5E Student Lesson Planning Template
|Teachers: Uhling, Escobar, Scherer, Moore |
|Date: 9/11/2014 |
|Subject / grade level: 8th Grade Math |
|Materials: |
|Double Sided counters |
|Grid paper |
|Square Roots Go Rational Student Worksheet |
|Calculators |
|Clothesline |
|Clothes pins |
|TEKS: |
|8.2.B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a|
|number line; |
| |
|KEY UNDERSTANDINGS: |
|That squaring a number and finding the square roots are inverse or opposite operations. |
|That irrational square roots can only be approximated. |
|We can start with figuring out which two perfect squares that they are between. |
|ENGAGEMENT |
|Teacher will put up the multiplication chart with the diagonal highlighted. |
|Ask students: |
|What numbers are highlighted? |
|What do you notice about the highlighted numbers? |
|Do you see any patterns in these numbers? |
|EXPLORATION |
|Teacher tells students that today we will be exploring making perfect and not so perfect squares. |
|Ask students: |
|What is a perfect square? |
|What is a square root? |
|What is a natural number? What is a rational number? An irrational number? (want to get across that irrational numbers can only be approximated, they are |
|non-repeating decimals that CAN’T be expressed as a fraction. |
|Tell students that we are going to make models of perfect and not so perfect squares to help us understand this concept. |
|Pass out double sided counters (one bag per student). |
|Have students create a square using 4 counters, 9 counters, 16 counters. |
|Next challenge students to create a square using 7 counters: They can’t do this. Model for them the process described below of estimating. Instead of using |
|x’s and o’s, use yellow for the 7 and then red for the two that they would need to fill in to get to the perfect square of 9: |
|Main Activity |
|The key to the rational roots students will be exploring during the lesson lies in the outer column and row of each perfect square. Ask students to predict |
|the square root of 7. |
|7 X's cannot fill a square, so 7 is not a perfect square. However, the square root of 7 can be estimated. The square root must be between 2 and 3 because 7 |
|lies between the perfect squares 4 and 9. |
|From this model, the largest perfect square is a square with side lengths of 2 with three remaining units in the outer column and row. 5 X's are needed in the|
|outer row and column to make the next larger perfect square. The missing units from the outer column and row are filled in with O's to reinforce the counting |
|of these elements. Therefore, an approximation to the square root of 7 is very close to 2 3/5. The 3 represents the extra number of units (X's) in the outer |
|row and column; and the 5 represents the total number of units (X's and O's) in the outer row and column. The meaning of a fraction is enforced with this |
|model. The fractional part of the square root is the part of units we have divided by the whole number of units needed in the outside column and row. |
|Challenge students to approximate the [pic]using the same process. Give them a few minutes to work on their own and then check in with them on their progress.|
|Allow the students to work on the first column, ‘Rational Root Expressed as a Fraction,’ independently. Circulate around the room assisting individual |
|students as needed. If students want to consult with a partner, they may but each student is expected to complete their own worksheet. |
| |
|EXPLANATION |
|After the majority of the class has completed the first column, invite individuals to share out their results. |
|Ask students to comment on any patterns they noticed. |
|ELABORATION |
|Tell the students that the next step will be to convert their fractional approximations to decimals. Tell them that you are going to let them use the |
|calculator to do this step BUT they need to know how to convert fractions to decimals. Call on a student to explain how to do this. |
|Pass out calculators. Complete the remaining columns, ‘Rational Roots Expressed as a Decimal,” and ‘Calculator Square Root Expressed as a Decimal,’ for the |
|numbers 2 and 3 together. |
|Allow students to complete the rest of the sheet independently using calculators. |
|If time allows, you can ask students this challenge question: What natural number would have 8[pic] as its rational root? |
|EVALUATION |
|Tell students that their ‘ticket out the door’ is going to be to arrange a variety of real numbers (which includes both rational and irrational numbers’ in |
|order on the clothesline. No one leaves until the numbers are arranged properly. Students may help each other out, but they are to explain to their classmates|
|their reasoning as they do it (not just snatch the number out of their hands). |
|Pass out numbers and allow students to work on ordering the numbers. Provide coaching/questioning as needed. |
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