Description

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. 

Description

In this module students learn the basics of integers, with plenty of real-world applications to ground their knowledge. Two short videos introduce the topic of integers and how to graph integers on the number line. A Quizlet activity allows students to practice the skill of identify positives, negatives, or zero. Four formative assessment items test a student's understanding of integers and graphing integers on a number line.  allow students to test their understanding of these topics.

For the problem solving activity, students learn about super-cooling electronic circuits for certain high-tech applications. Students use their knowledge of integers to arrange temperature values on a number line. 

This module can be used as an introductory lesson on integers for pre-algebra or algebra. The content aligns with the grade 6 Common 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.

Description

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.

Description

In this lesson students will use their basic understanding of circles to learn how circular structures are built. The example shown is that of the Roman Colosseum. Students will construct an oval shape from circular arcs to simulate the elliptical shape of the Roman Colosseum.

For this lesson make sure that students have ready access to a compass, ruler, grid paper (graph paper with x-y axes marked is preferred), and pencil with an eraser. The first construction has students creating a teardrop shape from circular arcs that have overlapping points of tangency. This first construction sets up the more elaborate second construction.

Students then look at a real-world application of using circular arcs to approximate the elliptical shape of the Roman Colosseum in a highly engaging video. Students analyze the architecture of the Roman Colosseum and are then shown how to build a scale model of the interior of  the Colosseum.

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

Description

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. 

Description

In this module, students explore algebraic expressions to model different quantities. They look at expressions that involve addition, subtraction, and multiplication. Then they look at real world data from the Star Wars movies since the Disney acquisition of the franchise. Students analyze whether the purchase of the Star Wars franchise has been profitable for Disney.

For this lesson make sure that students are familiar with the definitions of variables, unknowns, and constants. Review definitions are provided. 

Students will learn about modeling and evaluating algebraic expressions. In particular students will look at an expression of the form $px-C$, where p is the price and C is the cost of putting on an event (concert, movie).

Students then look at a real-world application of the Disney purchase of the Star Wars franchise. Students analyze box office data and arrive at an algebraic expression using this data set.

This lesson addresses Common Core standards from grades 6 and 7. This lesson can be assigned to individual students or teams of students. The lesson can be completed in about 20 to 25 minutes. 

Description

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.

Description

In this module model students will learn how to use algebra tiles to model positive numbers, negative numbers, and zero. For this module make sure students have access to set of algebra tiles to use to model integers. Students will then extend their knowledge of integers to learn about matter and anti-matter.

In this module we use red and yellow tiles. The yellow tiles are used to model positive integers, and the red tiles are used to model negative integers. Three short videos describe how to use these tiles to model positives, negatives, and zeros. This module does not address number operations.

As an extension activity students apply their knowledge of zero pairs to the context of matter and anti-matter. A short video describes the concept.

Throughout the lesson various assessment items are included, which are then scored. A teacher's guide includes a detailed description of all components of this lesson.

This lesson addresses the Grade 6 Common Core Standards but it can also be used at any point where algebra tiles are introduced.

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

Description

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.

Description

In this module students develop their skills at translating version 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 subtraction expressions. This includes numerical and algebraic expressions. Students progress through these form:

• a - b, for integers a and b
• x - a, for integer a
• ax - b, for integers a and b

As an extension of their work with translating words into mathematical expressions, students explore how the Inca used Quipus to identify numbers. This becomes an opportunity to translate the visual symbols from the Quipu into numbers in the proper place value. They also translate visual symbols into verbal mathematical expressions.

Description

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:

• y = ax
• y = 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.

Description

In this module students apply their knowledge of linear functions to the context of distance vs. time graphs. They look at data sets, graphs of coordinates, and algebraic representations of distance vs. time functions. Then students go on a field trip to a Nascar race to see how timing at the pit stop has an impact on distance vs. time data.

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:

• y = ax
• y = mx + b

The goal here is to connect the slope of the distance vs. time graph to the speed of the car. Students then explore the graphs of cars with different speeds and initial distances.

Students then watch a video about Nascar pit crews and learn about the rapid-response pit crews who change the tires on the race cars and how the timing of this affects the distance vs. time graph of the cars. Students use the information in the video to analyze linear function models for different pit crew times.

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

Throughout the lesson various assessment items are included, which are then scored. A teacher's guide includes a detailed description of all components of this lesson.

This lesson addresses the Grade 8 Common Core Standards but it can also be used in grades 9 and 10 for review purposes.

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

Description

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.

Description

In this lesson students learn how to use the slope formula to calculate steepness. In particular, students learn how to calculate steepness in the context of cycling. Cyclists use a measure called grade to calculate the steepness of a hill or mountain. Students apply their knowledge of slope to the concept of grade.

Student learn to use the slope formula and then apply it to the context of grade. Several instructional videos provide the background on using the slope formula. Examples of using the slope formula are then provided.

Assessments include two drag-and-drop activities that call on students to carefully analyze the use of the slope formula.

Description

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.

Description

In this module, students explore a physics-based application of linear functions: Hooke's Law. By exploring the properties of springs, a simple linear model is developed. Students then explore applications of Hooke's Law, from weight scales to bungee cords.

Students investigate the properties of springs and identify two variables: the displacement of the spring (extension or compression) and the amount of force involved. From this students identify the independent variable and dependent variable. A graphing calculator activity (using the Desmos graphing tool) allows students to explore the value of k in the function F = kx.

Description

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.

Description

When a rocket is launched into space, it starts from rest and within minutes reaches speeds of tens of thousands kilometers per hour. In other words, the rocket accelerates.

In this module, students apply their knowledge of linear functions to explore the speed vs. time function. In the process they learn about acceleration, as well as the properties of this linear function.

Students first explore the equation for calculating acceleration. Then they use that to develop the speed vs. time linear function. 

This module can be completed in about 20 minutes. Make sure that students understand the basics of linear functions in slope-intercept form.

Description

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.

Description

As the size of a circle changes, so does the size of the diameter and that of the circumference. In fact, there is a linear relationship between these two measures. This relationship can be modeled with a linear function. In this module students will study this linear function and examine its properties, including the fact that the slope of this function is π itself.

This is a hands-on module in which students will measure the diameters and circumferences of a number of different containers. This data gathering will lead to graphing the data. From that students develop a linear model using the Desmos graphing tool. Students will see that the relationship between circumference and diameter has to do with π. In fact, the slope of the linear function is π itself.

For the hands-on part of the lesson, make sure you have all the materials: Different size cylindrical containers (bottles, cups, etc.), string, marker, and a ruler (preferably a caliper). Collect all the student data and use the embedded Desmos graphing tool to graph the data and explore the linear function.

The module concludes with an overview video about the number π. 

Description

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.

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Description

What do drones have to do with domain and range? In this module, students learn about an emerging high-tech delivery system and use that as a vehicle for learning about a function's domain and range. Students will graph data from a table and explore domain and range, and then they graph a continuous function. This highly engaging module will give students a solid understanding of algebraic functions, specifically domain and range.

In this module students will learn the following concepts:

• Finding the domain and range for a set of coordinates that define a function
• Finding the domain and range of a continuous function that doesn’t extend to infinity
• Finding the domain and range of a continuous function that extends to infinity

Description

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.

Description

In this module students explore indirect measurement by seeing how simple angle measure, height measurements, and tangent ratios can be used to calculate distances. The context of castles provides a historically relevant military purpose for the tallness of castles.

This module explores Himeji Castle in Japan, as well as other castles. Some of the concepts explored in this module include:

• Angle measurements and alternate interior angles of parallel lines
• Tangent ratios
• Linear functions, in particular the functional relationship between a castle's height and its line of sight for a given angle

This module provides a nice blend of algebra and geometry topics and can be used in an algebra unit on linear functions, a geometry unit on tangent ratios, or even a pre-calculus lesson on tangent ratios and functions.

Description

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.

What your students will learn:

• 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.