#### 3.2

Number and operations. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:

(A)  compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate;

(B)  describe the mathematical relationships found in the base-10 place value system through the hundred thousands place;

(C)  represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers; and

(D)  compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =.

#### 3.3

Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to:

(A)  represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines;

(B)  determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line;

(C)  explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number;

(D)  compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b;

(E)  solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8;

(F)  represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines;

(G)  explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model; and

(H)  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.

#### 3.4

Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. The student is expected to:

(A)  solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction;

(B)  round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems;

(C)  determine the value of a collection of coins and bills;

(D)  determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10;

(E)  represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting;

(F)  recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts;

(G)  use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties;

(H)  determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally;

(I)  determine if a number is even or odd using divisibility rules;

(J)  determine a quotient using the relationship between multiplication and division; and

(K)  solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.

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