# What's Rational About That? Day 3

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## Objective

SWBAT find the rational approximation of irrational numbers and locate them on a number line.

#### Big Idea

Students will get practice truncating the decimal expansions of non-perfect square numbers in order to accurately place them on a number line.

## Continuous Improvement Quiz #2

25 minutes

In place of Warm-Up problems on Wednesdays, students take a 10-question non-graded (checked but not recorded) quiz that reinforces and assesses number sense concepts including problem-solving with fractions, decimals, percents and ratios as well as operations with integers and rational numbers. (See Welcome Back! Unit, Day 3 for additional information.) Students have 15 minutes to complete the ten questions.  We then go over the answers, which takes about 10 minutes.

## Perfect Square Roots?

10 minutes

The purpose of today's lesson is for students to practice simplifying squares and estimating the square roots of non-perfect squares. I have found in the past that students lack this skill which is an important number sense skill to have.  For this reason, I have added a day into my curriculum to focus on this.

At the end of the CI Quiz notebook, I inserted a quick sorting activity to provide students some practice with recognizing perfect squares and non-perfect square numbers.  While it was clear some students still needed practice, I wanted to move to Estimating Square Roots.

I began with the square root of 24.  I asked, "Between what two perfect square numbers would we find the square root of 24 on this double number line?" I moved the purple boxes to reveal 16 and 25 on either end. I then asked, "Where would you place the square root of 24 on this number line?

I then reveal the bottom of the double number line, which shows the square roots of the end numbers. I make a mark halfway between 9 and 10 and asked, "Who knows what number this location represents? I want students to apply their number sense, which

To check for class understanding, I asked for a "thumbs up" from the students.  I then tell them to turn to their shoulder partners (seat 1 with seat 2 and seat 3 with seat 4) and discuss. After the natural drop in conversation occurs, I asked, "So what number should we use to represent square root of 24?" I guide student thinking through questioning.

I then show the next number and ask a student to walk me through the process we just used to estimate a square root. Finally, for independent practice, I give the students four numbers on Let's Practice and tell them to use double number lines to estimate the values.