# NCTM Brain Teasers

Sliding Triangle The triangle at left lies on a flat surface and is pushed at the top vertex. The length of the congruent sides does not change, but the angle between the two congruent sides will increase, and the base will stretch. What is the maximum area achieved during this process? This brainteaser was written by Derrick Niederman. Solution: 200 square units; 32 units. For the first part of the question, the maximum area occurs when the angle between the sides is a right angle. For a more advanced trigonometry solution, remember that the area of a triangle can be calculated by taking half the product of two sides and the sine of the angle between those sides. For the second part of the question, note that if you bisect the original triangle, divide it into two right triangles, and rearrange the pieces, you can form a new triangle with exactly the same area. Again using a trig solution, A=(1/2)absinθ, where a and b are the side lengths. Related:  Math Gameslauriebworthyjtrivisonno

Illuminations Interactive Games Compound Interest Simulator This applet will allow you to investigate savings account earnings, credit card debt, and a stock market simulation. Mixtures Use this tool to explore mixture problems and percentages using colored circles in two different piles. Cyclic Figures Students will recognize rotation symmetry in figures and examining various rotation symmetries. Pick-a-Path Help Okta reach the target by choosing a path from the top of the maze to the bottom. Circle Area Use this tool to see the relationship between the area of a circle and its radius. Area of Parallelograms This applet shows the relationship between the area of a parallelogram and the lengths of its sides. Area of Trapezoids Investigate how changes in the base and height of a trapezoid affect its area.

Stick Pick Response to Intervention | RTI | RTI Resources | Intervention Central Math Tests and Quizzes That Are Aligned Core Math Curriculum Math Tests and Topic/Skill Based Quizzes We now have a full line of tests for each section of the common core curriculum. Test are fully available to members for immediate download. There is a test sampler in each section for those who haven't signed up yet and want to see what it is all about. Tests By Grade Level Kindergarten Level - You'll find a multiple choice version, short response, and all 5 individual content areas in their own quiz.Grade 1- The level of the material seems very difficult for first graders, but it is perfectly aligned.Grade 2- The extended response test form is difficult for most students at this level.Grade 3- Geometry comes to life, at least a little more.