Pre-Test Unit 7: Real Numbers KEY
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1 Pre-Test Unit 7: Real Numbers KEY No calculator necessary. Please do not use a calculator. Convert the following fraction to a decimal or decimal to a fraction. (5 pts; 3 pts for correct set-up/work, 2 pts for correct answer) Identify if the given number is rational or irrational and explain how you know. (5 pts; 2 pts for correct answer, 3 pts for explanation) Rational Irrational Irrational Rational Evaluate the following roots. (5 pts; no partial credit) Approximate the square roots to one decimal place. (5 pts; 2 pts for whole number accuracy, 1 pt if within 0.1) Compare the following irrational numbers using < or >. (5 pts; no partial credit) > < 15 List the following numbers in order from least to greatest. (5 pts; no partial credit) 13. 7,, 3, 4.15, 7, 3,, 4.15, , 23, 5, 23, 5, 27, 1
2 Match the given number with the letter that approximates that number s position on the number line. (5 pts; no partial credit) A B C D E C A E Estimate the value of the expressions to the nearest whole number. (5 pts; 3 pts for correct approximations) Answer the following question. (5 pts; partial credit at teacher discretion) 20. A calculator displays the following number in its display: 0.37 which does not fill the display screen. Is this enough to determine whether this number is rational or irrational? In at least one complete sentence, explain why. Yes, it is rational because the repeating digit is a zero at the end (otherwise known as a terminating decimal). This means it can be turned into a fraction. 2
3 Lesson 7.1 Unit 7 Homework Key Identify which of the following numbers are rational or irrational and explain how you know Rational Irrational Rational Irrational Integer root so Non-integer root Integer root so Non-integer root so it repeats a zero no repeating pattern it repeats a zero no repeating pattern Rational Rational Rational Rational Fraction meaning Repeats a zero Repeating pattern Integer root so it repeats a pattern it repeats a zero Irrational Irrational Rational Rational Non-integer root so Non-integer root so Fraction meaning Fraction meaning no repeating pattern no repeating pattern it repeats a pattern it repeats a pattern Rational Rational Rational Irrational Repeating pattern Repeats a zero Integer root so Non-integer root so it repeats a zero no repeating pattern 17. If the number 0.77 is displayed on a calculator that can only display ten digits, do we know whether it is rational or irrational? In one complete sentence explain why. Rational because it terminates (or repeats the digit zero). 18. If the number is displayed on a calculator that can only display ten digits, do we know whether it is rational or irrational? In one complete sentence explain why. We don t know. The decimal could repeat later making it rational or could never repeat making it irrational. 19. If the number is displayed on a calculator that can only display ten digits, do we know whether it is rational or irrational? In one complete sentence explain why. Our best guess is that it is rational because there appears to be a pattern, but we can t be sure. 20. If the number is displayed on a calculator that can only display ten digits, do we know whether it is rational or irrational? In one complete sentence explain why. We don t know. The decimal could repeat later making it rational or could never repeat making it irrational. 3
4 Lesson 7.2 Convert the following fractions to repeating decimals
5 Convert the following repeating decimals to fractions
6 Lesson 7.3 Evaluate the following roots giving the principal root Approximate the following irrational numbers to the nearest whole number
7 Approximate the following irrational numbers to one decimal place
8 Lesson 7.4 Place a point on the number line given for each of the following irrational numbers. 1. Point A: 2 2. Point B: Point C: Point D: 8 5. Point E: A E D C B 6. Point V: Point W: Point X: Point Y: Point Z: V Z Y Name the point on the number line associated with each irrational number E A D C B X W B 6.0 E D C A B A D C E 2.0 B E A D C
9 Compare the following numbers using < or > > < < < > < > < > < < < 3.01 List the following numbers in order from least to greatest , 4.2, 16, 4.2, , 33,5.1 24, 5.1, , 110,, 100, ,, 80 80, 9.4, , 32, 37, 32, 35, 37, , 3.5, 15, 10, 3.5, 15, , 60, 8.5, 60, 65, 8.5, , 25, 5.3, 26, 25, 26, 5.3,, , 15, 4.3, 9,, 9, 12, 15, , 63, 7.3, 38, 38, 49, 7.3,, 63 9
10 Lesson 7.5 Estimate the following expressions to the nearest whole number =
11 Review Unit 7: Real Numbers KEY No calculator necessary. Please do not use a calculator. Unit 7 Goals Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert to a decimal expansion which repeats eventually into a rational number. (8.NS.1) Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. (8.NS.2) Convert the following fractions into decimals or decimals into lowest terms fractions Identify if the given number is rational or irrational and explain how you know Irrational Rational Rational Rational Evaluate the following roots Approximate the square roots to one decimal place
12 Compare the following numbers using < or > < > > > 5 List the following numbers in order from least to greatest ,, 9, 3.1, , 40, 6.01, 23. 3, 1.1, 2,, 8, 3.1,, 9 35, 6.01, 40,, 1.1, 3, 2 Match the given number with the letter that approximates that number s position on the number line. A B C D E A D B C Estimate the value of the expressions to the nearest whole number Answer the following questions. 30. A calculator displays the following number in its display: which does not fill the display screen. Is this enough to determine whether this number is rational or irrational? In at least one complete sentence, explain why. Rational because it terminates (or repeats the digit zero). 12
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How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr.
Common Core Standard: 8.EE.2, 8.G.6 How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.3 How Can I Find
Bellwork Teacher selected Prior Knowledge Over the last few days we have been working with exponents and also learning about scientific notation.
Course: 8 th Grade Math DETAIL LESSON PLAN Student Objective 8EEA4 Perform operations (+, -, x, ) with numbers expressed in scientific notation Some problems may include one number written in standard
GRADE 8 ANSWER KEY NUMBER. 1. Squares and Square Roots (8.N.1) 2. Estimating Square Roots (8.N.2)
GRADE 8 ANSWER KEY Note: For more information on particular vocabulary, refer to Kindergarten to Grade 8 Mathematics Glossary (Manitoba Education). NUMBER 1. Squares and Square Roots (8.N.1) Level of Question
Radical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1:
Radical Expressions and Graph (7.1) Find roots of numbers EXAMPLE #1: Figure #1: Find principal (positive) roots EXAMPLE #2: Find n th roots of n th powers (Objective #3) EXAMPLE #3: Figure #2: 7.1 Radical
Unit 2: Accentuate the Negative
Unit 2: Accentuate the Negative Investigation 2: Adding and Subtracting Rational Numbers I can solve operations composed of rational numbers with an understanding of their properties. Investigation Practice
"No math concept is beyond the grasp of a child, if it is presented at the child's level." ~Jerry Mortensen. Mortensen Math
Fractions Mortensen Math http://crewtonramoneshouseofmath.blogspot.com/2014/07/base-ten-blocks-for-fractions-success.html When working with fractions, start with small denominators-keep the denominators
Irrational Numbers Can In-Spiral You
L e s l i e D. L e w i s Irrational Numbers Can In-Spiral You Introducing students to the Pytha - gorean theorem presents a natural context for investigating what irrational numbers are and how they differ