# Playing Around With Pythagoras- Day 5

## Objective

SWBAT use their knowledge of perfect square numbers and Pythagorean Theorem to estimate the lengths of unknown sides of right triangles.

#### Big Idea

Today, students will learn to estimate the lengths of unknown sides of right triangles by using their knowledge of perfect squares.

## Warm Up

8 minutes

Today's Warm Up reinforces the previous day's lesson on proving right triangles.  Triangle A is a right triangle (a triple, that some students may recognize), but Triangle B is not.  I intentionally include decimal side lengths to provide my students opportunities to continue to make sense of decimals.

## Estimating Unknown Side Lengths

10 minutes

Until today, students have been working with Pythagorean Theorem on triangles that have nice, neat side lengths (a.k.a. "Pythagorean Triples").  Today, I introduce triangles that include side lengths that must be estimated.  I want students to leave with a broad understanding of which two whole numbers a non-perfect square would fall on a number line.  This will help us build toward Day 6's lesson on estimating square roots using a double number line.

## Work Time

25 minutes

For Work Time, I have provided students a practice page that begins by asking students to think about what two whole numbers the square roots of non-perfect square numbers fall. Once students have completed the first five questions, they must verify their answers with a peer before moving on.  In this way, any confusion or misconceptions can be caught before students apply their skill to right triangle examples. I also circulate through the room, spot checking student work and questioning when responses are incorrect.

Once students have verified their estimates, they can move on to the application questions at the bottom of the page where they must use the Pythagorean Theorem to solve for unknown side lengths.  Each of the examples will require students to estimate.  The final question requires students to explain in words how to estimate.  The responses to this question will provide important feedback about individual student understanding.

## Quick Check

2 minutes

For closure today, I want to do a quick check for understanding, so I have created a slide that asks which of nine square roots will fall between 12 and 13 on the number line.  I ask students to jot them down in their journals. I then ask students to respond by holding up their fingers to represent the number of responses they found.  I quickly check responses and select one student holding up five fingers to list the numbers s/he felt were between 12 and 13 on the number line.  I ask for any discrepancies and ask these students to justify their answer for the class.  I then preview the next day's lesson by explaining that we will be learning a strategy for estimating square roots the following day.