Nicolas Mundy
8th grade algebra 1 block 5-6
Thinking with Mathematical Models
Additive inverses- Two numbers,a and b, that satisfy the equation a+b=0.Ex)3 and -3 are additive inverses.
inequality- A statement that two qauntites are not equal. The symbols <,>,are used to express inequalities. Ex) if a and b are two quantities like a=3 and b=4 so 3 is less than 4 so it is written as 3<4
inverse variation- A nonlinear relationship in which the product of two variables is constant. An inverse variation can be represented by an equation of y=kx, or xy=k where k is a constant.
Linear Relationship- A relationship in which there is a constant rate of change between two variables. A linear relationship can be represented by a straight-line graph and by an equation of the form y=mx+b.
Mathematical model-An equation or a graph that describes, at least approximately, the relationship between two variables. In this unit, mathematical models are made by inquiring data, plotting the data points, and, when the points showed a pattern, finding an equation or curve that fits the trend in the data.
Looking For Pythagoras
Conjecture- A guess about a pattern or relationship based on observations.
Hypotenuse-The side of a right triangle that is opposite the right angle. The hypotenuse is the longest side of a triangle.
Irrational number- A number that cannot be written as a fraction with a numerator and a denominator that are integers. The decimal representation of an irrational number never ends and never shows a repeating pattern of a fixed number of digits.
legs-The sides of a triangle that are adjacent to the right angle.
Perpendicular-Forming a right angle. For example, the sides of a right triangle that form the right angle are perpendicular.
Pythagorean Theorem- A statement about the relationship among the lengths of the sides of a right triangle. The theorem states that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a multiplied by a and b multiplied by b =c
rational number- A number that can be written as a fraction with a numerator and a denominator that are integers. The decimal representation of a rational number either ends or repeats.Ex)rational numbers.5,7,0.2, and 0.191919...
Real numbers- The set of rational numbers and all irrational numbers. The number line represents the set of real numbers.
Repeating decimal- A decimal with a pattern of a fix number of digits that repeats forever, such as 0.3333333... and 0.73737373... repearing decimals are rational numbers.
Square root- If A=s multiplied by s then s is the square root of A. For example,-3 and 3 are square roots of 9 because 3 times 3=9 and -3 times -3=9
Terminating decimal- A decimal that ends, or terminates, such as 0.5 or 0.125. terminating decimals are rational numbers.
Cube Root- A quantity in which the given quantity is cubed or multiplied by that number 3 times.
Acute triangle- A triangle that has all angles less than 90 degrees.
Obtuse triangle- A triangle with all angles greater than 90 degrees.
Right triangle- A triangle with a right angle.
Theorem- A rule in algebra or other branches of mathematics expressed by symbols or formulas.
Radius- A straight line from the center to the circumference of a circle or sphere.
Standard form- A way to write numbers using the digits 0-9.
Expanded form- A way to show how much each digit in a number represents.
Hypotenuse-The side of a right triangle that is opposite the right angle. The hypotenuse is the longest side of a triangle.
Irrational number- A number that cannot be written as a fraction with a numerator and a denominator that are integers. The decimal representation of an irrational number never ends and never shows a repeating pattern of a fixed number of digits.
legs-The sides of a triangle that are adjacent to the right angle.
Perpendicular-Forming a right angle. For example, the sides of a right triangle that form the right angle are perpendicular.
Pythagorean Theorem- A statement about the relationship among the lengths of the sides of a right triangle. The theorem states that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a multiplied by a and b multiplied by b =c
rational number- A number that can be written as a fraction with a numerator and a denominator that are integers. The decimal representation of a rational number either ends or repeats.Ex)rational numbers.5,7,0.2, and 0.191919...
Real numbers- The set of rational numbers and all irrational numbers. The number line represents the set of real numbers.
Repeating decimal- A decimal with a pattern of a fix number of digits that repeats forever, such as 0.3333333... and 0.73737373... repearing decimals are rational numbers.
Square root- If A=s multiplied by s then s is the square root of A. For example,-3 and 3 are square roots of 9 because 3 times 3=9 and -3 times -3=9
Terminating decimal- A decimal that ends, or terminates, such as 0.5 or 0.125. terminating decimals are rational numbers.
Cube Root- A quantity in which the given quantity is cubed or multiplied by that number 3 times.
Acute triangle- A triangle that has all angles less than 90 degrees.
Obtuse triangle- A triangle with all angles greater than 90 degrees.
Right triangle- A triangle with a right angle.
Theorem- A rule in algebra or other branches of mathematics expressed by symbols or formulas.
Radius- A straight line from the center to the circumference of a circle or sphere.
Standard form- A way to write numbers using the digits 0-9.
Expanded form- A way to show how much each digit in a number represents.
Growing, Growing, Growing
Base-The number that is raised to a power in an exponential expression. In the expression 3 to the 5th power, 5is the exponent and 3 is the base.
Compound growth- another term for exponential growth, usually used when talking about the monetary value of an investment. The change in the balance of a savings account shows compound growth because the bank pays interest not only on the original investment, but on the interest earned.
Decay Factor-The constant factor that each value in an exponential decay pattern is multiplied by to get the next value. The decay factor is the base in the equation A=64(0.5)n, where A is the area of a ballot and n is the number of cuts, the decay factor is 0.5.
Decay Rate- The percent decrease in an exponential decay pattern. A discount, expressed as a percent, is a decay rate. In general, for an exponential pattern with a decay factor b. The decay rate is 1-b
Exponent- A number that indicates how many times another number(the base) is to be used as a factor. Exponents are written as raised numbers to the right of the base.
Exponential decay- A pattern of decrease in which each value is found by multiplying the previous value by a constant factor greater than 0 but less than 1, For example, the pattern 27,9,3,1,1/3,1/9,... shows exponential decay in which each value is 1/3 times the previous value.
Exponential form- A quantity expressed as a number raised to a power. In exponential form, 32 can be written as 2 to the power of 5.
Exponential growth- A pattern of increase in which each value is found by multiplying the previous value by a constant factor greater than 1.
Exponential relationship- A relationship that shows exponential growth or decay.
Growth factor- The constant factor that each value in an exponential growth pattern is multiplied by to get the next value. The growth factor is the base in an exponential growth equation. For example, in the equation A+25(3)d, where A is the area of mold and d is the number of days, the growth factor is 3.
Growth rate- The percent increase in an exponential growth pattern.
Scientific notation-A short way to write very large or very small numbers.
Standard form- The most common way to express quantities.
Exponential function- A function whose value is a constant raised to the power of the argument, especially the function where the constant is E.
Compound growth- another term for exponential growth, usually used when talking about the monetary value of an investment. The change in the balance of a savings account shows compound growth because the bank pays interest not only on the original investment, but on the interest earned.
Decay Factor-The constant factor that each value in an exponential decay pattern is multiplied by to get the next value. The decay factor is the base in the equation A=64(0.5)n, where A is the area of a ballot and n is the number of cuts, the decay factor is 0.5.
Decay Rate- The percent decrease in an exponential decay pattern. A discount, expressed as a percent, is a decay rate. In general, for an exponential pattern with a decay factor b. The decay rate is 1-b
Exponent- A number that indicates how many times another number(the base) is to be used as a factor. Exponents are written as raised numbers to the right of the base.
Exponential decay- A pattern of decrease in which each value is found by multiplying the previous value by a constant factor greater than 0 but less than 1, For example, the pattern 27,9,3,1,1/3,1/9,... shows exponential decay in which each value is 1/3 times the previous value.
Exponential form- A quantity expressed as a number raised to a power. In exponential form, 32 can be written as 2 to the power of 5.
Exponential growth- A pattern of increase in which each value is found by multiplying the previous value by a constant factor greater than 1.
Exponential relationship- A relationship that shows exponential growth or decay.
Growth factor- The constant factor that each value in an exponential growth pattern is multiplied by to get the next value. The growth factor is the base in an exponential growth equation. For example, in the equation A+25(3)d, where A is the area of mold and d is the number of days, the growth factor is 3.
Growth rate- The percent increase in an exponential growth pattern.
Scientific notation-A short way to write very large or very small numbers.
Standard form- The most common way to express quantities.
Exponential function- A function whose value is a constant raised to the power of the argument, especially the function where the constant is E.
Frogs, fleas, and painted cubes
Quadratic Function- A second-degree polynomial function of the form a, b, and c are real numbers.
Parabola- The graph of a quadratic function. A parabola has a line of symmetry that passes through the maximum point if the graph opens downward or through the minimum point if the graph opens upward.
Dependent Variable- A variable whose value depends on that of another.
Independent Variable- A variable whose variation does not depend on that of another.
X-Intercept- The point at which a line crosses the x- axis and where the y-value equals 0.
Y-Intercept- The point at which the line crosses the y-axis.
constant- A number on its own, or sometimes a letter such as a, b, and c to stand as a fixed number.
Quadratic Term- A part of an expression in expanded form in which the variable is raised to the second power.
Linear Term- A part of an algebraic expression in expanded form in which the variable is raised to the first power.
Minimum value- The least y-value a function assumes. If y is the cost of an item, then the minimum value of the cost, or simply the minimum cost, is the least cost possible for the item.
Maximum Value- The greatest y-value a function assumes. If y is the height of a thrown object, then the maximum value of the height is the greatest height the object reaches.
Line of Symmetry- A line that divides a graph or drawing into two halves that are mirror images of each other.
Like Terms- Terms with the same variable raised to the same power.
Binomial- an algebraic expression of the sum or the difference of two terms.
Trinomial- A polynomial consisting of three terms.
Distributive Property- For ant three numbers a, b, and c, a(b+c)=ab+bc.
Factored Form- The form of an expression composed of products of factors, rather than sums or differences of terms.
Expanded Form- The form of an expression composed of sums and differences of terms, rather than products of factors.
Difference of squares- A squared number subtracted from another squared number.
Triangular numbers- A number that gives the total number of dots in a triangular pattern.
Parabola- The graph of a quadratic function. A parabola has a line of symmetry that passes through the maximum point if the graph opens downward or through the minimum point if the graph opens upward.
Dependent Variable- A variable whose value depends on that of another.
Independent Variable- A variable whose variation does not depend on that of another.
X-Intercept- The point at which a line crosses the x- axis and where the y-value equals 0.
Y-Intercept- The point at which the line crosses the y-axis.
constant- A number on its own, or sometimes a letter such as a, b, and c to stand as a fixed number.
Quadratic Term- A part of an expression in expanded form in which the variable is raised to the second power.
Linear Term- A part of an algebraic expression in expanded form in which the variable is raised to the first power.
Minimum value- The least y-value a function assumes. If y is the cost of an item, then the minimum value of the cost, or simply the minimum cost, is the least cost possible for the item.
Maximum Value- The greatest y-value a function assumes. If y is the height of a thrown object, then the maximum value of the height is the greatest height the object reaches.
Line of Symmetry- A line that divides a graph or drawing into two halves that are mirror images of each other.
Like Terms- Terms with the same variable raised to the same power.
Binomial- an algebraic expression of the sum or the difference of two terms.
Trinomial- A polynomial consisting of three terms.
Distributive Property- For ant three numbers a, b, and c, a(b+c)=ab+bc.
Factored Form- The form of an expression composed of products of factors, rather than sums or differences of terms.
Expanded Form- The form of an expression composed of sums and differences of terms, rather than products of factors.
Difference of squares- A squared number subtracted from another squared number.
Triangular numbers- A number that gives the total number of dots in a triangular pattern.
Photo used under Creative Commons from Keith Allison