symbols, words, objects, and pictorial models. Readiness Standard Compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models. Readiness Standard Compare TWO FRACTIONS HAVING THE SAME NUMERATOR OR DENOMINATOR IN PROBLEMS BY REASONING ABOUT THEIR SIZES AND JUSTIFYING THE CONCLUSION USING SYMBOLS, WORDS, OBJECTS, AND PICTORIAL MODELS Including, but not limited to: Fractions greater than zero and less than or equal to one Fraction – a number in the form where a and b are whole numbers and b is not equal to zero. A fraction can be used to name part of an object or part of a set of objects. Relationship between the whole and the part Numerator – the part of a fraction written above the fraction bar that tells the number of fractional parts specified or being considered Denominator – the part of a fraction written below the fraction bar that tells the total number of equal parts in a whole or set Whole number denominators of 2, 3, 4, 6, and 8 Comparisons of fractions are only valid when referring to the same size whole. Comparison of two fractions with the same numerator Common numerators standardize the number of pieces; therefore, compare the size of each piece (denominator). Reason about the sizes of fractions with the same numerator. Larger denominator → smaller fractional piece → smaller fraction Smaller denominator → larger fractional piece → larger fraction Comparison of two fractions with the same denominator Common denominators standardize the size of the pieces; therefore, compare the number of pieces (numerator). Reason about the sizes of fractions with the same denominator. Larger numerator → more equal-size fractional pieces → larger fraction Smaller numerator → fewer equal-size fractional pieces → smaller fraction Justification of comparison Symbols Inequality words and symbols Greater than (>) Less than (
Understanding and applying place value and properties of operations to solve problems involving addition and subtraction of whole numbers within 1,000 TxCCRS: I. Numeric Reasoning II.D. Algebraic Reasoning – Representations VIII. Problem Solving and Reasoning IX. Communication and Representation X. Connections Represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations. Readiness Standard Represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations. Readiness Standard Represent, Solve ONE- AND TWO-STEP MULTIPLICATION AND DIVISION PROBLEMS WITHIN 100 USING ARRAYS, STRIP DIAGRAMS, AND EQUATIONS Including, but not limited to: Whole numbers Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n} Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n} Multiplication Product – the total when two or more factors are multiplied Factor – a number multiplied by another number to find a product Multiplication of whole numbers within 100 Products of up to a two-digit factor by a one-digit factor Division Quotient – the size or measure of each group or the number of groups when the dividend is divided by the divisor Dividend – the number that is being divided Divisor – the number the dividend is being divided by Division of whole numbers within 100 Quotients of up to a two-digit dividend by a one-digit divisor
value Multiplicative numerical pattern – a pattern that occurs when a constant non-zero value is multiplied by an input value to determine the output value Tables (horizontal or vertical) With and without a process column Ex: Missing data that may be at the beginning, middle, or end within a table Ex: Verbal descriptions Words, numbers, and/or symbols Appropriate labels used to describe relationships of number pairs Ex: Relationships used to extend the pattern Ex: Ex: Note(s): Grade Level(s): Grade 4 will represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence. Various mathematical process standards will be applied to this student expectation as appropriate. TxRCFP: Grade Level Connections (reinforces previous learning and/or provides development for future learning) TxCCRS: II.D. Algebraic Reasoning – Representations IX. Communication and Representation Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties. The student is