CMP Content and Process Goals

The following is an overview of the Connected Math Program (CMP) content and process goals for each title in grades 6-8.  Title: Prime Time    Strand: Number  Project: CMP  Grade #: 6  Unit #: 1   Content & Process Goals: learn the basics of number theory - factors, multiples, prime and composite numbers, even and odd numbers, square numbers, greatest common factors and least common multiples discover the Fundamental Theorem of Arithmetic understand why 1 is not prime link area and dimensions of rectangles with products and factors develop strategies for finding factors and multiples of whole numbers solve problems involving factors and multiples using a variety of strategies  Title: Data About us    Strand: Data Analysis  Project: CMP  Grade #: 6  Unit #: 2   Content & Process Goals: Engage in the process:posing questions, collecting data, analyzing data, and making interpretations to answer qusetions Representing data using line plots, bar graphs, stem & leaf plots, and coordinate graphs Explore concepts that realte to ways of describing data, such as the shape of a distribution, what’s typical in the data, measures of center Develop a variety of strategies using comparative representations & concepts related to describing the shape of the data. Posing questions:formulate the key questions to explore and deciding what data to collect as well as collecting it. Analyzing the data: organizing, representing, summarizing, and describing the data Interpreting results:Predicting,comparing,and identifying relationships and using the results to makedecisions about question Reading the data, reading between the data, and reading beyond the data.  Title: Shapes and Designs    Strand: Number and Geometry  Project: CMP  Grade #: 6  Unit #: 3   Content & Process Goals: discover patterns and regularities in the relations among edges and angles of basic polygons use polygonal shapes to create interesting designs and useful structures discover the triangle inequality discover that there is only one triangular shape that can be created from three given edges recognize the shapes and properties of polygons estimate the size of any angle using reference to the right angle use an angle ruler to make accurate angle measurements  Title: Bits and Pieces, Part I    Strand: Number  Project: CMP  Grade #: 6  Unit #: 4   Content & Process Goals: Continue to build understanding of fractions,decimals,& percents and the relationships among these concepts and representations Explore operations with reational numbers, use strategies to estimate sum and products Develop strategies for adding or subtraction, develop ways to model sums and differences, understanding multiplication of fractions Develop understanding of the multiplication of decimals, explore relationship between two numbers and their product understand how to use percent as an expression of frequency when a data set contains more than or fewer than 100 pieces of a data use percents to estimate or compute taxes, tips, and discounts, draw pictorial models to represent a situation look for generalized pattern, use estimation to help decisions, use a problem’s context to help reason about the problem  Title: Covering and Surrounding    Strand: Measurement  Project: CMP  Grade #: 6  Unit #: 5   Content & Process Goals: develop students' understanding of the measurement of area and perimeter develop strategies for finding area and perimeter of rectangular and non-rectangular shaper discover relationships between perimeter and area understand the relationship between the area of a rectangle and a triangle develop formulas for finding area and perimeter of standard shapes apply finding perimeter and area to problems use multiple representations of data  Title: How Likely Is It?    Strand: Data Analysis  Project: CMP  Grade #: 6  Unit #: 6   Content & Process Goals: become acquainted with probability informally through experiments understand experimental and theoretical probability understand the concept of equally likely and unequally likely determine and interpret statements of probability organize date into lists or charts as a strategy for finding theoretical probability use graphs and tallies to summarize and display data and find experimental probabilities  Title: Bits and Pieces, Part II    Strand: Number  Project: CMP  Grade #: 6  Unit #: 7   Content & Process Goals: develop meaning for computations with rational numbers develop algorithms for computations with rational numbers use strategies to quickly estimate sums and products understand when addition or subtraction is the appropriate operation to use develop ways to model sums and differences change a fraction to a decimal estimate what fraction a given decimal is near explore the relationship between two numbers and their product use an area model to represent the product of two fractions understand how to use percent as an expression of frequency represent $1.00 as 100 cents to help solve problems use percents to estimate or compute taxes, tips and discounts draw pictorial models to represent products look for and generalize patterns use estimation to help make decisions  Title: Ruins of Montarek    Strand: Geometry  Project: CMP  Grade #: 6  Unit #: 8   Content & Process Goals: develop spatial visualization skills construct , manipulate and interpret 2 and 3 dimensional representations of objects communicate spatial information understand and recognize line symmetry construct 3 dimensional objects from 2 dimensional plans use models and representations of models to solve problems  Title: Variables and Patterns    Strand: Algebra  Project: CMP  Grade #: 7  Unit #: 1   Content & Process Goals: understand that variables in a situation are those quantities that change, such as time, temperature, feelings, TV shows popularity, distance traveled, and speed. understand that patterns describe a regular or predictable change in data search for pattern of change that show relationships among the variables select an appropriate range of values for the variables, create tables graphs, and simple symbolic rules that describe pattern of change understand the relationships among forms of representation words, tables, graphs and symbolic rules use a graphing calculator for making tables and graphs to find information about a situation  Title: Stretching and Shrinking    Strand: Geometry  Project: CMP  Grade #: 7  Unit #: 2   Content & Process Goals: enlarge figures using rubber band stretchers and coordinate plotting, informally visualize similar and distorted transformations identify similar figures and compare sides and angles, recognize that lengths between similar figures change by a constant factor build larger, similar shapes from copies of basic shape, divide a shape into smaller, similar shapes recognize the relationship between similarity and equivalent fractions, learn the effect of scale factor on length and area ratios observe and visualize ratios of lengths and area, recognize that triangles and rectangles with equal corresponding sides are similar determine and use scale factors to find unknown lengths, collect examples of figures and search for patterns in the examples use the concept of similarity to solve real-world problems, draw or construct counterexamples to explore similarity transformations make connections between algebra and geometry, use geometry software to explore similarity transformations  Title: Comparing and Scaling    Strand: Number  Project: CMP  Grade #: 7  Unit #: 3   Content & Process Goals: find the difference between two quantities find the ratio of pairs of quantities estimate ratio comparisons represent data in tables and graphs identify and compute equivalent ratios decide which is the most informative comparison, difference or ratio, for two quantities or pairs of quantities develop the ability to make judgments about rounding data to estimate ratios use equivalent ratios to make more accurate and insightful comparisons apply proportional reasoning to situations in which capture-tag-recapture methods are appropriate for estimating population counts set up and solve proportions that arise in applications connect unit rates with the rule describing a situation recognize that constant growth yields a straight line graph  Title: Accentuate the Negative    Strand: Number  Project: CMP  Grade #: 7  Unit #: 4   Content & Process Goals: perform four basic operations in the integers compare integers using <,>,= graph in four quadrants identify and compute integers and their inverses develop strategies for adding, subtracting, multiplying, and dividing integers represent integers on a number line determine if one integer is greater, less than, or equal to another use integers to solve problems understand and integer and its inverse are called opposites set up a coordinate grid on a calculator and name domain, range, and scale graph linear equations on a graphing calculator and observe effect of opposite coefficients of x and adding a constant  Title: Moving Straight Ahead: Linear Relationships    Strand: Algebra  Project: CMP  Grade #: 7  Unit #: 5   Content & Process Goals: understand the concept of slope and y-intercept solve equations through graphs, symbolic expressions, tables find the equation of a line given slope and y-intercept find slope of line given two points find y-intercept develop understanding of variables and patterns recognize and represent the relationships between variables graphically, symbolically, with tables or words identify variables and determine appropriate domain and range use graphing calculators to investigate linear relationships recognize linear representations in graphs, tables, equations, and descriptions recognize linearity is associated with a constant slope (rate of change) solve a linear function, y = mx +b, using tables, graphs, and equations find slope and y-intercept from a graph, equation or table write a linear equation given slope and y-intercept find the solution of two linear equations by graphing or making tables  Title: Filling and Wrapping    Strand: Geometry  Project: CMP  Grade #: 7  Unit #: 6   Content & Process Goals: conceptualize volume as measure of filling an object, develop the concept of volumes for prisms & cylinders as stacking layers of units conceptualize surface area as a measure of wrapping an object, determine the total number of blocks in a prism is equal to the area discover and apply strategies for finding the volume and surface area of a rectangular prism will work for any prism explore the relationship of the surface areas of rectangular prisms and cylinders to the total area of a flat pattern needed to wrap a solid discover the relationship among the volumes of cylinders, cones,and spheres determine which rectangular prism has the least(greatest)surface area for a fixed volume investigate the effects of varying dimensions of rectangular prisms and cylinders on volume and surface area vice versa estimate the volume of an irregular shape by measuring the amount of water displaced by the solid understand the relationship between a cubic centimeter and a milliliter reason about problems involving the surface areas and volumes of rectangular prisms, cylinders, cones, and spheres  Title: What Do You Expect?    Strand: Data Analysis  Project: CMP  Grade #: 7  Unit #: 7   Content & Process Goals: understand basic probability concepts- experimental and theoretical understand and use theoretical probability models - counting, constructing models expected value know the definition of and difference between independent and dependent events understand the relationship between theoretical and experimental probability analyze situations involving independent and dependent events understand how to find expected values from probabilities and equivalent fractions develop strategies for analyzing probabilities - list, counting trees, area models determine expected value for a chance situation, including drawing with and without replacement use probability and expected value to make decisions  Title: Data Around Us    Strand: Number, Measurement, and Data Analysis  Project: CMP  Grade #: 7  Unit #: 8   Content & Process Goals: have an awareness of magnitude develop a sense of measurement learn the systems of numeration compare numerical information perform operations on given data choose sensible units for measuring relate unfamiliar things to things that are personally meaningful read, write and interpret large numbers that occur in real life measurements using standard, scientific and calculator notation extend the use of exponents choose sensible ways of comparing counts and measurements including differences, rates, and ratios understand the two components of a measurement, count and unit  Title: Thinking With Mathematical Models    Strand: Algebra  Project: CMP  Grade #: 8  Unit #: 1   Content & Process Goals: fit a curve to given data enter data plot points test graph models understand and correct error messages in calculator use regression features of graphing calculators build and analyze mathematical models fit a line to experimental data identify the variables of interest in a situation conduct experiments to gather data about how variables are related  Title: Looking for Pythagoras    Strand: Number and Geometry  Project: CMP  Grade #: 8  Unit #: 2   Content & Process Goals: find slope, area, and distance discover and use the Pythagorean Theorem learn the different number systems identify and understand irrational numbers write repeating decimals as fractions calculate the distance between two points in the plane find areas of figures drawn on a coordinate grid with whole number vertices understand square roots as lengths of sides of squares understand the Pythagorean Theorem and how it relates the areas of the squares on the sides of a right triangle use the Pythagorean Theorem to solve problems investigate rational numbers written as decimals understand slope relationships of perpendicular and parallel lines  Title: Growing, Growing, Growing...    Strand: Algebra  Project: CMP  Grade #: 8  Unit #: 3   Content & Process Goals: understand and compute exponential growth and exponential decay graph exponential relationships identify and find patterns of exponential relationships use exponents build and analyze exponential models reason with and about exponential relationships explore the significance of shapes of graphs and patterns in tables make sense of the symbols in the equation y = a(bx) explore rates of growth recognize and describe situations that can be modeled with exponential functions  Title: Frogs, Fleas, and Painted Cubes    Strand: Algebra  Project: CMP  Grade #: 8  Unit #: 4   Content & Process Goals: solve and identify quadratic equations graph quadratic relationships-parabolas on a graphing calculator find the vertex of a parabola make tables of quadratic relationships identify the line of symmetry of a parabola find the intercepts of a parabola analyze quadratic relationships by examining tables, graphs, and equations compare characteristics of tables and graphs for quadratic relationships with those for linear and exponential relationships use the above relationships to predict the characteristics of a quadratic relation understand the significance of x- and y-intercepts, maximum and minimum points, and lines of symmetry  Title: Say It With Symbols    Strand: Algebra  Project: CMP  Grade #: 8  Unit #: 5   Content & Process Goals: evaluate expressions by applying the rules of order of operations, write sentences that communicate their reasoning develop tools for manipulating symbolic expressions in ways that are both connected to and independent from tabular and graphical recognize applications of the distributive and commutative properties, recognize and interpret equivalent expressions reason about and with equivalent expressions, explain the reasoning underlying the solution of linear equations to make sense of symbolic expressions involving addition, subtraction, multiplication, division, and exponents to judge the equivalency of two or more expressions by examining the underlying reasoning and the related tables and graphs apply the properties for manipulating expressions to solving linear equations solving simple quadratic equations with some sense of basic factoring and “undoing” techniques  Title: Kaleidoscopes, Hubcaps, and Mirrors    Strand: Geometry  Project: CMP  Grade #: 8  Unit #: 6   Content & Process Goals: learn the types of symmetry- rotational, translational, reflectional create symmetric designs perform symmetry transformations combine transformations understand congruence know the algebraic properties of transformational combinations recognize symmetry in designs determine the design element that has been rotated, reflected, or translated to produce a design with symmetry create designs with reflectional, rotational, or translational symmetries look for patterns that can be used to predict attributes of designs describe rigid motions in words and with coordinate rules compose symmetry transformations make tables of combinations of symmetry transformations for geometric figures and exploring the group structure in the tables  Title: Samples and Populations    Strand: Data Analysis  Project: CMP  Grade #: 8  Unit #: 7   Content & Process Goals: create different data representations - line plot, bar graph, stem and leaf, histogram obtain samples define and find measures of center - mean, median, mode understand the concept of randomness create a survey Use the process of statistical investigation to explore problems compose and decompose graphs recognize elements of graph and interrelationships between elements and impact of these elements on presentation of information in a graph describe the shape of data in a graph, including such elements as clusters, gaps, outliers, symmetry, skew, and peaks distinguish between a population and its sample raise questions about representativeness of sample data and sources of bias use different methods to generate samples especially random samples  Title: Clever Counting    Strand: Data Analysis  Project: CMP  Grade #: 8  Unit #: 8   Content & Process Goals: find combinations and permutations compute factorials find different counting possibilities create and identify networks consider order understand and compare large numbers construct organized lists and counting trees to enumerate possibilities recognize patterns, generalizing patterns, and using patterns to make predictions recognize situations that call for multiplication or division invent and use the fundamental counting principle « © John Holly