Unit One: First and Second Nine Weeks

Course: 1205020 M/J Mathematics 1ADVANCEDSTANDARDS (31)

Unit One: First and Second Nine Weeks

Numbers and Operations (MA.6.A.5 & MA.7.A.5)

Multiplication and Division of Fractions Decimals (MA.6.A.1)

This is an outline of the unit and is subject to revision as school events or directives require.

Data Analysis will be taught using bellringers and small projects/activities throughout the year.

MA.6.A.1 BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals.
MA.6.A.1.1 (Moderate): Explain and justify procedures for multiplying and dividing fractions and decimals. /

Ch. 1 and 2

MA.6.A.1.2(Low): Multiply and divide fractions and decimals efficiently. /

Ch. 1 and 2

MA.6.A.1.3(High): Solve real-world problems involving multiplication & division of fractions & decimals. /

Ch. 1 and 2

MA.6.A.5 Number and Operations /

Textbook Sections/Pages

MA.6.A.5.1 (Moderate): Use equivalent forms of fractions, decimals, and percents to solve problems. /

Ch. 5

MA.6.A.5.2(Moderate): Compare and order fractions, decimals, and percents, including finding their approximate location on a number line. /

Ch. 5

MA.6.A.5.3(Moderate): Estimate the results of computations with fractions, decimals, and percents, and judge the reasonableness of the results. /

Ch. 1 and 2

ADVANCED TOPICS

MA.7.A.5 Number and Operations
MA.7.A.5.1(Low): Express rational numbers as terminating or repeating decimals. / Ch 12-1 B
MA.7.A.5.2(High): Solve non-routine problems by working backwards. / Ch. 11-3C need additional resources

VOCABULARY

Algorithm: An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point.

Approximate: A number or measurement that is close to or near its exact value.

Denominator: The number b in a fraction a/b. If the fraction is representing a part-whole relationship, denominator is the number of equally-sized parts that make the whole or the complete set.

Equal: Having the same value (=).

Equivalent: Having the same value.

Estimate: Is an educated guess for an unknown quantity or outcome based on known information. An estimate in computation may be found by rounding, by using front-end digits, by clustering, or by using compatible numbers to compute.

Estimation: The use of rounding and/or other strategies to determine a reasonably accurate approximation, without calculating an exact answer.

Exponent (exponential form): The number of times the base occurs as a factor, for example 23 is the exponential form of 2 x 2 x 2. The number two (2) is called the base, and the number three (3) is called the exponent.

Fraction: A rational number expressed in the form a/b, where a is called the numerator and b is called the denominator. A fraction may mean part of a whole, ratio of two quantities, or may imply division.

Integers: The numbers in the set {…-4, -3, -2, -1, 0, 1, 2, 3, 4…}.

Number line: A line of infinite extent whose points correspond to the real numbers according to their distance in a positive or negative direction from a point arbitrarily taken as zero.

Numerator: The number a in a fraction a/b. If the fraction is representing a part-whole relationship, then the numerator tells how many equal parts of the whole are being considered.

Operation: Any mathematical process, such as addition, subtraction, multiplication, division, raising to a power, or finding the square root.

Procedure: A specific prescription for carrying out a mathematical task such as adding, multiplying, simplifying, and factoring.

Quotient: The result of dividing two numbers.

Multiples: The numbers that result from multiplying a given whole number by the set of whole numbers.

Non-routine problem: A problem that can be solved by more than one way, rather than a set procedure, having multiple decision points and multiple steps (grade level dependent).

Rational Number: A number that can be expressed as a ratio a/b, where a and b are integers and b≠0.

Whole Number: The numbers in the set {0, 1, 2, 3, 4, ...}

Course: 1205020 M/J Mathematics 1 ADVANCEDSTANDARDS (31)

Unit 2: Second and Third Nine Weeks

Ratios & Rates (MA.6.A.2)

Mathematical Expressions and Equations (MA.6.A.3)

This is an outline of the unit and is subject to revision as school events or directives require.

Data Analysis will be taught using bellringers and small projects/activities throughout the year.

MA.6.A.2 BIG IDEA 2: Connect ratio and rates to multiplication and division. /

Textbook Sections/Pages

MA.6.A.2.1(High): Use reasoning about multiplication and division to solve ratio and rate problems. /

Ch. 4

MA.6.A.2.2(Moderate): Interpret and compare ratios and rates. /

Ch. 4

MA.6.A.3 BIG IDEA 3: Write, interpret, and use mathematical expressions and equations.
MA.6.A.3.1(Moderate): Write and evaluate mathematical expressions that correspond to given situations. / Ch. 6-1 A,B,D
MA.6.A.3.2(Moderate): Write, solve, and graph one- and two- step linear equations and inequalities. / Ch. 7 and Ch. 8
MA.6.A.3.3(Moderate): Work backward with two-step function rules to undo expressions. / Ch. 7-1B, 7-3B, 8-1C, missing piece of data
MA.6.A.3.4(Moderate): Solve problems given a formula. / Ch. 9-1, 9-2, 9-3
MA.6.A.3.5(Moderate): Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent. / Ch. 6-2 ABC
MA.6.A.3.6(Moderate): Construct and analyze tables, graphs, and equations to describe linear functions and other simple relations using both common language and algebraic notation. / Ch. 8-1 ACDE

VOCABULARY

Distributive property: Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. [e.g., x(a + b) = ax + bx].

Equation: A mathematical sentence stating that the two expressions have the same value. Also read the definition of equality.

Expression: A mathematical phrase that contains variables, functions, numbers, and/or operations. An expression does not contain equal or inequality signs.

Formula: A rule that shows the relationship between two or more quantities; involving numbers and/or variables.

Linear equation: An algebraic equation in which the variable quantity or quantities are raised to the zero or first power.

Literal equations: An equation that contains more than one variable; an implicit equation; often mathematical formula.

Model: To represent a mathematical situation with manipulatives (objects), pictures, numbers or symbols.

Percent: Per hundred; a special ratio in which the denominator is always 100. The language of percent may change depending on the context. The most common use is in part-whole contexts, for example, where a subset is 40 percent of another set. A second use is change contexts, for example, a set increases or decreases in size by 40 percent to become 140% or 60% of its original size. A third use involves comparing two sets, for example set A is 40% of the size of set B, in other words, set B is 250 percent of set A.

Rate: A ratio that compares two quantities of different units.

Variable: Any symbol, usually a letter, which could represent a number. A variable might vary as in f(x)=2x+1, or a variable might be fixed as in 2x+1=5.

Number Sentence: A mathematical sentence that includes numbers, operation symbols, and a greater than or less than symbol or an equal sign. Note: 10 + 1 = 11 x 2 = 22 is continuing the number string with violating the equality because 10+1≠22. Therefore, it is not an acceptable representation for an equation or for showing computation with number sentences.

Ratio: The comparison of two quantities, the ratio of a and b is a:b or a to b or a/b, where b ≠ 0.

Linear function: A relationship between two variables such that for a fixed change in one variable, there is fixed change in the other variable. If there is one independent variable (e.g. f(x)=mx+b), then the graph of the function will be a line. If there are two independent variables (e.g. f(x,y)=ax+by+c) then the graph of the function will be a plane.

Pattern: A predictable or prescribed sequence of numbers, objects, etc. Patterns and relationships may be described or presented using multiple representations such as manipulatives, tables, graphics (pictures or drawings), or algebraic rules (functions).

Quadrant:Any of the four areas into which a plane is divided by the reference axes in a Cartesian coordinate system, designated first, second, third, and fourth, counting counterclockwise from the area in which both coordinates are positive.

Relation: A relation from A to B is any subset of the cross product (Cartesian product) of A and B.

Representations: Physical objects, drawings, charts, words, graphs, and symbols that help students communicate their thinking.

Rule: A general statement written in numbers, symbols, or words that describes how to determine any term in a pattern or relationship. Rules or generalizations may include both recursive and explicit notation. In the recursive form of pattern generalization, the rule focuses on the rate of change from one element to the next. Example: Next = Now + 2; Next = Now x 4. In the explicit form of pattern generalization, the formula or rule is related to the order of the terms in the sequence and focuses on the relationship between the independent variable and the dependent variable. For example: y=5t - 3 Words may also be used to write a rule in recursive or explicit notation. Example: to find the total fee, multiply the total time with 3; take the previous number and add two to get the next number.

Set: A set is a finite or infinite collection of distinct objects in which order has no significance.

Table: A data display that organizes information about a topic into categories using rows and columns.

Function: A relation in which each value of x is paired with a unique value of y. More formally, a function from A to B is a relation f such that every aA is uniquely associated with an object F(a)B.

Course: 1205020 M/J Mathematics 1 ADVANCEDSTANDARDS (31)

UNIT 3: Third and Fourth Nine Weeks

Geometry and Measurement (MA.6.G.4 & MA.7.G.2)

This is an outline of the unit and is subject to revision as school events or directives require.

Data Analysis will be taught using bell-ringers and small projects/activities throughout the year.

MA.6.G.4 Geometry and Measurement /

Textbook Sections/Pages

MA.6.G.4.1(Moderate): Understand the concept of Pi, know common estimates ofPi (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles. /

Ch. 9

MA.6.G.4.2(Moderate): Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies. /

Ch.9

MA.6.G.4.3(Moderate): Determine a missing dimension of a plane figure or prism given its area or volume and some of the dimensions, or determine the area or volume given the dimensions. /

Ch. 9

Enrichment: project based applications of previously learned concepts

ADVANCED TOPICS

MA.7.G.2 Big Idea 2 Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes. / Ch. 10
MA.7.G.2.1 (Moderate): Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. / Ch. 10
MA.7.G.2.2 (Moderate): Use formulas to find surface areas and volume of three-dimensional composite shapes. / Ch. 10
MA.7.G.4 Geometry and Measurement
MA.7.G.4.3(Low): Identify and plot ordered pairs in all four quadrants of the coordinate plane. / Ch. 11-1

Enrichment: project based applications of previously learned concepts

VOCABULARY

Area: The number of square units needed to cover a surface.

Circumference: The distance around a circle.

Cone: A pyramid with a circular base.

Cylinder: A three dimensional figure with two parallel congruent circular bases and a lateral surface that connects the boundaries of the bases. More general definitions of cylinder may not require circular bases.

Diameter: A line segment from any point on the circle (or sphere) passing through the center to another point on the circle (or sphere).

Dimension: The number of coordinates used to express a position.

Depth: The depth of a box is the horizontal distance from front to back.

Height: A line segment extending from the vertex or apex of a figure to its base and forming a right angle with the base or plane that contains the base.

Length: A one-dimensional measure that is the measurable property of line segments.

Line: A collection of an infinite number of points in a straight pathway with unlimited length and having no width.

Ordered pair: The location of a single point on a rectangular coordinate system where the first and second values represent the position relative to the x-axis and y-axis, respectively.

Parallelogram: A quadrilateral in which both pairs of opposite sides are parallel.

Perimeter: The distance around a two dimensional figure.

Plane figure: A two-dimensional figure that lies entirely within a single plane.

Plot: To locate a point by means of coordinates, or a curve by plotted points, or to represent an equation by means of a curve so constructed.

Point: A specific location in space that has no discernible length or width.

Prism: A polyhedron that has two congruent and parallel faces joined by faces that are parallelograms.

Pyramid: A three-dimensional figure whose base is a polygon and whose faces are triangles with a common vertex.

Rectangular prism: A six-sided polyhedron with congruent rectangular parallel bases, joined by faces that are parallelograms.

Side: The edge of a polygon (e.g., a triangle has three sides), the face of a polyhedron, or one of the rays that make up an angle.

Square: A rectangle with four congruent sides; also, a rhombus with four right angles.

Two-dimensional figure: A figure having length and width.

Circle: A closed plane figure with all points of the figure the same distance from the center. The equation for a circle with center (h, k) and radius r is: (x - h)2 + (y - k)2 = r2

Pi: The symbol designating the ratio of the circumference of a circle to its diameter. It is an irrational number with common approximations of either 3.14 of 22/7.

Volume: A measure of the amount of space an object takes up; also the loudness of a sound or signal.

Weight: The force with which a body is attracted to Earth or another celestial body, equal to the product of the mass of the object and the acceleration of gravity.

Course: 1205020 M/J Mathematics 1 ADVANCEDSTANDARDS (31)

Unit 4: Fourth Nine Weeks

Ratios, Rates, and Proportionality (MA.7.A.3)

Mathematical Expressions and Equations (MA.7.A.1)

Data Analysis will be taught using bellringers and small projects/activities throughout the year.

ADVANCED TOPICS

MA.7.A.3 BIG IDEA 3: Develop an understanding of operations on all rational numbers and solving linear equations.
MA.7.A.3.1(Moderate): Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers. / Ch. 11-1B
MA.7.A.3.2(Moderate): Add, subtract, multiply, and divide integers, fractions, and terminating decimals, and perform exponential operations with rational bases and whole number exponents including solving problems in everyday contexts. / Ch. 11-2, 11-3
MA.7.A.3.3(Moderate): Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients. / Ch. 11-2, 11-3
MA.7.A.3.4(Moderate): Use the properties of equality to represent an equation in a different way and to show that two equations areequivalent in a given context. / Ch. 12-3C
MA.7.A.1 BIG IDEA 1 Develop an understanding of and apply proportionality, including similarity.
MA.7.A.1.2(High): Solve percent problems, including problems involving discounts, simple interest, taxes, tips, and percents of increase or decrease. / Ch. 5

VOCABULARY

Absolute value: A number's distance form zero on a number line. Distance is expressed as a positive value.

Coefficient: The number that multiplies the variable(s) in an algebraic expression (e.g., 4xy). If no number is specified, the coefficient is 1.

Discount: An amount that is subtracted from the regular price of an item.

Distributive property: Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. [e.g., x(a + b) = ax + bx].

Equation: A mathematical sentence stating that the two expressions have the same value. Also read the definition of equality.

Expression: A mathematical phrase that contains variables, functions, numbers, and/or operations. An expression does not contain equal or inequality signs.

Linear equation: An algebraic equation in which the variable quantity or quantities are raised to the zero or first power.

Literal equations: An equation that contains more than one variable; an implicit equation; often mathematical formula.

Model: To represent a mathematical situation with manipulatives (objects), pictures, numbers or symbols.

Rate: A ratio that compares two quantities of different units.

Variable: Any symbol, usually a letter, which could represent a number. A variable might vary as in f(x)=2x+1, or a variable might be fixed as in 2x+1=5.

Ratio: The comparison of two quantities, the ratio of a and b is a:b or a to b or a/b, where b ≠ 0.

Quadrant:Any polygon with four sides, including parallelogram, rhombus, rectangle, square, trapezoid, kite.

Relation: A relation from A to B is any subset of the cross product (Cartesian product) of A and B.

Representations: Physical objects, drawings, charts, words, graphs, and symbols that help students communicate their thinking.