Mathematics Active Learning

Students match the graph of a quadratic, the x-intercepts, and the equation in standard form. Print out the file on card stock or laminate regular paper. Cut the cards apart to make a set for teams of two or three. The original has the cards that match placed together.

Students use the TI-84 Calculator to solve systems of equations using the Calculate Function. Systems include rational, linear, quadratic, exponential and absolute value functions. Even if students have not formally studied these functions, the activity works just fine and exposes them to different functions.

Students cut apart triangles and then match the sides to form a large parallelogram. Students match the standard form of the equation of a line to the slope-intercept form or point-slope form (equal number of each category).

These problems involve perfect square trinomials and the different of two squares. They may be used as a multiplying activity or a factoring activity. All binomials involve two variables. Students work in groups of two or three to match two binomials to a trinomial which is their product.

Students cut apart triangles and squares an then match the sides to form a topaz shape. Students match the numbers 2 and 3 raised to rational powers to the equivalent expression expressed as a radical.

Given the graph of a quadratic function, students write an equation in vertex form.

Students cut apart some small triangles. Then they match binomial and trinomial expressions with their greatest common monomial factor. Monomial factors include powers of x and y as well as three. A parallelogram will be formed.

Introduction to sets including vocabulary, set notation, subsets, union, intersection, disjoint, universal set, complement, Venn Diagrams, using Venn Diagrams to find GCF and LCM and multiplying sets.

Students use a graphing calculator to discover the parents functions of even radicals and odd radicals. They further discover what happens to a parent function if a number is added or subtracted outside the radical sign and if a number is multiplied outside a radical.

A pair of students use a number cube to create an ordered pair. Then they create a system with that ordered pair as a solution. This system is given to another pair to solve. This is repeated with different parameters and then students create their own parameters.

In class: 1. Give a card to each student. 2. Have students arrange themselves in order. 3. Then give commands that involve performing an operation on the number and have the students rearrange themselves, if necessary. For example: a. Add three b. Subtract negative two c. Multiply by negative one d. Divide by negative one e. You may introduce operations involving fractions and decimals as the skills of your class progress Included are cards that are integers, fractions and decimals with which y

Students explore like denominators briefly and then a more in-depth study of unlike denominators. This can be used as a class note sheet, with teacher direction at first. Then students practice in their groups.

The stations include graphing a line parallel to a line through a point. graphing a line perpendicular to a line through a point, writing the equation of a line through a point and perpendicular to the equation of a line, writing the equation of a line through a point and parallel to the equation of a line and determining whether the equations of two lines are parallel, perpendicular or neither. Masters for the stations and student answer sheet are included. It is recommended that a set of stati

This is a short exercise that may be completed as a class or in group work. I have not seen any problems like this and the concepts involved are important: Suppose we have a function f(x) = 7^(2x + 3) Using the properties of exponents, we can re-write this as f(x) = 7^2x × 7^3 Using the properties of exponents, we can re-write this as f(x) = (7^2)^x × 7^3 We can simplify further to f(x) = 49^x × 343 Questions also work the reverse way.

Students work in groups of two or three to arrange steps in the correct order to factor quadratics by splitting the middle term. These involve five steps.

Students cut apart triangles and then match the sides to form a larger triangle. Students match a radical expression to an equivalent expression written in rational exponent form. To make it a little more challenging than simply re-writing between radical form and rational exponent form, problems require students to find common powers inside the radical, for example: the cubed root of (9x^2) = (3x) to the 2/3 power. Also included are negative exponents.

Students work in groups of two or three to arrange steps in the correct order to solve a linear absolute value equation. These equations involve five steps including isolating the absolute value on one side. Two sets involve a variable inside and another variable outside the absolute value.

Stations involve writing the equation of a line given the slope and y-intercept and given the graph of a line. Also involved are transforming general form to slope-intercept form, finding the slope and y-intercept from slope-intercept form of an equation, graphing equations in slope-intercept form and finding the slope between two points. A students answer sheet is included.

Students match quadratic equations with their solutions found by using the quadratic formula. Solutions are given in (a+-SQR(b))/c and then reduced and simplified. This is intended as an introductory exercise where students plug numbers into the formula and are then shown how to simplify.

Students cut apart triangles and then match the sides to form a diamond shape. Students evaluate compositions of two functions involving radicals, polynomials, and exponents. Some compositions involve algebraic substitutions, but many involve numerical substitutions.