NUMBER SENSE - Poway Unified School District数感-宝威学区.doc

POWAY UNIFIED SCHOOL DISTRICTPRE-ALGEBRASTANDARDS AND EXEMPLARSSPRING, 2003NUMBER SENSEGrade 6:1.2*1.3*Interpret and use ratios in different context (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).Use proportions to solve problems (e.g., determine the value of N if 4/7=N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. 1 in. to 4 ft. = x to 12 ft. What is 20% of $60? Order from least to greatest: 250%, 3.1, , 1.7, , If you pay $35 for 7 CDs, what is the unit value? Joe drove 180 miles using 6 gallons of gas. How many miles/gallon?Grade 7:1.1Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation. Write 548,200 in scientific notation , .6(3.21) Write 7.28 x 10-4 in standard notation Write 0.00147 in scientific notation Write 0.00591 x 108 in standard notation The radius of the earths orbit is 150,000,000,000 meters. What is this number in scientific notation?a)b)c)d) 3.6 x 102 = a) 3.6000b) 36c) 360d) 3,6001.2*Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimal) and take positive rational numbers to whole-number powers. 34(6 3) 7 (4 + (2) The five members of a band are getting new outfits. Shirts cost $12 each, pants cost $29 each, and boots cost $49 a pair. What is the total cost of the new outfits for all of the members?a) $90b) $95c) $450d) $500 Simplify: a)b)c)d) 23.065 - (-10.5) 3(-4 +12) + 7(-3) 43 1.785 - 0.0984 (1.23)(4.78) Write the prime factorization of 72. Which of the following numerical expressions results in a negative number?a) (-7) + (-3)b) (-3) + (7)c) (3) + (7)d) (3) + (-7) - (11) One hundred is multiplied by a number between 0 and 1. The answer has to be a) Less than 0.b) Between 0 and 50 by not 25.c) Between 0 and 100 but not 50.d) Between o and 100. Which is the best estimate of 326 x 279?a) 900b) 9,000c) 90,000d) 900,000 The winning number in a contest was less than 50. It was a multiple of 3, 5, and 6. What was the number?a) 14b) 15c) 30d) It cannot be determined.1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. Convert to a decimal. Convert to a percent. is between which two whole numbers? There is a 20% off sale on sweaters. The list price is $25.00. Find the sales price. If Freya makes 4 of her 5 free throws in a basketball game, what is her free throw shooting percentage?a) 20%b) 40%c) 80%d) 90% Some students attend school 180 of the 365 days in a year. About what part of the year do they attend school?a) 18%b) 50%c) 75%d) 180% A pair of jeans regularly sells for $24.00. They are on sale for 25% off. What is the sale price of the jeans?a) $6.00b) $18.00c) $20.00d) $30.00 What is the fractional equivalent of 60%?a)b)c)d) A CD player regularly sells for $80. It is on sale for 20% off. What is the sale price of the CD player?a) $16b) $60c) $64d) $961.4*Differentiate between rational and irrational numbers. Define rational numbers. Define irrational numbers. Label the following numbers with an “R” for rational or an “I” for irrational: 1.27 1.2121121111.5*Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions. Convert the following into a decimal: Convert the following into a fraction: 0.27 1.45 0.27271.6Calculate the percentage of increases and decreases of a quantity. Calculate the percent of increase: From 1 to 1.2 From 3 to 6 From 5 to 18 Calculate the percent of decrease: From 1 to 0.8 From 14 to 7 From 15 to 4 The cost of an afternoon movie ticket last year was $4.00. This year an afternoon movie ticket cost $5.00. What is the percent of increase of the ticket from last year to this year?a) 10%b) 20%c) 25%d) 40% The price of a calculator has decreased from $12.00 to $9.00. What is the percent of decrease?a) 3%b) 25%c) 33%d) 75%1.7*Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.What is 15% of 36?16 is what percent of 64? A real estate agent earned 5% commission on a $200,000 house. What is her commission? If a shirt is on sale for $25 and it originally sold for $30, what is the percent of decrease? Sally puts $200.00 in a bank account. Each year the account earns 8% simple interest. How much interest will be earned in three years?a) $16.00b) $24.00c) $48.00d) $160.00* STUDENTS NEED TO BE ABLE TO ESTIMATE PERCENTS (MULTIPLES OF TEN) WITHOUT A CALCULATOR.2.2*Add and subtract fractions by using factoring to find common denominators. Simplify: Which of the following is the prime factored form of the lowest common denominator of ?a) 5 x 1b) 2 x 3 x 5c) 2 x 5 x 3 x 5d) 10 x 152.3*Multiply, divide, and simplify rational numbers by using exponent rules. Evaluate for x = 2, y = -3, and z = 5 x3 y2 z2 + y (x3)22.4Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why. Find the side of a square with an area of 81 units2. The square root of 150 is betweena) 10 and 11b) 11 and 12c) 12 and 13d) 13 and 142.5*Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. Simplify |9|, |8 3| True or false? If |x| = 3, what is the value of x?a) -3 or 0b) -3 or 3c) 0 or 3d) -9 or 9c) d) 4 What is the absolute value of -4?a) -4b)ALGEBRA AND FUNCTIONSe or inequalities that represent a verbal description (e.g., three less than a number, half as large as area A).1.1Use variable and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represent a verbal description (e.g., three less than a number, half as large as area A). Five less than 3 times a number. The length of a rectangle is four more than the width. If the perimeter is 20, find the width. Four times an unknown is less than 12. Which of the following inequalities represent the statement, “A number, x, decreased by 13 is less than or equal to 39”?a)b)c)d) A shopkeeper has x kilograms of tea in stock. He sells 15 kilograms and then receives a new shipment weighting 2y kilograms. Which expression represents the weight of the tea he now has?a)b)c)d) Divide a number by 5 and add 4 to the result. The answer is 9.Which of the following equations matches these statements?a)b)c)d) In a certain room, the number of chairs, c, is equal to 3 times the number of tables, t. Which equation matches the information?a) 3 c = tb) 3 t = cc) 3 c = 3 td) c t = 31.2Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5)2. If x = 2, y = 3 and z = 1, evaluate: x 5 3x + 2y z 8(x 2y) 3(2x + 5)2 Simplify: (5y) + ( 4) + ( x) + (2y) (7y) 4b 9b + 7b 3x 5 + 4x 2 2(2x + 1) 3 (x 4) -(2x - 4) If h =3, and k= 4, then a) 6b) 7c) 8d) 101.3*Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used. Simplify: 3(2x + 1) 32 + (-32) 95 + (5 + 278) 5( -13 + 13)1.4Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly. EmbeddedGrade 62.0Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions.1.5Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph. Consider the circle graph shown below. How many hours a day does Ramon spend in school?a) 2 hoursb) 4 hoursc) 6 hoursd) 8 hours After three hours of travel, Car A is about how many kilometers ahead of Car B?a) 2b) 10c) 20d) 25 The graph above shows the time of travel by pupils from home to school. How many pupils must travel for more than 10 minutes?a) 2b) 5c) 7d) 8 The cost of a long distance call charged by each of two telephone companies is shown on the graph below. Company A is less expensive than Company B fora) All callsb) 3 minutes call onlyc) calls less than 3 minutesd) calls longer than 3 minutes The graph below shows the value of Whistler Company stock at the end of every other year from 1994 to 2000. From this graph, which of the following was the most probable value of Whistler Company stock at the end of 1992?a) -$10b) $1c) $10d) $203.3* Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of the graph.What is the slope of the line shown in the graph to the left:a) -2b)c)d) 2 The slope of the line shown below is . What is the value of d ?a) 3b) 4c) 6d) 9 Identify the slope of Graph: y = 2x 4Graph using tables. Graph. Graph. Graph. Graph. What is the slope of the line below? a)b)c)d)3.4*Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. Given:xy1721031341604 Write a rule for the table. Graph the above table on a coordinate plane. Best Burger sells cheeseburgers for $1.75 each. Part of the table representing the number of cheeseburgers purchased and their cost is shown below. Which of the following is a portion of the graph of the data in the table? 4.1*Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Solve for x: 2x 3 = 7a) -5b) -2c) 2d) 5 A flower shop delivery van traveled these distances during one week: 104.4, 117,8, 92,3, 168,7, and 225.6 miles. How many gallons of gas were used by the delivery van during this week? What other information is needed in order information is needed in order to solve this problem?a) The average speed traveled in miles per hourb) The cost of gasoline per gallonc) The average number of miles per gallon for the vand) The number of different deliveries the van made x = 8 3x + 1 = 7 4x + 3.24 = 0.72 18 = 7MEASUREMENT AND GEOMETRY1.1Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). How many square feet are in 5 square yards? Order the following three speeds from fastest to slowest: 3,100 yd/hr, 160 ft/min, 9,200 ft/hr. A boy is two meters tall. About how tall is the boy in feet (ft) and inches (in)?(1 meter 39 inches)a) 5 ft 0 inb) 5 ft 6 inc) 6 ft 0 ind) 6 ft 6 in Juanita exercised for one hour. How many seconds did Juanita exercise?a) 60b) 120c) 360d) 3,600 One cubic inch is approximately equal to 16.38 cubic centimeters. Approximately how many cubic centimeters are there in 3 cubic inches?a) 5.46b) 13.38c) 19.38d) 49.14 The table below shows the flight times from San Francisco (S.F.) to New York (N.Y.). Which flight takes the longest?a) The flight leaving at 8:30 A.M.b) The flight leaving at 12:00 noonc) The flight leaving at 3:30 P.M.d) The flight leaving at 9:45 P.M.1.2 Construct and read drawings and models made to scale. If a half-inch represents a mile on a map, 3 inches represents how many miles? The actual width (w) of a rectangle is 18 centimeters (cm). Use the scale drawing of the rectangle to find the actual length (l). a) 6 cmb) 24 cmc) 36 cmd) 54 cm The scale drawing of the basketball court shown below is drawn using a scale of 1 inch (in) = 24 feet (ft). What is the length, in feet, of the basketball court?a) 90 ftb) 104 ftc) 114 ftd) 120 ft1.3*Use measures expressed as rates (e.g., speed, density) and measure expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. Sixty miles per hour is the same rate as which of the following?a) 1 mile per minuteb) 1 mile per secondc) 6 miles per minuted) 360 miles per second Beverly ran six miles at the speed of four miles per hour. How long did it take her to run that distance?a) hrb) hrsc) 4 hrsd) 6 hrs2.1Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Find the perimeter of a parallelogram with length 4.7 cm and width 27.2 cm. Find the area of a square with sides 16 cm long. Find the volume:1.7 cm7 cm14 cm In the figure below, the radius of the inscribed circle is 6 inches (in). What is the perimeter of square ABCD? a) 12p inb) 36p inc) 24 ind) 48 in What is the area of the shaded region in the figure shown below? (Area of a triangle )a) 4 cm2b) 6 cm2c) 8 cm2d) 16 cm2 The largest possible circle is to be cut from a 10-foot square board. What will be the approximate area, in square feet, of the remaining board (shaded region)?()a) 20b) 30c) 50d) 80 What is the area of the triangle shown above? a) 44 square unitsb) 60 square unitsc) 88 square unitsd) 120 square units A rectangular pool 42 feet by 68 feet is on a rectangular lot 105 feet by 236 feet. The rest of the lot is grass. Approximately how many square feet is grass?a) 2,100b) 2,800c) 21,000d) 28,000 What is the volume of the shoebox shown above in cubic inches (in3)?a) 29b) 75c) 510d) 675 Louis calculated the area of the circle above and got an answer of 50.769 cm2. He knows his answer was wrong because the correct answer should be abouta) 4 x 4 x 4 = 64b) 3 x 3 x 40 = 360c) 31 x 4 x 4 = 496d) 3 x 40 x 40 = 48002.2Estimate and compute the area of more complex or irregular two- and three- dimensional figures by breaking the figures down into more basic geometric objects. One-inch cubes are stacked as shown in the drawing below. What is the total surface area?a) 19 in2b) 29 in2c) 32 in2d) 38 in2 In the figure shown below, all the corners form right angles. What is the area of the figure in square units? a) 67b) 73c) 78d) 91 A right triangle is removed from a rectangle as shown in the figure below. Find the area of the remaining part of the rectangle. a) 40 in2b) 44 in2c) 48 in2d) 52 in22.4Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units. 1 square foot = _ square inches or 1ft2 = _ in2 1 cubic inch _ cubic centimeters or 1 in3 = _ cm3)3.1Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge. Construct the perpendicular bisector of .AB Construct the angle bisector of .DAR3.2Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translation and reflections. Which of the following triangles is the image of triangle RST that results from reflecting triangle RST across the y-axis? 3.3*Know and understand the Pythagorean Theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean Theorem by direct measurement. Which set of side lengths form a r