CMP Book: Investigation Number Objective: PASS: 1.1 Describe data distributions and display in line and bar graphs

Transcription

1 Data About Us (6th Grade) (Statistics) 1.1 Describe data distributions and display in line and bar graphs , 1.3, 1.4 Analyze data using range, mode, and median Display data in tables, line plots, and bar graphs Distinguish between horizontal & vertical bar graphs , Use stem - and - leaf plots Compare two data distributions using stem - and - leaf plots, median and range , , 2.4 Explore relationships between ordered pairs on coordinate graphs and explore scaling of the 6.5.1, vertical and horizontal axes. 3.1 Find the mean of data sets e 3.2 Create distributions with designated means e 3.3 Experiment with how data changes affect measures of central tendency b

2 Bits & Pieces I (6th Grade) (Understanding Fractions, Decimals, and Percents) 1.1, 1.2, 1.3 Explore fraction concepts a, b 1.4 Compare size of fractions and reason with fractions greater than b 2.1, 2.2 Find equivalent fractions b, 5.3.1b 2.3, 2.4 Use benchmarks to estimate size of fractions and compare and order fractions b, Develop concepts of fractions greater than one d 3.1 Develop decimal concepts c 3.2, 3.3 Read, write and understand place value of fractions and decimals b 3.3, 3.4 Find decimal equivalents for fractions b, 5.2.1c, Compare and order decimals Develop the concept of percent d 4.2 Compare percents , 4.4 Develop connections between fractions, decimals and percents c, 6.2.2

3 Prime Time (6th Grade) (Factors and Multiples) 1.1, 1.2 Find the factors of numbers and classify numbers as prime or composite , 5.2.2b 1.3 Develop understanding of the relationships of factors and multiples *6.2.4, 5.2.2b 2.1 Determine whether a number is prime/composite, square/non-square, and even/odd based on *6.2.4, 5.2.2b its factor pairs. 2.2 Make conjectures about the result of operations on even and odd numbers b 2.3 Classify numbers by their characteristics b, Develop strategies for finding common multiples and use the patterns to solve problems , 5.2.2b 3.3, 3.3, 3.4 Develop strategies for finding the least common multiple and least common factor and use 6.1.1, 5.3.2c patterns in common multiples and common factors to predict occurrences and solve problems. 4.1, 4.2 Find prime factorization of numbers c, 5.2.2b 4.3 Use prime factorization to find the LCM and GCF c 5.1 Use primes, composites, factors, multiples, and square numbers to solve problems b, *6.2.4, 7.2.3b

4 Covering & Surrounding (6th grade) (Two-Dimensional Measurement) 1.1 Introduce concepts of area and perimeter 7.4.1a 1.2 Understand area and perimeter relationships 7.4.1a 1.3 Develop area and perimeter formulas 7.4.1a, b 2.1, 2.2 Understand that the perimeters of figures with a fixed area can vary 7.4.1a 2.3 Find the minimum and maximum area of a rectangle with a fixed perimeter 7.4.1a 2.4 Apply area and perimeter concepts to nonrectangular figures 7.4.1a 3.1 Develop strategies for finding the area of triangles 7.4.1a 3.2 Distinguish among base, height, and sides of triangles 7.4.1a 3.3 Explore how triangles with the same base and height can look different but have the same area 7.4.1a 3.4 Apply area and perimeter in problem situations 7.4.1a 4.1, 4.2 Develop strategies for finding area and perimeter of parallelograms 7.4.1a 4.3, 4.4 Apply techniques for finding areas and perimeters of parallelograms to problem situations 7.4.1a 5.1 Find area and perimeter of irregular shapes 7.4.1a 5.2, 5.3, 5.4 Develop formulas to find circumference and area of a circle 8.4.3a, 7.4.1a, b

5 Shapes and Designs (6th grade) (Two-Dimensional Geometry) 1.1 Sort shapes according to properties b 1.2 Introduce rotation and reflection symmetry. *6.3.3, 7.3.3b 1.3 Decide which shapes will tessellate Use right triangles to estimate angle size b 2.2 Develop angle benchmarks. NA 2.3 Measure angles Introduce precision in angle measurement. NA 2.5 Explore angles created when parallel lines are cut by a transversal , 3.2 Find angle sums of polygons. NA 3.3 Decide which regular polygons will tile b, Explore the sum of the exterior angles of a polygon. NA 4.1 Determine that the sum of the side lengths of a triangle must be longer than the third side. NA 4.2 Determine that the sum of three side lengths of a quadrilateral must be longer than the fourth NA side length. 4.3 Build quadrilaterals according to specific properties b

6 Bits and Pieces II (6th grade) (Using Fraction Operations) 1.1, 1.2 Use benchmarks to develop estimation strategies for finding fraction and decimal sums and 6.2.3, 5.3.2c apply in problem situations. 2.1, 2.2, 2.3, 2.4 Develop strategies for adding and subtracting fractions and mixed numbers c 3.1, 3.2, 3.3 Estimate products of fractions and use models to represent the product of fractions , 3.5 Develop and use the multiplication algorithm , 4.2, 4.3 Develop and use strategies for dividing fractions Develop the division algorithm

7 How Likely Is It (6th grade) (Understanding Probability) 1.1 Develop the concept of probability through experiments a, , 1.3, 1.4 Find an experimental probability where the outcomes are not equally likely a, Compare experimental and theoretical probabilities a, Observe some properties (and, or, not) of probability Use organized lists and tree diagrams to find theoretical probabilities Extend probability understanding to include "possible" and "probably." , 3.2, 3.3 Analyze probability situations , , 4.2, 4.3 Develop strategies for making probability predictions , 7.5.2

8 Bits and Pieces III (6th grade) (Using Fraction Operations) 1.1 Develop estimation strategies for finding decimal sums using the relative size of a decimal a, 5.3.1a, Develop strategies for adding and subtracting decimal numbers a, 5.2.1b, 5.3.2a 1.3 Connect strategies for addition and subtraction of decimals to addition and subtraction of fractions c 1.4 Develop the algorithms for adding and subtracting decimals a 2.1 Solve problems that require decimal multiplication and estimate the relative size of a decimal product b, Use place value to reason about decimal multiplication Develop and use estimation strategies for finding decimal products a 2.4 Develop an algorithm for multiplying decimals b 3.1 Estimate and solve problems requiring operations involving decimals a, 5.3.2a, 5.3.2b 3.2, 3.3 Develop decimal division b, 5.2.1a 3.4 Understand and predict the decimal representation of a fraction , 5.2.1b, 5.2.1c 4.1 Introduce percents and use decimal computation to compute percents c, 5.2.1d, 7.2.2c 4.2, 4.3 Solve problems involving computation with percents c 5.1, 5.2 Use percents in estimating and computing taxes, tips and discounts c, 5.3.1b 5.3 Make and interpret circle graphs representing data involving percents , 5.5.1a

9 Variables and Patterns (7th Grade) (Introducing Algebra) 1.1 Collect and organize data in a table and identify patterns and relationships in the table , Identify relationships between variables in a table of data and create a coordinate graph , Compare table and graph representations of the same data , Create a table from a coordinate graph and compare patterns of change , 6.5.1, 6.5.2, 8.1.1c 1.5 Make a table and a graph from a problem situation , Compare data sets and use patterns to make predictions , 6.5.1, , 2.3 Construct a graph and analyze data to make decisions , , 3.2 Write and solve equations to represent relationships and describe the rate of change a,b,c 3.3 Write equations to represent situations a,b,c 4.1 Make and use graphing calculator tables. N/A 4.2 Make and use graphing calculator graphs. N/A 4.3 Make and use graphing calculators to solve problems. N/A

10 Stretching and Shrinking (7th Grade) (Understanding Similarity) 1.1, 1.2 Introduce similarity and make similar figures. *7.2.2a 1.3 Compare corresponding measurements of similar figures a, b 2.1 Produce similar figures on a coordinate graph and contrast similar and non-similar figures , 7.2.2a 2.2 Understand the role multiplication plays in similarity relationships. *7.2.2a 2.3 Understand the relationships of angles, side lengths, perimeters, and areas of similar polygon *7.2.2a 3.1, 3.2, 3.3 Use scale factors to make and analyze similar shapes. *7.2.2a 4.1, 4.2 Use ratios to determine and identify similar figures 7.2.2a, b, 8.2.1c 4.3 Use ratios of corresponding sides to find missing lengths in similar figures a, b, 8.2.1c, , 5.2, 5.3 Apply knowledge of similar triangles to develop a technique for indirect measurement c, 8.4.2

11 Accentuate the Negative (7th Grade) (Integers and Rational Numbers) 1.1 Explore the use of positive and negative numbers a 1.2 Compare and order positive and negative numbers a, 8.2.1a 1.3, 1.4 Use the number line and chips to develop addition and subtraction concepts with integers a, 7.2.1b 2.1, 2.2, 2.3, 2.4 Develop algorithms for adding and subtracting integers b 2.5 Graph positive and negative integers in all four quadrants a 3.1, 3.2, 3.3, 3.4 Multiply and divide integers b 4.1 Use the order of operations in computation b 4.2, 4.3 Develop and use the distributive property of multiplication over addition and subtraction , 7.2.1b

12 Filling and Wrapping (7th Grade) (Three Dimensional Measurement) 1.1, 1.2, 1.3, 1.4 Use nets to visualize, sketch, and calculate surface are of rectangular prisms , Connect the dimensions of a rectangular prism to its volume and surface area , Predict least surface area of rectangular prisms with common volumes Develop a formula for finding volume of a rectangular prism , 8.4.3a 3.1 Develop understanding of volume and surface area , Develop a strategy for finding the volume of a cylinder Develop a strategy for finding the surface area of a cylinder Apply understanding of volume to solve problems , , 4.2, 4.3 Explore volume relationships between cylinders, spheres and cones , Understand how changes in dimensions affect the volume of a prism. *7.2.2a, , 5.3 Understand the effect on surface area and volume of applying a scale factor to a rectangular prism. *7.2.2a

13 What Do You Expect? (7th grade) (Probability and Expected Value) 1.1 Review basic probability concepts , 5.5.2a 1.2, 1.3 Use probability to predict outcomes , 2.2, 2.3 Use an area model to analyze probability of two-stage outcomes , , 3.2, 3.3 Determine the expected value in a probability situation and use probability to make decisions7.5.1, , 4.2, 4.3 Analyze binomial situations , 7.5.2

14 Moving Straight Ahead (7th grade) (Linear Relationships) 1.1, 1.2 Explore patterns of change between independent and dependent variables for linear relationships. Alg I, 2.1c 1.3 Use tables and graphs to model problems of linear relationships. Alg I, 2.1b, 2.1d 2.1, 2.2 Solve problems using a table or graph. Alg I, Standard 2 2.3, 2.4 Connect tables, graphs, and equations. Alg I, Standard 2 3.1, 3.2, 3.3, 3.4 Solve linear equations using tables, graphs, and properties of equality. Alg I, 2.2a 3.5 Solve systems of equations by graphing Alg I, Introduce concept of slope c 4.2 Find and interpret the slope of a line from a table, graph, or equation. Alg I, 2.2cI 4.3 Explore patterns of slope in parallel and perpendicular lines. Alg I, 2.2cII 4.4 Write an equation for a situation when given two data points. Alg I, 2.2d

15 Comparing and Scaling (7th grade) (Ratio, Probortion, and Percent) 1.1, 1.2 Explore strategies for comparison of information *7.2.2a 1.3 Analyze and create comparison statements. *7.2.2a 2.1, 2.2, 2.3 Find equivalent ratios and compare ratios to solve problems b 3.1, 3.2, 3.3, 3.4 Connect the concept of unit rate to ratios and linear relationships b 4.1, 4.2, 4.3 Set up, solve, and apply proportions b, 8.4.2

16 Data Distributions (7th grade) (Describing Variability and Comparing Groups) 1.1 Recognize and describe the variability that occurs in data sets Interpret tables of data as related to percents and to making bar graphs , , 1.4 Use line plots and bar graphs to display data distributions and decide if a difference among data value matters , 2.2 Analyze data, recognize the variability that occurs, and make sense of the mean , 8.5.2a 2.3 Analyze data, recognize variability, and decide when to use the mean, median, or mode a 2.4 Analyze data, recognize variability, and understand how changes in data affect the mean or median b, 8.5.2a, , 3.2, 3.3, 3.4 Display and analyze data distributions, recognizing the importance of using the scales on graphs to compare data and decide when to use the mean or the median to describe a data distribution , 8.5.1, 8.5.2b, 8.5.2a 4.1, 4.2 Develop strategies for comparing unequal size data sets

17 Frogs, Fleas, and Painted Cubes (8th Grade) (Quadratic Relationships) This entire book correlates to Algebra I PASS - It is not appropriate for 8th grade PASS.

18 Kaleidoscopes, Hubcaps, and Mirrors (8th grade) (Symmetry and Transformations) 1.1, 1.2, 1.3, 1.4 Describe reflection, rotation, and translation symmetry b 2.1 Identify and perform line reflections. *6.3.3, 7.3.3b 2.2 Use properties of rotations to find the rotation image of a figure. *6.3.3, 7.3.3b 2.3 Examine and describe translation symmetries of a figure. *6.3.3, 7.3.3b 2.4 Give precise mathematical directions for performing reflections, rotations, and translations. *6.3.3, 7.3.3b 3.1, 3.2 Connect the concept of symmetry transformations to congruency and match corresponding 6.3.2, *6.3.3 parts of congruent figures. 3.3., 3.4 Use corresponding sides and angles of triangles to infer congruency. NA 4.1 Use triangle congruency conditions to deduce unknown side & angle lengths in figures. NA 4.2 Apply transformational geometry to shapes in the real world. * , 5.2, 5.3, 5.4 Specify coordinate rules for reflections, translations, and rotations in the direction of the *6.3.3, 7.3.3b x-axis, the y-axis, and the line y = x.

19 Looking for Pythagoras (8th grade) (The Pythagorean Theorem) 1.1 Explore distances on a coordinate grid. 7.3a 1.2 Review properties of quadrilaterals and draw shapes on a coordinate grid. NA 1.3 Find areas of irregular figures on a grid a 2.1 Draw squares on dot grids and find their area a 2.2 Introduce concept of square root b 2.3 Use square roots to find lengths c 3.1, 3.2, 3.3, 3.4 Develop and use the Pythagorean Theorem Estimate square roots and lengths of hypotenuses of right triangles c 4.2 Estimate lengths of hypotenuses of right triangles and apply the Pythagorean Theorem in problem situations. 4.3 Investigate properties of a triangle. NA 4.4 Use special right triangles to solve problems. NA

20 Growing, Growing, Growing (8th grade) (Exponential Relationships) 1.1 Introduce exponential growth and identify exponential patterns a 1.2, 1.3 Write an equation for an exponential relationship and solve problems involving exponential growth a, 8.2.2a 1.4 Compare and contrast exponential and linear growth. NA (Algebra I) 2.1, 2.2, 2.3 Solve problems involving exponents and exponential growth. NA (Algebra I) 3.1, 3.2, 3.3 Determine and connect growth rate and growth factors. NA 4.1, 4.2, 4.3 Analyze and solve problems involving exponents and exponential decay. NA 5.1 Use patterns in powers to estimate the ones digit for unknown powers a 5.2 Develop the rules for operating with exponents a 5.3 Explore exponential equations using a graphing calculator. NA

21 Thinking With Mathematical Models (8th grade) (Linear and Inverse Variation) 1.1, 1.2 Make tables and graphs to represent data, describe relationships between variables, and use Alg I, 2.1b,c,d data patterns to make predictions. 1.3 Distinguish between linear and non-linear relationships. Alg I, 2.1a 2.1 Fit a line to linear data and write an equation for the line. Alg I, Write linear equations. Alg I, 2.2d 2.3 Solve linear equations and write inequalities Alg I, 2.2a, 8.1.2a, 8.1.1a 2.4 Use equations to represent and interpret problem situations. Alg I, 2.2e 3.1, 3.2, 3.3 Explore situations that can be modeled by inverse variation relationships. Alg I, 1.1b, 8.4.3aI

22 Say It With Symbols (8th grade) (Making Sense of Symbols) 1.1, 1.2 Determine if two or more expressions are equivalent Interpret expressions in a given context. Alg I, 1.1a 1.4 Write equivalent expressions using the distributive property Use variables to write expressions and equations and interpret equivalent expressions. Alg I, 1.1a, 8.1.1a 2.2, 2.3 Rewrite algebraic expressions , 3.2 Develop strategies for solving equations involving distribution , Factor quadratic expressions Alg I 3.4 Solve quadratic equations by factoring. Alg I 4.1 Interpret rate of change Alg I 4.2, 4.3 Use patterns of change to write relationships and determine whether relationships are linear, exponential or quadratic. Alg. I 5.1, 5.2, 5.3 Translate verbal statements into algebraic statements and write conjectures about numbers. Alg. I

23 The Shapes of Algebra (8th grade) (Linear Systems and Inequalities) 1.1 Find equations describing coordinates for points on circles centered at the origin Alg I 1.2 Use slopes of parallel and perpendicular lines to reason about parallelograms and rectangles on coordinate grids. Alg I 1.3 Find midpoints Alg I 2.1 Use graphs to solve systems of linear equations and inequalities. Alg I, 8.1.2a, 8.1.2b 2.2, 2.3 Solve linear inequalities Alg I, 8.1.2a, 8.1.2b 3.1, 3.2 Introduce linear equations in two variables in standard form. Alg I 3.3 Solve systems of linear equations by graphing. Alg I 4.1, 4.2, 4.3,4.4 Solve systems of equations. Alg I 5.1, 5.2, 5.3 Solve linear inequalities in two variables Alg I 5.4 Solve systems of linear inequalities. Alg. I Samples and Populations (8th grade) (Data and Statistics)

24 Samples and Populations (8th grade) (Data and Statistics) 1.1, , 1.4 Compare distributions using measures of center (mean, median), measures of variability (range, percentiles), and data displays that group data (histograms, box-and-whisker plots) , *8.5.3, 8.5.2a 2.1 Distinguish between a sample and a population and use samples to make predictions about a population. * , 2.3, 2.4 Plan, select, compare, and describe random samples to estimate a characteristic of a population. *8.5.3, 7.5.1, 8.5.2a 3.1 Distinguish between samples and populations and use samples to draw conclusions about populations. *8.5.3, Apply probability concepts to select random samples , * , 4.2, 4.3 Explore relationships between paired values of numerical attributes. Alg I