Which number is greater? Compare rational and irrational numbers.

Focus 4 - Learning Goal #2: Students will work with radicals and integer exponents. 3 2 1 In addition to level 3.0 and above and beyond what was taught in class, students may: - Make connection with other concepts in math - Make connection with other content areas.   Students will work with radicals and integer exponents. - Use square root & cube root symbols to solve equations in the form x2 = p and x3 = p. - Evaluate roots of small perfect square. - Evaluate roots of small cubes. - Apply square roots & cube roots as it relates to volume and area of cubes and squares. Students will be able to: - Understand that taking the square root & squaring are inverse operations. - Understand that taking the cube root & cubing are inverse operations. With help from the teacher, I have partial success with level 2 and 3. Even with help, students have no success with the unit content.

Rodney thinks 𝟑 𝟔𝟒 is greater than 17/4 Rodney thinks 𝟑 𝟔𝟒 is greater than 17/4. Sam Thinks that 17/4 is greater. Who is right and why? 3 64 = 4 17/4 = 4 ¼ Because 4 < 4 ¼, then 3 64 < 17/4. So, 3 64 is smaller. On a number line 3 64 would be left of 17/4. Therefore, Sam is correct. 𝟑 𝟔𝟒 4 ¼ 4 5

Which number is smaller, 𝟑 𝟐𝟕 or 2.89? Explain. 3 27 =3 Because 2.89 <3, then 2.89 < 3 27 . On a number line, 2.89 is left of 3. Therefore, 2.89 is smaller than 𝟑 𝟐𝟕 . 2.89 𝟑 𝟐𝟕 2.5 3.5 3.0

Which number is greater, 𝟓𝟎 or 319/45? Explain. 50 is irrational. 7.1•7.1 = 50.41 7.09•7.09 = 50.2681 7.08•7.08 = 50.1264 7.07•7.07 = 49.9849 𝟓𝟎 is about 7.07 319/45 = 7 4/45 4/45 = .088888… 319/45 is about 7.09. Since 7.07 < 7.09, then 50 < 319/45. The greater number is 319/45.

Which number is greater, 5/11 or 0.4? Explain. 5/11 is equal to 0.45 Since 0.444444… < 0.4545454545…, then 0.4 < 5/11. The greater number is 5/11.