cms 2nd grade geometry unit - elementary...

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CMS 2nd Grade Geometry Unit

1st Grade Geometry 2nd Grade Geometry 3rd Grade Geometry Reason with shapes and their attributes. 1.G.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes. 1.G.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.1

Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5

Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

5Sizes are compared directly or visually, not compared by measuring.

Reason with shapes and their attributes. 3.G.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Lesson 1 2G1 Lesson 2-3 2G1 Lesson 4 2G2 Lesson 5 2.G2

Portions of this lesson are taken from Investigations Unit 2 Session 2.1-2.2 Categorize shapes by their attributes. Sort shapes by the number of sides.

Shapes workshop Consists of 4 stations one of which is optional. All stations are designed to develop an understanding of various attributes of shape. (This 2-day lesson includes several parts from Unit 2 Session 1.4 Ways to Fill)

Investigations Unit 2 Session 2.3 Ordering Rectangles Use as written

Investigations Unit 2 Session 2.4 Building Rectangles Use as written

Lesson 6 2.G2 Lesson 7 2.G1 Lesson 8 2.G1 Note: Several pages in the Student Activity Book for Unit 2 provide for practice with addition, subtraction, make ten combinations, and doubles combinations. This CMS unit does not include every session in the teacher guide. Therefore the following pages may be used at any point as needed to provide practice with Unit 1 concepts: Student Activity Book Pages: 1, 4, 12, 15, 23, 27, 28, 29, 30, 31, and 35

Investigations Unit 2 Session 2.5 Drawing Rectangles Use as written

2-d to 3-d shapes; making connections

Portions of this lesson were taken from Unit 2 Session 1.1 and 1.2

This session has students match Geoblocks to 2-d images. This session connects the work students have been doing with 2d shapes to identifying attributes of 3-dimensional shapes.

Investigations Unit 2 Session 1.5 Combining Shapes Use as written

Assessment tasks that may be used after this unit can be found here: http://www.illustrativemathematics.org/illustrations/1506

http://www.illustrativemathematics.org/illustrations/1506

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Lesson #1– Classify Shapes by the Number of Sides 2nd Grade Geometry Common Core State Standard: Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.


Common Core Math Practices SMP6 Attend to precision

Materials:

Set of shape cards (various polygons)

Set of shape cards for discussion (quadrilaterals only)

Sorting chart for groups of 3 or 4

Vocabulary: Pentagon Triangle Quadrilaterals Hexagon

Classroom Routine: What Time is It? Students work together with a partner to practice setting their individual clocks to the half hour. One student suggests a time and the other one sets the clock. They take turns with these two roles.

Introduction/ Mini-lesson Tell students, “Today we are going to be sorting using attributes. Attributes are the words that we use to describe people and things. Let’s practice sorting ourselves using attributes. If we were to sort ourselves what might the categories be? (Height, color of shirts, boy, girl, shoes, hair, type of uniforms.) Record the categories. Select one or two categories to sort the class. After this short exchange, explain that we were able to think of many ways to sort the same group of people. Tell students that shapes are like people in that they have lots of attributes that can be used to sort them. Provide each group of 3-4 students a set of shape cards and give the following directions: Today we are going to sort 2 dimensional (or flat) shapes. I would like for you to sort your shape cards into 3 or more categories. Shapes don’t have hair or wear different colors of shirts, so think with your partner about what categories you could use. Allow children time to sort their card set being sure to monitor and support children as they attempt to generate categories. Mid-Lesson Interruption: (After 15min.) Solicit specific children to quick share a category that their group generated being careful to solicit children who identified definable attributes. (number of sides, length of sides, corners and shape of corners) Focus the attention of the students on the number of sides and invite groups who have not already sorted using sides as a category to re-sort their shapes by the number of sides and create a poster of this sort.

Workshop Students are working in small groups to create a poster of shapes sorted by number of sides.

What to look/listen for: Students who struggle to generate a category: Let’s think about each shape. Are there some that seem to go together? Which ones? How do they go together?

Students who notice differences within the same attribute (sides: length, straight/slanted, long and short pairs, no sides the same) Questions to ask may include: What attributes are you using to sort? How do you know this shape goes here? How do you know that you have sorted them correctly?

Discussion “Many of you had an interesting sort for shapes with 4 sides (squares, rectangles). I am wondering how we can sort shapes that all have 4 sides. Does anyone have any ideas?” Make a new chart recording ways to sort quadrilaterals. Be sure to use the student’s language and attach correct vocabulary afterwards. (up and down sides and side to side sides might be used to describe opposite sides same.

Homework: How Many Sides? How Many Corners?

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CMS 2nd Grade Geometry Unit

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Polygon Sort

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Name: __________________ Geometry Lesson 1 Exit Ticket

Think about a category that you could put some of these shape in. What is the name of the category? _______________________________________ Circle the shapes that go in your category:

Name: __________________ Geometry Lesson 1 Exit Ticket Think about a category that you could put some of these shape in. What is the name of the category? _______________________________________ Circle the shapes that go in your category:

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Name: ___________________

How Many Sides? How Many Corners?

Directions: Tell how many sides and how many corners in each shape.

A

sides ___ corners ___

B


C


D


E


F


G


H


I


J


K


L


M


N


O


Pick 2 shapes above that you think fit in the same category.

What are the letters above your two shapes? _____ and _____

Why do these two shape go in the same category? ________________________

__________________________________________________________________

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Lesson #2–3 Working with Shapes 2nd Grade Geometry Common Core State Standard: Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5


Common Core Math Practices

Materials:

Teacher created poster with shapes glued on titled “Number of Angles”

Station Cards

Geoboards

Toothpicks

Vocabulary: Angles, attributes. Quadrilateral, hexagon, pentagon, octagon, triangle

Classroom Routine: Today’s Number: 18 Using Double Combinations Students generate expressions for the number 18 using double combinations. ( For more information see TE62 Example: 6+6+3+3) For more information see TE62

Introduction/ Mini-lesson

Review posters from yesterday. I made a poster using a different category (Show the teacher prepared poster prepared prior to this lesson). I used the category “Number of Angles.” Angles is the word mathematicians use for corners. So, when I sorted by the number of angles, that means that I sorted by the number of corners. Ask the children to compare the posters they made yesterday to the poster you have made. (You will want to have an example of a student poster sorted by sides from yesterday to display as well) Ask what they notice. *You are hoping that students will notice that the number of sides and the number of angles are the same. Ask students if they think that the number of sides in a shape is always the same as the number of angles in a shape. If students think so this would be a great statement to add to a “generalizations about shapes” poster that you would keep going.

We see that shapes have the same number of sides and angles. Mathematicians name shapes by the number of sides and angles. (Label your charts as you share the following information.) A triangle is a flat shape with 3 sides and 3 angles, a quadrilateral is a flat shape with 4 sides and 4 angles, a pentagon is a flat shape with 5 sides and 5 angles, and a hexagon is a flat shape with 6 sides and 6 angles. Tell students that some quadrilaterals have special names too because their corners are like the corners on a square tile like rectangles and squares. Squares are even more special because their sides are all the same length. Another special kind of quadrilateral is a trapezoid. The red pattern block is a trapezoid. Mathematicians, today and tomorrow we are going to explore shapes in several stations. Describe stations as needed.

Workshop

Station 1: Draw It! This station is designed to give students practice drawing shapes in a specified category. They work with a partner to create 2 different-looking examples of shapes in one category. Station 2: Geoboard Shapes! In this station, students create a specified shape on a geoboard, then record it on a paper geoboard and label the shape with its

What to look/listen for:

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name. *If all students create squares and rectangles challenge them to create a quadrilateral that is different from these. Correctly naming shapes as rhombus, parallelograms, etc. is not necessary). The key here is to get students to make the connection that these different 4-sided polygons are all quadrilaterals because of their 4 sides. Station 3: Toothpick Shapes! While at this station, students create a square and a rectangle by following the directions on the page. Students are then asked to consider what the angles look like in each shape. Optional Station 4: Find the shapes Students take turns finding the shapes that match the description given by the shape-caller. Be careful to listen to students play and bring up the language that they use to describe attributes as an opportunity to assign correct vocabulary. (“up and down sides” vs. “side-to-side sides” to describe opposite sides equal) Station 5: Ways to Fill (Investigations Unit 2: Session 1.4 Activity 2, TE page 47)

Discussion Day 2: Ask students whom you have identified to share descriptions of characteristics for polygons. Students may have said: “corners, up and down sides, pointies, etc” List the student language and the appropriate geometric term to support vocabulary development. This discussion will serve to support math vocabulary as well as emphasize the various attributes of shape. Day 3: See Investigations, Unit 2, Session 1.4 Discussion (TE page 48)

Homework

Day 2: Investigations Unit 2, Student Activity Book page 5 Day 3: Design a robot Students create a robot using the following criteria: - 2 hexagons - 4 quadrilaterals - 1 polygon with 5 angles - 2 closed shapes with 3 sides and 3 angles

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Station 1: Label it / Draw It! Materials: Pencils, paper, ruler, Draw It! cards Choose a card. Draw the shape. Have your partner draw a shape that is in the same category, but looks different. For example, partner 1 draws a quadrilateral; player 2 draws a differently shaped quadrilateral. Player 1 Player 2 For the teacher: Cut out the “Draw It!” cards below and place in the Draw It station.

Pentagon Hexagon Quadrilateral

Octagon Pentagon Hexagon

Triangle Octagon Pentagon

Quadrilateral

Directions: 1. Choose a card 2. Draw the shape 3. Partner draws the a different

example of the same type of shape

4. Choose another card and repeat

Triangle

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Station 2: Geoboard Shapes. Print 1 per student.

On a geoboard, create a shape with

4 sides of the same length. Draw your shape This shape is called a ________________________________


6 sides. Draw your shape This shape is called a ________________________________


8 angles. Draw your shape This shape is called a ________________________________


4 sides that are NOT all equal. Draw your shape This shape is called a ________________________________

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Station 3: Toothpick shapes. Print one copy for each student, or have students record in math journal.

Create a quadrilateral with no sides the same length.

Without breaking toothpicks, create a quadrilateral with one pair of sides (2 sides) the same length, and another pair of sides (2 sides) the same length. This shape should not have all 4 sides the same length. You will need more than 4 toothpicks to create this shape.

What do you notice about the angles of the two shapes you created?

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Station 4: Mystery Shapes “Which shapes could it be?” Player 1 - Draw a shape card. Say, “I have a shape that has…” Player 2 – Choose all of the shapes from the pile of shape cards that match

Lesson # 4 Notes: 2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Sizes are compared directly or visually, not compared by measuring.

Begin by asking students to get into groups of 4 and share their robot posters. Ask students in the group to identify the hexagons in each drawing then use the following as written. Investigations Unit 2 Session 2.3 Ordering Rectangles

Lesson #5 Notes: 2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Sizes are compared directly or visually, not compared by measuring.

Use Investigations Unit 2 Session 2.4 Building Rectangles as written: Encourage students to use “row” and “column” as they describe their rectangles.


Use Investigations` Unit 2 Session 2.5 Drawing Rectangles as written. In addition to finding the length and width of each rectangle, have students find the number of squares in each rectangle created on the geoboard.


Use Investigations Unit 2 Session 1.5 Combining Shapes as written continuing to focus the 2-D shapes that form the faces on the geoblocks as well.

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Lesson #7– Moving from 2 to 3-Dimensional Shapes 2nd Grade Geometry

Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5


Common Core Math Practices MP6 Attend to Precision

Materials:

Task Cards 1-6 (M7-9) Task Cards 7-12 (M10-M12), Shape Card (A), Geoblocks, Describing Geoblocks chart

Vocabulary: Faces, 3D, corners, edges, faces, attributes

Classroom Routine: Quick Images: Shapes Show 3 shape cards you haven’t used yet and continue with the Quick Images routine. Make sure to ask students how the shapes they drew today are alike, and how they are different.

Introduction/ Mini-lesson

Show Shape Card (A) the rectangle and have students draw it using the quick image routine. Next, hold up Geoblock K- the large rectangular prism and say, “This block that I’m holding is called a prism. Turn and talk to your partner; “How are the rectangle and the prism different?”

After students have had a few minutes to discuss, ask for a few students to share aloud.

Pass around a set of Geoblocks and have each students take out one block and examine it carefully. Ask students to describe one attribute of their block. List these on the “Describing Geoblocks” chart.

Explain that “When mathematicians talk about a 3-dimensional object, such as a Geoblock, they call this part of the block a face. When you put your block down on the floor or a table, it sits on one of its faces. What do you notice about a face of your Geoblock?”

Say, “The shape of a face is an important feature of a block. What shapes are the faces on your block?” - triangles or rectangles. Record student responses on a Describing Geoblocks chart.

Now as, “Count the number of faces on your block. How many faces does it have?” Record responses on the Describing Geoblocks chart. Ask students to keep their blocks and move to stand with classmates whose blocks have the same number of faces as their block. (You may employ a management technique here to assist children with moving to a group like holding up fingers to show the number of faces and using fingers as a guide for determining which group to get into)

Have students check to make sure all Geoblocks in the groups have the same number of faces.

As students are standing in a group, say, “Besides having the same number of faces, is there anything else that you notice about the blocks that are in your group? Compare the shapes of the faces of your blocks, what do you notice?

Write the following statement on the board: “I noticed that all of the blocks with ____faces have ____ shaped faces. Example for teacher: I noticed that all of the blocks with _(5) faces have triangular shaped faces. Challenge students to complete create several statements like the one above.

Workshop Introduce Find the Block: Provide each group Geoblock D (cube). Ask students to discuss the following with their team; what do you notice about this block? Students may notice it has 6 flat faces, 8 corners, and so on. Next, point to one face of the cube and ask partners to trace around one face of their cube. Ask students, what shape is the face of your Geoblock? Have partners trace around a different face and ask, “What do you notice?” Students should notice all faces are the same shape – square. Explain to students that this type of Geoblock is called a cube.

What to look/listen for: Do they comment on important features of shape and the number of sides and vertices.

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Hold up Task Card 1 from Find the Block Task Cards (M7). Tell students, “This card shows all of the faces of one Geoblock, and it was made by tracing around each face. Do you think this card matches the Geoblock you are holding?” Give students time to explore, then ask a few students to demonstrate how they know the cube matches Task Card 1. Explain to students that they will continue to find Geoblocks to match each of the task cards during workshop today

Discussion Post a picture of a square and a cube and ask students to discuss attributes of each. Are there attributes of the square that are not attributes for the cube? Are there attributes for the cube that are not for the square? What are they and why?

Homework: The Shape of a Face – Student Activity Book, Unit 2, page 2. Encourage students to bring in 3-d shaped objects that match the face of one or more on the SAB page.

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Copy and cut apart the following Workshop Task Cards and place around the room

Guess My Geoblock: Partner 1: Choose a Geoblock and hide it from your partner. Describe your Geoblock. Be sure to include… … My Geoblock has ______ faces …The faces on my Geoblock are shaped like ___________ Partner 2: Find or draw the Geoblock. Switch places and repeat

Double Arrays:

Take one primary number card

Color in that number of squares in one row on the Double Array Recording Sheet

Switch papers with your partner and double his/her number by coloring the same number of squares in the row underneath. Record the equation.

Switch papers and repeat

Draw a Face

Take one item from the table. Complete a “Draw a Face” recording sheet like the one below. If you finish, choose another item and complete a new sheet.

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Geometry Unit Assessment Grade 2 Name:_____________________

1. Color all the quadrilaterals blue 2. Color all pentagons green 3. Color all hexagons red 4. Circle 3 shapes with 2 sides that are equal length.

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Grade 2 Geometry Quiz

5. Draw a shape with 2 equal sides and 5 angles in the box below.

Mystery Rectangles Use the space below for work space.

4. Kevin was playing double it and his card was a 4. What would his array look like? What number sentence should he write?

5. My rectangle has 5 rows and uses 15 tiles. How many columns are in my rectangle?

6. Bekah is covering this rectangle with square tiles. How many square tiles does she need to cover the rectangle? Show your thinking below.

7. Susan wants to cover this rectangle with same-size squares. How many squares are needed to fill the rectangle? Show your thinking below.

8. What is the name of this 3-D shape? __________

9. Describe the faces on this prism: There are ____ faces.

What shapes are the faces?

________________________

cms 2nd grade geometry unit - elementary...

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