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Students use a geometric model to investigate common factors and the greatest common factor of two numbers.Key ConceptsA geometric model can be used to investigate common factors. When congruent squares fit exactly along the edge of a rectangular grid, the side length of the square is a factor of the side length of the rectangular grid. The greatest common factor (GCF) is the largest square that fits exactly along both the length and the width of the rectangular grid. For example, given a 6-centimeter × 8-centimeter rectangular grid, four 2-centimeter squares will fit exactly along the length without any gaps or overlaps. So, 2 is a factor of 8. Three 2-centimeter squares will fit exactly along the width, so 2 is a factor of 6. Since the 2-centimeter square is the largest square that will fit along both the length and the width exactly, 2 is the greatest common factor of 6 and 8. Common factors are all of the factors that are shared by two or more numbers.The greatest common factor is the greatest number that is a factor shared by two or more numbers.Goals and Learning ObjectivesUse a geometric model to understand greatest common factor.Find the greatest common factor of two whole numbers equal to or less than 100.

Material Type:
Lesson Plan
Author:
02/28/2022
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Subject:
Mathematics
Material Type:
Full Course
Provider:
Pearson
02/28/2022
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Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Subject:
Geometry
Mathematics
Provider:
Pearson
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Students will resume their project and decide on dimensions for their buildings. They will use scale to calculate the dimensions and areas of their model buildings when full size. Students will also complete a Self Check in preparation for the Putting It Together lesson.Key ConceptsThe first part of the project is essentially a review of the unit so far. Students will find the area of a composite figure—either a polygon that can be broken down into known areas, or a regular polygon. Students will also draw the figure using scale and find actual lengths and areas.GoalsRedraw a scale drawing at a different scale.Find measurements using a scale drawing.Find the area of a composite figure.SWD: Consider what supplementary materials may benefit and support students with disabilities as they work on this project:Vocabulary resource(s) that students can reference as they work:List of formulas, with visual supports if appropriateClass summaries or lesson artifacts that help students to recall and apply newly introduced skillsChecklists of expectations and steps required to promote self-monitoring and engagementModels and examplesStudents with disabilities may take longer to develop a solid understanding of newly introduced skills and concepts. They may continue to require direct instruction and guided practice with the skills and concepts relating to finding area and creating and interpreting scale drawings. Check in with students to assess their understanding of newly introduced concepts and plan review and reinforcement of skills as needed.ELL: As academic vocabulary is reviewed, be sure to repeat it and allow students to repeat after you as needed. Consider writing the words as they are being reviewed. Allow enough time for ELLs to check their dictionaries if they wish.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
03/01/2022
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Students will complete the first part of their project, deciding on two right prisms for their models of buildings with polygon bases. They will draw two polygon bases on grid paper and find the areas of the bases.Key ConceptsProjects engage students in the application of mathematics. It is important for students to apply mathematical ways of thinking to solve rich problems. Students are more motivated to understand mathematical concepts if they are engaged in solving a problem of their own choosing.In this lesson, students are challenged to identify an interesting mathematical problem and choose a partner or a group to work collaboratively on solving that problem. Students gain valuable skills in problem solving, reasoning, and communicating mathematical ideas with others.GoalsSelect a project shape.Identify a project idea.Identify a partner or group to work collaboratively with on a math project.SWD: Consider how to group students skills-wise for the project. You may decide to group students heterogeneously to promote peer modeling for struggling students. Or you can group students by similar skill levels to allow for additional support and/or guided practice with the teacher. Or you may decide to create intentional partnerships between strong students and struggling students to promote leadership and peer instruction within the classroom.ELL: In forming groups, be aware of your ELLs and ensure that they have a learning environment where they can be productive. Sometimes, this means pairing them up with English speakers, so they can learn from others’ language skills. Other times, it means pairing them up with students who are at the same level of language skill, so they can take a more active role and work things out together. Other times, it means pairing them up with students whose proficiency level is lower, so they play the role of the supporter. They can also be paired based on their math proficiency, not just their language proficiency.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
03/01/2022
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Students further explore scale, taking a scale drawing floor plan and redrawing it at a different scale.Key ConceptsStudents explore change from one scale to another, focusing on the ratios. Students will draw a scale model of a house.GoalsRedraw a scale drawing at a different scale.Find measurements using a scale drawing.

Subject:
Geometry
Ratios and Proportions
Material Type:
Lesson Plan
Author:
03/01/2022
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CC BY-NC
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Subject:
Geometry
Material Type:
Lesson Plan
Author:
03/01/2022
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Lesson OverviewStudents will work on the final portion of their project which includes creating the nets for the sides, making a slice in one of their buildings, and putting their buildings together. Once their two model buildings are complete, they will find the surface area and volume for their models and the full-size buildings their models represent.Key ConceptsThe second part of the project is essentially a review of the second half of the unit, while still using scale drawings. Students will find the surface area of a prism as well as the surface area of a truncated prism. The second prism will require estimating and problem solving to figure out the net and find the surface area. Students will also be drawing the figure using scale to find actual surface area.GoalsRedraw a scale drawing at a different scale.Find measurements using a scale drawing.Find the surface area of a prism.SWD: Students with disabilities may have a more challenging time identifying areas of improvement to target in their projects. It may be helpful to model explicitly for students (using an example project or student sample) how to review a project using the rubric to assess and plan for revisions based on that assessment.Students with fine motor difficulties may require grid paper with a larger scale. Whenever motor tasks are required, consider adaptive tools or supplementary materials that may benefit students with disabilities.Students with disabilities may struggle to recall prerequisite skills as they move through the project. It may be necessary to check in with students to review and reinforce estimation skills.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
03/01/2022
Educational Use
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This collection includes 6 videos and 3 media gallery on the topic of measurement and spatial sense.

Subject:
Mathematics
Material Type:
Module
Provider:
PBS LearningMedia
11/06/2023
Rating
0.0 stars

An interactive simulation in which students use a model of charged objects to explain how charges interact and construct an understanding of Coulomb's Law. It is concerned with comparing ions and neutral atoms. The model allows the user to investigate the relationships between sign of charge, magnitude of charge, and distance between ions. The model illustrates the operation of three types of electroscopes. Next it visually explores how a static charge can bend the path of a moving electron, and then graphically and numerically explores Coulomb's Law. Lastly a model that illustrates polarization of charge illustrates why a charged balloon is attracted to a neutral wall. The system allows students to enter their multiple choice and written answers throughout the activity and generate a report of their responses at the end even if they are not logged into the system.

Subject:
Physics
Science
Material Type:
Interactive
Provider:
National Science Teachers Association (NSTA)
Provider Set:
NGSS@NSTA
02/17/2021
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This article describes a number of creative projects that incorporate art and literacy skills into a science unit on biomes and ecosystems.

Subject:
Life Science
Science
Material Type:
Lesson Plan
Provider:
Ohio State University College of Education and Human Ecology
Provider Set:
Beyond Penguins and Polar Bears: An Online Magazine for K-5 Teachers
Author:
Jessica Fries-Gaither
02/09/2021
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This is the first instructional sequence in a teacher's guide built with the purpose of helping students build a deeper understanding of the Structures and Properties of Matter standard.Students have the opportunity to engage with interactive simulations, create poetry, drawing scientific diagrams, read complex text, develop evidence based explanations and design a model . The instructional sequence described in the lesson uses the 5 E learning model and includes a variety of online simulations, polls and model drawings.

Subject:
Physics
Science
Material Type:
Activity/Lab
Provider:
National Science Teachers Association (NSTA)
Provider Set:
NGSS@NSTA
02/18/2021
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Created by the Concord Consortium, the Molecular Workbench is "a modeling tool for designing and conducting computational experiments across science." First-time visitors can check out one of the Featured Simulations to get started. The homepage contains a number of curriculum modules which deal with chemical bonding, semiconductors, and diffusion. Visitors can learn how to create their own simulations via the online manual, which is available here as well. The Articles area is quite helpful, as it contains full-text pieces on nanoscience education, quantum chemistry, and a primer on how transistors work. A good way to look over all of the offerings here is to click on the Showcase area. Here visitors can view the Featured simulations, or look through one of five topical sections, which include Biotech and Nanotechnology. Visitors will need to install the free Molecular Workbench software, which is available for Windows, Linux, and Mac.

Subject:
Chemistry
Science
Material Type:
Activity/Lab
Interactive
Provider:
Concord Consortium
Provider Set:
Concord Consortium Collection
Author:
Concord Consortium Inc.
07/02/2012
Educational Use
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This detailed educator's guide provides a lesson in designing the structure of a spacecraft. The design challenge contains pre-lab activities and instructions for how to test the models.

Subject:
Science
Material Type:
Lesson Plan
Provider:
NASA
08/07/2023
Educational Use
Rating
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Subject:
Arts
English Language Arts
Material Type:
Student Guide
12/01/2023
Educational Use
Rating
0.0 stars

The Peg + Cat on-air series and online resources provide many opportunities for educators to introduce or reinforce early math concepts. In each 11-minute on-air episode of this animated, math-based series for 3-8 year olds, Peg and Cat find themselves thrust into the middle of a wacky word problem. This problem isn't just an academic exercise for them -- it's a messy, funny, real-life crisis they have to solve to get out of trouble. Peg and Cat grapple with all kinds of loopy obstacles under intense time pressure. They write out diagrams and charts on the graph paper that comprises their background. They interact with one another in their own quirky, comical way. And somehow, they always find a way to solve the math problem and save the day. The resources in this collection help you explore the concepts introduced in Peg + Cat with activity ideas, video clips, and online games. Use these resources to help your students explore real-life situations involving math that they'll be thrilled and entertained by.

Subject:
Mathematics
Material Type:
Module
Provider:
PBS LearningMedia
11/06/2023
Educational Use
Rating
0.0 stars

How did scientists figure out the structure of atoms without looking at them? Try out different models by shooting light at the atom. Check how the prediction of the model matches the experimental results.

Subject:
Science
Material Type:
Interactive
Provider:
Provider Set:
PhET Interactive Simulations
10/05/2022
Educational Use
Rating
0.0 stars

This video explores scale models, including 1:12 dollhouse models, 1:24 railroad models, and 1:192 architectural models. It explains what the different ratios represent and asks students to consider how they can use measurement and proportional reasoning to create their own scale models. The accompanying classroom activity gives students hands-on practice with creating models to scale and with real-world measurement.

Subject:
Mathematics
Material Type:
Audio/Video
Lesson
Provider:
PBS LearningMedia
11/06/2023
Educational Use
Rating
0.0 stars

The SciGirls decide to brainstorm what their favorite dress would look like and work together to design a dress that is totally outrageous and features technology. They reach out to a mentor to see what they can learn from her about incorporating technology into fashion. [2:20]

Subject:
Career and Technical Education
Mathematics
Material Type:
Audio/Video
Provider:
PBS LearningMedia
11/06/2023
Educational Use
Rating
0.0 stars

Eighteen-year-old inventor Ryan Patterson designed a sign language translator glove that works by sensing the hand movements of the American Sign Language and sending the data to a device that displays the words on-screen. The glove allows a deaf person to communicate easily with anyone. [2:37]

Subject:
Mathematics
World Language
Material Type:
Audio/Video
Provider:
PBS LearningMedia