Math
For children in kindergarten and up, geometry and spatial relationships are a part of their daily lives. Understanding an object’s position in space and learning the vocabulary to describe a position and give directions are important. Terms likeabove,below,left,right, orbetweenenable children to orient themselves with their surroundings and describe the world around them. They can apply these same terms when describing plane and solid shapes in the classroom.
Flat Plane Shapes
Most of the objects that we encounter can be associated with basic shapes. A closed two-dimensional, or flat, figure is called aplane shape. Different plane shapes have different attributes, such as the number ofsidesorcorners(orvertices). A side is a straight line that makes part of the shape, and a corner, or vertex, is where two sides meet.
- Key standard:Analyze and compare two- and three-dimensional shapes, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”), and other attributes. (Grade K)
![](https://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/blog/Into-Math_WF1390201.png)
尽管孩子们熟悉最通用的n shapes, before kindergarten, they may not have been able to verbalize what distinguishes a square from a rectangle or a circle from a triangle. They will learn to describe shapes in terms of their sides and corners.
Atriangleis a shape with three sides and three corners. Arectangleis a shape with four sides and four corners. They may notice that opposite sides are the same length.
Asquareis a rectangle in which all four sides are of equal length. Acircleis a round shape that has no sides or corners. These attributes, as well as size, can be used to sort and classify shapes.
Extend the Lesson
- For students who are ready, you may want to show how the sides must be straight and the corners must be right angles for the shape to truly be a rectangle.
- For students who are ready, you may want to show how all the points of a circle must be the same distance from a center point for the shape to truly be a circle.
- Flags around the world present colorful ways to showcase all sorts of shapes and designs. What countries interest your students? Showcase their flags and have students identify the flat plane shapes they see.
Solid Shapes
Many of the everyday objects that children are familiar with aresolid shapes.For example, blocks are oftencubesorrectangular prisms. They have sixfaces, or flat surfaces.
Other familiar solid shapes arespheres, which children might recognize as being shaped like balls. One shape children might not immediately recognize is apyramid, which has one rectangular face and four triangular faces. They will likely, however, recognizecylinders, which are shaped like cans, andcones, like ice cream cones or traffic cones.
As with plane shapes, children will learn to describe solid shapes in terms of their attributes. For example:
- Roundness or flatness
- Ability to roll or slide
- Number of sides or corners
They will also come to see how the plane shapes comprise the faces of solid shapes. This is an important idea, as the real world around us is three dimensions and made of solid shapes! The place where people see flat plane shapes is generally on the faces of 3-D objects. Because of this, it is common to teach solid shapes first before moving on to plane shapes, which we practice inHMH Into Math.
Tracing around the face of solids will help a child understand a cube differs from a rectangular prism because all six of its faces are squares. This will enrich the ways in which they can describe and compare solids. For example, a child might see that although both a cylinder and a sphere can roll, a sphere has no faces and cannot slide. A cylinder, on the other hand, has two circular faces, so it can both roll and slide. (But some cylinders will slide more easily than others!)
Extend the Lesson
- For students who are ready, you may want to show how the faces of cubes and rectangular prisms must meet at right angles, or all the points on a surface of a sphere are the same distance from a central point.
- Does your school have access to a 3-D printer? Don’t just describe shapes like cubes or spheres—actuallycreatethem! Present the 3-D printed objects to the class and have them share what they notice and wonder.
- Have students identify solid shapes in the real world! Either bring objects, such as an ice cream cone, number cube, or soccer ball, for students to describe and classify, or have students look for objects outside of school to share. Consider what interests your students. Look for buildings near the school and around the world with interesting shapes or balls from sports that your students like to play.
- Origami presents an exciting way to transform a flat plane shape into a solid shape. Look online for folding ideas, such as creating a cube. You can also look for printouts that let students construct 3-D shapes or have students create cubes, pyramids, and other solid shapes using toothpicks and marshmallows.
Once children can recognize and describe the attributes that distinguish plane and solid shapes, such as those that make a triangle different from a square or a cylinder different from a cone, they can begin to create and continue patterns. When children create or find patterns, they are using the attributes of not just one but of a series of shapes to determine the order or pattern.
***
Grow student confidence in mathematics withHMH Into Math, our core math solution for Grades K–8.
Get our FREE guide "Optimizing the Math Classroom: 6 Best Practices."
Related Reading
-
The Importance of Hands-On Science Activities: Learning by Doing
Alicia Ivory
ShapedEditor -
7 ELL Strategies for Reading Success
Rebecca Salinas
Learning Architect, HMHRichard Blankman
ShapedEditor -
11 Essential 9/11 Activities & Lesson Plans for the Classroom
Brenda Iasevoli
ShapedExecutive Editor
CORE CURRICULUM
HMH Social Studies, 6-12
SEE ALL SOCIAL STUDIES
AP & ELECTIVES
AP Human Geography
Personal Finance
SEE ALL SOCIAL STUDIES
AP & ELECTIVES
SUPPLEMENTAL
Connected Teaching and Learning
HMH’s Connected Teaching and Learning integrates assessment, core instruction, supplemental practice, intervention, and professional learning all on one platform.
Professional Development
Providing professional development for teachers, HMH’s professional learning courses, coaching, and leadership advisory supports educators every step of the way.
Keeping It Current For Grades 6–12
Each month we bring you videos, articles, and current events designed to build cultural awareness, media literacy, and a deeper understanding of significant historical figures and events.
For Teachers
Coaching Membership
Teacher's Corner
Live Online Courses
SEE ALL PROFESSIONAL DEVELOPMENT
For Leaders
The Center for Model Schools (formerly ICLE)
Intervention Curriculum
HMH's K-12 intervention programs are built on 20+ years of proven results. We can help teachers develop an intervention curriculum that meets students' needs.
Science of Reading eBook
In this exclusive Science of Reading eBook you’ll find research-backed information that will walk you through the experience new readers face as they build their reading brain.
Model Schools Conference
加入我们学校到第32届模型es presented by The Center for Model Schools. We showcase the success of districts, schools, and educators.
AP & Electives
Assessment
Early Learning
English Language Development
Homeschool
Intervention
Literacy
Mathematics
Professional Development
Science
School Improvement
Social and Emotional Learning
Social Studies
Special Education
Summer School
SEE ALL SOLUTIONS
Intervention Curriculum
HMH's K-12 intervention programs are built on 20+ years of proven results. We can help teachers develop an intervention curriculum that meets students' needs.
BROWSE RESOURCES
Classroom Activities
Customer Success Stories
Digital Samples
Events & Webinars
Grants & Funding
International
Research Library
Shaped - HMH Blog
CUSTOMER SUPPORT
Contact Sales
Customer Service & Technical Support Portal
Platform Login
免费教学Resources: Fun Classroom Activities and Lesson Plan Ideas
Here you'll find free learning activities, lessons, downloadables, and videos for students in Grades K–12 to keep learning and growing at grade level.
2023–2024 Monthly Calendar Themes for School
Check out these monthly calendar themes for school, complete with teaching resources for holidays and other days of significance for all grade levels.
Learn about us
About
Diversity, Equity, and Inclusion
Environmental, Social, and Governance
News Announcements
Our Legacy
Social Responsibility
Supplier Diversity
Join Us
Careers
Educator Input Panel
Suppliers and Vendors
Divisions
Heinemann
Center for Model Schools (formerly ICLE)
NWEA