In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations.

The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning.

The purpose of this task is to assess studentsŐ understanding of multiplicative and additive reasoning.

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).

In these lessons students will explore the paintings of Horace Pippin and Wayne Thiebaud and the mobiles of Alexander Calder to discover and practice math and visual art concepts. Background and biographical information about the work of art and artist, guided looking with class discussion, and activities with worksheets using mathematical formulas and studio art provide the framework for each lesson.

One common mistake students make when dividing fractions using visuals is the confusion between remainder and the fractional part of a mixed number answer.

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

In this problem students practice basic addition and subtraction skills along with logical reasoning to satisfy three interdependent conditions. Solvers use the clues provided to determine the number of eggs in each of three baskets. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, a PowerPoint presentation, and vocabulary cards (pdf).

This task allows students to relate addition and subtraction problems to money in a context that introduces the concept of scarcity.

This problem reinforces addition fact fluency, develops reasoning, and encourages working systematically. Solvers determine which seven cards, out of a set of 15 numbered cards 1-15, are used to satisfy the given sums of each consecutive pair of cards. The resource includes hints for getting started, printable copies of the problem and number cards, suggestions implementation and differentiation, discussion questions, and sample student solutions.

In this task students are asked to write an equation to solve a real-world problem. There are two natural approaches to this task. In the first approach, students have to notice that even though there is one variable, namely the number of firefighters, it is used in two different places. In the other approach, students can find the total cost per firefighter and then write the equation.

This task is the first in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.

This task provides a context for some of the questions asked in "6.NS Multiples and Common Multiples." A scaffolded version of this task could be adapted into a teaching task that could help motivate the need for the concept of a common multiple.

In this problem students study motion along a path and the properties of a parallelogram. Students must navigate back to a starting point after traveling three legs in cardinal directions on a compass. Ideas for implementation, extension and support are included.

This problem gives students practice in calculating with fractions, using factors and multiples, finding equivalent fractions, logical reasoning, and working systematically. Students use clues to determine the total number of discs in a game and the fraction represented by each color. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable (pdf) worksheet of the problem.