Activating Prior Knowledge M7:LSN13 Comparing Irrational Numbers Activating Prior Knowledge Which is greater? (calculator allowed) 1. √2 or 1.4 2. 8 7 or 1.15 3. √7 or ∛8 Tie to LO

Learning Objective Students use finite decimal approximations of irrational numbers to compare the size of irrational numbers. Students place irrational numbers in their approximate locations on a number line. CFU

Exploratory Challenge – Exercise 1 M7:LSN13 Comparing Irrational Numbers Concept Development Exploratory Challenge – Exercise 1 Rodney thinks that 3 64 is greater than 17 4 . Sam thinks that 17 4 is greater. Who is right and why? What strategy might you use to figure this out? Now do the work: CFU

End CFU Skilled Development/Guided Practice M7:LSN13 Comparing Irrational Numbers Skilled Development/Guided Practice Exploratory Challenge – Exercises 2-11 In your table groups, please complete exercises 2-11 and be prepared to share your work with the class. You have 15 minutes! 15 minutes End CFU

CFU Skilled Development/Guided Practice M7:LSN13 Comparing Irrational Numbers Skilled Development/Guided Practice Exploratory Challenge – Exercises 2-3 Which number is smaller, 3 27 or 2.89? Explain. Which number is smaller, 121 or 3 125 ? Explain. CFU

CFU Skilled Development/Guided Practice M7:LSN13 Comparing Irrational Numbers Skilled Development/Guided Practice Exploratory Challenge – Exercises 4-5 Which number is smaller, 49 or 3 216 ? Explain. Which number is greater, 50 or 319 45 ? Explain. CFU

CFU Skilled Development/Guided Practice M7:LSN13 Comparing Irrational Numbers Skilled Development/Guided Practice Exploratory Challenge – Exercises 6-7 Which number is greater, 5 11 or 0.4? Explain. Which number is smaller, 38 or 154 25 ? Explain. CFU

CFU Skilled Development/Guided Practice M7:LSN13 Comparing Irrational Numbers Skilled Development/Guided Practice Exploratory Challenge – Exercises 8-9 Which number is greater, 2 or 15 9 ? Explain. Place each of the following numbers on a number line: 25, 28 , 30 , 32 , 35 and 36 ? CFU

CFU Skilled Development/Guided Practice M7:LSN13 Comparing Irrational Numbers Skilled Development/Guided Practice Exploratory Challenge – Exercise 10 Challenge: Which number is larger, 5 or 3 11 ? Explain. CFU

CFU Skilled Development/Guided Practice M7:LSN13 Comparing Irrational Numbers Skilled Development/Guided Practice Exploratory Challenge – Exercise 11 A certain chessboard is being designed so that each square has an area of 3 in2. What is the length of one edge of the board rounded to the tenths place? (A chessboard is composed of 64 squares as shown.) CFU

Concept Development - Notes M7:LSN13 Comparing Irrational Numbers Concept Development - Notes How do we know if a number is rational or irrational? Numbers that can be expressed as a fraction are by definition, rational numbers. Any number that is not rational is irrational. Is the number 1. 6 rational or irrational? Explain. The number 1. 6 is rational because it is equal to 15 9 . Is the number 2 rational or irrational? Explain. Since 2 is not a perfect square, then 2 is an irrational number. This means that the decimal expansion can only be approximated by rational numbers. CFU

Closure Homework – Module 7 page 70 Problem Set #1-7 CFU What did we learn today? Why is it important to you? 3. Which strategy do you use to write the decimal expansion of a fraction? 4. What strategy do you use to write the decimal expansion of square and cube roots? Homework – Module 7 page 70 Problem Set #1-7 CFU