What's At the Root? Day 2

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SWBAT evaluate square roots of small perfect squares and cube roots of small perfect cubes to represent solutions to equations in the form of x^2 = p and x^3 = p, where p is a positive rational number.

Big Idea

This lesson provides student additional practice with perfect square and cube roots, this time in equation format. Students also practice applying these concepts to a real world problem.

Warm Up

7 minutes

Today's Warm Up problems build on the previous day's lesson.  The first problem asks students to determine the dimensions of the largest cube that can be made with 216 cubes.  The second problem asks students to critique the thinking of a student (MP 3), Jesse, who believes 42 is a square number because he is able to create what he believes is a square using color tiles.  This problem will help to quickly identify students who may lack the foundational understanding from previous day's lesson. It is important that these students are then paired with a stronger student for today's lesson.

Objective & Proficiency Scale

2 minutes

Included in the notebook slides are today's objective and proficiency scale so that students are aware of the targets for learning. 

Work Time Part I: Root Trains

15 minutes

To give students additional exposure to and practice with perfect square and cubic roots, they will spend the first half of work time solving a "Train" puzzle. This involves beginning with any piece from the "train" that includes a solution and an equation (that do not match). Students ignore the solution on the left side of the card, but find the answer to the simplified equation on the right side. They then sort through the remaining train pieces to find the match for the equation. They continue in this manner until they have created a full loop. Making this task more challenging is that several solutions appear more than once and students must be able to create the train using all the pieces. Once students finish ordering the first train, train #2 is available. 

(On the Math Trains 1 & 2 for students, the cards have been mixed so that students can cut them out. In the other file, the cards are in solution order.)

Work Time Part II : Think-Pair-Share

18 minutes

For the second part of Work Time, I have provided an application problem that will require students to use what they have learned about roots to solve a problem. Because I want students to have some purposeful struggle, I ask that the spend the first four minutes of this time thinking about the problem and how they are going to use what they know to solve it. I will encourage students to record their thinking in their journals so that I can circulate through the room encourage "stumped" students through questioning (e.g., "What information does the picture provide to you?" "How can you use that information?"). Once the timer sounds, I ask students to share their ideas with their partner.

I continue to circulate the room so that I can listen in on conversations that I will refer during the "share" portion of the work time. I encourage the groups to determine an answer that they will share after the six-minute timer sounds. For student pairs who quickly arrive at the answer, I ask them to add additional data to the picture that helped them to arrive at their answer. 

When the six minute timer sounds, I ask for "volunteers" (some I have intentionally pre-selected for their unique approaches) to share their work. Typically, a variety of answers yields great discussion that requires students to fully explain their approach. If no variation in answers exists, I ask if anyone has another way to approaching this problem. I want to instill in my students the idea that there is almost always more than one way to solve a problem.

Line Up and Out

3 minutes

For closure, distribute the square and cube root cards (prepared from the previous day's lesson) to twenty students. Student who do not receive a card will serve as the judges.  Instruct the students with cards to simplify the given expression and then order themselves from least to greatest as if on a number line.  Once students are lined up, the remaining students verify their work by announcing the values. This provides a great opportunity to see which students need additional support for simplifying radical expressions.