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Math Quarter 1 Benchmark Study Guide The 1st Quarter Math Benchmark will be on Tuesday, October 28, 2013 Homework Schedule: Due: Tuesday, October 21st Integers and Absolute Value (pages 2-3) Due: Wednesday, October 22nd. Graphing Inequalities & Measures of Central Tendency (pages 4-6) Due: Thursday, October 23rd. Fractions, Decimals & Percents (pages 7-9) Due: Friday, October 24thBasic Skills & Multi-Step Word Problems (pages 10-12) Remember to show all work, even for multiple choice questions. Credit will not be given if work is not shown. It is ok to show your work on a separate sheet of paper. Be sure to bring the work paper with you! 1 Benchmark 1 Study Guide Integers Name: Integers- all whole numbers and their opposites […-3, -2, -1, 0, 1, 2, 3…] NOT a fraction, decimal, or percent -4.5, ¾, 85% Draw a number line to represent the integers -5 to 5 Practice Use your knowledge of integers to answer the following questions. 1. Circle the numbers below that ARE integers. 1.3 ⅜ 5 -23 6.6666 0 49% 17 What makes a number NOT an integer? ____________________________________________ _____________________________________________________________________________ 2. Write the following phrases numerically. A loss of 20 yards ____________________ 5 inches taller ____________________ An altitude of 3800 feet ____________________ 7 units to the left of zero on the number line ____________________ A profit of $10 ____________________ A debit of $48 ____________________ A credit of $65 ____________________ A debt of $3 ____________________ 3. Draw a comparison sign to complete each number statement. -19 ____ 5 30 ____ -25 -6 ____ -7 -15 ____ 0 20 ____ -11 -10 ____ -3 Remember positive numbers are ALWAYS greater than negative numbers. When comparing two negative numbers, the number closer to zero is always greater. 2 Answer the following questions by looking at the number line. E -6 -5 F -4 -3 -2 G -1 0 1 2 3 H I 4 5 6 4. At what point do you find H? _____ 5. Which point represents -5? _____ Ascending- order from least to greatest Descending- order from greatest to least 6. Put the following integer in ascending order: 1, –8, 7, -12 –4, –1, 2, -5 7. Circle the set of integers that are in descending order. A) -6, -3, 5, 10 B) -3, 5, -6, 10 C) 10, 5, -3, -6 D) 10, -6, 5, -3 Absolute Value Absolute Value: the number of units a number is away from zero. –4says “the absolute value of negative four” –2 11 +5says “the absolute value of positive five” 7 26 3 Graphing Inequalities < Less than > Greater than ≤ Less than or equal to ≥ Greater than or equal to Open dot means < or > “less than” or “greater than” Closed dot means ≤ or ≥ “less than or equal to” or “greater than or equal to” Always read the answer starting with the variable to find out which direction the arrow points. Practice Graph each inequality. 1. r > -1 2. p≤3 Name each inequality. n n Measures of Central Tendency Mean- the average (add up all of the numbers and divide by the number of items) * Mean works well for sets of data with no very high or low numbers Example: Test scores from the last unit test 82 95 73 100 85 79 64 88 91 76 833 10 = 83.3 % 4 Median- the middle number in a set of data * Median is a good choice when data sets have a couple of values much higher or lower than most of the others Example: The number of fish in a pond 3, 6, 1, 0, 5, 3, 4 Put the numbers in order 0, 1, 3, 3, 4, 5, 6 3 is the median Example: The number of cookies each student ate at lunch 4 1 5 2 0 8 4 3 0 6 Put numbers in order 0 0 1 2 3 4 4 5 6 8 3.5 is the median Mode- the number that occurs most often * There can be more than one mode or no mode at all * If there are exactly two modes, it is called bimodal * Mode is a good descriptor to use when the set of data has some identical values Example: The number of points Victoria scores in each basketball game 12 5 18 10 12 9 18 12 7 15 Put numbers in order: 5 7 9 10 12 12 12 15 18 18 12 is the mode 5 Find the mean, median, and mode of the following sets of data. Example: The number of hours kids watch TV per week 11 Mean- 5 22 = 14 8 13 6 16 Median- Mode- Mean as a balance point- the point on a number line where the data distribution is balanced Find the mean as a balance point for the following set of data. “Number of Siblings” 6 Fractions, Decimals, and Percents Fractions- the representation of a number expressed in the form a/b Numerator-the number above a fraction bar 3 numerator Denominator- the number below a fraction bar 7 denominator Decimals- the representation of a number based on tenths, hundredths, and thousandths Place values Percents- the representation of a number out of 100 Find the percent of each grid _____% _____% _____% Converting Fractions, Decimals, and Percents Fraction Decimal if the denominator is 10 or 100, read the fraction as a decimal reduce to simplest form and divide the numerator by the denominator 3 = 0.3 10 10 (simplify to 5/6 and do long division) = 0.833 12 7 Decimal Percent Dr. Pepper move the decimal point two places to the right (multiply by 100) .DP 0.82 = 82% Percent 0.7 = 70% Decimal Revers Dr. Pepper move the decimal point two places to the left (divide by 100) DP. 94% = 0.94 16.2% = 0.162 Comparing Fractions, Decimals, and Percents Fractions find a common denominator change both fractions into decimals or percents Decimals align decimal points add zeros to even up place values compare numbers according to their place values Percents compare the whole numbers Mixed Forms change all numbers to the same form (percents are the easiest to compare) Compare the following numbers using a <, >, or = sign. 0.9 ____ ½ 82% ____ 1.4 2/3 ____ 5/6 ¼ ____ 2/7 Put the following numbers in ascending order. 0.64, 1/5, 43%, ½ ________________________________ 8 Put the following numbers in descending order. 2/3, 0.09, 16%, 3/8 ________________________________ Complete the chart below. Fraction Decimal Percent 1/4 2/4 3/4 1/5 2/5 3/5 4/5 1/3 2/3 1/8 2/8 3/8 4/8 5/8 6/8 7/8 9 Basic Skills Adding and Subtracting Decimals Line up the decimal points Fill in zeros when necessary Multiplying Decimals Decimals do NOT need to be lined up Count how many digits are after each decimal point and write it to the side of the problem Multiply Put the decimal point in the answer Dividing Decimals If only one number has a decimal point, do long division and bring the decimal point straight up into your answer If both numbers have a decimal point, move both decimal points to the right so the divisor (the number at the door) becomes a whole number Practice- Show all of your work and circle the best answer. 1. Add: $1.36 + $9.44 A $9.08 B $9.74 C $9.80 D $10.80 2. Subtract: A B C D 0.298 1.072 1.928 2.928 3. Multiply: A B C D 4.298 2.37 0.23 x 1.6 1.38 0.138 3.58 0.368 10 4. Find the quotient of: 9 6.669 A 0.0741 B 0.741 C 7.41 D 74.1 5. Find the quotient. 0.942 ÷ 0.003 A B C D 0.314 3.14 31.4 314 Multistep Word Problems Six Step method to solving a word problem 1) The Question 2) The Facts 3) The Plan 4) The Picture 5) The Action 6) The Check Practice- Show all of your work and circle the best answer. 1. At a trip to the grocery store, you buy 4 lbs. of bananas for $0.49 per pound, 2 boxes of oatmeal each at $3.79 per box, and 4 yogurts advertised at 2 for $1.00. If you give the cashier a $20.00 bill, how much change should you get back? A $7.75 B $8.28 C $8.46 D $11.54 11 2. The sixth-grade band is raising money to help buy new instruments. They are selling $21 magazine subscriptions. If 56 students sell one subscription each, how much money will they raise? A B C D $1,000 $1,076 $1,176 $1,680 3. Johanna rented a car. Rental costs were $29.00 per day plus $0.49 for each mile driven. If she kept the car for 1 day and drove 50 miles, how much did she owe? A $29.49 B $31.45 C $53.50 D $78.00 4. Mr. Rico’s class decided to invite their parents to their National Hugging Day party. Amber, Jordan, and Brian made the invitations. Item Cost Package of Paper $3.92 Package of Stickers Box of Envelopes $3.42 $5.13 Stamps $0.32 each It took one package of paper and one package of stickers to make the invitations. They used one box of envelopes and twenty five stamps. About how much did it cost in all to make the invitations? 12