# What's At the Root? Day 4

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## Objective

SWBAT use area models to find relationships between numbers and square roots and use square root symbols to represent solutions.

#### Big Idea

Students are going to learn square root notation while tackling this mathematical task where the take on the role of a sign maker.

## Warm Up

5 minutes

For today's Warm Up assignment, I have posted two word problems that focus on cube and square roots. In the first problem, students must determine the smallest perfect square that is a factor of 64. The second problem requires students to think in three dimensions to determine the measures of the sides of the largest cube that can be formed from 75 snap cubes. The second problem may pose a challenge for some students, so I will encourage them to use problem solving strategies (guess and check, work backwards, draw a picture, etc.) to assist them.

Once the timer sounds after 5 minutes, we work to find consensus from the group by selecting volunteers to give their answers. The students then decide if they agree or disagree and show their stance using a thumbs up or thumbs down signal. If discourse occurs, I ask additional students to share their answers and explain their thinking to the class in an effort to sway their peers. I use questioning, as needed to guide the class to full consensus.

## Learning Objective

1 minutes

After warm up, I quickly introduce today's Learning Objective. It is important that students understand what we expect to learn during today's work session so that we know our destination for the day.

## Work Time

20 minutes

As I distribute worksheets to the class, I introduce today's Work Time assignment, Squareville Sign Company Task 1 to the students and show two examples. The first is a perfect square model with an area of 4. I ask the students to tell me measurements of the sides of the square and they report "2". I record their answer, however, as the square root of 4 instead. I then ask, "Is it okay to write your answer this way? Give me a thumbs up if you agree, a thumbs down if you disagree and a thumbs sideways if you are not sure."

The vast majority of the class show a thumbs up sign, so I select a student to explain why it's okay.

I then move to the next example and ask students how the two signs differ. I want them to recognize that the sign is slightly larger than 2 x 2. I note that the area of the second square is 5 units. I then ask how we could note the length of one side. Once a student volunteers "square root of 5", I ask how we can estimate this number. While I get several suggestions along the line of guess and check, I ask about tools we might use. One student finally suggests using a calculator.

I then distribute calculators to each group and encourage them to use them to help with today's task.

## Consensus Building

6 minutes

When the work timer sounds after 20 minutes, I call the students' attention to the Smart board where I have copied the image from the task's second page to facilitate Building Consensus. I then select name sticks at random to report their group's findings for each of the numbered signs.

I explain that we are going to build on today's task for part 2 the following day. In the meantime, I display a prompt for a Ticket Out the Door.

## Ticket Out the Door

5 minutes

For closure, I reveal a Ticket Out the Door prompt for students to answer on the back of their task sheet, which they will turn in at the end of class. I remind students of our objective and explain I would like to see their answer in two different forms, if possible. I am interested to see which students are able to write their response as radical 56 followed by an estimation as well as those who simply write radical 56. Based on student responses, I will adjust my Warm Up assignment in the subsequent lesson.