MATH NUMBER SENSE 7 Performance Objective Task Analysis Benchmarks/Assessment Students:

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1 Students: 1. Students know the properties of and 1. Read, write and compare rational compute with rational numbers numbers in scientific notation (positive expressed in a variety of forms. and negative powers of 10 ), approximate numbers using scientific notation. Write negative exponents as decimals Complete the pattern. 1,000 = = = 1 = = = = Express numbers using scientific notation 1 Light travels at a speed of 18,000,000,000 meters per minute. Write this number in scientific notation. Write in scientific notation. 7,540,000 5,001,000 6, x Write the following as a power of 10 or the product of a whole number and a power of 10: a) b) ten billion c) 6,000,000 d) 3 hundred thousand ( FW)

2 Are 74.5 x 10 2 and x 10-3 written in scientific notation? Explain. Write in standard form Write each number in standard notation x x x x 10-3 Read numbers using scientific notation Decide which is larger. Explain 1 x 10 9 or 9 x 10 8 Compare numbers using scientific notation Compare using >,<, or = 4 x x x x 10-5 Which number is smaller than ? a) 4.7 x 10-4 b) 4.7 x 10-3 c) 4.7 x 10-5 Approximate numbers using scientific notation Approximate 12,300,000 x 1,500 Convert to scientific notation, compute and express your answer in scientific notation as well as decimal. ( FW) (350,00)(.0049)/.25 ( )(.0063)/((140,000)(70,000)(.18)) 2

3 * 2. Add, subtract, multiply and divide rational numbers, integers, fractions and decimals and take rational numbers to whole number powers. Add rational numbers, integers fractions and decimals Subtract rational numbers, integers fractions and decimals Multiply rational numbers, integers fractions and decimals Divide rational numbers, integers fractions and decimals 1/8 + - (1/3), -7 + (-15), (-3.1) -1/3-1/4, , /2 + 1/4-1/3 x 3, (-5)(-5), -1/3 of 15-1/3 1/12, 15-5, Take rational numbers to whole number powers (1/3) 4 5x5x5 = (3 x 10 5 )(6 x 10 3 ) Find prime factors Write the prime factorization of the following numerals: ( FW) 804, 396, 605, 1, Convert fractions to decimals and percents and use these representations in estimation, computation and applications. 3

4 Write decimals and fractions as percents Write as a percent /4 1/3 9/4 Describe how the position of the decimal point is changed in writing a percent as a decimal. Write percents and fractions as decimals Write as a decimal. -17/4, 3 5/16, 2 2/5, 23.5%, 2%, 235% Change to decimals. ( FW) 7/8 7/11 Write decimals and percents as fractions Write as a fraction % 175% 8% Order and compare Put 75%, 7/8, and.723 in order from largest to smallest. Application Peter got 15 out of 20 problems correct on a math test. What % of the problems did he get wrong? A bicycle is on sale for $115. This is 80% of the original cost. What was the original cost? Estimation Use estimation skills to find 26% of 40. 4

5 *4. Differentiate between rational and irrational numbers. Write as rational numbers Determine whether the real numbers are rational or irrational Why is π irrational? *5. Know that every fraction is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions. Which of the fractions are repeating decimals? terminating decimals? 1/2 1/3 1/4 1/5 1/6 1/7 Use bar notation Express each decimal using bar notation Write the first ten decimal places of each decimal Write each fraction as a decimal. 2/3 2/5 6 4/25 1/33 Find the period of the repeating part of 41/13. ( FW) 5

6 Convert terminating decimals to reduced fractions Write the decimal of a fraction or mixed number in simplest form..08 = -3.4 = = Change to fractions. ( FW) Calculate percent of increases and decreases of a quantity. Calculate percent of increases of a quantity The price of strawberries went from $1.00 to $1.50. What is the percent of the price increase? Hockey Goals Scored Kim Marlene Kim and Marlene compared their records from 1997 to Which player improved more? Calculate percent of decreases of a quantity Find the percent of change in price if the old selling price was $19.95 and the new selling price is $ *7. Solve problems that involve discounts, markups, commissions, profit and simple compound interest. 6

7 Discounts A pair of tennis shoes that normally sells for $89.95 is on sale for $ What is the rate of discount? A new bike sells for $198. You can get it on sale at 25% off. How much will the bike cost? Markups A store owner s cost for a computer game is $30. If it sells for $48, what is the markup rate? Commissions Dexter sells sports equipment on commission. He sold $15,000 of equipment last month. If he earns 14% commission, how much commission did he earn last month? Profit A department store bought Levi s for $12 each. To make a profit the store must sell the pants at a 100% markup. What will the Levi s cost the customer? Simple interest Calculate simple interest. I = prt p = $5,000 r = 5% t = 2 years 7

8 Compound interest Calculate compound interest. A = p(1 + r/n) nt p = $5,000 r = 5% n = 4 t = 5 Don deposited $5,000 in a savings account. The account earned 4% annual interest compounded twice a year. How much money did he have at the end of 2 years? Joe borrowed $800 at 10% interest compounded semi-annually. How much interest will there be in 4 years? ( FW) What will be the monthly payments on a loan of $50,000 at 12% annual interest so that it will be paid off at the end of 10 years? How much total interest will have been paid? Same problem with 8% annual interest over 10 years. Same problem with 10% annual interest over 15 years. ( FW) 8

9 Students: 2. Students use exponents, powers, and 1. Understand negative whole number Using 5 4, label and explain what the roots and use exponents in working with fractions. exponents. Multiply and divide expressions involving exponents with a common base. base and exponent represent. Understand negative whole number exponents Continue the pattern. ( FW) 3 3 = = = = = 1/3 = = Extend the pattern. 2 5, 2 4, 2 3, 2 2, 2 1,,, Use powers and exponents in expressions Write each product using exponents /3 1/3 1/3 1/5 1/5 1/4 1/4 Multiply and divide expressions Simplify. (3 x 3 x 3) (3 x 3 x 3 x 3) = (4 x 4 x 4 x 4) (4 x 4 x 4) = = = 9

10 Raise to a power Evaluate. (-2) 2 (-1) (2) -2 (7) -1 *2. Add and subtract fractions using factoring to find common denominators. *3. Multiply, divide, and simplify fractions using exponent rules. Multiply and divide using exponent rules Use prime factors to solve. 3 1/ /3 8 1/3 + (-5 1/6) 8 1/3-5 1/6 3 1/5-7 1/3 2/28 + 1/49 ( FW) -5/63 + (-7/99) ( FW) Use prime factorization to simplify the fraction. Evaluate Use prime factors and compute. (42/22 (75/63) ( FW) Write fractions in simplest form Use prime factors to write the fractions in simplest form. 18/24 24/52 Reduce 910/1859 ( FW) 10

11 4. Use the inverse relationship between raising to a power and root extraction for square integers; and, for integers which are not square, determine without a calculator, the two integers between which its square root lies, and explain why. Determine the two integers between which its square root lies, and explain why. *5. Understand the meaning of the absolute value of a number, interpret it as the distance of the number from zero on a number line and determine the absolute value of real numbers. Determine the absolute value of real numbers If the area of a square is 9, what is the length of the sides? Find the edge of a square that has an area of 81. ( FW) - 7 lies between what two integers? Explain. Find the square root. Estimate if it is not a perfect square / 9-25/ 100 Find the distance between -20 and 6 on a number line. Find the absolute value. -7 = +7 = Solve for x. x = 9 Is -15 > or < -25? Find the absolute value of 12, 1/4. 11

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