# Unit 7 Overview: Reasoning with Shapes

## Overview

**Unit Overview/Summary - FOCUS: **

This unit focuses on Geometry. Learning in this unit will enable students to:

Reason with shapes and their attributes

# Relevant Standards:

**Major work of the grade is in bold. **

The standards to be addressed during this unit of study include:

2.G.A.1. Recognize 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.

2.G.A.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.

# Examples and Explanations:

2.G.A.1. 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. Students use the vocabulary word “angle” in place of “corner” but they do not need to name angle types. Interactive whiteboards and document cameras may be used to help identify shapes and their attributes. Shapes should be presented in a variety of orientations and configurations.

2.G.A.3 This standard introduces fractions in an area model. Students need experiences with different sizes, circles, and rectangles. For example, students should recognize that when they cut a circle into three equal pieces, each piece will equal one third of its original whole. In this case, students should describe the whole as three thirds.

If a circle is cut into four equal pieces, each piece will equal one fourth of its original whole and the whole is described as four fourths.

Students should see circles and rectangles partitioned in multiple ways so they learn to recognize that equal shares can be different shapes within the same whole. An interactive whiteboard may be used to show partitions of shapes.

# Transfer Goal: Aligned to district portrait or vision of the learner

**Aligned to district portrait or vision of the learner **

In this unit students will develop the skills of perseverance, reasoning, and precision. This will be accomplished through focus on the following Standards for Mathematical Practice:

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Model with mathematics.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

**Grade level content is in bold **

## Coherence:

## How does this unit build on and connect to prior knowledge and learning?

Students build on their previous understandings of:

- Reasoning with shapes and their attributes.
**Partitioning a rectangle into rows and columns of same-size squares**

## How does this unit prepare students for future learning?

The learning of this unit serves as a foundation for content that will be addressed in future years. Specifically, students will utilize this learning to:

- Further reason about shapes and their attributes.
- Develop understanding of fractions as numbers.

# Essential Questions:

**Essential Questions can be approached in multiple ways. There should be no more than 2-3 essential questions and they should align with your topics. Questions can be repeated throughout a course or over years, with different enduring understandings. **

- How can plane and solid shapes be described?
- How does decomposing shapes into halves, thirds, or fourths relate to equal shares and shapes?

# Enduring Understanding:

**Enduring Understanding: The major ideas you want students to internalize and understand deeply. These understandings should be thematic in nature. They are not the end all, be all of the question. They are focused to align to the focus (unit overview). **

Students understand:

- Objects can be described and compared using their geometric attributes.
- When decomposing circles and rectangles into halves, thirds, or fourths, equal shares of identical wholes need not have the same shape. e.g., a rectangle divided into fourths vertically results in rectangular parts or diagonally results in triangular parts.

# What Students Will Know:

- Properties of polygons.
- Names of shapes.
- Two-dimensional shapes (that are closed and have straight sides meeting at corners/vertices) can be classified by the number of sides and/or vertices.
- When decomposing circles and rectangles into halves, thirds, or fourths, equal shares of identical wholes need not have the same shape.

# What Students Will Do:

- Identify shapes that have specified attributes.
- Draw shapes that have specified attributes.
- Identify triangles, quadrilaterals, pentagons, hexagons and cubes.
- Section circles and rectangles into 2, 3, or 4 equal parts.
- Describe the parts of the shape as halves, thirds, and fourths.
- Identify the combinations of the whole (2 halves = 1 whole, etc...).
- Use manipulatives, pictures and words to show that equal sized sections of the same whole need not have the same shape.
- Explore classifying triangles, quadrilaterals, pentagons, and hexagons based on the number of sides or vertices.
- Provide real-world experiences to recognize and name cubes, rectangular prisms, cones, and cylinders.
- Explore and describe part-whole relationships.
- Relate two, three, or four equal shares to circles and rectangles.
- Describe equal shares using the terms halves, thirds, fourths, quarters and the phrases half of, third of, fourth of, quarter of in real-world contexts.
- Explore the decomposition of shapes into halves, thirds, and fourths; equal shares of identical wholes need not have the same shape, e.g., a rectangle divided into fourths vertically results in rectangular parts or diagonally results in triangular parts.

# Demonstration of Learning:

**Additional Assessment Samples: **

# Unit Specific Vocabulary and Terminology:

The purpose of vocabulary work should be to allow all students to access mathematics. Vocabulary is a way to provide opportunities for students to use mathematical language to communicate about how they solved a problem, describe their reasoning, and demonstrate understanding of mathematical content. Vocabulary is inclusive of key words and phrases.

Often multilingual learners/English learners (MLs/ELs) are perceived as lacking academic language and needing remediation. Research shows that MLs/ELs bring standards-aligned background knowledge and experiences to the task of learning, and they need opportunities to extend their language for academic purposes. When considering the language demand of a lesson (at the word level), you can check for cognates and polysemous words. Pointing out these words to students can help them activate and build background knowledge assumed in lessons. TESOL professionals can assist with the identification of cognates and polysemous words, and they can provide guidance about the background knowledge MLs/ELs bring or may need.

**Academic Vocabulary **

- 2-dimensional
- 3-dimensional
- attribute
- corner
- edge
- face
- flat
- fourth
- half
- side
- solid
- straight
- third
- whole

**Content Vocabulary **

- angle
- circle
- cubes
- hexagon
- octagon
- Pentagons
- plane
- polygon
- quadrilateral
- rectangle
- rhombus
- septagon
- square
- trapezoid
- triangle
- vertice

**Vocabulary resources: **

- Bilingual Glossaries and Cognates
- Using Cognates to Develop Comprehension in English
- Challenges for EL Students to Overcome
- Cognates and Polysemous Words
**Granite School Vocabulary Cards:**Each card has the word and a picture. They are designed to help all students with math content vocabulary, including ELL, Gifted and Talented, Special Education, and Regular Education students.

# Aligned Unit Materials, Resources and Technology:

High-quality instructional resources are critical for improving student outcomes. The alignment guidance is intended to clarify content and support understanding for clear implementation and coherence.

Materials selection is a local control decision and these documents have been provided from participating publishers to assist districts in implementation. Use of the materials from these publishers is not required. These aligned core programs meet expectations as reported by edReports. Strong alignment of curricula and instructional materials have the potential to support student engagement and teacher growth.

# Opportunities for Interdisciplinary Connections:

**Science**

**SP 2:**Developing and using model**SP 5:**Using mathematics and computational thinking

**Computer Science**

**CS3:**Recognizing and Defining Computational Problems**CS4:**Developing and Using Abstractions**CS7:**Communicating Around Computing

# Opportunities for Application of Learning:

**Defined Learning** provides an open access online library of standards-aligned project-based lessons to help students meet the expectations of the Standards. Each project is based on a situation in a relevant career to help students connect classroom content to career pathways. This supplemental resource is available at no cost to teachers and districts.* Create an account and log in to access this free resource to support your curriculum.*

*The tasks below provide additional opportunities to apply the content of this unit.*

# Critical Consciousness for Diversity and Equity:

Culturally relevant mathematics engages and empowers students. Opportunities for teachers to orchestrate discussions where students share not only connections to prior mathematics learned but also to their lived experiences must be provided. It is important to dig deep to find ways to link students’ home cultures and the mathematics classroom. Build authentic relationships with families through two-way, reciprocal conversations that acknowledge families’ cultures as assets for teaching and learning. As you plan to implement this unit, focus on designing experiences that have students at the center. In addition to keeping students engaged, ensure the learning experiences have a context that reflects lived experiences (mirror) or provide opportunities to view and learn about the broader world (window).* *

One crucial link to students’ home cultures is through their language. Students’ language repertoires –all the languages and language varieties they use everyday– are a valuable resource to be engaged in the mathematics classroom. This approach is referred to as a translanguaging stance. It is based on a dynamic view of bilingualism that understands individuals as having one linguistic repertoire composed of various named languages (such as English and Spanish) and/or language varieties on which they draw to make meaning.

The following questions are intended to assist in promoting diverse voices and perspectives while avoiding bias and stereotyping:

- How will students share their experiences with others while attending to the mathematics in the unit?
- What opportunities are there for students to make connections from their life to the mathematics?
- What do I know or need to learn about my students to create lessons free from bias and stereotypes?
- In what ways can the mathematical thinking already taking place in the classroom and community be honored?
- How is relevant background knowledge developed so that all students can access the mathematics of the unit?
- What opportunities are there for students to use their full language repertoires during mathematical discussions and practice? Where can I create these opportunities?
- What do I know or need to learn about students’ languages and how they use them? How can I learn this?

*** Resources to support diversity and equity in the classroom please visit the **DEI collection

# Multilingual Learners/English Learners (ML/EL):

Mathematical symbols, expressions, and methods are not universal; ways of doing math differ across cultures. When working with diverse students, especially with those from different countries, it is important to be aware that these differences exist.

It is also important to remember that communicating about mathematical content and practices requires complex language. Since conceptual learning and language learning are interconnected and acquired through participation in meaningful activities, the research-based strategies listed below focus on making content comprehensible (accessible) and creating opportunities for student voice, both verbal and written.

*Additional resources for ML/EL*

CELP Standards--Linguistic Supports

ML/EL Support Collection for Math

- Concrete models for various shapes

This unit presents opportunity to address the following CELP Standards:

**CELP Standard 1: **Construct meaning from oral presentations and literary and informational text through grade-appropriate listening, reading, and viewing

**CELP Standard 2: **Participate in grade-appropriate oral and written exchanges of information, ideas, and analyses, responding to peer, audience, or reader comments and questions

**CELP Standard 3: **Speak and write about grade-appropriate complex literary and informational texts and topics

**CELP Standard 4: **Construct grade-appropriate oral and written claims and support them with reasoning and evidence

**CELP Standard 5:** Conduct research and evaluate and communicate findings to answer questions or solve problems

**CELP Standard 6: **Analyze and critique the arguments of others orally and in writing

**CELP Standard 7:** Adapt language choices to purpose, task, and audience when speaking and writing

**CELP Standard 8:** Determine the meaning of words and phrases in oral presentations and literary and informational text

**CELP Standard 9:** Create clear and coherent grade-appropriate speech and text

**CELP Standard 10:** Make accurate use of standard English to communicate in grade appropriate speech and writing

The document below provides guidance on these standards that is grade appropriate and broken down by language level descriptors which will assist the teacher in making the content of the unit accessible to all students.