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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