have them return to the How Many Rectangles? activity.Students who want more of a challenge can try to cut their own pieces- instead of starting with a prepared set- to make boxes in shapes and sizes of their own choosing.

Making Boxes Rubric Student’s Name: Date:

Total Points: / 40


Category 0- Below Expectations

5- Meets Expectations

10- Exceeds Expectations

Student demonstrates understanding that opposite faces of a rectangular prism are the same size and shape.

Student cannot demonstrate understanding that opposite faces of a rectangular prism are the same size and shape.

Student demonstrates some knowledge of understanding, missing one attribute, size or shape.

Student demonstrates understanding that opposite faces of a rectangular prims have both the same size and shape.

Student explains the process in which they created the box.

Student cannot explain the process in which they created the box.

Student vaguely explains the process in which they created the box.

Student explains in full detail the process in which they created the box.

Students creates a rectangular prism with 6 faces.

Student does not create a rectangular prism with 6 faces.

Student creates a rectangular prism with 6 faces.

Student can describe the rectangular prism using correct vocabulary and attributes.

Student cannot describe the rectangular prism.

Student can describe the rectangular prism, but lacks correct vocabulary and attributes.

Student describes the rectangular prism using correct vocabulary and attributes.

Unit: GeometryTitle: Post-AssessmentMain Focus Points:

Students will demonstrate the knowledge they gained throughout the unit.Resources needed for the lesson: Post-assessment worksheet, Jeopardy Game, SmartBoard,

privacy shields.Vocabulary: Polygon, geometry, two-dimensional shape, three-dimensional shape, rectangle,

rectangular prismTime Required: 40 minutesEnvironment: Students sitting individually sitting at desks, students gathered in front of

document camera.

Procedures:1. Activity: Geometry Review

a. Create an interactive Jeopardy game for the SmartBoard. The Jeopardy game should be based on the unit. The Jeopardy game should be used for students to reflect on the unit and review on what they learned.

2. Assessment: Post-Assessmenta. Have students clear their desks and each student should put up their privacy shields. Distribute the post-assessment to each student. Explain that the post-assessment should be natural for them since it is everything that they had learned over the last few weeks.b. To grade the post-assessment use the answer key. Each question has an amount of points assigned for each right answer.


Post-Assessment: Geometry Name:

Number:


3. Circle the rectangles?

4. Explain two attributes which makes a shape a rectangle:


2. Circle the polygon?

1. Draw a line to match the 3D object to their 2D look alike:

6. How is a rectangular prism different from a rectangle?


Pre-Assessment: Geometry Name: Answer Key

Number:


3. Circle the rectangles (each rectangle is a point)?

4. Explain two attributes which makes a shape a rectangle (2 points- one for each correct attribute):

-Each angle is 90 degrees

-The sides parallel to each other are equal

-Has two pairs of parallel lines


2. Circle the polygon (1 point)?

1. Draw a line to match the 3D object to their 2D look alike ( each correct match is 1 point):

6. How is a rectangular prism different from a rectangle (1 point, bonus points for extra reasons)?

-A rectangular prism is a 3-D solid of a rectangle.

-A rectangle is a plane shape.


Teacher Reflection- reflect on the unit by answering the following questions:

1. Describe the unit as far as subject area and duration of instruction.

2. What went well during the instruction of the unit? How did you know it went well?

3. What would you consider doing differently if you taught the unit again?

4. How did you assess student learning? Did you use a pretest prior to the beginning of the unit?

5. How did you provide for individual differences in abilities and learning styles?

6. What kinesthetic activities did you incorporate while teaching this unit and why did you choose those particular activities?

7. How was technology incorporated into the unit instruction?

8. How would you enhance the unit to better suit your particular teaching style?


Curriculum Rubric for Understanding By Design Units(retrieved October 10, 2011 and adapted from Kinnelon Public Schools, www.kinnelonpublicschools.org/.../UBD_Review_Rubric_0607.doc)

Name: Leah ManiaceDate:12/8/12Unit Name and grade level: Geometry, 2 Grade

Excellent (8-10 points) Fair (6-8 points) Poor (0-5 points)

Bas

ic In

clus

ions

(x 1

)

Unit Plan contains five to ten lessons (how many: 16 )

Unit Plan pages are numbered, include author’s name and year in footer

Unit Plan learning experiences are referenced when “adapted” from others’ work

Unit Plan includes appropriate pre-test and post-test (pages: 5-6, 39-40 )

Unit Plan includes teacher reflection component (pages: 43 )

Unit Plan contains four lessons (how many: )

Unit Plan pages are not numbered, include author’s name and year in footer

Unit Plan learning experiences are sometimes referenced when “adapted” from others’ work

Unit Plan includes appropriate pre-test or post-test (pages: )

Unit Plan includes modest teacher reflection component (pages: )

Unit Plan contains three lessons (how many: )

Unit Plan pages are not numbered, don’t include author’s name or year in footer

Unit Plan learning experiences are not referenced when “adapted” from others’ work

Unit Plan don’t include appropriate pre-test and post-test

Unit Plan don’t include teacher reflection component


Stud

ent L

earn

ing

(x 2

)

Unit Plan requires students to interpret, evaluate, theorize, and/or synthesize information

Targeted enduring objectives are clearly defined, well articulated, and supported by the Essential and Unit Question

All enduring objectives clearly align with the Common Core State Standards, essential questions, the learning plan, and the assessment

Unit plan has well-defined accommodations to support a diversity of learners including gifted and struggling

Unit Plan requires students to analyze and apply information, solve problems, and/or make conclusions

Targeted enduring objectives are defined and moderately supported by the Essential and Unit Questions

Some enduring objectives align with the Common Core State Standards, essential questions and learning plan

Unit plan offers minimal accommodations to support a diversity of learners

Unit Plan requires students to define, identify, describe, and/or summarize. Very little higher-order thinking is required to complete the learning objectives

Targeted learning objectives are vague and not clearly supported by the Essential and Unit Questions

Relationship between enduring objectives and the Common Core State Standards, but relationship to learning plan, essential questions, and learning plan is unclear

Unit Plan does not accommodate a diversity of learners

Stud

ent A

sses

smen

t an

d E

valu

atio

n (x

2)

Instrument(s) for authentic assessment of big idea objectives are included (pages: 2, 5-6, 37, 39-40 )

A clear relationship is evident between learning objective and assessment of student learning

Assessment tools include a topic-specific rubric that builds towards criteria for excellence in order to serve as a helpful scaffold for students (formative assessment)

Assessment tools are diverse and include performance as well as self assessment and more traditional tools

Instrument(s) for assessment of big idea objectives are included (pages: )

Some relationship is evident between learning objectives and assessment

Assessment tools contain some topic-specific criteria, but may be unclear to students and are structured as a checklist without establishing a clear continuum of expectations that would be found in a rubric

Instrument(s) for assessment of big idea objective are not included or the assessment(s) does not match the targeted objectives

Relationship between objectives and assessment tools is unclear

Assessment tools contain only general criteria

Inte

grat

ion

of L

itera

ture

and

So

ng (x

2)

Proposed literature (at least one) and song (at least one) use is engaging, age appropriate, beneficial to student learning and supportive of higher-order thinking skills (pages: 11, 19, 23, 27 )

Children’s Literature and other song/dance is integral to the success of the Unit Plan

A clear relationship between the use of literature and song and student learning is exhibited by the anticipated student samples

Proposed literature (at least one) and song (at least one) use is engaging, age appropriate, but it is unclear as to how it enhances student learning (pages: )

Children’s Literature and other song/dance is important, but not integral to the Unit Plan

A limited relationship between the use of literature and song and student learning is exhibited by the anticipated student samples

Proposed literature (at least one) and song (at least one) is not age appropriate, nor engaging, and does not enhance student learning

Importance of literature and song/dance to the Unit Plan is unclear

No relationship between the use of literature and song and student learning is exhibited by the anticipated students samples


Inte

grat

ion

of v

irtu

al a

nd n

on-v

irtu

al m

anip

ulat

ives

, Int

erne

t tut

oria

ls,

calc

ulat

ors,

gam

es a

nd a

pple

ts (x

3)

Proposed technology use is engaging, age appropriate, beneficial to student learning and supportive of higher-order thinking skills

Technology (at least five of the following) is integral to the success of the Unit Plan (non-virtual manipulatives pages:9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 34, 36; virtual manipulatives pages:13, 15, 17, 27, 29; Internet tutorials pages: 4, 9, 13, 15, 17, 27, 29, 31; games for practice pages: 38; SmartBoard pages: 17, 38; \document camera pages: 4, 9, 11, 15, 17, 25, 27, 29, 31)

A clear relationship between the use of technology and student learning is exhibited by the anticipated student samples

Use of technology enhances the Unit Plan by using the computer as a research tool, a publishing tool (students use the computer and disseminate a product), and a communication device

Proposed technology use is engaging, age appropriate, but it is unclear as to how it enhances student learning

Technology (at least three of the following) is important, but not integral to the Unit Plan (non-virtual manipulatives pages: ; virtual manipulatives pages: ; Internet tutorials pages: ; applets pages: ; calculators integration pages: ; games for practice pages: ; SmartBoard pages: ; document camera pages: ; other: )

A limited relationship between the use of technology and student learning is exhibited by the anticipated student samples

Use of technology is limited to using the computer as a tool, a publishing tool (students use the computer and disseminate a product), or a communication device

Proposed technology is not age appropriate, nor engaging, and does not enhance student learning

Importance of technology to the Unit Plan is unclear

No relationship between the use of technology and student learning is exhibited by the anticipated student samples

Unit Plan does not take advantage of research, publishing (students use the computer and disseminate a product), and communication capabilities


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