What's Rational About That? Day 3

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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.