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This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
01/21/2013
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The purpose of this task is to study some patterns in a small addition table. Each pattern identified persists for a larger table and if more time is available for this activity students should be encouraged to explore these patterns in larger tables.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
08/15/2012
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In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012
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In this problem students are comparing a very small quantity with a very large quantity using the metric system. The metric system is especially convenient when comparing measurements using scientific notations since different units within the system are related by powers of ten.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012
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This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass.

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
08/21/2012
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This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012
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In this real world problem students solve questions based on the relationship between production costs and price.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012
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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.

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012
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This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
08/21/2012
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This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
10/21/2013
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This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012
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This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
08/20/2012
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This task provides a good entry point for students into representing quantities in contexts with variables and expressions and building equations that reflect the relationships presented in the context.

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
08/15/2012
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This is a task where it would be appropriate for students to use technology such as a graphing calculator or GeoGebra, making it a good candidate for students to engage in Standard for Mathematical Practice 5 Use appropriate tools strategically.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012
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This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
01/05/2013
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This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.

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Illustrative Mathematics
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Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
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This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

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Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics