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All Things Second Grade Math!

Unit 4- 2D and 3D Shapes

This unit bundles student expectations that address creating, sorting, and classifying two- and three-dimensional figures, as well as composing and decomposing geometric

figures based on geometric attributes. According to the Texas Education Agency, mathematical process standards including application, tools and techniques,

representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in

everyday life, society, and the workplace.

Prior to this unit, in Grade 1, students used both formal and informal geometric language to identify two- and three-dimensional figures based on attributes. Students also created, composed, and partitioned two-dimensional figures.

During this unit, students analyze attributes of two-dimensional shapes and three-dimensional solids in order to develop generalizations about their properties. Using formal geometric language, students classify and sort polygons with 12 or fewer sides by identifying the number of sides and number of vertices. While mastery of the names of

polygons with seven or more sides is not expected according to the standards, students should be aware that all two-dimensional polygons have a specific name based on the

number of sides and vertices in the figure. It is also important that students are exposed to both regular figures where sides are the same length and irregular figures where

sides are not the same length. While exploring two-dimensional figures, students not only determine the number of vertices and sides, but also examine if the sides are equal

in length, and if the corners are square. Although students at this grade level are expected to use formal geometric language, the term “right angle” when referring to corners is not an expectation until Grade 4. However, teachers may begin to associate the words “square” and “right” when describing corners of two-dimensional

figures. Students use attributes based on formal geometric language to classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prism (including cubes as special rectangular prisms), and triangular prisms. Students develop spatial visualization skills, meaning the creation and manipulation of mental representations of shapes, as they investigate creating two-dimensional shapes based on given attributes of the figures. Spatial visualization is also reinforced as students compose two-dimensional shapes and three-dimensional solids with given properties or attributes. Students also decompose two-dimensional shapes into equal or unequal parts and use geometric attributes to identify and name the resulting parts.

Concrete Progression-Still Applies to Shapes

Due to unit and state testing, we often rush students to the abstract form of understanding before they are ready. Students have to learn by doing and that means using manipulatives 50% of daily instructional time. And smart boards, apps and the book are not manipulatives...they are tools! Now, I am not saying you cannot use these great resources, I am just reminding you that a manipulative is something the kids are handling and learning from. Think of \knowledge in these stages

  1. Using-This is the time when there is no algorithm-just the materials (counters, beans, cubes) Looks like-lots of questioning that leads to student discovery. Kids are talking and “playing”.

  2. Modeling-In this stage, the students have the materials and the teacher is modeling the procedure while using manipulatives. The students are still not writing the procedures/algorithm. Instead they are seeing patterns and predicting.

  3. Materials & Procedures-Here students are copying procedures you are modeling and beginning to try problems on their own. They still have materials and you are watching to see who is using them for necessity vs. comfort or out of habit.

  4. No Materials-This is where students understand the concept and can generalize their problem solving. They may not get to this during the unit-remember mastery may not come until the end of the year. “But on a test…?”-If you have truly covered the concept concretely, students will know they can draw a picture to solve. That is why it is important to transition from concrete to pictorial throughout the unit! In one lesson I may fluctuate between concrete materials and pictorial representations. Another day I may try to go from pictorial to abstract and back to concrete in small groups.

Composing 2D Shapes

2.8D says that students will compose two-dimensional shapes by by given properties. Pattern blocks and tangrams are a great way to address this TEK. It is more than just creating pictures with pattern blocks and tangrams though. It is important that students be given time to create new SHAPES from other shapes. For example, use 2 pieces from the tangrams to create a square.
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Composing 3D Shapes

Create a 3D Shape Attribute Movie