Students begin the lesson with a critique of their own work on the Self Check using questions and comments from you to reflect on their work. They then critique three examples of student work on the task, each with its own tools for modeling the given relationship between quantities. Finally, they apply what they learned to a closely related problem.Key ConceptsStudents reflect on their work and connect different ways of representing ratio relationships: tape diagrams, double number lines, and ratio tables.Goals and Learning ObjectivesUse teacher comments to refine solution strategies for ratio problems.Deepen understanding of ratio relationships.Synthesize and connect strategies for representing and investigating ratio relationships.Critique given student models created to solve ratio problems.Apply deepened understanding of ratio relationships to a new ratio problem.

Students use tape diagrams to model relationships and solve problems about types of DVDs.Key ConceptsTape diagrams are useful for visualizing ratio relationships between two (or more) quantities that have the same units. They can be used to highlight the multiplicative relationship between the quantities.Goals and Learning ObjectivesUnderstand tape diagrams as a way to visually compare two or more quantities.Use tape diagrams to solve ratio problems.

Students focus on interpreting, creating, and using ratio tables to solve problems.Key ConceptsA ratio table shows pairs of corresponding values, with an equivalent ratio between each pair. Ratio tables have both an additive and a multiplicative structure:Goals and Learning ObjectivesComplete ratio tables.Use ratio tables to solve problems.

This lesson teaches about Rates, Ratios, and Unit Rates, using visually appealing art and real-life examples that will engage teenagers.

Normally we find things using landmark navigation. When you move to a new place, it may take you awhile to explore the new streets and buildings, but eventually you recognize enough landmarks and remember where they are in relation to each other. However, another accurate method for locating places and things is using grids and coordinates. In this activity, students will come up with their own system of a grid and coordinates for their classroom and understand why it is important to have one common method of map-making.

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

This lesson unit is intended to help sixth grade teachers assess how well students are able to: Analyze a realistic situation mathematically; construct sight lines to decide which areas of a room are visible or hidden from a camera; find and compare areas of triangles and quadrilaterals; and calculate and compare percentages and/or fractions of areas.

Two besotted rulers must embrace proportional units in order to unite their lands. It takes mathematical reasoning to identify the problem, and solution, when engineers from Queentopia and Kingopolis build a bridge to meet in the middle of the river.

Learn about the dynamic relationships between a jet engine's heat loss, surface area, and volume in this video adapted from Annenberg Learner's Learning Math: Patterns, Functions, and Algebra.

This lesson is about ratios and proportions using candy boxes as well as a recipe for making candy as situations to be considered. It addresses many Mathematical Reasoning standards and asks students to: Use models to understand fractions and to solve ratio problems; think about a ratio as part/part model and to think about the pattern growing in equal groups or a unit composed of the sum of the parts; find a scale factor and apply it to a ratio. (5th Grade Math)

Students reinforce their knowledge of the different parts of the digestive system and explore the concept of simulation by developing a pill coating that can withstand the churning actions and acidic environment found in the stomach. Teams test the coating durability by using a clear soda to simulate stomach acid.

The battle is on in this game where you build your own potions! Check your ratios to win this mixture mix-off. Ratio Rumble guides students in: identifying ratios when used in a variety of contextual situations; providing visual representations of ratios; solving common problems or communicating by using rate, particularly unit rates; and explaining why ratios and rates naturally relate to fractions and decimals.

Students often think additively rather than multiplicatively. For example, if you present the scenario, "One puppy grew from 5 pounds to 10 pound. Another puppy grew from 100 pounds to 108 pounds." and ask, "Which puppy grew more?" someone who is thinking additively will say that the one who now weighs 108 grew more because he gained 8 pounds while the other gained 5 pounds. Someone who is thinking multiplicatively will say that the one that now weighs 10 pounds grew more because he doubled his weight while the other only added a few pounds. While both are correct answers, multiplicative thinking is needed for proportional reasoning. If your students are thinking additively, you can nudge them toward multiplicative thinking with this activity.

In this lesson designed to enhance literacy skills, students learn how to use fractions to interpret the nutritional information contained on food labels.

In some textbooks, a distinction is made between a ratio, which is assumed to have a common unit for both quantities, and a rate, which is defined to be a quotient of two quantities with different units (e.g. a ratio of the number of miles to the number of hours). No such distinction is made in the common core and hence, the two quantities in a ratio may or may not have a common unit. However, when there is a common unit, as in this problem, it is possible to add the two quantities and then find the ratio of each quantity with respect to the whole (often described as a part-whole relationship).

Why do we care about air? Breathe in, breathe out, breathe in... most, if not all, humans do this automatically. Do we really know what is in the air we breathe? In this activity, students use M&M(TM) candies to create pie graphs that show their understanding of the composition of air. They discuss why knowing this information is important to engineers and how engineers use this information to improve technology to better care for our planet.

Proportional relationships are everywhere. They are used to compare professional athletes and to help shoppers get the “best bang for their buck” at the grocery store. They help us build models and designs and are used in many business applications. This lesson plan introduces proportional relationships, ratios and unit rates at the grade 6/7 (C) level and requires adult learners to identify and compare ratios using the Padlet application.

Proportional relationships are everywhere. They are used to compare professional athletes and to help shoppers get the “best bang for their buck” at the grocery store. They help us build models and designs and are used in many business applications. This lesson plan introduces proportional relationships, ratios and unit rates at the grade 6/7 (C) level and requires adult learners to identify and compare ratios using the Padlet application.

Measure relative humidity in the air using a simple device made of a temperature sensor, a plastic bottle, and some clay. Electronically plot the data you collect on graphs to analyze and learn from it. Experiment with different materials and different room temperatures in order to explore what affects humidity.

A very short video introduction to how photosynthesis cycles energy through an ecosystem and a "real-world" application of ratios! Lindsay Hollister, JPPM's horticulturalist, taps a black walnut tree for its sap and park staff boil it down to create syrup. Included in this video are an animated food web showing the directions of energy flow during photosynthesis and when sap is "rising," which can be extended by students to include humans or more parts of their local ecosystem. Use the video as an introduction to activities about sugar and biological storage, and an excuse to sample maple syrup to taste the sugar. Alternatively, research trees nearby students could help tap and witness the biological transfer of energy themselves.

Always be sure you can successfully identify a plant before using it and take precautions to avoid negative reactions.

This resource is part of Jefferson Patterson Park and Museum’s open educational resources project to provide history, ecology, archaeology, and conservation resources related to our 560 acre public park. More of our content can be found here on OER Commons or from our website at jefpat.maryland.gov. JPPM is a part of the Maryland Historical Trust under the Maryland Department of Planning.