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2 7.N.4 Develop the laws of exponents for multiplication and division Directions: Rewrite as a base with an exponent. 1) = 2) x 7 x 17 = 3) = 5) 12-3 = ) y 20 y 10 = 4) p9 = 10 p 7) Rewrite in extended form in the space below: x 6 x 5 Using what the expression above looks like in extended form, explain why the law of exponents works for multiplication (why you add the exponents). 8) Rewrite in extended form in the space below: n10 n 5 = Using what the expression above looks like in extended form, explain why the law of exponents works for division (why you subtract the exponents). 7.N.1 Distinguish between the various subsets of real numbers (/natural numbers, whole numbers, integers, rational numbers, and irrational numbers) 7.N.2 Recognize the difference between rational and irrational numbers (e.g., explore different approximations of π.) 7.N.17 Classify irrational numbers as non-repeating/non-terminating decimals 2

3 Directions: Circle the names of the all the subsets to which the number belongs. 9) 24 10) ) 19 12) ) 2,103,722 14) Using what you know about subsets of real numbers, explain how you know that 24 is a natural/ number, a whole number, an integer, a rational number, and a real number. 7.N.15 Recognize and state the value of the square root of a perfect square (up to 225) 7.N.16 Determine the square root of non-perfect squares using a calculator 7.N.18 Identify the two consecutive whole numbers between which the square root of a nonperfect square whole number less than 225 lies (with and without the use of a number line) 15) 196 = 16) 81 = 17) 9 = 18) 16 = 19) When someone asks you, What is the perfect square of n? what exactly is he/she asking? Directions: Between what two integers do you find the following square roots: 20) 37 and 21) 63 and 22) 2 and 23) 255 and 3

4 7.N.3 Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers 24) Graph the following numbers on the number line below: {-3.4, π, 1 3, - 2 } Explain why you placed each number where you did. 7.N.14 Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals (e.g., 10 - ² =.01 = 1/100.) 24) Complete the chart below. (Do not fill in the dark areas.) ,000 7.N.5 7.N.6 7.N.7 Write numbers in scientific notation Translate numbers from scientific notation into standard form Compare numbers written in scientific notation Directions: Change to scientific notation. 25) 7,001,100 = 26) = 27) 45.8 = 28) 0.07 = 4

5 Directions: Change to standard form. 29) 5.06 x 10-3 = 30) 4.11 x = 31) 6.70 x 10 1 = 32) x 10-4 = 7.N.8 7.N.9 7.N.10 Find the common factors and greatest common factor of two or more numbers Determine multiples and least common multiple of two or more numbers Determine the prime factorization of a given number and write in exponential form 33) Find the greatest common factor of 54, 117, 207. GCF = 34) Find the least common multiple of 16, 24, and 44.. LCM = 35) What is the prime factorization of 1350 in exponential form? 7.N.12 Add, subtract, multiply and divide integers 7.N.13 Add and subtract two integers (with and without the use of a number line). 7.N.11 Simplify expressions using order of operations. Note: Expressions may include absolute value and/or integral exponents greater than 0 36) (5-7) 2-2x3-7 = 37) 3-4x = 5

6 7.N.19 Justify the reasonableness of answers using estimation Directions: For the estimation problems, show how you found your answer. Exact answers will be marked wrong! 37) Sara and Jill work part-time in a shoe store. Last week Sara earned $ Jill earned $29.35 more than Sara. About how much did Jill earn last week? 38) Jody's car gets about 25 miles to the gallon. Which is the best estimate of the number of gallons he will need in order to travel 976 miles? (a) 4 (b) 30 (c) 40 (d) 50 6.A.2 Use substitution to evaluate algebraic expressions (may include exponents of one, two and three) Directions: What is the value of 2a 2 6ab when 39) a = -3; b = 5 40) a = 4; b = -2 6.A.3 Translate two-step verbal sentences into algebraic equations 6.A.4 Solve and explain two-step equations involving whole numbers using inverse operations 7.A.1 Translate two-step verbal expressions into algebraic expressions Directions: Translate into an algebraic equation and solve, showing your work. 41) Three more than twice a number is negative 5. 42) Twenty-one is the same as twelve less than three times a number. Explain how you solved the above equation. 6

7 7.A.5 7.G.10 line Solve one-step inequalities (positive coefficients only) (See 7.G.10) Graph the solution set of an inequality (positive coefficients only) on a number Directions: Solve and graph the equation on the number line. 43) 6y 18 44) x 7 > -13 7

Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers.

Real Numbers and The Number Line Properties of Real Numbers Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers. Square root, radicand,