# Playing Around with Pythagoras- Day 7

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## Objective

SWBAT use double-number lines to accurately estimate the lengths of unknown sides of right triangles.

#### Big Idea

Students will continue to practice using double number lines to estimate the square roots of non-perfect square numbers. They will also evaluate others' work to gain consensus on determined values.

## Warm Up

8 minutes

Today's Warm Up questions provide two opportunities for students to practice applying the Pythagorean Theorem. The first example is a Pythagorean Triple, which many students will likely recognize. However, because the previous day's lesson focused on estimating square roots, the second example requires students to estimate the answer. While some students may have mastered this strategy, I use the answer to the second problem to launch into a review of the previous day's lesson.  In this way, students can directly connect today's work to previous learning.

## Estimating Square Roots Using Double Number Lines

5 minutes

Building upon the second problem from the Warm Up, I provide students two additional opportunities for guided practice with estimating square roots using a double number line.  This allows students time to make sense of the strategy while giving me time to wander the room and watch for struggling students. If I determine particular pairs are stuggling, I make seat changes at this time in preparation for Work Time. In this way, I can better support students by pairing them with students who have a stronger understanding of the strategy.

## Work Time

20 minutes

During Work Time, students work independently estimating the square roots of six different non-perfect square numbers by drawing double number lines in their journals.  Once finished, the partners compare answers and discuss any discrepancies to come to consensus by listening to and critiquing the work of their partners. Once the timer sounds, I bring partners together in the larger group to gain class consensus. For student pairs who finish before the timer sounds, I challenge them to continue to test each other on the less familiar perfect square roots, especially for 169-361.

## Building Consensus

12 minutes

As students work during Work Time, I discreetly select students who will help build class consensus by effectively modeling the use of the double number line for their classmates on the SmartBoard.  In this way, struggling students will see six peer examples and I am able to facilitate Consensus Building more efficiently.

## Quick Check

2 minutes

Becuase it has been almost a week since students have been assessed on their recall of perfect squares, today's closure is a quick check using the perfect square flash cards.  Each student is shown a perfect square root card and s/he must tell me the perfect square that falls before and after the number on the card.  For example, if a student is shown the square root of 49, s/he must tell me 36 and 64.  This quick check not only help build fluency and recall, it will also alert me to the students who are struggling and need more attention and support.