Bianca visits a bike shop and learns how bicycle gears work in this Cyberchase video segment.

In this problem students explore the concept of proportion by comparing the relative strengths of different mixes of juice flavor and water in a visual context. Given four mixtures represented by purple and white rectangles, students order the drinks from strongest to weakest flavor and explain their reasoning. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support.

In this investigation students explore the concept of ratios and their relationship with factors and multiples. Given an assortment of cogs (gears) with different numbers of teeth, solvers are asked to find which pairs allow for each tooth of one to fit into every gap of the other, and to form conjectures regarding which pairs would work generally. The problem is well-suited for group work. The Teachers' Notes page offers suggestions for implementation, key questions, student sheets, and links to articles, videos, and an interactive Cog Environment (cataloged separately).

This brief article discusses the Count the Beat project, which incorporates music into math instruction. The instructors in this project began each lesson with a brief math exercise followed by a more in-depth music task utilizing number lines, fractions, ratios, and/or probability. While music professionals carried out this project the article does offer some suggestions for application in the math classroom without music professional.

With this flexible Flash applet students can explore a wide range of concepts, including addition and subtraction, factors and multiples, fractions, ratios, and combinations. Users place, move and rotate virtual Cuisenaire Rods on a grid which can be enlarged, reduced, moved or printed. It contains a link to page of challenges which can take advantage of this tool.

This activity gives students an opportunity to discuss the quantities involved in statements about measurements or statistics and may involve estimation, calculation and/or research. Ideas for implementation, extension and support are included.

This brief article describes some methods of indirect measurement that have been applied throughout history to the problem of estimating the height of tall trees. Several methods involving scaling, angles, ratios, and tools are discussed.

This activity gives students a chance to make estimates and comparisons of the measures of length (height) and capacity. It presents an image of a tiny elf next to a normal size mug. Students are asked to estimate the Little Man's height and compare it with that of other objects. Next, they are asked to estimate the height and volume of the Little Man's mug. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension and support.

This problem, based on the story of Goldilocks and the Three Bears, provides a context for children to apply ratio and proportion concepts as well as fraction computation skills. Using the given size relationships among the bears, solvers determine the sizes of various objects in the bears' house. The Teachers' Notes page offers suggestions for implementation, key questions, ideas for extension and support, a printable pdf of the problem, and links to related problems.

This problem provides an opportunity for students to reason about ratio and proportion in the realistic context of mixing a fruit drink from concentrate. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and links to related problems (Blackcurrantiest is cataloged separately).

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.

In this problem students apply basic proportional reasoning in the context of a pie recipe. Given a recipe for 80 pies, Peter needs to determine whether the ingredients he has on hand are enough to make 2 pies. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension, and printable lists of ingredients (doc).

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

This activity builds student knowledge of ratios by using Cuisenaire rods to determine proportion and form equivalent ratios. Students may use the Cuisenaire rod environment embedded in this resource or they may use actual Cuisenaire rods depending on preference/ability/accessibility. This resource includes teacher notes, solution, and suggestions for questioning.

In this lesson designed to enhance literacy skills, students examine how to use fractions to measure and help conserve freshwater resources.

This lesson is meant to introduce students to the concept of unit rate. It uses a Canva presentation to introduce the concept. For practice, student will calculate the population density of various countries and compare it to the population density of Utah. There is a worksheet to complete during independent practice, an exit ticket, and an extension activity for fast finishers. Image Credits:"Flag Map Of The World" by GDJ is in the public domain through OpenClipArt.org upload agreement"Utah" by Arohletter1 is in the public domain through OpenClipArt.org upload agreementImage Credit: Christian Cragun