#### 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.

4.1.6 A: Number Sense

4.1.6 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).

4.1.6 A.1.a: All integers

4.1.6 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

4.1.6 A.1.c: All decimals

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

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

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

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

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

4.1.6 A.7.b: Common multiples, common factors

4.1.6 A.8: Compare and order numbers.

4.1.6 B: Numerical Operations

4.1.6 B.1: Recognize the appropriate use of each arithmetic operation in problem situations.

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

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

4.1.6 B.2.b: Mental math

4.1.6 B.2.c: Calculator

4.1.6 B.3: Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.

4.1.6 B.5: Find squares and cubes of whole numbers.

4.1.6 B.6: Check the reasonableness of results of computations.

4.1.6 B.7: Understand and use the various relationships among operations and properties of operations.

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

4.1.6 C: Estimation

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

4.1.6 C.2: Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

4.1.6 C.3: Determine the reasonableness of an answer by estimating the result of operations.

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

4.2.6 A: Geometric Properties

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

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

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

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

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

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

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

4.2.6 A.3: Identify similar figures.

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

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

4.2.6 A.6: Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives.

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

4.2.6 B: Transforming Shapes

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

4.2.6 C: Coordinate Geometry

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

4.2.6 D: Units of Measurement

4.2.6 D.1: Select and use appropriate units to measure angles, area, surface area, and volume.

4.2.6 D.2: Use a scale to find a distance on a map or a length on a scale drawing.

4.2.6 D.3: Convert measurement units within a system (e.g., 3 feet = ___ inches).

4.2.6 D.4: Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).

4.2.6 E: Measuring Geometric Objects

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

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

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

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

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

4.2.6 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.

4.3.6 A: Patterns

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

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

4.3.6 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)

4.3.6 B: Functions and Relationships

4.3.6 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).

4.3.6 C: Modeling

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

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

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

4.3.6 D: Procedures

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

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

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

4.3.6 D.2: Understand and apply the properties of operations and numbers.

4.3.6 D.2.a: Distributive property

4.3.6 D.3: Evaluate numerical expressions.

#### 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.

4.4.6 A: Data Analysis

4.4.6 A.1: Collect, generate, organize, and display data.

4.4.6 A.1.a: Data generated from surveys

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

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

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

4.4.6 B: Probability

4.4.6 B.1: Determine probabilities of events.

4.4.6 B.1.b: Multiplication rule for probabilities

4.4.6 B.1.c: Probability of certain event is 1 and of impossible event is 0

4.4.6 B.1.d: Probabilities of event and complementary event add up to 1

4.4.6 B.2: Determine probability using intuitive, experimental, and theoretical methods (e.g., using model of picking items of different colors from a bag).

4.4.6 B.2.a: Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked

4.4.6 B.2.b: Given data obtained experimentally, what is the likely distribution of items in the bag

4.4.6 B.3: Explore compound events.

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

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

4.4.6 C: Discrete Mathematics-Systematic Listing and Counting

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

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

4.4.6 C.1.b: Venn diagrams

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

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

4.4.6 C.2.c: Number of ways of selecting a slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21)

4.4.6 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: 5/18/2018

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