3rd Grade Mathematics MISSOURI LEARNING STANDARDS: GRADE-LEVEL EXPECTATIONS DLM ESSENTIAL ELEMENTS DLM LINKAGE LEVELS CODE Expectation Code Essential Element 3: Essential Elements Use place value understanding and properties of operations to perform multi-digit arithmetic. Understand place value. 3.NBT.A.1 Round whole numbers to the nearest 10 or 100. EE.3.NBT.1 Use decade numbers (10, 20, 30) as benchmarks to demonstrate understanding of place value for numbers 0-30. This essential element is not currently being assessed. 3.NBT.A.2 Read, write, and identify whole numbers within 100,000 using base ten numerals, number names, and expanded forms. Not applicable. Not applicable. Not applicable. 3.NBT.A.3 Demonstrate fluency with addition and subtraction within 1000. EE.3.NBT.2 Demonstrate understanding of place value to tens. Initial Precursor: Recognize separateness. Recognize set. Distal Precursor: Explain ten as a composition of ten ones. Proximal Precursor: Recognize multiple tens and something. Compose numbers based on tens. Target: Explain place value for tens and ones. Successor: Explain the relationship between rounding and place value. Explain place value for hundreds. 3.NBT.A.4 Multiply whole numbers by multiples of 10 in the range 10-90. EE.3.NBT.3 Count by tens using models such as objects, base ten blocks, or money. Initial Precursor: Recognize before. Recognize after. Distal Precursor: Explain number sequence pattern.
4.RA.B.2 Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. Generate and analyze patterns. Generate and analyze patterns. 4.RA.C.1 Generate a number pattern that follows a given rule. EE.4.OA.5 Use repeating patterns to make predictions. Initial Precursor: Recognize attribute values. Arrange objects in pairs. Distal Precursor: Recognize patterns. Proximal Precursor: Recognize symbolic patterns. Recognize repeating patterns. Recognize pictorial patterns. Target: Recognize the core unit in a repeated pattern. Successor: Extend a pictorial pattern by applying the rule. Extend a symbolic pattern by applying the rule. 4.RA.C.2 Use words or mathematical symbols to express a rule for a given pattern. Classify 2-dimensional shapes by properties of their lines and angles. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.GM.A.1 Draw and identify points, lines, line segments, rays, angles, perpendicular lines, and parallel lines. EE.4.G.1 Recognize parallel lines and intersecting lines. Initial Precursor: Recognize attribute values. Distal Precursor: Recognize point. Proximal Precursor: Recognize line. Recognize line segment. Target: Recognize intersecting lines/line segments. Recognize parallel lines/line segments. Successor:
Multiply and divide rational numbers. EE.7.NS.2.a Solve multiplication problems with products to 100. Initial Precursor: Recognize separateness. Recognize set. Distal Precursor: Solve repeated addition problems. Represent repeated addition with an equation. Explain repeated addition. Proximal Precursor: Demonstrate the concept of multiplication. Target: Multiply by 1, 2, 3, 4, 5, 6, 7, 8, 9, and/or 10. Successor: Divide by 1, 2, 3, 4, 5, 6, 7, 8, 9, and/or 10. Apply the relationship between multiplication and division. Determine that a number and its reciprocal have a product of 1 (multiplicative inverse). Understand that every quotient of integers (with divisor) is a rational number. EE.7.NS.2.b Solve division problems with divisors up to five and also with a divisor of 10 without remainders. Initial Precursor: Recognize subset. Recognize set. Recognize separateness. Distal Precursor: Solve repeated subtraction problems. Represent repeated subtraction with an equation. Explain repeated subtraction. Proximal Precursor: Demonstrate the concept of division. Target: Divide by 1, 2, 3, 4, 5, and/or 10. Successor: Explain the relationship between multiplication and division. Convert a rational number to a decimal. Understand that all rational numbers can be written as EE.7.NS.2.c-d Express a fraction with a denominator of 10 as a zero
and reproducing the drawing at a different scale. Recognize same. Recognize different. Proximal Precursor: Match the same two-dimensional shape with same size and same orientation. the same three-dimensional shapes with same size and same orientation. Target: Match the same two-dimensional shape with different sizes and same orientation. Match the same three-dimensional shapes with different size and same orientation. Successor: Match the same two-dimensional shapes with different size and different orientation. Match the same three-dimensional shapes with different size and different orientation. 7.GM.A.2 Use a variety of tools to construct geometric shapes. Determine if provided constraints will create a unique triangle through construction. Construct special quadrilaterals given specific parameters. EE.7.G.2 Recognize geometric shapes with given conditions. Initial Precursor: Recognize same. Recognize different. Distal Precursor: Recognize squares. Recognize circles. Recognize triangles. Recognize rectangles. Recognize cubes. Recognize cones. Recognize cylinders. Recognize spheres. Proximal Precursor: Describe attributes of shapes. Target: Recognize shapes with specified attributes.
Successor: Classify shapes with specified attributes. 7.GM.A.3 Describe two-dimensional cross sections of pyramids, prisms, cones, and cylinders. EE.7.G.3 a two-dimensional shape with a three-dimensional shape that shares an attribute. This essential element is not currently being assessed. 7.GM.A.4 Understand concepts of circles. Analyze the relationships among the circumference, the radius, the diameter, the area and Pi in a circle. Know and the formulas for circumference and area of circles to solve problems. EE.7.G.4 Determine the perimeter of a rectangle by adding the measures of the sides. Initial Precursor: Recognize attribute values. Distal Precursor: Describe measurable attributes. Recognize measurable attributes. Proximal Precursor: Explain length. Explain perimeter. Target: Calculate the perimeter of a rectangle by counting unit lengths on a grid. Calculate perimeter by adding all the side lengths. Successor: Use coordinates to calculate perimeters of polygons. Apply and extend previous understanding of angle measure, area and volume. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.GM.B.5 Use angle properties to write and solve equations for an unknown angle. EE.7.G.5 Recognize angles that are acute, obtuse, and right. Initial Precursor: Recognize attribute values. Distal Precursor: Recognize line. Recognize point. Recognize ray. Proximal Precursor: Recognize angle. Target: Recognize obtuse angles. Recognize acute angles. Recognize right angles. Successor: Compare angles to a right angle.
expansion that terminates or repeats. Convert decimal which repeat into fractions and fractions into repeating decimals Generate equivalent representations of rational numbers. Recognize parts of a given whole or unit. Proximal Precursor: Decompose a fraction into a sum of unit fractions with the same denominator. Explain the concept of addition and subtraction of fractions. Target: Subtract fractions with common denominators. Successor: Add or subtract fractions with denominators of 10 and 100. 8.NS.A.2 Estimate the value and compare the size of irrational numbers and approximate their locations on a number line. EE.8.NS.2.a Express a fraction with a denominator of 100 as a decimal. Initial Precursor: Recognize separateness. Recognize set. Distal Precursor: Partition sets into subsets. Explain unit fraction. Proximal Precursor: Explain the decimal point. Represent a fraction with a denominator of 10 as a decimal. Target: Represent a fraction with a denominator of 100 as a decimal. Successor: Compare two decimals to the tenths using symbols. Compare two decimals to hundredths symbols. EE.8.NS.2.b Compare quantities represented as decimals in real-world examples to hundredths. Initial Precursor: Recognize separateness. Distal Precursor: Recognize one tenth in a set model. Recognize tenths in a set
intersection as the solution to the system. Explain why solution(s) to a system of two linear equations in two variables correspond to point(s) of intersection of the graphs. Explain why systems of linear equations can have one solution, no solution or infinitely many solutions. Solve systems of two linear equations. Understand congruence and similarity using physical models, transparencies, or geometry software. Understand congruence and similarity using physical models, transparencies, or geometry software. 8.GM.A.1 Verify experimentally the congruence properties of rigid transformations. Verify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations. Investigate if orientation is preserved under rigid transformations. EE.8.G.1 Recognize translations, rotations, and reflections of shapes. Initial Precursor: Recognize attribute values. Distal Precursor: Recognize the defining attributes of a shape. Recognize the non-defining attributes of a shape. Proximal Precursor: Explain transformations. Target: Recognize translation. Recognize reflection. Recognize rotation. Successor: Explain the properties of lines and line segments in transformations. Explain the properties of angles in transformations. Explain the properties of parallel lines in transformations. 8.GM.A.2 Understand that two-dimensional figures are congruent if a series of transformations can be performed to map the pre-image of the image. EE.8.G.2 Identify shapes that are congruent. Initial Precursor: Recognize same. Recognize different. Distal Precursor:
Demonstrate the concept of multiplication. Target: Evaluate expressions with whole number exponents. Successor: Explain perfect cubes. Explain perfect squares. A1.NQ.A.2 Rewrite expressions involving radicals and rational exponents the properties of exponents (Limit to rational exponents with a numerator of 1). Not applicable. Not applicable. Not applicable. Use to solve problems. Reason quantitatively, and use units to solve problems. A1.NQ.B.1 Use units of measure as a to understand and solve problems involving quantities. Identify, label, and use appropriate units of measure within a problem. Convert and rates. Use units within problems. Choose and interpret the and the origin in graphs and data displays. EE.N-Q.1-3 Express quantities to the appropriate precision of measurement. Initial Precursor: Use perceptual subitizing. Distal Precursor: Round decimals to any place. Proximal Precursor: Solve word problems involving multiplication with rational numbers. Solve word problems involving subtraction with rational numbers. Solve word problems involving addition with rational numbers. Target: Express numerical answers with a degree of precision appropriate for the problem context. Successor: Solve multi-step problems with rational numbers. A1.NQ.B.2 Define and use appropriate quantities for representing a given context or problem. A1.NQ.B.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Interpret and use structure. Interpret the structure of expressions.
Recognize direction of covariation. Describe rate of change in a graph. Target: Analyze linear function graphs. Interpret a point on the graph of a linear function. Successor: real-world problems by interpreting linear function graphs. Perform operations on polynomials. Perform arithmetic operations on polynomials. A1.APR.A.1 Add, subtract, and multiply polynomials, and understand that polynomials follow the same general of arithmetic and are closed under these operations. Not applicable. Not applicable. Not applicable. A1.APR.A.2 Divide polynomials by monomials. Not applicable. Not applicable. Not applicable. Understand the concept of a function and use function notation. Understand the concept of a function and use function notation. A1.IF.A.1 Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range. Represent a function using function notation. Understand that the graph of a function labeled f is the set of all ordered pairs (x,y) that satisfy the equation y = f(x) EE.F-IF.1-3 Use the concept of function to solve problems. Initial Precursor: Order objects. Arrange objects in pairs. Distal Precursor: Explain x-coordinate. Explain y-coordinate. Explain coordinate pairs (ordered pairs). Proximal Precursor: Describe the rate of change in a table. Describe rate of change in a graph. Target: Solve real-world problems by interpreting linear function graphs. real-world problems by interpreting linear function tables. Successor: Use graphs to read beyond the data. Use tables to predict function values. A1.IF.A.2 Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
variables are related; determine and use a function that models the relationship. Construct a linear function to bivariate data represented on a scatter plot that minimizes residuals. Construct an exponential function to model bivariate data represented on a scatter plot that minimizes residuals. A1.DS.A.6 Interpret the slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data. Not applicable. Not applicable. Not applicable. A1.DS.A.7 Determine and interpret the correlation coefficient for a linear association. Not applicable. Not applicable. Not applicable. A1.DS.A.8 Distinguish between correlation and causation. Not applicable. Not applicable. Not applicable. Geometry
symmetry of figures. G.CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Given a geometric figure and a rotation, reflection, or translation of that figure, identify the components of the two figures that are congruent. Initial Precursor: Recognize same. Recognize different. Distal Precursor: Match the same three-dimensional shapes with same size and different orientation. Match the same two-dimensional shape with the same sizes and different orientations. Proximal Precursor: Recognize translation. Recognize rotation. Recognize reflection. Recognize congruent figures. Target: Explain the relationship between congruent figures and transformation. Successor: Use a sequence of transformations to describe congruence of 2 given figures. G.CO.A.5 Demonstrate the ability to rotate, reflect, or translate a figure, and determine a possible sequence of transformations between two congruent figures. Understand congruence in terms of rigid motions. Understand congruence in terms of rigid motions. G.CO.B.6 Develop the definition of congruence in terms of rigid motions. Identify corresponding congruent and similar of shapes. Initial Precursor: Recognize same. Recognize different. Distal Precursor: Match the same two-dimensional shape with different sizes and same orientation. Match the same two-dimensional shape with same size and same orientation. G.CO.B.7 Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.
Match the same three-dimensional shape with same size and same orientation. Proximal Precursor: Recognize congruent figures. Recognize similar figures. Target: Explain congruent figures. Explain similar figures. Successor: Explain the relationship between congruent figures and transformation. Explain the relationship between similar figures and transformation. Prove geometric theorems. Prove geometric theorems. G.CO.C.8 Prove theorems about lines and angles. Not applicable. Not applicable. Not applicable. G.CO.C.9 Prove theorems about triangles. Not applicable. Not applicable. Not applicable. G.CO.C.10 Prove theorems about polygons. Not applicable. Not applicable. Not applicable. Make geometric constructions. Make geometric constructions. G.CO.D.11 Construct geometric figures using various tools and methods. Not applicable. Not applicable. Not applicable. Understand similarity in terms of similarity transformations. Understand similarity in terms of similarity transformations. G.SRT.A.1 Construct and analyze scale changes of geometric figures. Not applicable. Not applicable. Not applicable. G.SRT.A.2 Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures. Not applicable. Not applicable. Not applicable. G.SRT.A.3 Use the properties of similarity transformations to Not applicable. Not applicable. Not applicable.
establish the AA criterion for two triangles to be similar. Prove theorems involving similarity Prove theorems involving similarity G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Not applicable. Not applicable. Not applicable. Define trigonometric ratios, and problems involving right triangles. Define trigonometric ratios, and solve problems involving right triangles. G.SRT.C.6 Understand that side ratios in right triangles define the trigonometric ratios for acute angles. Not applicable. Not applicable. Not applicable. G.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. Not applicable. Not applicable. Not applicable. G.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles. Not applicable. Not applicable. Not applicable. G.SRT.C.9 Derive the formula A=1/2ab sin (c) for the area of a triangle. Not applicable. Not applicable. Not applicable. Understand and apply theorems about circles. Understand and theorems about circles. G.C.A.1 Prove that all circles are similar using similarity transformations. Not applicable. Not applicable. Not applicable. G.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords of circles. Not applicable. Not applicable. Not applicable. G.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove Not applicable. Not applicable. Not applicable.
Apply geometric concepts in modeling situations. geometric concepts in modeling situations. G.MG.A.1 Use geometric shapes, their measures and their properties to describe objects. Use properties of geometric shapes to describe real-life objects. Initial Precursor: Recognize same. Recognize different. Distal Precursor: Match the same two-dimensional shape with same size and same orientation. Match the same two-dimensional shape with different size and same orientation. Match the same three-dimensional shapes with same size and same orientation. Match the same three-dimensional shapes with same size and same orientation. Match the same three-dimensional shapes with different size and same orientation. Proximal Precursor: Recognize squares, circles, triangles, rectangles, cubes, cones, cylinders, and/or spheres. Target: Use geometric shapes to describe objects. Successor: Use geometric methods to solve design problems. G.MG.A.2 concepts of density based on area and volume in modeling situations. G.MG.A.3 Apply geometric methods to solve design mathematical modeling problems. Understand independence and conditional probability and use them to interpret data. Understand independence and conditional probability, and use them to interpret data. G.CP.A.1 Describe events as subsets of a sample using characteristics of the Identify when events are independent or dependent.
outcomes, or as unions, intersections or complements of other events. Contrast objects. Distal Precursor: Classify. Proximal Precursor: Recognize possible outcomes. Explain simple events. Recognize impossible outcomes. Target: Determine if 2 events are independent or dependent. Successor: Explain compound events. G.CP.A.2 Understand the definition of independent events and use it to solve problems. G.CP.A.3 Calculate conditional probabilities of events. G.CP.A.4 Construct and interpret frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. G.CP.A.5 Recognize and explain the concepts of conditional probability and independence in a context. G.CP.A.6 and interpret the Addition Rule for calculating probabilities. Not applicable. Not applicable. Not applicable. G.CP.A.7 Apply and interpret the general Multiplication Rule in a uniform probability model. Not applicable. Not applicable. Not applicable.
A2.NQ.B.3 Know and apply the Fundamental Theorem of Algebra. Not applicable. Not applicable. Not applicable. Define and use logarithms. Construct and compare linear, quadratic, and exponential models, and solve problems. A2.SSE.A.1 Develop the definition of logarithms based on properties of exponents. Not applicable. Not applicable. Not applicable. A2.SSE.A.2 Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations. Not applicable. Not applicable. Not applicable. A2.SSE.A.3 Use properties of logarithms to equations or find equivalent expressions. Not applicable. Not applicable. Not applicable. A2.SSE.A.4 Understand why logarithmic scales are used, and use them to solve problems. Not applicable. Not applicable. Not applicable. equations and inequalities. Create equations that describe numbers or relationships. A2.REI.A.1 Create and equations and inequalities including those that involve absolute value. Create an equation involving one operation with one variable, and use it to solve a real-world problem. Initial Precursor: Combine sets. Partition sets. Distal Precursor: Represent multiplication with equations. Represent division with equations. Represent subtraction with equations. Represent addition with equations. Proximal Precursor: Represent expressions with variables. Represent the unknown in an equation. Target: real-world problems using equations with non-negative rational numbers. Represent problems as equations. A2.REI.A.2 Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.
Successor: Solve rational equations in 1 variable. Solve general systems of equations and inequalities. Solve systems of equations. A2.REI.B.1 Create and solve systems of equations that may include non-linear equations and inequalities. Not applicable. Not applicable. Not applicable. Perform operations on polynomials and rational expressions. Understand the relationship between zeros and factors of polynomials. A2.APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients. Not applicable. Not applicable. Not applicable. A2.APR.A.2 Understand the Remainder Theorem, and use it to solve problems. Not applicable. Not applicable. Not applicable. A2.APR.A.3 Find the least common multiple of two or more polynomials. Not applicable. Not applicable. Not applicable. A2.APR.A.4 Add, subtract, multiply, and divide rational expressions. Not applicable. Not applicable. Not applicable. A2.APR.A.5 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial. Not applicable. Not applicable. Not applicable. Use and interpret functions. Interpret functions that arise in applications in terms of the context. A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to problems. EE.F-IF.4-6 Construct graphs that represent linear functions with different of change and interpret which is faster/slower, higher/lower, etc.