Standard
Benchmark
Indicator | Description | Lesson Plans | Thinkfinity | Resources |
|
1
|
The student uses numerical and computational concepts and procedures in a variety of situations.
|
|
|
|
|
1.1
|
The student demonstrates number sense for real numbers and algebraic expressions in a variety of situations.
|
|
|
|
|
1.1.A1
|
generates and/or solves real-world problems using equivalent representations of real numbers and algebraic expressions (2.4.A1a) ($), e.g., a math classroom needs 30 books and 15 calculators. If B represents the cost of a book and C represents the cost of a calculator, generate two different expressions to represent the cost of books and calculators for 9 math classrooms.
|
|
|
|
|
1.1.K1
|
knows, explains, and uses equivalent representations for real numbers and algebraic expressions including integers, fractions, decimals, percents, ratios; rational number bases with integer exponents; rational numbers written in scientific notation; absolute value; time; and money (2.4.K1a) ($), e.g., –4/2 = (–2); a(-2) b(3) = b3/a2.
|
|
|
|
|
1.1.K2
|
compares and orders real numbers and/or algebraic expressions and explains the relative magnitude between them (2.4.K1a) ($), e.g., will (5n)² always, sometimes, or never be larger than 5n? The student might respond with (5n)² is greater than 5n if n > 1 and (5n)² is smaller than 5 if o < n < 1.
|
|
|
|
|
1.1.A2
|
determines whether or not solutions to real-world problems using real numbers and algebraic expressions are reasonable (2.4.A1a) ($), e.g., in January, a business gave its employees a 10% raise. The following year, due to the sluggish economy, the employees decided to take a 10% reduction in their salary. Is it reasonable to say they are now making the same wage they made prior to the 10% raise?
|
|
|
|
|
1.1.K3
|
knows and explains what happens to the product or quotient when a real number is multiplied or divided by (2.4.K1a):
|
|
|
|
|
1.1.K3A
|
a rational number greater than zero and less than one,
|
|
|
|
|
1.1.K3B
|
a rational number greater than one,
|
|
|
|
|
1.1.K3C
|
a rational number less than zero.
|
|
|
|
|
1.2
|
The student demonstrates an understanding of the real number system; recognizes, applies, and explains their properties, and extends these properties to algebraic expressions.
|
|
|
|
|
1.2.A1
|
generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning (2.4.A1a) ($):
|
|
|
|
|
1.2.A1A
|
commutative, associative, distributive, and substitution properties, e.g., the chorus is sponsoring a trip to an amusement park. They need to purchase 15 adult tickets at $6 each and 15 student tickets at $4 each. How much money will the chorus need for tickets? Solve this problem two ways.
|
|
|
|
|
1.2.A1B
|
identity and inverse properties of addition and multiplication, e.g., the purchase price (P) of a series EE Savings Bond is found by the formula ½ F = P where F is the face value of the bond. Use the formula to find the face value of a savings bond purchased for $500.
|
|
|
|
|
1.2.A1C
|
symmetric property of equality, e.g., Sam took a $15 check to the bank and received a $10 bill and a $5 bill. Later Sam took a $10 bill and a $5 bill to the bank and received a check for $15. $ addition and multiplication properties of equality, e.g., the total price for the purchase of three shirts in $62.54 including tax. If the tax is 3.89, what is the cost of one shirt, if all shirts cost the same?
|
|
|
|
|
1.2.A1D
|
addition and multiplication properties of equality, e.g., the total price for the purchase of three shirts is $62.54 including tax. If the tax if $3.89, what is the cost of one shirt?
|
|
|
|
|
1.2.A1E
|
zero product property, e.g., Jenny was thinking of two numbers. Jenny said that the product of the two numbers was 0. What could you deduct from this statement? Explain your reasoning.
|
|
|
|
|
1.2.K1
|
explains and illustrates the relationship between the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] using mathematical models (2.4.K1a), e.g., number lines or Venn diagrams.
|
|
|
|
|
1.2.K2
|
identifies all the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs (2.4.K1m).
|
|
|
|
|
1.2.A2
|
Jenny said that the product of the two numbers was 0. What analyzes and evaluates the advantages and disadvantages of using integers, whole numbers, fractions (including mixed numbers), decimals or irrational numbers and their rational approximations in solving a given real-world problem (2.4.A1a) ($), e.g., a store sells CDs for $12.99 each. Knowing that the sales tax is 7%, Marie estimates the cost of a CD plus tax to be $14.30. She selects nine CDs. The clerk tells Marie her bill is $157.18. How can Marie explain to the clerk she has been overcharged?
|
|
|
|
|
1.2.K3
|
names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects (2.4.K1a) ($):
|
|
|
|
|
1.2.K3A
|
commutative (a + b = b + a and ab = ba), associative [a + (b + c) = (a + b) + c and a(bc) = (ab)c], distributive [a (b + c) = ab + ac], and substitution properties (if a = 2, then 3a = 3 x 2 = 6);
|
|
|
|
|
1.2.K3B
|
identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity: a + 0 = a, multiplicative identity: a • 1 = a, additive inverse: +5 + –5 = 0, multiplicative inverse: 8 x 1/8 = 1);
|
|
|
|
|
1.2.K3C
|
symmetric property of equality (if a = b, then b = a);
|
|
|
|
|
1.2.K3D
|
addition and multiplication properties of equality (if a = b, then a + c = b + c and if a = b, then ac = bc) and inequalities (if a > b, then a + c > b + c and if a > b, and c > 0 then ac > bc);
|
|
|
|
|
1.2.K3E
|
zero product property (if ab = 0, then a = 0 and/or b = 0).
|
|
|
|
|
1.2.K4
|
uses and describes these properties with the real number system (2.4.K1a) ($):
|
|
|
|
|
1.2.K4A
|
transitive property (if a = b and b = c, then a = c),
|
|
|
|
|
1.2.K4B
|
reflexive property (a = a).
|
|
|
|
|
1.3
|
The student uses computational estimation with real numbers in a variety of situations.
|
|
|
|
|
1.3.A1
|
adjusts original rational number estimate of a real-world problem based on additional information (a frame of reference) (2.4.A1a) ($), e.g., estimate how long it takes to walk from here to there; time how long it takes to take five steps and adjust your estimate.
|
|
|
|
|
1.3.K1
|
estimates real number quantities using various computational methods including mental math, paper and pencil, concrete objects, and/or appropriate technology (2.4.K1a) ($).
|
|
|
|
|
1.3.K2
|
uses various estimation strategies and explains how they were used to estimate real number quantities and algebraic expressions (2.4.K1a) ($).
|
|
|
|
|
1.3.A2
|
estimates to check whether or not the result of a real-world problem using real numbers and/or algebraic expressions is reasonable and makes predictions based on the information (2.4.A1a) ($), e.g., if you have a $4,000 debt on a credit card and the minimum of $30 is paid per month, is it reasonable to pay off the debt in 10 years?
|
|
|
|
|
1.3.A3
|
determines if a real-world problem calls for an exact or approximate answer and performs the appropriate computation using various computational strategies including mental math, paper and pencil, concrete objects, and/or appropriate technology (2.4.A1a) ($), e.g., do you need an exact or an approximate answer in calculating the area of the walls to determine the number of rolls of wallpaper needed to paper a room? What would you do if you were wallpapering 2 rooms?
|
|
|
|
|
1.3.K3
|
knows and explains why a decimal representation of an irrational number is an approximate value (2.4.K1a).
|
|
|
|
|
1.3.K4
|
knows and explains between which two consecutive integers an irrational number lies (2.4.K1a).
|
|
|
|
|
1.3.A4
|
explains the impact of estimation on the result of a real-world problem (underestimate, overestimate, range of estimates) (2.4.A1a) ($), e.g., if the weight of 25 pieces of paper was measured as 530.6 grams, what would the weight of 2,000 pieces of paper equal to the nearest gram? If the student were to estimate the weight of one piece of paper as about 20 grams and then multiply this by 2,000 rather than multiply the weight of 25 pieces of paper by 80; the answer would differ by about 2,400 grams. In general, multiplying or dividing by a rounded number will cause greater discrepancies than rounding after multiplying or dividing.
|
|
|
|
|
1.4
|
The student models, performs, and explains computation with real numbers and polynomials in a variety of situations.
|
|
|
|
|
1.4.A1
|
generates and/or solves multi-step real-world problems with real numbers and algebraic expressions using computational procedures (addition, subtraction, multiplication, division, roots, and powers excluding logarithms), and mathematical concepts with ($):
|
|
|
|
|
1.4.A1A
|
applications from business, chemistry, and physics that involve addition, subtraction, multiplication, division, squares, and square roots when the formulae are given as part of the problem and variables are defined (2.4.A1a) ($), e.g., given F = ma, where F = force in newtons, m = mass in kilograms, a = acceleration in meters per second squared. Find the acceleration if a force of 20 newtons is applied to a mass of 3 kilograms.
|
|
|
|
|
1.4.A1B
|
volume and surface area given the measurement formulas of rectangular solids and cylinders (2.4.A1f), e.g., a silo has a diameter of 8 feet and a height of 20 feet. How many cubic feet of grain can it store?
|
|
|
|
|
1.4.A1C
|
probabilities (2.4.A1h), e.g., if the probability of getting a defective light bulb is 2%, and you buy 150 light bulbs, how many would you expect to be defective?
|
|
|
|
|
1.4.A1D
|
application of percents (2.4.A1a), e.g., given the formula A = P(1+rdivided by n) to the nt, when A = amount, P= principal, r = annual interest, n = number of compounding periods per year, t= number of years. If $1,000 is placed in a savings account with a 6% annual interest rate and is compounded semiannually, how much money will be in the account at the end of 2 years?
|
|
|
|
|
1.4.A1E
|
simple exponential growth and decay (excluding logarithms) and economics (2.4.A1a) ($), e.g., a population of cells doubles every 20 years. If there are 20 cells to start with, how long will it take for there to be more than 150 cells? or If the radiation level is now 400 and it decays by ½ or its half-life is 8 hours, how long will it take for the radiation level to be below an acceptable level of 5?
|
|
|
|
|
1.4.K1
|
computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1a) ($).
|
|
|
|
|
1.4.K2
|
performs and explains these computational procedures (2.4.K1a):
|
|
|
|
|
1.4.K2A
|
addition, subtraction, multiplication, and division using the order of operations
|
|
|
|
|
1.4.K2B
|
multiplication or division to find ($):
|
|
|
|
|
1.4.K2Bi
|
a percent of a number, e.g., what is 0.5% of 10?
|
|
|
|
|
1.4.K2Bii
|
percent of increase and decrease, e.g., a college raises its tuition form $1,320 per year to $1,425 per year. What percent is the change in tuition?
|
|
|
|
|
1.4.K2Biii
|
percent one number is of another number, e.g., 89 is what percent of 82?
|
|
|
|
|
1.4.K2Biv
|
a number when a percent of the number is given, e.g., 80 is 32% of what number?
|
|
|
|
|
1.4.K2C
|
manipulation of variable quantities within an equation or inequality (2.4.K1d), e.g., 5x – 3y = 20 could be written as 5x – 20 = 3y or 5x(2x + 3) = 8 could be written as 8/(5x) = 2x + 3;
|
|
|
|
|
1.4.K2D
|
simplification of radical expressions (without rationalizing denominators) including square roots of perfect square monomials and cube roots of perfect cubic monomials;
|
|
|
|
|
1.4.K2E
|
simplification or evaluation of real numbers and algebraic monomial expressions raised to a whole number power and algebraic binomial expressions squared or cubed;
|
|
|
|
|
1.4.K2F
|
simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents;
|
|
|
|
|
1.4.K2G
|
matrix addition ($), e.g., when computing (with one operation) a building’s expenses (data) monthly, a matrix is created to include each of the different expenses; then at the end of the year, each type of expense for the building is totaled;
|
|
|
|
|
1.4.K2H
|
scalar-matrix multiplication ($), e.g., if a matrix is created with everyone’s salary in it, and everyone gets a 10% raise in pay; to find the new salary, the matrix would be multiplied by 1.1.
|
|
|
|
|
1.4.K3
|
finds prime factors, greatest common factor, multiples, and the least common multiple of algebraic expressions (2.4.K1b).
|
|
|
|