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Grade 1 Mathematics Frameworks

Unit 3Shapes and Fractions

Georgia Performance Standards FrameworkGrade 1 Mathematics Unit 3 1st Edition

Unit 3: Shapes and Fractions (4 weeks)

TABLE OF CONTENTS

Overview................................................................................................................................4

Key Standards and Related Standards...................................................................................5

Enduring Understanding........................................................................................................8

Essential Questions................................................................................................................8

Concepts and Skills to Maintain............................................................................................9

Selected Terms and Symbols.................................................................................................10

Classroom Routines...............................................................................................................11

Strategies for Teaching and Learning....................................................................................11

Evidence of Learning.............................................................................................................11

TasksGraphing Attributes.....................................................................................................13Build a Shape...............................................................................................................20 Pattern Block Pictures..................................................................................................24Which One Doesn’t Belong.........................................................................................29Describe It, Chart It, Find It, Make It..........................................................................33Listen and Do...............................................................................................................37 I Want Half! ................................................................................................................41Where Does it Live?....................................................................................................43Fractions Are As Easy As Pie! ....................................................................................47Culminating Task: Monster Math..............................................................................50

Georgia Department of EducationKathy Cox, State Superintendent of Schools

MATHEMATICS GRADE 1 UNIT 3: SHAPES AND FRACTIONSOctober 2009 Page 2 of 57

The following tasks represent the level of depth, rigor, and complexity expected of all first grade students. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. It is important that all elements of a task be addressed throughout the learning process so that students understand what is expected of them. While some tasks are identified as a performance task, they also may be used for teaching and learning (learning task).

Task Name Task Type/Grouping Strategy Content Addressed

Graphing Attributes Performance TaskLarge Group, Individual

Classify shapes by attributesCreate graphs

Build a Shape Learning TaskLarge Group

Study and create shapes, Classify, compare, contrast, and

describe shapes

Pattern Block Pictures Learning TaskLarge Group, Partners Create, classify, and describe shapes

Which One Doesn’t Belong? Performance TaskPartners Compare, classify, and contrast shapes

Describe It, Chart It, Find It, Make It

Performance TaskSmall Group Study and create 2D and 3D shapes

Listen and Do! Performance TaskIndividual

Arrange and describe proximity, position, and direction

I Want Half! Learning TaskLarge Group, Small Group

Share objects between people,Identify, describe, label, create fractions

Understand whole

Where Does it Live? Performance TaskLarge Group, Small Group

Understand whole

Fractions Are as Easy as Pie! Performance TaskLarge Group, Small Group

Understand wholeCulminating Task : Monster Math Performance Task

Individual

Understand whole

OVERVIEW

In this unit, students will: study and create two- and three-dimensional figures identify basic figures within two- and three-dimensional figures compare, contrast, and/or classify geometric shapes using position, shape, size, number of

sides, and number of corners arrange and describe objects in space by proximity, position, and direction solve simple problems, including those involving spatial relationships investigate and predict the results of putting together and taking apart two- and three-

dimensional shapes create mental images of geometric shapes using spatial memory and spatial visualization relate, identify, and label fractions (halves, fourths) as equal parts of whole objects, AND

on the number line between ANY two whole numbers

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics such as counting, time, money, positional words, patterns, and tallying should be addressed on an ongoing basis through the use of calendar centers and games.

To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under “Evidence of Learning” be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely replace, the textbook. Textbooks not only provide much needed content information, but excellent learning activities as well. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources.

STANDARDS ADDRESSED IN THIS UNIT

KEY STANDARDS

M1G1. Students will study and create various two and three-dimensional figures and identify basic figures (squares, circles, triangles, and rectangles) within them.

a. Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.b. Build, represent, name, and describe cylinders, cones, and rectangular prisms.c. Create pictures and designs using shapes, including overlapping shapes.

M1G2. Students will compare, contrast, and/or classify geometric shapes by the common attributes of position, shape, size, number of sides, and number of corners.

M1G3. Students will arrange and describe objects in space by proximity, position, and direction (near, far, below, above, up, down, behind, in front of, next to,

and left or right of).

M1N3. Students will add and subtract numbers less than 100 as well as understand and use the inverse relationship between addition and subtraction.

h. Solve and create word problems involving addition and subtraction to 100 without regrouping. Use words, pictures and concrete models to interpret story problems and reflect the combining of sets as addition and taking away or comparing elements of sets as subtraction.

M1N4. Students will count collections of up to 100 objects by dividing them into equal parts and represent the results using words, pictures, or diagrams.

c. Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of objects or a whole using pictures and models.

d. Understand halves and fourths as representations of equal parts of a whole.

RELATED STANDARDS

M1N1. Students will estimate, model, compare, order, and represent whole numbers up to 100.

a. Represent numbers up to 100 using a variety of models, diagrams, and number sentences. Represent numbers larger than 10 in terms of tens and ones using manipulatives and pictures.

b. Correctly count and represent the number of objects in a set using numerals.c. Compare small sets using the terms greater than, less than, and equal to.d. Understand the magnitude and order of numbers up to 100 by making ordered sequences and representing them on a number line.

M1N2. Students will understand place value notation for the numbers 1 to 99. (Discussions may allude to 3-digit numbers to assist in understanding place value.)

c. Decompose numbers from 10 to 99 as the appropriate number of tens and ones.

M1N3. Students will add and subtract numbers less than 100, as well as understand and use the inverse relationship between addition and subtraction.

a. Identify one more than, one less than, 10 more than, and 10 less than a given number.

b. Skip-count by 2s, 5s, and 10s, forward and backwards; to and from numbers up to 100.

c. Compose/decompose numbers up to 10 (e. g. 3+5=8, 8=5+2+1).d. Understand a variety of situations to which subtraction may apply: taking away from

a set, comparing two sets, and determining how many more or how many less.e. Understand addition and subtraction number combinations using strategies such as

counting on, counting back, doubles and making tens.

f. Know the single-digit addition facts to 18 and corresponding subtraction facts with understanding and fluency. (Use strategies such as relating to facts already known, applying the commutative property, and grouping facts into families.)

g. Apply addition and subtraction to 2 digit numbers without regrouping (e.g.15 + 4, 80-60, 56 + 10, 100-30, 52 + 5).

M1M2. Students will develop an understanding of the measurement of time.b. Begin to understand the relationship of calendar time by knowing the number of days in a week and months in a year.

M1D1. Students will create simple tables and graphs and interpret them.a. Interpret tally marks, picture graphs, and bar graphs.b. Pose questions, collect, sort, organize and record data using objects, pictures, tally

marks, picture graphs, and bar graphs.

M1P1. Students will solve problems (using appropriate technology).a. Build new mathematical knowledge through problem solving.b. Solve problems that arise in mathematics and in other contexts.c. Apply and adapt a variety of appropriate strategies to solve problems.d. Monitor and reflect on the process of mathematical problem solving.

M1P2. Students will reason and evaluate mathematical arguments.a. Recognize reasoning and proof as fundamental aspects of mathematics.b. Make and investigate mathematical conjectures.c. Develop and evaluate mathematical arguments and proofs.d. Select and use various types of reasoning and methods of proof.

M1P3. Students will communicate mathematically.a. Organize and consolidate their mathematical thinking through communication.b. Communicate their mathematical thinking coherently and clearly to peers, teachers,

and others.c. Analyze and evaluate the mathematical thinking and strategies of others.d. Use the language of mathematics to express mathematical ideas precisely.

M1P4. Students will make connections among mathematical ideas and to other disciplines.

a. Recognize and use connections among mathematical ideas.b. Understand how mathematical ideas interconnect and build on one another to produce

a coherent whole.c. Recognize and apply mathematics in contexts outside of mathematics.

M1P5. Students will represent mathematics in multiple ways.a. Create and use representations to organize, record, and communicate mathematical

ideas.

b. Select, apply, and translate among mathematical representations to solve problems.c. Use representations to model and interpret physical, social, and mathematical

phenomena.

ENDURING UNDERSTANDINGS

The properties of shapes make them alike or different. Some shapes have sides, angles, and faces which can be counted. Patterns can be created, extended, and transferred through the use of geometric shapes. Location of shapes can be described using positional words. Fractions are numbers on the number line that represent equal parts of a whole or set.

ESSENTIAL QUESTIONS

What makes shapes different from each other? How do shapes fit together and come apart? How can shapes be sorted? Where can we find shapes in the world? How can we create a pattern using shapes? How can we divide shapes into equal parts? How can we divide quantities into equal parts? How do we know where a fraction belongs on the number line (where does it live)? How can we group certain shapes together? Why do they belong together? How are shapes used in our world? How can a shape be described? How can we combine shapes to create different shapes? How do direction words help us find an object or place? How can we be sure that we have equal parts? Why is it important to divide into equal parts? How can shapes share the same attributes?

CONCEPTS/SKILLS TO MAINTAIN

Counting to 30 Patterning Sorting Number words through 10 Writing numbers through 20 Ordinal numbers (1st – 10th) Comparing sets of 1-10 objects (using terms equal to, more than, or less than) One to one correspondence Equivalence Basic geometric shapes Spatial relationships – positional words Estimation using five or ten as a benchmark Modeling addition and subtraction Name and value of coins

Calendar time and daily schedule Measurement – comparing and ordering

SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and how their students are able to explain and apply them.

The definitions below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers.

Circle: the set of all points in a plane that are the same distance from a given point

Cone: a hollow or solid object that has a flat, round base and narrows to a point at the top

Cube: a special kind of rectangular prism with all six faces being squares.

Cylinder: a hollow or solid object shaped like a round pole or tube

Far: a positional word, a long way off

Fractions: are numbers that represent equal parts of a whole or set

Fourths: the parts you get when you divide something into four equal parts

Halves: the parts you get when you divide something into two equal parts

Hexagon: a closed plane figure (2D) with six straight sides

Left of: a positional word, on or to the left

Near: a positional word, close; not far

Next to: a positional word, beside

Pentagon: a closed plane figure (2 D) with five straight sides

Quadrilateral: closed plane figure (2D) with four straight sides (rectangles and squares are quadrilaterals)

Rectangular prism: a hollow or solid object with six rectangular faces

Right of: a positional word; on or to the right

Sphere: a hollow or solid circular object

Triangle: a closed plane shape ( 2D) with three straight sides

Whole: unit; an entire object or set

Teacher Note: The definitions for SQUARE and RECTANGLE can be found in Kindergarten Unit 2.

Classroom RoutinesThe importance of continuing the established classroom routines cannot be overstated. Daily routines must include such obvious activities as taking attendance, doing a lunch count, determining how many items are needed for snack, lining up in a variety of ways (by height, age, type of shoe, hair color, eye color, etc.), daily questions, 99 chart, and calendar activities. They should also include less obvious routines such as how to select materials, how to use materials in a productive manner, how to put materials away, in addition, how to do just about everything! In addition children need to have plenty of time to explore new materials before attempting any directed activity with these materials. The regular use of these routines are important to the development of students’ number sense, flexibility, and fluency which will support students’ performances on the tasks in this unit. See unit 1 for suggestions concerning specific ideas for classroom routines.

99 Charts Post several 99 charts in the classroom. Have one at your math calendar/bulletin board area. It is important to use a 99 chart rather than a hundred’s chart for several reasons. First, a 99 chart begins with zero where a hundred’s chart begins with 1. We need to include zero because it is one of the ten digits and just as important as 1-9. Second, a 99 chart puts the decade numerals (10, 20, 30, etc.) in the correct row. For instance, the number 20 is the beginning of the 20’s family; therefore it is at the beginning of the 20’s row. Lastly, the 99 chart ends with the last two digit number, 99. The number 100 should begin a whole new chart because it is the first three digit number. Please see unit 1 for additional ideas for using a 99 chart.

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

STRATEGIES FOR TEACHING AND LEARNING

Students should be actively engaged by developing their own understanding. Mathematics should be represented in as many ways as possible by using graphs, tables,

pictures, symbols, and words. Appropriate manipulatives and technology should be used to enhance student learning. Students should be given opportunities to revise their work based on teacher feedback,

peer feedback, and metacognition which includes self-assessment and reflection. Math journals are an excellent way for students to show what they are learning about a

concept. These could be spiral bound notebooks that students could draw or write in to describe the day’s math lesson. First graders love to go back and look at things they have done in the past so journals could also serve as a tool for a nine week review.

EVIDENCE OF LEARNING By the conclusion of this unit, students should be able to demonstrate the following competencies:

Sort shapes into groups made up of members sharing the same attributes. Compare shapes based on attributes. Find and name shapes in the environment. Use shapes to create representations of items in the environment. Compose and decompose shapes. Create shapes, both 2 and 3 dimensional. Divide a collection of objects into equal parts (halves, fourths). Divide wholes into equal parts (halves, fourths). Locate where a number lives on a number line and tell who its neighbors are. Locate where a fraction (halves, fourths) lives on a number line.

Performance Task: Graphing Attributes

STANDARDS ADDRESSED

ESSENTIAL QUESTIONS

How can shapes be sorted? How are shapes used in our world?

MATERIALS

Student shape page Large drawing paper or construction paper Scissors Glue

GROUPING

Large, Individual

TASK DESCRIPTION, DISCUSSION AND DEVELOPMENT

Background KnowledgeStudents should have had prior experiences sorting, classifying, creating, and interpreting graphs using appropriate mathematical language.

Part IDisplay a variety of the shapes from the task sheet on an overhead or chart. Have the students brainstorm ways to describe the shapes. Chart their responses. (Please save this for further shape studies.) Guide students to look for ways other than color and size when describing the shapes such as by number of sides, number of corners, or no corners. Have students give examples of things they have seen in their environment that have some of these same shapes. Some examples may be badges, buttons, awards, stickers, signs, etc.

Note:You can save time by cutting out the shapes on the student page in advance. Store each set in a zippered plastic bag, paperclip, or envelope. Another idea would be to have a set copied onto cardstock and laminated so that they could be used again for activities or in a center.

Part IIStudents should organize their shapes into groups for a graph. Students will be able to create various ways to display their information (picture graph, bar graph, or tally charts.) They should create these graphs on their own and then write what they know about their graphs.

As students sort shapes and make their graph, make sure to ask open-ended questions so the students can verbalize how they are thinking. Questions may include:

What can you tell me about the way you sorted your shapes? Can you think of another way to sort them? Why do you think there is more than one way to sort the shapes? Where do you see these kind of shapes (listen for and encourage examples from in your

classroom, outside, at home, etc.) What helped you decide how you were going to make your graph? How will you describe your graph to the class? What question can you write for the rest of the class to answer using your graph?

Questions for Teacher Reflection

Am I allowing students to make their own sorting discoveries? Too often we want to tell a student how to get an answer and miss out on opportunities for them to show other valid ways to solve a problem.

How are the students sorting the shapes? Are students recognizing how these shapes are used in our world? Does their graph make sense? Can they explain it to the class? Did the student write a question for the class to answer (using the graph they made)?

DIFFERENTIATION

Extension For students who are easily sorting the shapes into two groups try having them sort the

shapes into three or four groups. Have them create a graph for each of the groupings.

Intervention For students who are having difficulty sorting the shapes, give them a set of attribute

blocks they can pick up and feel. The teacher can choose the type of graph for the student. Premade graph template could

also be available.

Technology Link Students can access interactive attribute blocks at The National Library of Virtual Manipulatives website: http://nlvm.usu.edu/en/nav/topic_t_3.html

Learning Task: Build a Shape

STANDARDS ADDRESSED

a. Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.c. Create pictures and designs using shapes, including overlapping shapes.

ideas.b. Select, apply, and translate among mathematical representations to solve problems.c. Use representations to model and interpret physical, social, and mathematical

phenomena.

ESSENTIAL QUESTIONS

What makes shapes different from each other? How do shapes fit together and come apart? How can a shape be described?

MATERIALS

The Greedy Triangle by Marilyn Burns or other similar book Toothpicks

1 piece of construction paper for each student Glue or mini marshmallows (see task for choice) 10-12 die-cut squares per student (can be different colors) 3-4 large squares for teacher demonstration Small zippered plastic bags (1 per student to be used for investigation)

Other LiteratureWhen a Line Bends…A Shape Begins by Rhonda Gowler GreenThe Shape of Things by Dayle Ann Dobbs

GROUPING

Large Group

TASK DESCRIPTION, DISCUSSION AND DEVELOPMENT

CommentThis task will take a few days.

Part IRead The Greedy Triangle, a book about a shape that wanted to be something else (or other similar book about various shapes). As you are reading, record any new information from the story to be used for the second part of the task.

Part IICompare and contrast information from The Greedy Triangle and the chart made in Graphing Attributes task. Ask students to use this information to create new more specific statements on sentence strips. Record student responses about these shapes: rectangle, square, triangle. Save these statements to be used in the third task, Pattern Block Picture.

Possible students questions for formation assessment: How many sides are in a triangle, rectangle, pentagon, etc.? Can you show me? How are these shapes different from one another? How are they alike?

Part IIIStudents will use toothpicks to recreate a triangle, rectangle, square, pentagon, and a hexagon. These shapes are to be glued to a sheet of paper and labeled with the correct shape name and the number of toothpicks used to make the shape. As the students work, ask the students if they see a relationship between the number of toothpicks they used and the number of sides in the shape.As an alternative to gluing them on paper, students could use small marshmallows and toothpicks.

Part IV

CommentThis portion of the task should be completed in small groups on the next day.

Task DirectionsTell students, “Today, we want to see how many different shapes we can create using a square.” Display a large square to the students and ask, “What will happen if I cut this shape straight down the middle? What shapes will be created?”

Possible conversation, student responses may be “Another square, two squares, or a rectangle and a square.” After the teacher makes the cut and the students discuss the result, now would be a good time to have a squares and rectangle discussion.

Good questions to ask: “Why do we call these two shapes rectangles, not squares? How do you know a shape is a rectangle, but not a square? How are rectangles and squares alike? Are all rectangles squares? DO NOT ASK WHAT MAKES A SQUARE DIFFERENT THAN A RECTANGLE BECAUSE ALL SQUARES ARE RECTANGLES, BUT NOT ALL RECTANGLES ARE SQUARES. Instead, ask something like this: What makes a square special? A square is a rectangle, but what makes it a square?

Ask students, “What characteristics does a rectangle have? To be a rectangle, what characteristics do I have to have? Are those the same characteristics needed to be a square?”

You are leading the students to an understanding that all squares are rectangles, but not all rectangles are squares. Discussion should continue with idea that squares are special kinds of rectangles. Horizontal, vertical and diagonal vocabulary could be used. Emphasize the lines that students cut have to be straight horizontal, vertical, or diagonal and then demonstrate these to the students. Example cuts should include ones that are not just straight through the middle, instead the teacher should snip off one corner demonstrating a small cut. This will show students their cuts can be of various lengths. Take turns having one student demonstrate a cut and then other students model the same cut. As one piece is cut off, teacher will lead students in a discussion of vocabulary terms of possible shapes such as: pentagon, triangle, rectangles, and quadrilaterals. Be sure to save pieces that are snipped off in the individual zippered plastic bags for students, so that they can use them later in a center to compose and decompose shapes. As students create various shapes, they can label for future investigations.

Examples of cuts that can be made:

Questions for Teacher ReflectionIn this activity, the goal is for students to see the relationship between different plane shapes. Becoming familiar with the characteristics of these shapes will help them to make the connection to solid figures and their similar characteristics.

What makes shapes different from each other? How do shapes fit together and come apart? Do students see this activity as just a geometry lesson or do some recognize the built-in

addition and subtraction concepts as strips or toothpicks are added or taken away to make new shapes?

DIFFERENTIATION

Extension Challenge students to make larger shapes that use more toothpicks but still have the same characteristics. Ask students: “Would you still have a triangle if two sides were longer than the third side? Why or why not?” Ask students, “What kind of shapes would be created by making 2 cuts?” New shapes could include: quadrilaterals that are not rectangles and hexagons.

Intervention Allow students who may be having a difficult time describing or making the shapes extra

time with the toothpicks and pattern or attribute blocks as a model. Also students could use tangram pieces if they are having difficulty with the cuts.

Learning Task: Pattern Block Pictures

STANDARDS ADDRESSED

a. Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.c. Create pictures and designs using shapes, including overlapping shapes.

M1P4. Students will make connections among mathematical ideas and to other disciplines.a. Recognize and use connections among mathematical ideas.b. Understand how mathematical ideas interconnect and build on one another to produce

a coherent whole.c. Recognize and apply mathematics in contexts outside of mathematics.

phenomena.

ESSENTIAL QUESTIONS

How can a shape be described? How do shapes fit together and come apart? What makes shapes different from each other?

MATERIALS

Pattern blocks (in bags for each student) Construction paper or die cutouts of pattern blocks (1 bag per student with enough to

create picture) Construction paper Pattern Block Picture recording sheet Glue sticks (1 for each student)

Comments: The bags should contain enough shapes so that students can easily make a picture with 12 shapes (See task for description.)

GROUPING

Large Group, Partners

TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

Part IGather students on class meeting area. Display a picture of a triangle, rectangle (that is not a square), and a square rectangle. Use sentence strips from previous task and have students place statements under the correct shape. You need to add pentagon and possibly hexagon to your display.

CommentMany statements will fit under square will also fit under rectangle because again, all squares are rectangles. Additional statements could be added about where we find these shapes in the real world.

Part II

CommentFormal discussions about a trapezoid and rhombus have not necessarily occurred in kindergarten; therefore the red, blue and tan pieces may not be familiar to your students. They were probably introduced to these shapes as quadrilaterals. It is okay to introduce the more specific name for these shapes, but please keep in mind, first graders do not have to master identification of these shapes. Keep in mind a first grader does not have to be able to identify a shape as a parallelogram, rhombus or trapezoid.

Next give each student a zippered plastic bag of pattern blocks. Have students trace pattern blocks on paper and discuss attributes of each shape. Be sure to name the number of sides, number of corners, as well as shapes that can be combined to create other shapes. For example “I combined two squares to make a rectangle.”

Special NoteStudents will likely combine a trapezoid and a triangle, which will create a parallelogram. You can choose to introduce the term parallelogram or stick with term quadrilateral.

Allow students a few minutes to practice tracing shapes. Collect pattern blocks. Then distribute zippered plastics bags that contain the cutout paper pattern blocks. Have students create a picture using at least a dozen of the pattern block shapes. Encourage students to combine multiple pieces together so that the picture is made up of pattern block shapes touching. You may want to provide an example for students to see how pattern blocks can be combined.

Once students have created their pictures, glue the picture onto a sheet of construction paper.

Ask questions such as: Which shape did you use the most of? Least of? What are you noticing about these shapes? What do they have in common? How are

they different? Did any of your shapes combine to form other shapes? Which shapes are easy to combine? Why do you think this? Are any hard to

combine? Why? What else did you discover?

Part IIIUsing the Pattern Block Recording Sheet, have students place a tally mark to record the number of each shape used to create their picture. Then students should write a story about their picture.

Part IVAs a class, students share their individual shape totals in order to create a class shape total. This could be started in picture graph format. At some point (probably after 8 to 10 students have placed their shapes on the graph,) students will notice that they are running out of space; therefore, this may not be the best way to record this information. Discussion about this not being the best way to record this information needs to occur. Then ask students what other kind of graph they could create. You are leading them into creating a bar graph. Create class bar graph. Students could then generate questions that could be answered using this information.

Questions for Teacher Reflection

Are students correctly describing shapes? Are students noticing how shapes fit together and come apart? Can students identify what makes shapes different from each other? Are students able to generate questions related to the bar graph?

DIFFERENTIATION

Extension Have students create questions about their own shape tally chart and create a graph about

their picture. “Which shape did you have more/fewer of? How many more/fewer?” Students could glue shapes down and create shape again on top. This would help them as

they count tallies for the chart.

Intervention If tracing is too time consuming for some students, skip this part and give them the precut

shapes. Ask the student to identify the name of the shape and the number of sides it has verbally.

Students may also make their pattern block picture and tally the number of shapes before gluing them down. This will allow the student to sort them into like groups first.

Pattern Block Picture Chart

Performance Task: Which One Doesn’t Belong?

Adapted from Math Connections: Linking Manipulatives and Critical Thinking by David J. Glatzer and Joyce Glatzer (1997) by Dale Seymour Publications.

STANDARDS ADDRESSED

M1G2. Students will compare, contrast, and/or classify geometric shapes by the common attributes of position, shape, size, number of sides, and number of corners

ESSENTIAL QUESTIONS

What makes a shape different from other shapes? How can we group certain shapes together? Why do they belong together?

MATERIALS

Attribute blocks “Which One Doesn’t Belong?” task sheet

GROUPING

Small Group

TASK DECRIPTION, DEVELOPMENT AND DISCUSSION

Part IThe students will be shown four attribute blocks, three of which have some similar properties or characteristics (based upon, shape, size, color, thickness.) Discuss which three belong together and why. Have students justify their reasoning. The teacher can decide how the students share their choices and their reasoning. Provide several examples, then allow students to work on their own to create their own examples. Then allow students time to share their example and have other students identify which one doesn’t belong and why.

Part IIStudents complete “Which One Doesn’t Belong” task sheet. Comment: Having students explain WHY they respond to the answer that they give is extremely important. Encouraging student discussions about how or why other answers could also be correct will enrich student understanding. Once students are familiar with the game, they are able to make-up their own questions. Please note there are some examples that could have multiple correct answers. Answers are correct as long as students are able to justify them.

Suggested questions for summative student assessment: Are there any ways that all pieces are the same? What makes your one piece different from the other shapes? Is there more than one difference? Could you have grouped your shapes any other way? Can you think of another shape that would fit into the group with the other three shapes?

Questions for Teacher Reflection Can students explain what makes the one shape different from the other shapes? Do they notice if there is more than one difference? Did they group the shapes more than one way? Can students identify another shape that would fit into the group? Are students able to justify their choices for sorting?

DIFFERENTIATION

Extension Have students create a booklet of their own problems. It could be placed in a center for

future review.

Intervention Use a smaller simpler set of shapes, for instance a set of three where two of the shapes

are obviously alike (square and rectangle) and one that is obviously different (circle).

Which One Doesn’t Belong?

A B C D

Shape _________ doesn’t belong because _______________________________________________

_________________________________________________________________________________

_________________________________________________________________________________.

A B C D

_________________________________________________________________________________

_________________________________________________________________________________.

A B C D

_________________________________________________________________________________

_________________________________________________________________________________.

A B C DShape _________ doesn’t belong because _______________________________________________

_________________________________________________________________________________

_________________________________________________________________________________.

Performance Task: Describe It, Chart It, Find It, Make It

STANDARDS ADDRESSED

b. Build, represent, name, and describe cylinders, cones, and rectangular prisms.

phenomena.

ESSENTIAL QUESTIONS

Where can we find shapes in the real world? How can a shape be described?

MATERIALS

Geometric solid models for: cylinder, cone, and rectangular prism Graphic organizer chart Student copy of graphic organizer Names of geometric solids on index cards Index cards (for student labeling) Modeling clay or play dough Captain Invincible by Stuart J. Murphy

GROUPING Small Group

CommentPrepare a chart/graphic organizer to record the characteristics of the three-dimensional figures as you read the story.

Part I

Read Captain Invincible and the Space Shapes by Stuart J. Murphy or other book about 3D shapes.

Pass solids (cylinder cone, and rectangular prism) around and ask students to describe how each one looks and feels and record these characteristics in the graphic organizer. Students will complete the Describe It, Chart It, Find It, Make It Task Sheet. Allow students to use solids to trace around with a pencil to determine the shape of its face.

CommentsOne way to talk about how 3-D shapes are different than 2-D shapes is to refer to 3-D shapes as having a body. This is why it is easy hold them in our hand. 2-D shapes do not have a body, which is why it is easy to draw them on paper. If you use the term “body” when talking about 3-D shapes then discussing “face” on the 3-D shape is a little easier. Our bodies have a face, and likewise most 3-D shapes have a face, some have more than one face. How funny would we look if we had more than one face?!

It is natural for students to initially talk about the faces as “sides” but as you talk about them make sure to use the word faces not sides. Gradually the students will pick up on this and will start calling the “sides” face. This is important because “side” actually refers to a two dimensional shape. When you are talking about a three dimensional shape, for instance a cube, it has 6 faces but 12 edges! Each face has four sides.

Part IIHave students go on a geometric solid shape hunt in the classroom to fill in the last column of the chart. Students tell the name of the solid it represents, write its name on an index card, and attach it to the item. Shapes can then be displayed in a “Solid Shapes Museum.”

As you circulate, observe the student’s choices and listen to their conversations. Help students to understand they can learn to recognize the shapes even though they are not exactly the same as the model. During their shape hunt and as students share their 3-D findings, ask the students questions like:

Is this object exactly like our model? How is it the same? How is it different? Which solid is the hardest to find in the classroom? Why? What do you notice about the faces of the objects?

After their hunt, students will use modeling clay or play dough to create solids. As students work on their models, ask them to name and describe their solids. These can also be labeled and added to the museum display using notecards.

Questions for Teacher Reflection Are students able to talk about where we find shapes in the real world? How are the students describing the shapes they are finding? Are they able to choose something easily from the classroom without referring back to

the solid example? Do most students choose the solid they are most familiar with, such as a rectangular

prism? Which ones are they not choosing?

DIFFERENTITATION

Extension Students could determine attributes and then use that information to graph objects from

the “Shape Museum”. Students could extend their search to the rest of the school and /or use cameras to take

pictures of other items that represent 3-D solids. A home connection could be made by sending a parent letter asking for students to search

for solids they could bring back to school to add to the “Shape Museum.”

Intervention Give students who struggle cards with examples of 3-D solids that can be used when they

are looking for objects for the “Shape Museum.”

Describe It, Chart It, Find It, Make It Task Sheet

Number of corners

Number of faces

Is the facea circle,

square, or a

rectangle?

Everyday object

Cylinder

Rectangular

Performance Task: Listen and Do!

STANDARDS ADDRESSED

M1G3. Students will arrange and describe objects in space by proximity, position, and direction (near, far, below, above, up, down, behind, in front of, next to, and left or right of).

phenomena.

ESSENTIAL QUESTIONS

How do direction words help us find an object or place?

MATERIALS

Drawing paper Crayons or markers

GROUPING Individual

Students will listen to the directions and draw objects according to where something is to be placed. They will listen to entire direction the first time without drawing. After hearing the direction a second time the students will draw.

Give time for students to draw, closely monitor to see when you need to move to the next direction. Have students pair/share after the activity. As students share their work with a partner, they should be using positional words to describe the picture they drew.

Ask the students questions such as: How is your picture the same or different from your neighbor’s? Which directions would look similar? How do you know? Which direction was the hardest for you to follow? What made it so hard? Which direction was the easiest to follow? Why?

Questions for Teacher Reflection Which directional words are students having the most difficulty with? Can students follow a list of directions accurately? Are students able to explain how direction words help us find an object or place?

DIFFERENTIATION

Extension While on the playground, students could set up their own “Listen and Do” activity. One

person would be the leader and give others directions such as; going over three objects, around one object, and under two objects, etc.

Provide partners with pattern blocks and a folder. One student will call out directions as he or she creates a pattern train on one side of the folder. Other student will listen and create pattern train on the other side of the folder. Once directions are finished, folder is removed and students check to see if pattern trains match.

Intervention Provide students with left/right reminder cards if needed. Some students may need fewer

directions to begin the task and then can progress to more as they master four or five directions. Below is an example of how to structure such an activity:

Draw a small house in the middle of your paper. Draw two big trees, so that the house is between the two big trees. Draw a basket near the house. Draw a cat inside the basket. Draw a dog outside the basket. Draw a snake close to the dog. Write your name on the top left corner of your paper. Draw a sun on the top right corner of your paper. Draw a butterfly before the dog. Now color your picture.

Divide a sheet of paper into fourths and then give directions specific to one box at a time. For example: “In the top left box, write your name. In the top right box draw a circle with a triangle inside of it. In the bottom left box, write the numeral three and draw three flowers. In the bottom right box, draw a puppy close to a boy.” Have students describe what they did using positional words.

Listen and Do

Read each direction to students two times.

Draw a small house in the middle of your paper.Draw two big trees, so that the house is between the two big trees.Draw a basket near the house.Draw a cat inside the basket.Draw a dog outside the basket.Draw a snake close to the dog.Write your name on the top left corner of your paper.Draw a sun on the top right corner of your paper.Draw a butterfly before the dog.Now color your picture.

Learning Task: I Want Half!

STANDARDS ADDRESSED

a. Use informal strategies to share objects equally between two to five people.c. Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of

objects or a whole using pictures and models.d. Understand halves and fourths as representations of equal parts of a whole.

phenomena.

ESSENTIAL QUESTIONS

How can we divide shapes into equal parts? How can we be sure that we have equal parts? Why is it important to divide into equal parts?

MATERIALS

I Want Half by Stuart J Murphy or similar book Set of Pattern Blocks for each pair of students Paper for drawing and writing

GROUPING

Large group, small group

Part IAsk students if they have ever had to share something with someone. Have them turn to tell a neighbor (elbow buddy) about their experience. Then have students share the story that their partner shared with them. Next, share with the class the title of the book you are about to read, Give Me Half by Stuart J Murphy or similar book. Have them make predictions about the story before reading.

At the conclusion of the story review what having “half” of something means…that there are two equal parts. Make sure students can explain this and understand that having half means that each person gets one of the two parts.

Part IIGive each pair of students a bag full of pattern blocks. Tell them they are going to act like the children in the story and share their materials. Have them pull out the yellow hexagon and instruct them to search through their shapes to try and find one that they think would cover up only half of the hexagon. Facilitate the investigation with a discussion like, “Think about the two children in the story. If they have to share this hexagon, how much will each one get? (half) What shape represents half of the hexagon? (red trapezoid) How do you know?(it takes two to cover it up). Why didn’t you say the triangle? (because it takes 6 of those to cover it up) What if you only had triangles to use, could they still get half of the hexagon? Prove it: how many would each child get? (3) Would that be half of the hexagon? (yes) How do you know? (because each person gets the same amount. Is there another shape that covers the hexagon? (yes, blue rhombus) How many does it take? (3) Would one of those three pieces make half of the hexagon? (no) How do you know? (it can’t be shared equally by two people).

Part IIIHave students draw a picture of something being shared equally. They can draw a picture of the story they told their partner (elbow buddy) or what their buddy told them at the beginning of the lesson or they can draw a picture of something else. You can provide pictures for the students to look at if you think this will help them create their own drawing. Once they have their picture completed have them write a few sentences explaining what is going on in the picture.

Questions for Teacher Reflection Which directional words are students having the most difficulty with? Can students follow a list of directions accurately? Are students able to explain how direction words help us find an object or place?

DIFFERENTIATION

Extension Provide partners with pattern blocks and a folder. One student will call out directions as

he or she creates a pattern picture on one side of the folder. Other student will listen and create pattern picture on the other side of the folder. Once directions are finished, folder is removed and students check to see if pattern trains match.

Performance Task: Where Does it Live?

STANDARDS ADDRESSED

b. Use informal strategies to share objects equally between two to five people.e. Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of

objects or a whole using pictures and models.f. Understand halves and fourths as representations of equal parts of a whole.

phenomena.

ESSENTIAL QUESTIONS

How can we divide shapes into equal parts? How can we be sure that we have equal parts? Why is it important to divide into equal parts? How do we know where a fraction belongs on the number line (where does it live)?

MATERIALS

10 large notecards with the numbers 0-10 and a picture of yellow pattern block hexagons that represents the number on the card

Scissors- one pair per set of partners Glue Half sheets of paper, 2 for each student Baggie with 20 yellow paper hexagons per partners

GROUPING

Comments Prepare a space for the number line to be 10 to 12 feet long. Allow for 10 to 12 inches in between each number, so it will be easy to place hatch marks.

Part I Begin with the essential question, “How do we know where a fraction belongs on the number line (where does it live)?” Draw a number line on the board, but do not put numbers on it. You will use a set of notecards that has one numeral (0-10) on it as well as a picture that represents the amount. For example, the number four will have four regular yellow hexagons either drawn on it or you can paste paper cut outs of the yellow hexagons on it. It is recommended that you use the yellow hexagons from a set of pattern blocks because students are familiar with these shapes and they can easily be cut in half (for later in the lesson). Show the students the set of notecards and ask “Can anyone tell me where we would put 0 on our number line?” Listen for them to say at the front or beginning. Then ask questions like, “Why do you think it needs to go at the beginning? What number would we put up next? How do you know? What about after that? So who lives next door to the number one? How many neighbors does the number one have?”Next ask, “What should our number line end with? (10) How do you know? (10 is the largest number we are working with at the moment) What about 5, where do you think it should go?(in the middle between 0 and 10) How did you figure that out?” Allow several students to share reasoning on benchmark number placement. It is important to listen for the reasoning that 5 is half of 10.

Place the remaining numbers in a bucket and have students come up and draw out one card at a time. This will be done randomly. Ask students to place the number they draw out where they think it “lives” on the number line. Ask questions such as, “Is the number you have closer to 0, 5, or 10? Who lives next door to that number? Is there another number that lives next door to your number? What two numbers does your number live in between? Is your number larger or smaller than the one we just put up? How do you know? How far away from 8 (or 4, 2, 10, etc) is your number?”

CommentThe numbers will be drawn randomly; therefore numbers may not be in the appropriate space on the number line. It is important to encourage discussion of why the placement of numbers is important. Students should use their knowledge of 5 and 10 as benchmark numbers to help them figure out where the other numbers they draw out should be placed.

Part IIOnce all the numbers are up on the number line again ask: “How do we know where a fraction belongs on the number line (where does it live)?” Say something like, “We have the numbers 0-10 up on our number line, but what about the question we asked a little while ago, how do we know where a fraction belongs on the number line (where does it live)?” Refer back to the “I Want Half” learning task they did previously. Write down some of the numbers they used from

that lesson, i.e. 2 ½ , 4 ½ , etc. Ask, “Where do you think we would place these numbers on the number line? Where do you think they live?” Allow students to share their reasoning. Record ideas on chart paper or on the board to address at the end of the lesson. Show students the materials they will need for the fraction exploration. Each set of partners will share scissors, glue, several half sheets of paper, and a set of 20 yellow hexagons (paper/dye cut outs of the pattern blocks NOT the wooden or plastic ones). Ask the students to think about how they could use their materials to create a picture for 3½ . Have them discuss this with their partner. After a couple minutes have several groups share their ideas. Listen for someone to suggest placing three hexagons on the paper and then cutting one of the hexagons in half and putting it on too. If this is offered then have the students elaborate on their idea and actually show and explain their picture. If this idea is not suggested then have an example of 3½ ready to show the students and ask “What does this picture show (3½ hexagons)? How do you know?” Once all agree on the correct representation then ask “Where should we hang this up on the number line? Should it go before or after 0? What about 2, 3, 4…why?” You are listening for students to say something along the lines of, “ It is more than 3 but less than 4” or “ We have 3 whole hexagons and part of another” or “ We have less than four because we need another half to make four hexagons”. Once the class agrees that the 3½ picture should be placed in between the 3 and 4, then move on to Part III.

Part IIIGive each set of partners two of the following fractional numbers to create (1½ - 9½.) Instruct them to use their materials to make a picture for the fractional numbers they have been given. Then have each set of partners share with another set of partners to “check” each of the representations. When a group of 4 students has agreed on their representations then have them work together to decide where their pictures should “live” on the number line. When they all agree then have them attach their picture to the number line on the board. Once each group is finished gather everyone back together as a whole class and talk about what they have created. Ask questions like, “What was the biggest number you created a picture for? How did your group decide where to place your picture? Who lives next door to 5½? Are these the only fractions? What number do you think lives in between 10 and 11? What about between 0 and 1?” Then ask… “Is there a way to have less than one but more than zero?” If students seem confused then show one yellow hexagon in your right hand and say, “I have one whole hexagon in my right hand but zero in my left hand. What could I do to make it so I have more than zero in my left hand but less than one in my right hand?” Students will probably say cut it so then get more specific and say, “If I want to ‘share it” exactly, like in the story Give Me Half, then how should I cut it?” Once you have cut it in half ask, “How much am I holding in my hand now? Do I have more than 0? Less than One? What amount do I have? Where should it go on our number line?” Have someone come up and place the hexagon in between 0 and 1 and then label it ½ .

Part IVHave magazines for students to look through to search for real life examples of halves. Have them post their examples on a bulletin board titled “For Real Fractions”. Allow students time to share their work and discuss their findings. It is important to discuss and share similarities and differences.

DIFFERENTIATION

Extension Have students work with the trapezoid, rhombus, and triangle pattern blocks. Have them

compare them to the yellow hexagon. Tell them that the yellow hexagon is the one whole and they need to come up with a fraction name for each of the other pieces based on the hexagon being one.

Performance Task: Fractions Are As Easy as Pie!

STANDARDS ADDRESSED

a. Use informal strategies to share objects equally between two to five people.c. Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of

objects or a whole using pictures and models.d. Understand halves and fourths as representations of equal parts of a whole.

phenomena.

ESSENTIAL QUESTIONS

How can we divide shapes into equal parts? How can we be sure that we have equal parts? Why is it important to divide into equal parts?

MATERIALS

Large sheet of paper to represent cake Crayons 3 pieces of construction paper per student Wooden or plastic dice labeled 1 whole, ½, ¼ A Fair Bear Share by Stuart J Murphy or similar book

GROUPING

CommentThis task is designed to take 3 or more class periods.

Part IThis activity is designed to help students “see” that how they divide/fold one large piece of paper into multiple pieces does matter! Demonstrate this by taking a sheet of paper, saying the sheet of paper is a cake that four students won at the fair, and then fold it unevenly. Tear off three small pieces to give to the three of the volunteers and then give the one big piece to the fourth student. Ask, “Is this fair? Why do you say that? What should I do to make it fair?” Invite further discussion with students about situations where they have had to share things, like cookies, candy or toys, and listen for them to verbalize the importance of making sure everyone gets a fair share!

Part IIGather students together and read A Fair Bear Share by Stuart J Murphy or similar book.

After the story do the following activity: Remind students of the cake scenario you discussed before reading the story. Ask “Is

there a way to cut the cake so it will be fair?” Allow students to share ideas. Give each student 3 sheets of construction paper that are the same size. Tell the students

that these represent 3 whole cakes. Have them label one of the sheets with the number one (because it represents one whole cake). It should also be labeled “one whole.”

Next, tell the students they are going to share the second cake (piece of construction paper) with one friend. Tell them to fold the paper in a way that it will create two equal pieces. Keep in mind some students may fold their paper vertically and some may fold it horizontally. Allow both representations to be shared and discussed. Ask questions such as: “Are these two representations of ½ the same size?” How do you know ? Can you prove it? Is there a way to cut one and rearrange it to fit into the other one?” Remind students of their work from Build a Shape task where they cut and rearranged shapes. The teacher should demonstrate through cutting and rearranging that the two representations of ½ are the same size.

Label each part of the second “cake” with both the fraction ½ and the word one-half. Be sure to revisit the meaning of half discussed in a previous task, I Want Half!

For the third sheet of construction paper, tell the students they are going to share this cake with 3 friends and again fold it in a way that creates four equal pieces. Some students may fold it vertically (like a fan) or vertically and horizontally (making a grid). Allow both representations to be shared and discussed. The discussion for ¼ should be similar to the one you had related to ½.

Label each part of the third “cake” with both the fraction ¼ and the word one-fourth. Make sure to ask students “What is happening to our pieces as we add more folds to the

paper? Why is this happening? What if we shared this cake with ten people, would we get more or less cake? How do you know? Which is bigger ½ or ¼? Can you prove it?”

While students are working, look to see that the children are dividing the rectangles into equal portions. The measurements do not have to be exact, but they should be very close in size. Part III

Preparation for Fraction Cover Up Game Students will be given 3 sheets of white construction paper. 1 sheet should be labeled as “one whole” 1 sheet should be folded and labeled as halves. Color the halves and cut them apart. 1 sheet should be folded and labeled as fourths. Color the fourths a different color

than the halves and cut them apart. Students will use the six fractional pieces to play a Fraction Cover Up game. The

game board is the “one whole” sheet of white construction paper that has not been folded or cut yet.

Directions for Fraction Cover Up Game The object of the game is to be the first one to completely cover your mat. Students will work with a partner. Each partner will use their own mat and fraction pieces they just created. They will take turns rolling a die that is labeled with ½ and ¼ (3 of each). Students will place the fractional piece that is rolled onto their mat. If they are

unable to play a piece, then they lose their turn. Play continues until one partner has covered their mat.

Questions for Teacher Reflection Are students able to divide the paper into fourths and halves? Are the students checking to make sure they have created equal parts? Can the students explain why it is important to divide into equal parts? Are students able to divide shapes into equal parts? Can students determine if two things are equal? Are they able to explain how they know

that these things are equal? Can students explain how they know ½ is bigger than ¼?

DIFFERENTIATION

Extension Allow students to explore dividing up shapes equally that are not rectangles, such as

circles, triangles, trapezoids, pentagons, hexagons, etc.

Intervention Have two sets of large precut rectangles. One set should already be divided into fractions

and labeled. Students can match the fractional rectangle puzzle pieces to the whole rectangle shape. Using this as a guide they will then divide, label, and color their own rectangle.

Culminating Performance Task: Monster MathThis culminating task represents the level of depth, rigor, and complexity expected of all first grade students to demonstrate evidence of learning.

STANDARDS ADDRESSED

M1G1. Students will study and create various two and three-dimensional figures and identify basic figures (squares, circles, triangles, and rectangles) within them

a. Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.b. Build, represent, name, and describe cylinders, cones, and rectangular prisms.c. Create pictures and designs using shapes, including overlapping shapes.

M1N1. Students will estimate, model, compare, order, and represent whole numbers up to 100.

a. Represent numbers up to 100 using a variety of models, diagrams, and number sentences. Represent numbers larger than 10 in terms of tens and ones using manipulatives and pictures.

b. Correctly count and represent the number of objects in set using numerals.c. Compare small sets using the terms greater than, less than, and equal to.

c. Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of objects or a whole using pictures and models.

d. Understand halves and fourths as representations of equal parts of a whole.

ideas.b. Select, apply, and translate among mathematical representations to solve problems.

c. Use representations to model and interpret physical, social, and mathematical phenomena.

ESSENTIAL QUESTIONS

How can shapes share the same attributes? How can shapes be divided into equal parts? How do shapes fit together and come apart? How can we combine shapes to create different shapes? How are shapes used in our world?

MATERIALS

Construction paper Crayons and/or markers Various “junk”: ribbon, shredded paper, tissue, buttons, etc. Monster Math by Anne Miranda or similar book

GROUPING

Large Group

TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

After reading Monster Math by Anne Miranda or similar book (this book can also be used as an introduction to addition and subtraction to 50), have students help create a list of “musts” for monster creation.

Help the class create a list of “musts” for the creation of monsters. Include in the list all shapes and fractional parts we have studied in this unit. Tell students to be creative, but include all the “musts” in their monster. Make and post the criteria list for the monster. Reminding students of attributes listed on the chart and “musts” determined as a class, have them create their own monsters using construction paper and various decorative “junk” such as ribbon, shredded paper, tissue, etc. Remind them to refer to the list of attributes created at the beginning of the lesson. Make sure students have created a list of attributes for their personal monster that includes things like number of claws, number of horns, length of tail, color of fur, etc. For example:

Monsters must contain a minimum of: The following shapes (allow students to list all the shapes they have investigated) 1 tail 4 claws be at least as tall as a chair leg have stripes or a pattern somewhere all pieces must be cut

no drawing have an example of fractional parts of a whole ( fourths or halves) in the design

Once all monsters are completed ask students to come up with some different ways in which they could organize their monsters. Brainstorm a list of way to organize the monsters, such as:

Way to organize our monsters: less than 5 claws more than 5 claws scary looking friendly looking has stripes has polka dots

Then partner students up and have them: Check to see if their partner’s monster complies with all the “musts” the class has

decided on. Talk about similarities and differences between your monsters. Have them work together to write a number sentence to describe their monsters

characteristics on a strip of paper and share with the class. Have the students write a story problem to describe your number sentence. Be

sure to use words and pictures in your story problem.

After partners have had time to work through the above tasks together then have groups of four students work together asking them to…

Choose a way to group or organize the monsters with all the friends in your group Choose a way to graph the monster groupings. Create a graph with your friends to share with the class.

Display monsters so all can see. Using the monsters, line them up according to some of the organizational ideas. Show how each can generate number sentences using +, -, =, or words such more than, less than, or equal to etc.

For example: 3 eyes is less than 5 claws 2 horns = 2 horns 4 arms is more than 1 head

Write number sentences on sentence strips. Have participants turn them into story problems. Then students return to seat, after choosing a number sentence/story problem to illustrate.

My Monster, Horrible Huckleberry, has 5 claws on his purple furry hand. He has 3 green eyes on his enormous purple head. How many more claws does he have than eyes?

These pages can also become a class book to be used along with monster sculptures. Using monster sculptures, graph attributes of the monsters. Have students share their graphs to discuss what data they collected about the class monsters.

For example: (gathering data) Monster Claws

Number of Claws Number of Monsters with that number of claws

5 claws 2 monsters

6 claws 4 monsters

8 claws 0 monsters

10 claws 5 monsters

10+ claws 9 monsters

Questions for Teacher Reflection Are students noticing how shapes can share the same attributes? Can they point these

attributes out? Are students able to identify both the similiarities and differences of two (or three or

four) given shapes? Can they explain how certain shapes fit together and come apart? Can students use given shapes to create new shapes? Are students able to divide shapes into equal parts? Can students explain the importance of equal parts? Do students recognize how shapes are used in our world?

DIFFERENTIATION

Extension Move this to a math center where students can create a pet or other monster family

member. The theme could also be changed as long as the attributes are determined ahead of time and the similar rules are followed.

Students could create clues about a monster and write questions to solve.

Intervention

Students may work with a partner or a small group to complete this task if needed. Encourage students to describe their work as they are creating their monster to assess understanding.

Important Teacher Note about Geometry and Fractions: Student work should be evaluated using appropriate rubrics; perhaps even rubrics created by the students. It is important that students are able to discuss and prove their knowledge of shapes, (triangles, rectangles, pentagons, hexagons, squares, and circles) and their attributes. Position, shape, size, number of sides, and number of corners, as well as fractional parts can be discussed. Vocabulary words would be terrific additions to a word wall that includes a picture or example for reference. Students could help create these with their own work throughout the unit. Further investigations of fractions can be found Elementary and Middle School Mathematics: Teaching Developmentally, 5th Ed. By Jon Van DeWalle

unit 3 organizer: - compton coaches · web view01/08/2009 · cone: a hollow or solid object...

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