Global Concept Guides:Three Dimensional Shapes, Two Dimensional Shapes, Equal Partitioning
Prior Learning:MFAS.1.G.1.1, MAFS.1.G.1.2, MAFS.1.G.1.3
Progressions Document Link
Sample Show What You Know Task:Use the Go Math Ch. 11Show What You Know (TE p. 506) or Diagnostic Interview Task (TE p. 506)
Mathematics Florida Standards for Mathematical Content:
Reason with shapes and their attributes.
MAFS.2.G.1.1Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces.* Identify triangles, quadrilaterals, pentagons, hexagons and cubes. (*Sizes are compared directly or visually, not compared by measuring)
MAFS.2.G.1.2 -Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
MAFS.2.G.1.3 Partition circles and rectangles into two, three or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. / Comments:
This parent flyer and included video can be utilized by both you and parents to build content knowledge and understanding of the strategies highlighted in this unit.
Notes on Assessment:
Unit 10 AssessmentGo Math Ch. 11
See common performance task link below.
Unpacking the Standards for this Unit:
“Students identify, describe and draw triangles, quadrilaterals, pentagons, and hexagons. Pentagons, triangles and hexagons should appear as both regular (equal sides and equal angles) and irregular. Students recognize all four sided shapes as quadrilaterals (squares, rectangles and trapezoids).”
Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: attribute, feature, angle, side, triangle, quadrilateral, square, rectangle, trapezoid, pentagon, hexagon, cube, face, edge, vertex, surface, figure, shape, closed, open, partition, equal size, equal shares, half, halves, thirds, half of, a third of, whole, two halves, three thirds, four fourths, partition, rows and columns.”
“It is important for students to see circles and rectangles portioned in multiple ways so they learn to recognize that equal shares can be different shapes within the same whole. For more information see PowerPoint on GCG 3 of this unit.
Common Performance Task with Rubric for this Unit:
Auntie Em’s Cookies has the student partition cookies into halves, thirds, and fourths. Students have to draw the other half of a cookie already cut into half and explain how they knew how to do that.
Click here for the performance task and rubric.
Future learning:
“It is vital that students understand different representations of fair shares.” By students having a deep understanding of fair shares they develop a strong foundation for the understanding of fractions. By partitioning rectangles into rows and columns, students will also develop a foundation for arrays and multiplication.
2nd / Global Concept 1 of 3 for this Unit of Study: ThreeDimensional Shapes / Projected Time Allotment: 3 Days
Sample Essential Questions:
Day 1: How can you identify three-dimensional shapes in the real world?
Day 2: How can I sort three-dimensional shapes based on their attributes?
Day 3: How are rectangular prisms and cubes alike and different?
Related Unit 10 Assessment: Go Math Ch. 11 # 6, 7, 10
Instructional Resources
Manipulatives:
- Three-dimensional solids (in the GO Math Kit) provide students opportunities to hold, explore, and manipulate these shapes. Pictures from a book do not replace this experience.
- Relational Geosolids
- Real life examples of three-dimensional solids (cans, boxes, balls, etc.).
- Venn diagram rings to sort actual three-dimensional shapes based on different attributes.
- Real-world objects to expose students to three-dimensional shapes in the real world.
- Go Math Lesson 11.1 Essentials: On Your Own p. 511, Problem Solving p. 512 # 7 -9
- Go Math Lesson 11.2 Essentials: Go Deeper TE p. 515, On Your Own;and Problem SolvingTE p. 515-516 # 3-6
- iTools(Geometry; Solid Figures activity)
- Mega Math- Sort Solid Figures- Stack, Roll, Slide
- Mega Math- Sort Solid Figures- Faces, Edges, Vertices
- Mega Math- Match Solid Figures with Real-Life Objects
- Mega Math- Identify Solid Figures
- Mega Math Classify Solid Figures
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- How are cubes and rectangular prisms the same? How are they different?
- How many more faces does a cylinder have than a cone?
- What do cones and cylinders have in common? What makes them different?
- How are spheres, cones, and cylinders similar? How are they different?
- How are the faces of a cube different than the faces of a rectangular prism?
Our students arebetter able to…
- Describethe similarities and differences between three-dimensional shapes by identifying the number of edges, vertices, and faces(SMP 3).
- Make connections between real-world objects and three-dimensional shapes. (SMP 4, 7)
- Sort three-dimensional figures based on various attributes (SMP 5, 7).
- Identify three--dimensional shapes based on attributes (SMP 5, 7).
- Provide opportunities for students to find three-dimensional figures in the real world and connect them to three-dimensional shapes (SMP 4).
- Provide hands on experiences with three-dimensional shapes (SMP 5).
- Use precise vocabulary when discussing three-dimensional figures such as three-dimensional, edges, faces, vertex/vertices, rectangular prisms, cube, cone, cylinder, sphere(SMP 6).
2nd / Global Concept 2 of 3 for this Unit of Study: Two Dimensional Shapes / Projected Time Allotment:4 Days
Sample Essential Questions:
Day 1: How can you name shapes based onthe number of sides and vertices?
Day 2: How do you find and count angles in two-dimensional shapes?
Day 3: How can you use the number of sides and angles to sort two-dimensional shapes?
Day 4: What are different ways to sort polygons?
Related Unit 10 Assessment: Go Math Ch. 11: 1, 2, 3, 4, 12, 13, 14, 15
Instructional Resources
Manipulatives:
- Two-dimensional figuresto sort, compare, contrast, and analyze.
- Pattern blocksto sort and name shapes based on attributes.
- Polygon sort cardsto sort and discuss attributes.
- Venn Diagram ringsto sort polygon cards or figures.
- Anglegsto create polygons by connecting sides.
- Geoboardsto create polygons based on given attributes.
- Go Math Lesson 11.3Essentials:Listen and Draw TEp 517, p. 518, p. 519, p. 520
- Go Math Lesson 11.4Essentials: Listen and Draw TE p 521, p. 522, p. 523, p. 524
- Go Math Lesson 11.5Essentials: p. 527 # 5-9, p. 528.
- Farm Fences - Students create polygons based on specific rules.
- It’s All About the Shapes–Cpalms lesson using The Greedy Triangle, Geoboards, concentration game and a Venn diagram.
- Shape Up- Students can identify shapes based on attributes
- Interactive Online Resources:
- Shape Riddles lesson- Students create polygons from riddles.
- Mega Math- Identify Plane Shapes
- Mega Math- Sort Plane Shapes
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- Create riddles such as: I am a polygon. I have 4 vertices and four sides. What shape could I be?
- How are squares and rectangles alike? How are they different?
- How can you sort the quadrilaterals into three separate categories?
- How can you create more than two different triangles using your Anglegs?
- Is a circle a polygon why or why not?
Our students arebetter able to…
- Use precise vocabulary when discussing polygons: vertex/vertices, side, angle, triangle, quadrilateral, pentagon, hexagon(SMP 6).
- Identify shapes based on attributes: i.e., sides, angles, and vertices (SMP 6).
- Identify differences and similarities between polygons by the use of manipulatives(SMP7).
- Use precise vocabulary when discussing polygons: vertex/vertices, side, angle, triangle, quadrilateral, pentagon, hexagon (SMP 6).
- Allow students to sort plane shapes by attributes (SMP 6).
- Facilitate discussions about attributes of shapes (SMP 3).
- Provide opportunities for students to apply their knowledge of polygons to compare and contrast polygons (SMP 3, 7).
2nd / Global Concept 3 of 3 for this Unit of Study: Equal Partitioning / Projected Time Allotment:4 Days
Sample Essential Questions:
Day 1: How do you find the total of same-size squares that will cover a rectangle?
Day 2: What are halves, thirds and fourths of a whole?
Day 3: How do you find a half of, a third of and a fourth of a whole?
Day 4: How can drawing a diagram help when solving problems about equal shares?
Related Unit 10 Assessment: Go Math Ch. 11: #5, 8, 9, 11, 16
Instructional Resources
Manipulatives:
- Color tiles/pattern blocks to fill rectangles and to model fourths, halves, and thirds.
- Ruler/straight edge to draw straight lines when dividing shapes into equal parts.
- Geo boards & rubber bands to divide the board into equal parts.
- Post-It Notes
- Grid paper for students to draw shapes and easily see the equal parts.
- Shape Puzzles - Students work together to partition rectangle.
- Go Math Lesson 11.6 Essentials: RtI Tier 2 TE p. 529B, Listen and Draw p. 529 and On Your Own p. 531
- Go Math Lesson 11.7 Essentials: RtI Tier 1 & 2 TE p. 533B, Listen and Draw TE p. 533 (use the margin in the TE to guide instruction), Model and Draw TE p. 534 (use guiding questions in the margin and refrain from using student page), Problem Solving TE p. 536 # 16-17.
- Go Math Lesson 11.8 Essentials: RtI Tier 1 & 2 TE p. 537B, Explain TE p. 539 # 16, Problem Solving TE p. 540 #17-18
- Go Math Lesson 11.9 Essentials: RtI Tier 2 TE p. 541B, Listen and Draw TE p. 541 (use TE margins to guide instruction), On Your Own p. 543 # 7-15, Problem Solving TE p. 544 #16-17
- Go Math Lesson 11.10 Essentials: Unlock the Problem TE p. 545 (use TE margin to guide instruction, refrain from using student page), Try Another Problem TE p. 546 (use TE margin to guide instruction, refrain from using student page), Share and Show TE p. 547, On Your Own TE p. 548 # 6, 7
- CPALMS: Problem Solving Tasks - Which show One Half
- Dividing Circles into halves, thirds, and fourths
- Divide Shapes-This website goes through shapes divided up and you select which one is split into equal parts.
Sample HOT Questions: Use these to facilitate student discussions. (SMP 1, 3)
- How do you know if a shape has been cut into fourths, thirds, or halves?
- What are all the different rectangles you can make with 12 color tiles?
- What do the words “thirds” and “fourths” tell you the number of equal-sized pieces that make up your whole?
- How can you use pattern blocks to help model half of a hexagon? A third of a trapezoid?
- How do you know if something is divided in equal parts?
Our students arebetter able to…
- Partition shapes into equal parts and identify equal parts (SMP 4).
- Use precise vocabulary when discussing the equal parts of a shape: i.e., rows, columns, halves, thirds, fourths, equal parts, whole, half of, third of, fourth of, partition (SMP 6).
- Give our students ample opportunities to partition shapes into equal parts (SMP 4).
- Model using precise vocabulary when discussing equal parts: i.e., rows, columns, halves, thirds, fourths, equal parts, whole, half of, third of, fourth of, partition (SMP 6).