Solve problems involving ratios and rates.

a. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane.
b. Solve unit rate problems.

Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Ratio errors confuse a dodgeball coach as two teams face off in an epic tournament. See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.

True love has the right ratio. In this humorous animation, the number of words spoken by each partner predicts whether a date goes well or horribly. What do you do when someone asks if you listen to country music backwards, but won't let you get a word in edgewise?

Play with objects on a teeter totter to learn about balance. Test what you've learned by trying the Balance Challenge game.

Open middle problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking.

The Finding Equivalent Ratios problem asks students to use the digits 1-9 to create 3 equivalent ratios made up of single and double digit numbers.

Student facing mathematics units. Covers area and surface area, ratios, dividing fractions, arithmetic in base ten, expressions and equations, rational numbers, and data sets/distributions.

Students begin their sixth grade year investigating the concepts of ratio and rate. They use multiple forms of ratio language and ratio notation, and formalize understanding of equivalent ratios. Students apply reasoning when solving collections of ratio problems in real world contexts using various tools (e.g., tape diagrams, double number line diagrams, tables, equations and graphs). Students bridge their understanding of ratios to the value of a ratio, and then to rate and unit rate, discovering that a percent of a quantity is a rate per 100. The 35 day module concludes with students expressing a fraction as a percent and finding a percent of a quantity in real world concepts, supporting their reasoning with familiar representations they used previously in the module.

In this problem-based learning module, students will be given the chance to plan their idea of the perfect party.  They are given a budget of $2,500, this is the maximum amount of money they can use.  The goal is for students to plan a party that they think people would want to attend and would enjoy being a part of.  The students will need to come up with categories of what their party will need (food/drink, decorations, entertainment, location, etc).  These will then be the stations students will move at their own pace through to complete the party planning.  At each station they will need to identify what they are doing to have/do for the party and how much it will cost.  They will then have to figure out the unit cost (cost per person) for that category. The final station should allow for students to find the total cost of their part and total unit cost per person for the party.  If the total cost exceeds $2,500 students should make adjustments as needed.Students will then create an advertisement (commercial, flyer, poster etc.) to promote their party as the “PARTY OF THE YEAR!”Students will then present these advertisements to school staff, parents, administrators etc. to vote on the party they would want to throw for their own child. They should take into consideration cost per person, entertainment, and enjoyment of the party.

This lab exercise exposes students to a potentially new alternative energy source hydrogen gas. Student teams are given a hydrogen generator and an oxygen generator. They balance the chemical equation for the combustion of hydrogen gas in the presence of oxygen. Then they analyze what the equation really means. Two hypotheses are given, based on what one might predict upon analyzing the chemical equation. Once students have thought about the process, they are walked through the experiment and shown how to collect the gas in different ratios. By trial and error, students determine the ideal combustion ratio. For both volume of explosion and kick generated by explosion, they qualitatively record results on a 0-4 scale. Then, students evaluate their collected results to see if the hypotheses were correct and how their results match the theoretical equation. Students learn that while hydrogen will most commonly be used for fuel cells (no combustion situation), it has been used in rocket engines (for which a tremendous combustion occurs).

Brigitte Tennis uses the visual aid of spraying water from one point of a triangle to illustrate to her students opposite and adjacent sides. She then beats out a rhythm on drums to teach her students the mnemonic device SOH-CAH-TOA for finding sine, cosine, and tangent.

This lesson is regarding the introduction to ratios.  Students will learn what a ratio is, practice finding ratios, and work on making their own ratios. There are YouTube videos, worksheets, and funny images to help students understand ratios.