# Content Showcase: Media4Math Classroom Modules

1. FREE

## Construction Site Math: Ratios

In this real-world application of ratios, students will learn what a ratio is, including ratios with three terms. They will see different ways of writing ratios, including fractions in simplest form.

a:b     $\frac{a}{b}$     a to b

Two short videos introduce the concept of ratios and each video includes real-world examples of ratios. Then several formative assessments are used to test for understanding.

Students then look at the application of ratios to the mixing of concrete at a construction site, starting with a video then followed by an assessment.

This lesson can be assigned to individual students or teams of students. The lesson can be completed in about 20 minutes.

#### Math Concepts

• Ratios and Rates
• Algebra

#### Learning Objectives

• Identifying ratios
• Simplifying ratios
• Working with ratios with three items

#### Prerequisite Skills

• Writing fractions
• Simplifying fractions
Common Core Standards CCSS.MATH.CONTENT.6.RP.A.1, CCSS.MATH.CONTENT.7.RP.A.2 20 mins 6th - 7th Grade

## Isosceles Triangles

In this lesson students explore and use the properties of isosceles triangles to solve real world problems. After learning the basics of isosceles triangles they apply what they learn to the structure of the Eiffel Tower.

A video introduces the topic of isosceles triangles, along with two isosceles triangle theorems. Students are shown how to find the values for the isosceles pair, given the third angle, by solving a multi-step equation.

Students then apply what they have learned about isosceles triangles by learning about the triangular trusses in the Eiffel Tower. Students learn about what a truss is, what their function is in a building, and why isosceles triangle trusses are an effective form of a truss. Students then learn about two important properties of isosceles triangles involve the perpendicular bisector of the base and the angle bisector of the third angle. Another video ties together triangular trusses, perpendicular bisectors, and angle bisectors.

Students then complete a cloze assessment, in which they identify key words that are missing from a reading passage.

This module can be used as an introductory lesson on isosceles triangles in a middle school geometry unit. The content aligns with grade 7 Core State Standards, but this module can be used as a refresher for higher grades.

This module can be assigned to individual students or groups of students. Students should be able to complete this lesson in 20 minutes.

• Triangles
• Equations

#### Learning Objectives

• Define what an isosceles triangle is
• Describe the isosceles triangle theorems
• Solve real world problems using isosceles triangles

#### Prerequisite Skills

• Basic knowledge of triangles
• Solving multi-step equations
Common Core Standards CCSS.MATH.CONTENT.7.G.B.5 20 mins 6th - 7th Grade

## Integers and Absolute Value

In this module students learn how to measure distances on a number line by finding the absolute value of integer values. In the process students also learn about integers and their opposites, as well as how to compare and order integers. Finally, students apply their skills in a real-world scenario involving scuba diving.

In this lesson students view a number of instructional videos, play a math game, and practice their developing skills with absolute value. Students then look at a real-world example: A video describes an exploration around a sunken ship off the coast of San Diego. Students analyze a schematic diagram of the sunken ship using their skills with absolute value.

This lesson addresses Grade 6 Common Core Standards but it can also be assigned to higher grades for concept review.

This lesson can be assigned to individual students or teams of students. The lesson can be completed in about 20 to 25 minutes.

#### Math Concepts

• Graphing Numbers
• Number Concepts

#### Learning Objectives

• Identify integers and their opposites
• Define absolute value
• Calculate absolute value on a number line
• Compare and order integers

#### Prerequisite Skills

• Definition of an integer
• Working with Number Lines
Common Core Standards CCSS.MATH.CONTENT.6.NS.C.7 20 mins 6th - 7th Grade

## Regular Polygons

In this module, students explore the properties of regular polygons and use their skills to construct tile patterns. Students learn about Arabesque tile patterns found throughout the Middle East. These tile patterns are based on Euclidean geometric principles.

Students learn about the characteristics of polygons, including regular polygons. There are two geometric constructions, one for constructing a square and one for constructing a regular hexagon. Students need to use a compass and ruler for these activities.

Students also learn the formula for calculating the sum of the interior angles of a polygon. This provides an opportunity for algebraic work in the context of geometry.

This lesson addresses the high school Common Core Standards but it can also be used in an informal geometry class in middle school.

#### Math Concepts

• Geometric Constructions
• Circles

#### Learning Objectives

• Define polygons
• Construct a square using a compass and ruler
• Construct a hexagon using a compass and ruler
• Calculate the sum of the interior angles of a polygon

#### Prerequisite Skills

• Know how to use a compass and ruler
• Familiarity with algebraic formulas
Common Core Standards CCSS.MATH.CONTENT.HSG.MG.A.3 20 mins 8th - 10th Grade

## The Language of Math: Addition Expressions

In this module students develop their skills at translating verbal expressions into mathematical ones. This is a crucial skill that often doesn't get enough attention. A student's ability to successfully translate words into mathematical expressions and equations puts that student on a path to successfully solving more complicated problems.

In this module students focus on addition expressions. This includes numerical and algebraic expressions. They work on addition expressions of the following form:

• a + b, for various integers a and b
• x + a, for integer a
• ax + b, for various integers a and b

As an extension of their work with translating words into mathematical expressions, students explore the various symbols used by meteorologists with weather maps. Students analyze the symbols on a weather map. They also translate words into mathematical expressions using the context of weather.

#### Math Concepts

• Expressions
• Number Concepts
• Problem Solving

#### Learning Objectives

• Translate verbal expressions into algebraic expressions
• Solve problems using algebraic expressions

#### Prerequisite Skills

• Familiarity with integers
• Familiarity with algebraic expressions
Common Core Standards CCSS.MATH.CONTENT.6.EE.A.2.A, CCSS.MATH.CONTENT.6.EE.B.6 20 mins 6th - 7th Grade

## Linear Function Models

In this module students learn the properties of linear functions. They look at data sets, graphs of coordinates, and algebraic representations of functions. Then students go on a field trip to the US Mint to see how money is printed. From this they develop linear function models for calculating the number of bills printed, along with their dollar value.

Students begin by analyzing linear function data by identifying the common difference. The goal is to see the relationship among the common difference and the slope of the linear function.

Students use the Desmos graphing calculator to explore graphs of data and equations. Both types of linear functions are explored:

• ax
• mx b

Students then watch a video about the US mint and how currency is created. Students use the information in the video to develop two linear function models: one for calculating the number of bills produced for every sheet of printed bills, plus another for calculating the dollar value of the printed bills.

Note: Be sure students are familiar with the concept of slope and the basic definition of a function.

#### Math Concepts

• Functions
• Problem Solving
• Algebra

#### Learning Objectives

• The definition of a linear function
• How to graph linear functions
• How to display linear function data
• Mathematical modeling

#### Prerequisite Skills

• Slope formula
• Definition of a function
Common Core Standards CCSS.MATH.CONTENT.8.F.A.2, CCSS.MATH.CONTENT.8.F.A.3, CCSS.MATH.CONTENT.8.F.B.4 20 mins 8th - 10th Grade

## Reflection and Symmetry: Da Vinci's Mirror Writing

In this module explore reflection and symmetry in the context of Leonardo Da Vinci's mirror writing. Many of Da Vinci's handwritten notes were written in reverse script that could only be read correctly in a mirror. This provides an opportunity to explore geometric reflections, but also the symmetric properties of certain letters of the alphabet.

The module begins by looking at reflections and axes of reflection. Through this exploration students come to recognize that some letters, in spite of a reflection, are unchanged. This creates an opportunity to explore vertical and horizontal line symmetry.

• Geometry

#### Learning Objectives

• Understanding of axis of reflection
• Understanding of vertical line symmetry
• Understanding of horizontal line symmetry
• Encoding messages using the properties of reflection and symmetry

#### Prerequisite Skills

• Understanding of geometric points and lines
• The letters of the alphabet are made up of basic geometric shapes
Common Core Standards CCSS.MATH.CONTENT.8.G.A.3 20 mins 6th - 8th Grade

## Halloween Math Activities

Turn the Halloween season into an opportunity to do some math activities! In this module, you'll find a clever collection of arithmetic, algebra, and geometry activities.

1. Geometry activity: Watch a video about how spiders build webs and analyze the result geometrically. Students build polygon-based web designs in this hands-on activity.
2. Algebra activity: Going to the pumpkin patch? Use different sized pumpkins on this data-gathering activity, where students measure diameters and circumferences and graph the results.
3. Arithmetic activity: Two addictive divisibility games based on whack-a-mole.

#### Math Concepts

• Functions
• Graphing Numbers
• Number Concepts
• Geometric Constructions

#### Learning Objectives

• Using polygons to construct shapes
• Gathering and analyzing data
• Analyzing linear function data and graphs

#### Prerequisite Skills

• Understanding of basic polygon shapes
• Understanding of diameter and circumference of a circle
• Understanding of basic divisibility rules
Common Core Standards CCSS.MATH.CONTENT.6.G.A.3, CCSS.MATH.CONTENT.7.G.B.4, CCSS.MATH.CONTENT.8.F.A.3 20 mins 6th - 8th Grade

## Applications of Linear Functions: Cricket Chirps

Crickets are known for their chirping sounds. But did you know that the number of times a cricket chirps per minute is an indicator of the outside temperature? In fact, the relationship between cricket chirps and the outside temperature can be modeled by a linear function. In this module, students will explore the function that can be used to determine the outside temperature based on the number of times a cricket chirps per minute.

First, students watch a video that describes the chirp-temperature phenomenon. Students are then walked through the process of developing the linear model. They look at inputs and outputs, determine the dependent and independent variables, and explore the linear function with a graphing calculator activity.

#### Math Concepts

• Functions
• Problem Solving

#### Learning Objectives

• Build a linear function model
• Test a function model
• Graph a linear function

#### Prerequisite Skills

• Basic understanding of a linear function in slope-intercept form
Common Core Standards CCSS.MATH.CONTENT.8.F.A.3, CCSS.MATH.CONTENT.8.F.A.1 20 mins 6th - 8th Grade

## Applications of Linear Functions: Temperature Conversion

Temperature is one of the most important measurements that we deal with on a daily basis. Weather, climate, food preparation, health, and other phenomena involve some type of temperature measure. The two most common units of temperature measure are Fahrenheit and Celsius.

There is a linear function that allows you to convert from one unit to another. In this module, you'll learn about this linear function. In fact, students will learn about this function and its inverse.

The module starts with an analysis of Celsius-to-Fahrenheit data. They look at the functional relationship between the variables and develop a linear model using the Desmos graphing calculator. They analyze the properties of this linear function and look at its graph.

Next, students analyze Fahrenheit-to-Celsius data. They also develop a linear function model using the Desmos graphing calculator.

Finally, they compare the graphs of the first function and its inverse to identify properties of functions and their inverses.

#### Math Concepts

• Functions
• Problem Solving

#### Learning Objectives

• Create a linear function model for temperature conversion
• Graph the temperature function and interpret slope, y-intercept, domain, and range
• Explore the inverse of a function

#### Prerequisite Skills

• Understands the basics of linear functions
Common Core Standards CCSS.MATH.CONTENT.8.F.A.3, CCSS.MATH.CONTENT.8.F.B.4 20 mins 8th - 10th Grade

## What Is a Function?

In algebra, the topic of functions is extremely important. But what is a function? In this module students will learn what a function is and how to represent it. They'll explore data tables, graphs, and equations. Plus, they'll see the connection from one to the other.

Students will learn about function machines, and we draw an analogy to actual machines. A short video shows how a flat disk of aluminum (the input) is turned into a soda can (the output) by a series of machines that stretch and shape the disk into the can.

#### Math Concepts

• Functions
• Graphing Numbers

#### Learning Objectives

• Defining a function
• Graphing a function
• Using the vertical line test

#### Prerequisite Skills

• Organizing data in tables
• Graphing data from tables
Common Core Standards CCSS.MATH.CONTENT.8.F.A.1, CCSS.MATH.CONTENT.8.F.B.5 20 mins 8th - 10th Grade

## What Is Function Notation?

Cheetahs can accelerate up to 75 mph and can easily outpace a gazelle. But gazelles have adapted to keep cheetahs at bay long enough to tire them out. We can analyze this phenomenon mathematically through the use of some basic concepts involving functions.

In this highly engaging module students learn about functions, domain, range, and mathematical modeling. They will look at the following types of functions:

• Speed vs. distance
• Distance vs. time
• Displacement vs. time

These three functions are analyzed using function notation, and the domains and ranges are clearly defined. Students explore a mathematical model that shows whether a cheetah will catch the gazelle or if the gazelle escapes.

This module also uses the Desmos graphing calculator extensively.

#### Math Concepts

• Functions
• Graphing Numbers
• Problem Solving

#### Learning Objectives

• Defining a function using function notation
• Developing a mathematical model using function notation
• Identify the domain and range of a function

#### Prerequisite Skills

• Understands the basics of linear functions
Common Core Standards CCSS.MATH.CONTENT.8.F.B.4, CCSS.MATH.CONTENT.8.F.B.5 20 mins 8th - 10th Grade

## Why Do Elephants Have Wrinkled Skin?

Have you noticed how wrinkled an elephant's skin is? What purpose does it serve and what does math have to do with explaining this phenomenon? Well, the explanation for an elephant's wrinkled skin is almost entirely a math story.

In this module students explore rational expressions and functions in the context of the ratio of surface area and volume for various three-dimensional figures. Such figures can be used to model the basic shapes of animals.

This ratio reveals a lot about how an animal is able to retain heat or lose it rapidly, depending on the animal's habitat. The geometry of heat transfer also has applications in architecture and design.

• Calculate the ratio of surface area and volume
• Graph rational functions
• Solve real-world problems using rational functions

Make sure your students know the basics of rational numbers and functions.

#### Math Concepts

• Functions
• Ratios and Rates
• Geometry
• Algebra

#### Learning Objectives

• Calculate the ratio of surface area and volume
• Graph rational functions
• Solve real-world problems using rational functions

#### Prerequisite Skills

• Understanding of rational numbers
• Understanding of the basic properties of functions
• Understanding of area and volume formulas for simple geometric shapes
Common Core Standards CCSS.MATH.CONTENT.HSF.BF.A.1.B, CCSS.MATH.CONTENT.7.NS.A.3, CCSS.MATH.CONTENT.HSG.MG.A.1 30 mins 8th - 11th Grade