Global Concept Guides: Describe and Sort Two-Dimensional Shapes, Compose Two-Dimensional Shapes, Decompose Two-Dimensional Shapes, Equal and Unequal Parts
Prior Learning:MAFS.K.G.1.2,MAFS.K.G.1.3,MAFS.K.G.2.4, MAFS.K.G.2.6
Progressions Document Link
Show What You Know Task:Show What You Know with Vocabulary Builder (p. 183-184)
Common Core State Standards for Mathematical Content :
Reason with shapes and their attributes.
MAFS.1.G.1.1Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
MAFS.1.G.1.2Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.1
MAFS.1.G.1.3Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
Footnotes:
1 Students do not need to learn formal names such as “right rectangular prism.” / Comments:
Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should use with increasing precision are: shape, closed, open, side, attribute, feature, two-dimensional, rectangle, square, trapezoid, triangle, half-circle, quarter-circle, equal shares, halves, fourths, quarters, half of, fourth of, quarter of
This parent flyercan be utilized by both you and parents to build content knowledge and understanding of the strategies highlighted in this unit.
Notes on Assessment:
Use Chapter 12 Form B Go Math Assessment
The performance task should be given after GCG 2.
Seecommonperformance tasklink below
Unpacking the Standards for this Unit:In this unit, students identify attributes of shapes as defining (triangles are closed and three sided) or non-defining (color, orientation, overall size). Students compose shapes to create a composite shape (a triangle and a rectangle composed together create a different shape). This concept of defining vs.non-definingattributes is new to students.
Children’s ideas about shapes do not come from passive looking. Instead, they come as children’s bodies, hands, eyes, and minds engage in active construction. In addition, children need to explore shapes extensively to fully understand them; merely seeing and naming pictures is insufficient. (A Research Companion to Principles and Standards for School Mathematics, pg. 152)
Common Performance Task with Rubric for this Unit: Two Dimensional Shapes
Students identify shape by attributes and show how to compose a shape using other shapes.
Click here for Performance Task and Rubric.
Future learning:In second grade, this unit’s geometry concepts are built upon by decomposing shapes into equal shares of halves, thirds, or fourths (2.G.3). These equal shares are used to show a connection between the decomposed shape, rows, columns, and the array interpretation of multiplication as repeated addition (2.G.2). In second grade, students will be able to draw a shape given a set of attributes such as given number of angles, faces, etc.(2.G.1). In third grade, students will also be able to partition shapes into equal areas and describe these sections in fractional terms (3.G.2).
1st / Global Concept 1 of 4for this Unit of Study (Click to view PowerPoint in slide show mode): Describe and Sort Two-Dimensional ShapesStudents will use defining attributes to sort and describe two-dimensional shapes / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1:What attributes can you use to sort two-dimensional shapes?
Day 2:What is the difference between a defining attribute and a non-defining attribute?
Day 3: What attributes can you use to define two-dimensional shapes?
Related Go Math Chapter Test Questions: Unit 13 (Go Math Ch. 12) #3, 5, 12, 15-16, 24
Instructional Resources
Manipulatives:
- Pattern Blocks to sort by rules or attributes
- Models of real-world two-dimensional shapes
- Geoboard/Rubber bands- In the Illuminations lesson: Investigating Shapes linked below there is a good activity utilizing Geoboard in lesson 3
- Pattern Block Cut-outs Black line Master to help build fine motor skills while developing a connection to the number of sides of a shape
- Go Math Lesson 12.1 Essentials: Listen and Drawp. 485 allows students to sort shapes by attributes, Math Talk in Action p. 487 probes students to think deeper about attributes, On Your Own p.487 provides rules which students have to find shapes that apply, Problem Solving (p.488as an independent check.
- Illuminations: Investigating Shapes – Lesson 3 with Geoboard students select shape from a bag without removing it from the bag and describes the shapes by defining attributes. Other students can ask yes or no questions to help give clues then the shape can be guessed.
- Go Math Lesson 12.2 Essentials: On Your Own p.491 relates the number of sides to the number of vertices and Problem Solving p. 492 students draw shapes to match the clues.
- Comparing Polygons Writing Activity to have students compare two shapes. It is recommended that you choose shapes that are similar and will have comparisons (such as triangles, rectangles, squares).
- Voyages Gr. 1 Excursions:Making Pictures (TE p.43-44 & SE p.59-60) Setting the Stage students build a square and a rectangle with toothpicks, and discuss attributes, then inBuilding Conceptual Knowledge students make a book of shapes, including their names, numbers of sides, and numbers of vertices.
- Animated Math Model: Skill 48: Sort and Classify Plane Figures
- Mega Math: Shapes in Different Orientations
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- How are ____ and ____ alike? Different? Explain.
- How can you prove a shape is a triangle? Square? Rectangle? Trapezoid? Rhombus? Pentagon? Hexagon?
- What is the difference between sides and vertices?
- What is a defining attribute? What is a non-defining attributes? Give examples of each
Our students are better able to…
- Use concrete objects to define and justify the attributes of shapes (SMP 5)
- Use appropriate terminology to explain verbally and through journaling how the attributes of shapes help to sort and define them. (SMP 6)
- Compare and contrast the attributes of shapes(SMP 7)
- Provide opportunities for students to explore the attributes of different shapes with concrete representations (SMP 5)
- Emphasize the use of correct vocabulary: shape, closed, open, side, attribute, feature, two-dimensional, rectangle, square, trapezoid, triangle (SMP 6)
- Provide opportunities to compare and contrast the attributes of shapes(SMP 7)
1st / Global Concept 2 of 4for this Unit of Study (Click to view PowerPoint in slide show mode): Compose Two-DimensionalShapes
Students combine two-dimensional shapes to make a new composite shape / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1:How can you combine two-dimensional shapes to make new shapes?
Day 2:How can you compose a two-dimensional shape?
Day 3:How can you use three or more two-dimensional shapes to make a new shape?
Related Go Math Chapter Test Questions:Unit 13 (Go Math Chapter 12) # 8, 11, 18, 22, 23
Instructional Resources
Manipulatives:
- Pattern Blocks- Use to explore what happens when shapes are combined
- Tangram Pieces- Use to explore what happens when shapes are combined
- Geoboard/Rubber bands- Use to compose new two-dimensional shapes
- Pattern Block Cut-outs- Black line Master to use to cut apart shapes to compose new shapes
- Engage NY Lesson 4 -Create composite shapes from two‐dimensional shapes:Concept Development p. 5.B.5-5.B.7 questions guide class discussion on using pattern blocks to build new shapes, Student Debrief p. 5.B.7- 5.B.8 is intended to invite reflection and active processing of the total lesson experience.Independent Practice p. 5.B.9-5.B.10 #1-5 and 7 students create new shapes based on rule.
- Go Math Lesson 12.4 Essentials: Listen and Draw p. 497 use Two Dimensional Shapescut out shapes to combine to make a new shape,On Your Own p. 498-499 #3-6 work in small groups or partners to identify which two shapes are used to make the new shape, Problem Solving p. 500 #8-11 as a check for understanding.
- More Two Dimensional Shapes - cut out shapes used with Lesson 12.5 Engage
- Go Math Lesson 12.5 Essentials:Unlock the Problem p. 501Try Another Problem p.502 with book closed. It is important to have deep conversations combining shapes.
- Animated Math Model- Skill 49: Combine Plane Figures
- Illuminations: Shape Cutter- interactive tool that allows you to create and manipulate shapes
- Illuminations: Shape Tool- interactive tool that allows you to create and manipulate shapes
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- You use me six times to create a hexagon. What shape am I? How do you know?
- Katrina predicts that if a triangle has 3 vertices and a square has 4 vertices, when she combines the two, the new shape will have 7 vertices. Do you agree or disagree with her prediction? Explain
- How many different ways can you combine three rectangles to make a new shape? Prove your answer in your journal
Our students are better able to…
- Use two or more two-dimensional shapes to compose new shapes (SMP 5)
- Use appropriate terminology to describe how definable attributes change when composing new two-dimensional shapes (SMP 3, 6)
- Provide ample opportunities for students to use concrete materials to compose new two-dimensional shapes (SMP 5)
- Facilitate discussion among students about the changes in defining attributes of newly composed shapes (SMP 3, 6)
1st / Global Concept 3 of 4for this Unit of Study (Click to view PowerPoint in slide show mode):Decompose Two-Dimensional Shapes
Students break apart composite shapes into smaller two-dimensional shapes / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1:How can you find shapes in other shapes?
Day 2:How can you decompose two-dimensional shapes?
Day 3:How can you decompose shapes without manipulatives?
Related Go Math Chapter Test Questions:Unit 13 (Go Math Chapter 12) # 4, 10, 14, 21
Instructional Resources
Manipulatives:
- Pattern Blocks- Use to explore what happens when shapes are combined
- Tangram Pieces- Use to explore what happens when shapes are combined
- Super Source Tangram Puzzles:Tangrams Make Sense -Toy Cat, More Toys, Sailboat
- Activity Village- Tangram Puzzles contains numerous puzzles to challenge students
- Pattern Block Cut-outsBlack line Master to use to cut apart shapes to decompose shapes
- Go Math Lesson 12.6 Essentials: Listen and Draw p. 505 students use a hexagon and 2 triangles to draw as many new shapes as possible, Problem Solving p.508 with a partner, and On Your Own p. 507 independently
- More Two Dimensional Shapes - cut out shapes used with Lesson 12.7 Engageto cut into smaller shapes.
- Go Math Lesson 12.7 Essentials:On Your Own p. 511 draw a line where shapes can be cut apart Use Math Talk in Action to guide discussion
- Read Aloud Three Pigs, One Wolf and Seven Magic Shapes: pick a few animals to make predictions how the animal would be made by drawing the lines to represent the tangram pieces in the shape outline, then students can check by using tangram pieces.
- Math Model- Skill 50: Combine and Separate Plane Figures
- Mega Math- Combine and Separate Shapes
- Finding Shapes in the Real Worldthis has students use 2/3 dimensional figures and relate to real world objects.
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- Will you always get the same two shapes if you draw the line in a different place? Why or why not?
- How can you decompose the same shape with different tangrams?
- Compare and contrast your model with your partners.
Our students are better able to…
- Decompose 2D shape models/pictures and describe which shapes are used (SMP 3)
- Persevere when solving problems (SMP 1)
- Use precision when explaining their models of decomposed shapes (SMP 6)
- Provide various hands-on experiences for decomposing composite shapes (SMP 3)
- Model the Trial and Error strategy and encourage students to persevere when solving problems (SMP 1)
- Emphasize the use of correct vocabulary: decompose, compose, composite shape, appropriate shape terminology (SMP 6)
1st / Global Concept 4 of 4for this Unit of Study (Click to view PowerPoint in slide show mode):Equal and Unequal Parts
Students identify equal and non-equal parts, halves, fourths, and quarters / Projected Time Allotment:
4 days
Sample Essential Questions:
Day 1:How can you define equal and unequal parts of two-dimensional shapes?
Day 2:How can a shape be separated into two equal shares? (halves)
Day 3:Howcan a shape be separated into four equal shares? (fourths, quarters)
Day 4:How can you prove if a model is separated into halves, fourths, or quarters?
Related Go Math Chapter Test Questions:Unit 13 (Go Math Chapter 12) # 1, 2, 6, 7, 9, 13, 17, 19, 20
Instructional Resources
Manipulatives:
- Circles, Squares, and Rectangles: Students will fold and cut to explore halves and quarters.
- Georgia Dept. of Ed Fractions Are As Easy As Pie: (PDF p. 51-56)Part 1 and Part 2 can be used to introduce equal parts using literature and folding paper to show the parts.
- Go Math Lesson 12.8 Essentials:Listen and Draw p. 513 can be used to have a discussion about equal vs. unequal parts. Problem Solving p 516 can be used as partner work on Day 1 for students to practice drawing equal and unequal parts. On Your Own p. 515 can be used on Day 1 as independent practice.
- Go Math Lesson 12.9 Essentials: The scenario from the Listen and Draw on p. 517 can be used without the book. The students should be given squares of paper to fold and then cut to demonstrate different ways to show 2 equal parts (halves). On Your Own p. 519 # 5-7 can be used to lead a class discussion about whether the parts are halves or not. Problem Solving p. 520 #17-18 can be used as independent practice. Math Journal p. 520 can be used with paper shapes as closure. The teacher can choose to use circles or rectangles.
- Go Math Lesson 12.10 Essentials:Extend the Math Activity p. 523 can be used as an engage on Day 3. Students will use circular pieces of paper to show a whole, a half, and a fourth. The teacher should use the math talk to facilitate a discussion about how the number of equal shares affects the size of the pieces. On Your Own p. 523 can be used as independent practice to demonstrate mastery of the concept of fourths. #16 can be used as a check for understanding.
- Partition the Pizza: This CPALMS formative assessment can be used to lead a discussion about fourths. This task includes a rubric which gives teaching implications and questions based on the student’s ability to create fourths.
- Voyages Grade 1 Excursion Lesson-Fraction Fish and Other Friends: Students will explore different area models to show halves and fourths. Be sure NOT to write the fractions in numerator and denominator form or introduce eighths to the students. The fraction pictures task is also not an appropriate part of the lesson to use.
- Animated Math Model- Skill 51: Equal Parts
- Fraction Shoot: Equal and Unequal parts
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- Can a shape have more than two equal parts? Explain.
- If the square showed 6 equal shares, do you think the equal shares would be larger or smaller than fourths? Explain.
Our students are better able to…
- Analyze and create models of equal and unequal shares, halves and fourths/quarters (SMP 3, 4)
- Use precise language when describing shapes and attributes (SMP 6)
- Provide students with opportunities to decompose shapes into equal and unequal parts, halves, and fourths and justify their partitioning (SMP 3,4)
- Model precise language: halves, fourths, quarters, half-of, fourth of, quarter of (SMP 6)