New ReviewNot a perfect square? Not a problem! Scholars determine rational approximations of the square roots of "not-so-perfect" squares. The use of area models helps with this task.

New ReviewPythagoras sure was a smart man. Learners explore diagonals of rectangles by measuring a few of them with a ruler in the second and final installment of a two-part series. Based on the results, they try to come up with a relationship...

New ReviewTake me out to the ball game, if we don't measure the diagonal, it's a shame. Pupils investigate the diagonals of squares using the measurements of a baseball field as an example in the first of two lessons. Hopefully, they'll realize...

New ReviewIrrational numbers can make perfect sense, thanks to a creative activity! The second lesson in a two-part series introduces strategies for handling those not-so-perfect squares that contain irrational side lengths. Groups build on prior...

New ReviewBreak down the heights of squares. Groups investigate square roots by finding squares that stack up to the same height. Given the area of a square, teams find other squares that have an equivalent height when stacked up. Then, classmates...

New ReviewAccuracy is in the eye of the beholder. Scholars use an iterative process and a computer software program to determine the square root of two to a given number of decimal places. Examining their answers, they consider how accurate the...

New ReviewTake a radical look at square roots. The presentation examines square roots as the lengths of the sides of a square with a given area on the coordinate plane. Using this method, it is clear why the square root of a number can be positive...

An assessment presents class members with four quadratic equations. Pupils must  determine which strategies for solving each quadratic equation are most efficient and justify their choices. The strategies include solving by taking square...

Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...

Use an iterative process to find an approximation of a square root. Pupils use the interactive to find an approximation to find the positive root of a quadratic function with Newton's method. With the graphs, learners position the...

Take the next step in simplifying radical expressions. The video shows how to rationalize the denominator that contains square roots. Examples contain simple radicals and ones that require using conjugates.

Get classmates to think rationally about roots. A short assessment asks pupils to rewrite a square root using exponents and then explain why their exponent creates an equivalent expression. 

Two-step into the quadratic formula. Pupils take over transforming the general standard formula of a quadratic into the quadratic formula. Given the equation after the first major transformations, learners continue with the second major...

The rules still hold. By reviewing the meaning of exponents in arithmetic, the video takes a look at exponents in algebra. The resource develops the meaning of any number raised to the zero power. Taking the idea of exponents further,...

Is your smartphone really doing its best work when it comes to color? The narrator describes technology's lazy approach to recreating colors in an insightful video. Science scholars discover how digital cameras store images, and why the...

Try out a resource using triangles to estimate radicals. An interactive app allows learners to approximate some irrational numbers involving square roots. They find the two consecutive numbers that an irrational number lies between by...

Walking in the park can be good for the body and for mathematics skills. Young scholars use an interactive app to investigate the relationship between squares and square roots using a square with adjustable length. The program also takes...

How can you draw a number? A set of questions takes learners through the reasoning for why a geometric construction can be drawn to represent the square root of a number. An interactive helps visualize the construction.

Square away any doubts about using a new resource. Pupils learn about squares and square roots in the mini-lesson. They complete a worksheet identifying roots of perfect squares up to 400.

Think outside the box and use an engaging, interactive app that shows the relationship between square roots and squares using an actual square. Pupils find that moving a slider increases the side length of a square and its associated area.

Get two answers from a single equation. Pupils use the interactive to take the square root of nine and see the graphical representation of the two solutions. Individuals realize that solutions to quadratic equations that are solved by...

What is the relationship between the sides of a right triangle? Learners use an interactive to create models of right triangles and view the relationship between the lengths of the sides. They finish by using the Pythagorean Theorem to...

Simplify your life by using a resource on simplifying square roots. Pupils review square roots and calculate values of given radical expressions using a calculator. The lesson concludes by having them consider the results to develop the...

Assess pupil understanding of rational and irrational numbers with a mid-module assessment that is the 15th lesson in the 25-part series. The questions represent the objectives in the first half of the series. Topics include decimal...