This unit is centered on designing a shoe for a customer. Students decide on a particular type of shoe that they want to design and utilize ideas of force, impulse, and friction to meet the needs of a particular customer. Force plates are used study the relationship between force, time, and impulse to allow students to get the mathematical models that allow them to make data informed decisions about their shoe design.

This resource is intended for students to work with a partner to determine equivalent fractions to find the sum. Students need to have a background knowledge of connecting fractions and decimals, along with equivalent fractions prior to this activity. It may be helpful to have each row be printed on different colored paper, so it may help organize their thinking.

VIDEO 3 OF 3 - This video addresses NC standard 5.NF.1. It explains how to connect the use of models for addition/subtraction of fractions to the standard algorithm for adding/subtracting fractions.

VIDEO 1 OF 3 - This video addresses NC standard 5.NF.1. It explains WHY we create equivalent fractions when adding unlike denominators, and HOW to create equivalent fractions when adding unlike denominators.

In this activity, students will work in collaborative groups to create 9M x 9M models of plant and animal cells. Class population can be split into 2 or 4 groups, with half the students constructing animal cells and the other half constructing plant cells. Students must organize and assign duties, provide materials for this activity, and write a written report. They will also give "Cell Tours" to other students and/or classroom guests.

This lesson is Day 12 in a series of 12 lessons around fraction equivalences and comparisons.

Use your math skills to help detectives solve the crime. This video lesson reviews fractions of an area, fractions on a number line, and equivalent fractions. No materials are required.

This lesson is Day 2 in a series of 12 lessons around fraction equivalences and comparisons.

This video lesson introduces the idea that fractions can be used to represent 1 whole. To engage in this lesson, students may use virtual circle models from Toy Theater (https://toytheater.com/fraction-circles/)

This lesson is Day 4 in a series of 12 lessons around fraction equivalences and comparisons.

This video lesson looks at how we use fractions in the kitchen. Students are challenged to use circle models to find equivalent fractions for a recipe. Students may use virtual circe models from the Toy Theater (https://toytheater.com/fraction-circles/).

This video lesson introduces the idea that when comparing two fractions, they must refer to the same size whole. Then, students use fraction strips to compare fractions. Students may use virtual fraction strips from Toy Theater (https://toytheater.com/fraction-strips/)

In this STEM lesson, students use the NASA Future Flight Design Challenge activity and website to help them learn how NASA engineers develop and test experimental aircraft to solve a specific problem by using the engineering design process. Students will solve an engineering design challenge based on specific criterion and build and design four paper aircraft based on actual NASA experimental aircraft. They will conduct and test their models and gather data of the results based on the design process and a specific challenge. Lastly, students will evaluate the performance of each aircraft based on engineering requirements.

Flowering plants keep the world cooler and wetter than it would be otherwise.

This 5-E lesson introduces the use of nonfiction materials from the library with a maker component. Students willexamine nonfiction materials,draw diagrams,make models,ask questions of others,and explain their work. 

This 6-E lesson introduces the use of nonfiction materials from the library with a maker component. Students willuse critical thinking skills,examine nonfiction materials,draw diagrams,make models,ask questions of others,and explain their work. 

Expressions

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Write and evaluate simple expressions that record calculations with numbers.
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.
Interpret numerical expressions without evaluating them.

Lesson Flow

Students learn to write and evaluate numerical expressions involving the four basic arithmetic operations and whole-number exponents. In specific contexts, they create and interpret numerical expressions and evaluate them. Then students move on to algebraic expressions, in which letters stand for numbers. In specific contexts, students simplify algebraic expressions and evaluate them for given values of the variables. Students learn about and use the vocabulary of algebraic expressions. Then they identify equivalent expressions and apply properties of operations, such as the distributive property, to generate equivalent expressions. Finally, students use geometric models to explore greatest common factors and least common multiples.

Lesson OverviewStudents use a geometric model to investigate common multiples and the least common multiple of two numbers.Key ConceptsA geometric model can be used to investigate common multiples. When congruent rectangular cards with whole-number lengths are arranged to form a square, the length of the square is a common multiple of the side lengths of the cards. The least common multiple is the smallest square that can be formed with those cards.For example, using six 4 × 6 rectangles, a 12 × 12 square can be formed. So, 12 is a common multiple of both 4 and 6. Since the 12 × 12 square is the smallest square that can be formed, 12 is the least common multiple of 4 and 6.Common multiples are multiples that are shared by two or more numbers. The least common multiple (LCM) is the smallest multiple shared by two or more numbers.Goals and Learning ObjectivesUse a geometric model to understand least common multiples.Find the least common multiple of two whole numbers equal to or less than 12.

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.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

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.

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.