CK-12 Foundation
Integers: Tiling a Chessboard with Dominoes
Ten questions make up an interactive all about integers. Scholars answer multiple choice, short answer, and discussion questions using a 4x4 chessboard and dominoes.
Concord Consortium
Proportional Representation
Sometimes the solution is all a matter of perspective. The short assessment task presents a problem to pupils that requires them to make sense of a diagram. Once learners see two similar triangles, the rest of the solution is solving a...
Concord Consortium
Perfect Ten
How many ways can you make 10? Class members tackle three problems to find all possible ways three numbers add to be 10. The first is with positive integers, secondly with non-negative integers, and finally with real numbers. Pupils also...
Concord Consortium
People and Places
Graph growth in the US. Given population and area data for the United States for a period of 200 years, class members create graphs to interpret the growth over time. Graphs include population, area, population density, and population...
Concord Consortium
Parameters and Clusters II
Let's give parameters a second try. Scholars take a second look at a system of linear equations that involve a parameter. Using their knowledge of solutions of systems of linear equations, learners describe the solution to the system as...
Concord Consortium
Parameters and Clusters I
Chase the traveling solution. Pupils analyze the solutions to a system of linear equations as the parameter in one equation changes. Scholars then use graphs to illustrate their analyses.
Concord Consortium
Painted Stage
Find the area as it slides. Pupils derive an equation to find the painted area of a section of a trapezoidal-shaped stage The section depends upon the sliding distance the edge of the painted section is from a vertex of the trapezoid....
Concord Consortium
Outward Bound
Just how far can I see? The short assessment question uses the Pythagorean Theorem to find the distance to the horizon from a given altitude. Scholars use the relationship of a tangent segment and the radius of a circle to find the...
CK-12 Foundation
Integers that Represent Different Situations: Football Field
A football-themed interactive focuses on integers. Seven questions challenge scholars to show what they know by way of short answers, multiple-choice, and true or false. An open-ended question followed by a discussion concludes the...
College Board
AP Calculus: Slope Fields
Ready to field questions about slope fields? An article on AP® Calculus teaching methods describes how to teach about slope fields to solve differential equations. It gives some sample problems to consider with the class and how to...
College Board
Beginning the Year with Local Linearity
Local linearity isn't the first thing that comes to mind to start off an AP® Calculus course. A scholarly article discusses one possible beginning to the AP® Calculus course: investigating and introducing derivatives through activities...
College Board
Calculus at the Battle of Trafalgar
All's fair in math and war. Scholars examine the Battle of Trafalgar using calculus. They set up and solve a system of differential equations to determine the number of ships remaining in each fleet over time.
Concord Consortium
Poly I
Root for young mathematicians learning about functions. A set of two problems assesses understanding of polynomial functions and their roots. Scholars select values for a, b, and c, and then create two functions that meet given...
College Board
Approximation
Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...
College Board
Extrema
No need to go to extreme lengths to find resources on extrema. The central focus of an AP® curriculum module is on critical points and extrema, and how to cover these concepts throughout the course. A set of three worksheets helps assess...
College Board
Reasoning from Tabular Data
Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...
College Board
Engaging the Intuition in Statistics to Motivate
Motivation is key to learning. The author points out that it is important to engage intuition for aspects of statistics that pupils find counter-intuitive. Three strategies—using multiple representations, using intuitive analogies, and...
College Board
Calculations Aren't Enough!
Unlike mathematics, statistics comes with a context. The author reminds teachers that data analysis involves using the context to make sense of the numbers. The article stresses good communication skills by highlighting the scoring...
College Board
Teaching Students How to Write AP Statistics Exam Responses
But this is math—we don't need to know how to write! The article makes a point that class members in AP® Statistics should be comfortable writing as the exams require it. Individuals quickly realize that quality writing is crucial to a...
College Board
2002 AP® Statistics Free-Response Questions Form B
Develop a deeper understanding of statistics. The six released free-response items from the 2002 AP® Statistics Form B involve several concepts that are currently in the regular statistics standards. Teachers see how AP® assessed the...
College Board
2004 AP® Statistics Free-Response Questions Form B
Over the years, data analysis has been important. Looking back to the 2004 AP® Statistics Form B free-response questions, pupils and teachers see the importance of analysis of data sets. The six questions contain analysis of data on...
College Board
2005 AP® Statistics Free-Response Questions Form B
Here's another great way to learn from the past. Released free-response questions provide a look into how concepts measured on the 2005 AP® Statistics Exam on Form B. Teachers and pupils review questions that cover concepts such as...
College Board
2007 AP® Statistics Free-Response Questions Form B
So that is how they do it! Pupils and teachers see how College Board assesses topics using the free-response questions from Form B of the 2007 AP® Statistics test. The six questions are divided in two sections, the first five being more...
College Board
2008 AP® Statistics Free-Response Questions Form B
To know what is on the test would be great. The six free-response question from the second form of the 2008 AP® Statistics gives pupils an insight into the format and general content of the exam. Each question requires the test taker to...