#### 4.1: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

4.1.A: Number Sense

4.1.A.1: Use real-life experiences, physical materials, and technology to construct meanings for numbers (unless otherwise noted, all indicators for grade 6 pertain to these sets of numbers as well).

4.1.A.1.b: All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers

4.1.A.4: Explore the use of ratios and proportions in a variety of situations.

4.1.A.5: Understand and use whole-number percents between 1 and 100 in a variety of situations.

4.1.A.6: Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.

4.1.A.7: Develop and apply number theory concepts in problem solving situations.

4.1.A.7.a: Primes, factors, multiples

4.1.A.8: Compare and order numbers.

4.1.B: Numerical Operations

4.1.B.2: Construct, use, and explain procedures for performing calculations with fractions and decimals with:

4.1.B.2.a: Pencil-and-paper

4.1.B.2.b: Mental math

4.1.B.8: Understand and apply the standard algebraic order of operations for the four basic operations, including appropriate use of parentheses.

4.1.C: Estimation

4.1.C.1: Use a variety of strategies for estimating both quantities and the results of computations.

#### 4.2: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

4.2.A: Geometric Properties

4.2.A.1: Understand and apply concepts involving lines and angles.

4.2.A.1.b: Properties of parallel, perpendicular, and intersecting lines

4.2.A.1.c: Sum of the measures of the interior angles of a triangle is 180°

4.2.A.2: Identify, describe, compare, and classify polygons and circles.

4.2.A.2.a: Triangles by angles and sides

4.2.A.2.b: Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi

4.2.A.2.c: Polygons by number of sides.

4.2.A.2.d: Equilateral, equiangular, regular

4.2.A.2.e: All points equidistant from a given point form a circle

4.2.A.4: Understand and apply the concepts of congruence and symmetry (line and rotational).

4.2.A.5: Compare properties of cylinders, prisms, cones, pyramids, and spheres.

4.2.A.7: Identify a three-dimensional shape with given projections (top, front and side views).

4.2.A.8: Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape).

4.2.B: Transforming Shapes

4.2.B.1: Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.

4.2.B.2: Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.

4.2.C: Coordinate Geometry

4.2.C.1: Create geometric shapes with specified properties in the first quadrant on a coordinate grid.

4.2.E: Measuring Geometric Objects

4.2.E.2: Develop and apply strategies and formulas for finding perimeter and area.

4.2.E.2.a: Triangle, square, rectangle, parallelogram, and trapezoid

4.2.E.2.b: Circumference and area of a circle

4.2.E.3: Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders.

4.2.E.4: Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa.

4.2.E.5: Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).

#### 4.3: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

4.3.A: Patterns

4.3.A.1: Recognize, describe, extend, and create patterns involving whole numbers and rational numbers.

4.3.A.1.a: Descriptions using tables, verbal rules, simple equations, and graphs

4.3.A.1.b: Formal iterative formulas (e.g., NEXT = NOW * 3)

4.3.A.1.c: Recursive patterns, including Pascal’s Triangle (where each entry is the sum of the entries above it) and the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, . . . (where NEXT = NOW + PREVIOUS)

4.3.B: Functions and Relationships

4.3.B.1: Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).

4.3.C: Modeling

4.3.C.1: Use patterns, relations, and linear functions to model situations.

4.3.C.1.a: Using variables to represent unknown quantities

4.3.C.1.b: Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities

4.3.C.2: Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.

4.3.C.2.a: Changes over time

4.3.C.2.b: Relations between quantities

4.3.C.2.c: Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

4.3.D: Procedures

4.3.D.1: Solve simple linear equations with manipulatives and informally.

4.3.D.1.a: Whole-number coefficients only, answers also whole numbers

4.3.D.1.b: Variables on one or both sides of equation

#### 4.4: All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

4.4.A: Data Analysis

4.4.A.2: Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.

4.4.A.2.a: Bar graph, line graph, circle graph, table, histogram

4.4.A.2.b: Range, median, and mean

4.4.B: Probability

4.4.B.3: Explore compound events.

4.4.B.4: Model situations involving probability using simulations (with spinners, dice) and theoretical models.

4.4.B.5: Recognize and understand the connections among the concepts of independent outcomes, picking at random, and fairness.

4.4.C: Discrete Mathematics-Systematic Listing and Counting

4.4.C.1: Solve counting problems and justify that all possibilities have been enumerated without duplication.

4.4.C.1.a: Organized lists, charts, tree diagrams, tables

4.4.C.2: Apply the multiplication principle of counting.

4.4.C.2.b: Number of ways a specified number of items can be arranged in order (concept of permutation)

4.4.C.3: List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person’s hand once).

Correlation last revised: 11/13/2008

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