Peg Board for Area etc. of Quadrilaterals

This toy peg board is useful for helping students (and their parents) visualize everything from identification of various types of quadrilaterals to using the Pythagorean Theorem to find the distance along a right triangle's hypotenuse. Just let students explore and discover the relationships by manipulating the vertices of a general quadrilateral. Types identified include the square, rhombus, parallelogram, rectangle, kite, trapezoid, concave, and bow-tie quadrilaterals. (Mathematica)

Decimal Approximations for Rational Numbers

This brief demonstration allows you to select two whole numbers and see the decimal approximation for the quotient of the two whole numbers selected using slider controls. It illustrates that every rational number that can be represented as the quotient of two integers has a repeating or terminating decimal part. (Mathematica)

Least Common Multiple for Grade 6+

This tool will provide the least common multiple for up to four whole numbers, 1 to 20. The Common Core mathematics curriculum standard provides for sixth graders finding the least common multiple for only two whole numbers, 1 to 12, but we have decided to be a little more challenging. In addition to the least common multiple, we also show the complete prime factorization for each of the whole numbers entered, considered to be a step in one of the most efficient ways to find the least common multiple. We also plot the multiples of each number up to about 100. (Mathematica)

Greatest Common Factor for Grade 6+

This tool will provide the greatest common factor for up to four whole numbers, 1 to 100. The Common Core mathematics curriculum standard provides for sixth graders finding the greatest common factor for only two whole numbers, but we have decided to be a little more challenging. In addition to showing the list of whole number divisors for each number, we also plot those factors on four number lines stacked on top of each other. (Mathematica)

Area of Rectangle on a Peg Board for Grade 2

Grade 2 Mathematics, Common Core, says, "Partition a rectangle into rows and columns of same-size squares and count to find the total number of them." This demo allows students to manipulate a small rectangle (max size 5 by 5 units) on a grid and count the squares inside to determine the area. The word "area" is not used at this level, but to make it more interesting, the student's rectangle will change to a random color every time they move the pegs on the peg board. (Mathematica)

New and Old Soccer Balls, Grade 1

The soccer coach has a bag with a lot of soccer balls in it, but some of them are old. She wants to know how many new soccer balls she has for use in today's soccer match. Use the sliders below to find out how many soccer balls she can use. (Mathematica)

Graphs of Linear and Quadratic Functions

For the high school algebra standard Reasoning with Equations & Inequalities, 7, "Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3."

This demo provides graphical solution strategies for a parabola of the generalized form y = Ax2 + Bx + C and a line in the slope-intercept form. A, B, C, m, and b can be varied as needed, and the graph will be modified. (Mathematica)

Construct a Regular Hexagon Given Side Length

This lesson is one we built a few years ago, but it has since been updated with some colorful drawings illustrating how to construct a regular hexagon given the length of the side. Tools needed include a compass and a straight edge. (Adobe)

Compare Fractions, Unlike Denominators, with Fraction Bar

The US Common Core curriculum for mathematics in fourth grade has, among other concepts students might be tested on, the following:

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

This tool will let students explore, make mistakes without the consequences of a high-stakes test, and learn at their own pace. Let them explore what happens to the shaded area as they increase the denominator. Let them find out if 1/3 and 4/12 actually line up, representing equivalent fractions. Just let them play with it. (HTML 5)

Compare Fractions, Unlike Denominators, with Circles

The Common Core curriculum for math (grade 4) has the following:

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

This tool uses fraction wheels (a.k.a. circle graphs or pie graphs) to explore fraction comparisons. (HTML 5)