The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc) shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The problem combines the ideas of ratio and proportion within the context of density of matter.

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.

This problem is part of a very rich tradition of problems looking to maximize the area enclosed by a shape with fixed perimeter. Only three shapes are considered here because the problem is difficult for more irregular shapes.

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.

This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.

This activity is designed to determine the appropriate instructional level for a student in a one-on-one interaction with the teacher.

This activity is designed to determine the appropriate instructional level for a student in a one-on-one interaction with the teacher.

In this assessment in a one-to-one setting, a student is shown the numbers from 1Đ10, one number at a time, in random order. The teacher asks, Ňwhat number is this?"

This assessment task can be used with a single student or a small group of students. Each student needs his or her own set of numeral cards.

This assessment may be used in a small group or whole group setting, give each student a piece of paper. Students who have trouble writing certain numbers can then get targeted practice.

In this real world problem students solve questions based on the relationship between production costs and price.

This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.

The purpose of this task is to help students develop fluency in their understanding of the relationship between fractions and ratios. It provides an opportunity to translate from fractions to ratios and then back again to fractions.

This series of word problems requires students to apply the concepts of factors and common factors in a context.

The purpose of this task is to provide students with a multi-step problem involving volume and to give them a chance to discuss the difference between exact calculations and their meaning in a context.

The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction.

This real world task requires students to answer questions about equations for calculating compound interest.