Repeated motion is present everywhere in nature. Learn how to 'make waves' with your own movements using a motion detector to plot your position as a function of time, and try to duplicate wave patterns presented in the activity. Investigate the concept of distance versus time graphs and see how your own movement can be represented on a graph.

This is a three-credit course which covers topics that enhance the students’ problem solving abilities, knowledge of the basic principles of probability/statistics, and guides students to master critical thinking/logic skills, geometric principles, personal finance skills. This course requires that students apply their knowledge to real-world problems. A TI-84 or comparable calculator is required. The course has four main units: Thinking Algebraically, Thinking Logically and Geometrically, Thinking Statistically, and Making Connections. This course is paired with a course in MyOpenMath which contains the instructor materials (including answer keys) and online homework system with immediate feedback. All course materials are licensed by CC-BY-SA unless otherwise noted.

This Pre-Calculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems.
Use parentheses to evaluate numerical expressions.
Identify and use the properties of operations.

Lesson Flow

In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work.

The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

Putting Math to Work

Type of Unit: Problem Solving

Prior Knowledge

Students should be able to:

Solve problems with rational numbers using all four operations.
Write ratios and rates.
Use a rate table to solve problems.
Write and solve proportions.
Use multiple representations (e.g., tables, graphs, and equations) to display data.
Identify the variables in a problem situation (i.e., dependent and independent variables).
Write formulas to show the relationship between two variables, and use these formulas to solve for a problem situation.
Draw and interpret graphs that show the relationship between two variables.
Describe graphs that show proportional relationships, and use these graphs to make predictions.
Interpret word problems, and organize information.
Graph in all quadrants of the coordinate plane.

Lesson Flow

As a class, students use problem-solving steps to work through a problem about lightning. In the next lesson, they use the same problem-solving steps to solve a similar problem about lightning. The lightning problems use both rational numbers and rates. Students then choose a topic for a math project. Next, they solve two problems about gummy bears using the problem-solving steps. They then have 3 days of Gallery problems to test their problem-solving skills solo or with a partner. Encourage students to work on at least one problem individually so they can better prepare for a testing situation. The unit ends with project presentations and a short unit test.

Rate

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers.
Understand quantity as a number used with a unit of measurement.
Solve problems involving quantities such as distances, intervals of time, liquid volumes, masses of objects, and money, and with the units of measurement for these quantities.
Understand that a ratio is a comparison of two quantities.
Write ratios for problem situations.
Make and interpret tables, graphs, and diagrams.
Write and solve equations to represent problem situations.

Lesson Flow

In this unit, students will explore the concept of rate in a variety of contexts: beats per minute, unit prices, fuel efficiency of a car, population density, speed, and conversion factors. Students will write and refine their own definition for rate and then use it to recognize rates in different situations. Students will learn that every rate is paired with an inverse rate that is a measure of the same relationship. Students will figure out the logic of how units are used with rates. Then students will represent quantitative relationships involving rates, using tables, graphs, double number lines, and formulas, and they will see how to create one such representation when given another.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Understand ratio concepts and use ratios.
Use ratio and rate reasoning to solve real-world problems.
Identify and use the multiplication property of equality.

Lesson Flow

This unit introduces students to the routines that build a successful classroom math community, and it introduces the basic features of the digital course that students will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the routines of Opening, Work Time, Ways of Thinking, Apply the Learning (some lessons), Summary of the Math, Reflection, and Exercises. Students learn how to present their work to the class, the importance of students’ taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems, to further explore the resources and tools and to learn how to organize their work.

The mathematical work of the unit focuses on ratios and rates, including card sort activities in which students identify equivalent ratios and match different representations of an equivalent ratio. Students use the multiplication property of equality to justify solutions to real-world ratio problems.

The Mathematics of Nutrition Science is a workbook designed to integrate and contextualize developmental mathematics into an introductory college level Nutrition class. Definitions and skills from Community College Level Elementary Algebra and Quantitative Literacy courses are explained through examples analyzing the nutritional content of different foods. The book contains exercises for students to practice these skills, and also to reflect on the concepts through short writing assignments aligned with developmental English. These materials could be used by Nutrition course instructor in many different ways, and are designed to be self-contained and require minimal mathematical instruction.

Students obtain a basic understanding of microfluidic devices, how they are developed and their uses in the medical field. After conducting the associated activity, they watch a video clip and learn about flow rate and how this relates to the speed at which medicine takes effect in the body. What they learn contributes to their ongoing objective to answer the challenge question presented in lesson 1 of this unit. They conclude by solving flow rate problems provided on a worksheet.

A work in progress, CK-12's Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.

This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.

The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.

This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.

In Monster School Bus, students play a newly hired bus driver with a certain number of seats on the bus. The mission: to pick up each neighborhood’s little monsters and bring them to school – without dividing up groups (monsters don’t like that).
In early levels, each little monster takes up one seat and players combine integers to add up to 10. Each new neighborhood exposes learners to a more complex set of numbers, including decimals and fractions. The design of characters and locations gives the game an edgy look, and provides a more mature atmosphere to a game covering fairly juvenile content (e.g., buildings transform into punk Monster Buildings as a reward for picking up kids). This is important: though students learn this concept of number chunking in earlier grades, they often fail to understand it conceptually. Therefore, this content could turn off older students if they feel the game is “below them.” The edgy character design helps make the content feel more age-appropriate, and the graphical details impact gameplay and motivate players to visualize numbers as sets and quantities and think harder about relationships among numbers and number systems.

In this seminar you will learn how to complete multiple step equations. You will apply techniques you have learned about inverse operations to solve for a missing variable. You will use the techniques learned in this seminar to verify solutions to various other types of problems as you move forward. When solving multiple step equations, you will identify which operation to address first, which second, and so on, until you have the variable all alone and a solution for it. The best part? You can always substitute your answer into the original problem to make sure your answer is correct.StandardsCC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a given variable.