Geometry+Investigation+1+2010

=__Investigations 1 and 2__= Vocabulary for Investigation 1:
 * attribute
 * angle
 * side
 * triangle
 * quadrilateral
 * square
 * rectangle
 * trapezoid
 * hexagon
 * pentagon
 * cube
 * face
 * edge
 * vertex
 * surface
 * figure

Do Now ideas:
 * Put a shape in the middle of the page, students list attributes.
 * Or, there are shapes on the rug, they list attributes on a white board or with sticky notes.
 * Draw a polygon on the board.

=__Week 1__=

Day 1:
(This lesson comes from the data unit).

Learning Targets:

 * I can list attributes of 2D and 3D shapes. This means I can say what they look like or feel like.
 * I can sort shapes by an attribute.
 * I can figure out how shapes have been sorted. This means I can say what is the same about a group of shapes.

1. Begin with listing attributes of shapes. Put out many shapes and have a “gallery walk” of shapes (2D and 3D, math manipulatives but other things as well if they have a distinct shape, like boxes). Students list words that describe shapes using this sentence frame: “I see a shape that is_” or “I see a shape that has _.” (Be sure to put these stems on the board or, even better, on a poster.) Have them list as many different words as you can. (You will get colors, etc which aren’t parts of the definitions of shapes – that is fine.) //10 minutes//

2. Introduce the learning targets: listing attributes and sorting. Model sorting using only paper 2D shapes. Do a think-aloud, using the same sentence frames: "My rule is shapes that are..." or "My rule is shapes that have...". Model looking for shapes with an attribute the class listed before (three sides, four points, round, etc.) Ask if anyone else wants to try. //10 minutes//

3. Groups of 3 get envelopes of paper shapes. Spread them out and start to list attributes of these shapes. First have everyone think of an attribute, then share with their group, then share with the group. List the words on cards and display them.

4. Decide with your group on a way to sort the shapes. Remind them of the sentence frames. Share a few ways groups sorted, and ask them to find 2 more ways. Remind them of the stem: "My rule is shapes that are..." or "My rule is shapes that have...". //10 minutes//

5. Ask for self-evaluation of the learning target: can you sort shapes by an attribute?

6. Now tell them they are going to see if they can guess how other people sorted. (Point out that learning target.) Show Guess My Rule paper and how to put the shapes that fit your rule on one side and the shapes that don’t on the other side. //10 minutes//

7. Model how to play Guess My Rule with a partner – your partner sets up a board, then you try to add 3 or 4 shapes to one side or the other, then you guess how they sorted. [My rule is shapes that are (blank) or My rule is shapes that have (blank).] //10 minutes//

8. Exit ticket: Draw two shapes with an attribute that is the same, and write the attribute.

Day 2 (Based on Session 2.1)

 * I can list attributes of 2D and 3D shapes. This means I can say what they look like or feel like.
 * I can sort shapes by an attribute.
 * I can figure out how shapes have been sorted. This means I can say what is the same about a group of shapes.
 * I can explain what a polygon is.

Materials:
 * 2D shape cards
 * Other shape cards with shapes that are NOT polygons: open shapes, half curved, half straight lines, etc.

//1.// Quick images with shapes (as described in lesson 1.1, p. 25) //15 minutes; optional// § Introduce learning target and connect to visualizing in reading; visualizing helps you remember, understand, and notice new things. § As you debrief, connect also to learning target about naming attributes: how can you use attributes of a shape to help you remember the shape?

2. Review how to play Guess My Rule. Talk about how to guess a rule. Get a few suggestions, and then do a think-aloud: "Hmmm, let me see. First I'm going to look on the "My Rule" side and try to find something that is the same about all the shapes." (Remind them that good mathematicians look for similarities and differences, from the Big Ideas list.) "Okay, I see that all the shapes on this side have 3 points. Now I'm going to check each shape on that side. Let's see, I'll point to the shape, and if it has 3 points, you give a thumbs-up. Now that I've checked ALL the shapes on this side, I'm going to check all the shapes on the other side, to make sure they are a thumbs-down for 3 points. I'll point, and you give a thumbs-up or a thumbs-down."

3. Make an anchor chart for playing Guess My Rule:


 * Look for an attribute all the shapes have in common on the "My Rule" side.
 * Check each shape to be sure it has that attribute. (Thumbs up)
 * Check each shape on the "Not My Rule" side to be sure it's a Thumbs Down for that attribute.

4. Today you are going to see if you and a partner can trick another pair with Guess My Rule. Have pairs at tables set up a Guess My Rule board with the shapes and write their rule on a slip of paper. Use a slip with the stem on it.

Then they move to another table to guess the rule and write their guess on the back of the slip. They get to check what the other pair wrote to see if they were right. Then go guess another pair’s. //12 minutes//

//5.// Tell them you have a mystery for them to solve. There is this new word you want them to learn: //polygon.// A polygon is a kind of shape with certain attributes. But what a polygon is is a mystery. You are going to play a guessing game where they guess if a shape is or is not a polygon, and you tell them if they are right or not. Point out the learning target about figuring out what a polygon is.

6. Set up a Guess My Rule board and put a couple polygons on the My Rule side and a couple of non-polygons on the other side. Have students add shapes to one side or the other and take suggestions of what a polygon is. DO NOT tell them if they are right or not, but ask them for evidence. What is your evidence that all polygons have straight sides? What on my board makes you think that? etc. Keep repeating the mystery: What is a polygon? How do you know if a shape is a polygon? //15 minutes//

Pull out the following ideas and record them on a class anchor chart: § closed shapes § all the sides are straight § have corners or angles

Congratulate them on figuring out the mystery, and mastering the learning target!

Learning targets:

 * I can identify shapes that are polygons and shapes that are not polygons.
 * I can explain what 2D and 3D shapes are.
 * I can list attributes of 2D and 3D shapes. This means I can say what they look like or feel like.

1. Review what is a polygon. Make an anchor chart of what are polygons. Put some up, ask if they are a polygon or not, and ask for proof of why.

2. List attributes of 2D shapes. Put shapes on the rug, and have students say attributes (or use cards you already made and sort them.) Put heading on an anchor chart: Under Number of Points, write 3 points, 4 points, etc, as they name them. For each attribute named, put it under the heading it matches.
 * Number of points (angles) Tell them "angle" is another word for point, a place where 2 lines come together.
 * Number of sides
 * Open or closed shape
 * Straight sides or curved sides

3. Give them a new Guess My Rule with your rule being 3D shapes. Put geoblocks on the My Rule side and 2D paper shapes on the Not My Rule side. Have them guess your rule. //5 minutes//

4. Point out the learning target of explaining 2D and 3D. How would you explain what 2D shapes are? How would you explain what 3D shapes are? Jot down notes on a 2-column anchor chart. //10 minutes//

5. Quick Guess my Rule Quiz

Learning Targets:

 * I can explain what 2D and 3D shapes are.
 * I can list attributes of 2D and 3D shapes. This means I can say what they look like or feel like.
 * I can determine how many faces a 3D shape has.

1. Review what is a polygon -- have students tell partners and share out. Review 2D and 3D shapes: have students tell partners and then share out.

Look at day's learning targets and self-assess. Hand out 3D shapes to each student. They try to list attributes of the 3D shapes with a partner. First have everyone think of an attribute, then share with their partner, then share with the group. List the words on under categories, as you did for 2D shapes. You will need to introduce vocabulary such as EDGES, FACES://15 minutes//
 * number of edges (sides)
 * number of points
 * number of faces
 * shape of faces

2. Introduce the idea of a //face.// Ask them what their face is. Tell them 3D shapes have faces too. Give each student one geoblock. Define a face – if you sit the geoblock down on the ground, it is sitting on one //face//. Each side of the geoblock is called a face. What does it feel like if you touch one face of your geoblock? (It feels flat – it feels like a 2D shape!)

3. Their job now is to come up with a way to count the faces on a geoblock. Give all pairs the same 3D shape (probably a cube). They try to count the sides. Write down all their answers. //10 minutes//

4. Do some practicing//:// have up some posters with pictures of geoblocks. Kids pick a block, count the faces, write the number of faces on the poster under that block. See if the numbers are consistent; check any disparities as a class.

5. Exit ticket: 2 attributes of a 3D shape (have them record the letter of the shape, and its two attributes.)

=__Week 2__=


 * //Be sure to introduce the protocol of a Math Talk at morning circle on Day 1 or 2 this week. Use the question "What is the best kind of ice cream?" Create a list of norms, practice as a group, and see if you need to add to or change the list of norms.//**

//**If necessary, repeat later in the week to get ready to discuss what is a rectangle? during a math talk.**//

Day 1
based on Session 2.2

Learning Targets:

 * I can identify shapes that are quadrilaterals.
 * I can identify shapes with right angles.


 * 1) Warm up with some sorting. In groups of 3, students sort 2D shape cards, including non-polygons. Give them ways to sort: //(10 minutes)//
 * 2) **Polygons** and non polygons (review what is a polygon)
 * 3) Tell them to make groups of shapes that have the same number of sides. Let them make as many groups as they want (not just 2 groups). See what groups come out: 3 sides, 4 sides, etc., but also maybe no sides (for round shapes).
 * 4) Shape posters: give each pair 2 small "posters" with shapes on them, one 2D and one 3D. For the 3D shape, give them the corresponding geoblock. Students must complete the poster.
 * 5) Give sentence starters: Our shape is... Our shape has... Ask them to write in complete sentences.
 * 6) Have vocabulary up clearly visible so they can check it, and spell words correctly.
 * 7) [[file:yasecondgrade/2D shape poster.doc|2D shape poster.doc]]
 * 8) [[file:yasecondgrade/3D shape poster.doc|3D shape poster.doc]]
 * 9) Define **quadrilaterals**. (A shape with 4 sides.) Ask them to pull out the quadrilaterals they have sorted and put away the rest of the shapes. //(10 minutes)//
 * 10) Ask how many points the quadrilaterals have. Find out that the quadrilaterals have 4 points as well. (There may be confusion about what a point is. Some kids seem to think that points made with wider angles are not points. Come to a consensus about what a point is: it is a place where 2 sides come together. If necessary, have them count points on shapes other than quadrilaterals.)
 * 11) Draw a picture of a point on chart paper. Explain that another word for a point is a "vertex." And on the inside of a vertex is an angle. When 2 lines comes together, they make an angle. An angle is the space between the 2 lines. (see p. 65) Be sure to point out that there are 2 angles around the point, one on the outside and one on the inside.
 * 12) Add "number of **angles**" to the list of 2D attributes.
 * 13) Tell students to turn to a partner and explain what a quadrilateral is. Then ask them to define an angle.
 * 14) Thumbs assessment of learning target of defining a quadrilateral.
 * 15) Have everyone look for Shape A. Ask them to point to an angle on Shape A. "This kind of angle is a special kind of angle. It is called a right angle. It is a right angle because it looks like a corner, or an L." Show them how a square tile fits just perfectly in a right angle.
 * 16) "Now let's look at Shape N. Does Shape N have right angles? How can you tell? Check it." Have students explain how they knew it did NOT have right angles.
 * 17) Then try with Shape Q. Again have some students explain how they knew.
 * 18) Today or tomorrow, do a "right angle" hunt around the room. Students draw and label what they find. [[file:yasecondgrade/right angle hunt.doc|right angle hunt.doc]]

Learning targets:

 * I can list attributes of 2D and 3D shapes. This means I can say what they look like or feel like.
 * I can identify shapes with right angles. This means I can say if a shape has right angles or not.

//Do Now: Find shapes with right angles and trace them.// / draw something in the room that has a right angle.

Quick game: find a quadrilateral! Find a polygon! Find a shape with right angles! Each time, turn to the person next to you and explain how you know.
 * Hand out square tiles and tell them that right angles are like "square angles." If you put a square in a right angle, it will match up just right, no overlapping.
 * Add "has right angles" to the list of attributes of 2D shapes.
 * In groups of 3, have students sort 2D shapes into shapes with right angles and shapes that don't have right angles, using square tiles.
 * If there's time, play some Guess My Rule with something new: buttons? rocks? Have pairs try to create a challenge for another pair, and leave their games out for others to guess.
 * Exit ticket: have students put an X in each right angle of a 2D shape. [[file:yasecondgrade/right angle practice.doc|right angle practice.doc]]

Learning Targets:

 * I can list attributes of 2D and 3D shapes. This means I can say what they look like or feel like.
 * I can identify right angles.

1. Sorting quadrilaterals (see p. 73). In small groups or pairs, have students sort quadrilaterals into shapes with 4 sides and 4 right angles and 4 sides but not 4 right angles. Refer back to the learning target. (15 minutes) With a partner from another group, they look at each others' sorting and see if they have questions or changes to suggest. 2. Shape attributes assessment: Put geoblocks at each table and use the 3D attribute sheet to write attributes of one or two shapes. (15 minutes) 3. Ticket to leave: quick Guess my Rule quiz.

Day 4

 * based on Session 2.3**

Learning Targets:

 * I can list attributes of 2D and 3D shapes. This means I can say what they look like or feel like.
 * I can reason about which rectangles are bigger and smaller, and put them in order from biggest to smallest.
 * I can explain my thinking to a partner.


 * 1) 2 D attributes quiz [[file:yasecondgrade/2Dattributes.doc|2Dattributes.doc]]
 * 2) Comparing shapes activity: [[file:yasecondgrade/comparing shapes.doc|comparing shapes.doc]]
 * 3) //OMIT//Chocolate Factory Challenge: You work at a chocolate factory making chocolate bars. All of your chocolate bars are rectangular. Some are bigger than others. You need to figure out which ones are biggest and which ones are smallest so you know which ones should cost more. (Which ones do you think should cost more? Bigger ones or smaller ones?)
 * 4) Point out the new learning target of ordering rectangles.
 * 5) In pairs, give students a set of rectangles to put in order. Tell them they need to put them in a line of biggest to smallest (or most expensive to least expensive). Have them lay them out on colored paper on a desk so other students can walk and look at their work afterwards. Teachers should tape the rectangles down as students finish so they are portable. Make sure pairs' names are on the work in big, dark letters so students know whose work it is.
 * 6) Pairs join another pair and compare their work. Each person may say one thing (go around in a circle) about what they notice or wonder about the work of the pairs.
 * 7) Bring all the rectangles to the rug and put in the middle, or on the board. Everyone sits and looks at the ordering silently for a few minutes. Then they may ask questions of each other.
 * 8) If students have ordered from tallest to smallest, turn rectangle C on its side and ask: "Is this one still the biggest now? Why or why not?" Turn and talk about the answer.
 * 9) If there's time, ask them to talk to a partner about how we could find out FOR SURE which chocolate bars are bigger and smaller -- which ones have more chocolate and which ones have less. What tools in the classroom could we use?
 * 10) End with sorting something new: Yekti cards? insects?

Day 4

 * Based on Session 2.3**

Learning Targets:
//OMIT//
 * I can find the area of a rectangle. That means I can say how many squares it would take to cover the whole rectangle.


 * 1) Vocabulary game: have cards (or pieces of paper) with math vocabulary on one side and a definition on the other side. Children stand in two lines, or two circles, one facing out and one facing in. You are facing a partner. One person shows his / her vocabulary word, and the other one says what it is. The first shows the answer. Then the second student shows his / her word and the first explains what it is. They swap cards, and move one down the line to meet a new partner with their new words.
 * 2) Back to the chocolate factory problem.
 * 3) Share ideas for how to measure exactly how much chocolate is in each bar. Talk about the new learning target.
 * 4) Show a real chocolate bar that has squares of chocolate. Ask if that gives them any ideas of how to measure how much chocolate is in a bar. What tools in the classroom could they use?
 * 5) Get to the idea of covering a rectangle with square tiles. On the rug, have each student cover one triangle with square tiles and share with his / her partner how many squares it took.
 * 6) Explain the word **area**: a word we use when we measure how many squares can fill a shape.
 * 7) Students work in pairs to confirm which chocolate bars have the most / least area. They put a new set of rectangles in order by counting how many squares cover them, and taping them on paper again. This time, they record the area: 12 square inches.
 * 8) As they work and you discuss their work, use the words "row" and "column." Bring a picture of a column and a row. Make columns with your bodies by holding hands straight up above your head and pretending to hold up a building. Make rows with your bodies by holding your arms out to the side and pretending to inch down a skinny aisle to your seat. [[file:yasecondgrade/rows and columns.doc|rows and columns.doc]]
 * 9) In half groups, share their work on the board or on the floor. Ask each pair to say briefly what they did. They may ask for questions or comments. Ask students what they notice / wonder / learned.
 * 10) Self-assessment with thumbs: area of rectangles learning target.
 * 11) Ticket to leave: write on a scrap of paper how you can find the area of a rectangle.

Learning Targets:

 * I can find the area of a rectangle. That means I can say how many squares it would take to cover the whole rectangle.
 * I can make a shape that is **congruent** to another shape. This means I can make a rectangle that is the same size and shape as another rectangle.
 * I can use clues about area, rows, and columns to solve a rectangle riddle.


 * 1) Quick area quiz: Give students 2 rectangles to find the area of.
 * 2) Give each student 6 squares. Tell them they should make a rectangle with an area of 6 square inches, or using 6 square tiles. On graph paper, they draw their rectangle. Share with a partner whose rectangle looks different from yours. (See page 85-87)
 * 3) Introduce the word **congruent**: two shapes that are the same size and shape, even if they are turned in different directions. Have each student make a rectangle with an area of fewer than 12 squares. They give it to a partner, and their partner makes a congruent rectangle.
 * 4) Do one rectangle riddle with a partner (see page 89). Give them time and space for these: don't rush through them.

=Week Four=

Day 1
Learning Targets:
 * I can make as many rectangles as possible with an area of 12.
 * I can find the area of a rectangle. That means I can say how many squares it would take to cover the whole rectangle.


 * 1) Review what **area** means. Show them some rectangles to find the area of, or hand each pair a rectangle and have them find the area. (Use inch graph paper to make these.)
 * 2) Give them the challenge, in pairs, to make as many rectangles with an area of 12 as possible. This means, if they own a chocolate factory and they are trying to make chocolate bars that have 12 squares, how many different shaped chocolate bars could they make?
 * 3) Give each pair graph paper (either inch graph paper or centimeter graph paper) to record the triangles they make. Model for the class the process of making one rectangle out of 12 squares, then counting how many rows and outlining that many boxes, counting the columns, outlining those boxes, and then shading in the rectangle. They should cut out their rectangles and tape them on big paper, then record the area. (Many rectangles can be made using the inch graph paper but they may need centimeter graph paper for long, skinny rectangles.)
 * 4) Each pair joins another pair and compares what they did to see if they missed any possibilities.
 * 5) If there is time, make a class chart with all the rectangles. How can we be sure we found all the possible rectangles you can make with 12 squares? Continue to practice language of **rows, columns,** and **area** throughout this lesson**.**

Day 2
//OMIT// Learning Targets:
 * I can make as many rectangles as possible with an area of 12.
 * I can find the area of a rectangle. That means I can say how many squares it would take to cover the whole rectangle.


 * 1) Finish rectangles with 12 squares if you're not done.
 * 2) Do the vocabulary game with the vocab cards from the unit to review for the test.
 * 3) Centers:
 * 4) rectangle riddles (do one as a group to model how you might approach it, but do an easier one than the ones you are handing out.)
 * 5) basic facts (Boom or flash cards)
 * 6) collect 25 cents
 * 7) Sharing of all rectangles with 12 squares and looking for patterns: have a poster of all possible rectangles organized in a way that makes sense (such as 12 x 1, 6 x 2, 3 x 4, etc.) Ask if anyone sees patterns.

Day 3
End of unit assessment

Next week:
 * Centers:
 * Unit assessment

////