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### 3.1 Number Sense, Properties, and Operations

- 3.1.1 The whole number system describes place value relationships and forms the foundation for efficient algorithms
- 3.1.1.a Use place value and properties of operations to perform multi-digit arithmetic.
- 3.1.1.a.i Use place value understanding to round whole numbers to the nearest 10 or 100.
- 3.1.1.a.ii Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- 3.1.1.a.iii Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations.

- 3.1.1.a Use place value and properties of operations to perform multi-digit arithmetic.
- 3.1.2 Parts of a whole can be modeled and represented in different ways
- 3.1.2.a Develop understanding of fractions as numbers.
- 3.1.2.a.i Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; describe a fraction a/b as the quantity formed by a parts of size 1/b.
- 3.1.2.a.ii Describe a fraction as a number on the number line; represent fractions on a number line diagram.
- 3.1.2.a.iii Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- 3.1.2.a.iii.1 Identify two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- 3.1.2.a.iii.2 Identify and generate simple equivalent fractions. Explain why the fractions are equivalent.
- 3.1.2.a.iii.3 Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
- 3.1.2.a.iii.4 Compare two fractions with the same numerator or the same denominator by reasoning about their size.
- 3.1.2.a.iii.5 Explain why comparisons are valid only when the two fractions refer to the same whole.
- 3.1.2.a.iii.6 Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

- 3.1.2.a Develop understanding of fractions as numbers.
- 3.1.3 Multiplication and division are inverse operations and can be modeled in a variety of ways
- 3.1.3.a Represent and solve problems involving multiplication and division.
- 3.1.3.a.i Interpret products of whole numbers.
- 3.1.3.a.ii Interpret whole-number quotients of whole numbers.
- 3.1.3.a.iii Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
- 3.1.3.a.iv Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
- 3.1.3.a.v Model strategies to achieve a personal financial goal using arithmetic operations.

- 3.1.3.b Apply properties of multiplication and the relationship between multiplication and division.
- 3.1.3.b.i Apply properties of operations as strategies to multiply and divide.
- 3.1.3.b.ii Interpret division as an unknown-factor problem.

- 3.1.3.c Multiply and divide within 100.
- 3.1.3.c.i Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.
- 3.1.3.c.ii Recall from memory all products of two one-digit numbers.

- 3.1.3.d Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- 3.1.3.d.i Solve two-step word problems using the four operations.
- 3.1.3.d.ii Represent two-step word problems using equations with a letter standing for the unknown quantity.
- 3.1.3.d.iii Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 3.1.3.d.iv Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

- 3.1.3.a Represent and solve problems involving multiplication and division.

### 3.3 Data Analysis, Statistics, and Probability

- 3.3.1 Visual displays are used to describe data
- 3.3.1.a Represent and interpret data.
- 3.3.1.a.i Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.
- 3.3.1.a.ii Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.
- 3.3.1.a.iii Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

- 3.3.1.a Represent and interpret data.

### 3.4 Shape, Dimension, and Geometric Relationships

- 3.4.1 Geometric figures are described by their attributes
- 3.4.1.a Reason with shapes and their attributes.
- 3.4.1.a.i Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category.
- 3.4.1.a.i.1 Identify rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

- 3.4.1.a.ii Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

- 3.4.1.a.i Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category.

- 3.4.1.a Reason with shapes and their attributes.
- 3.4.2 Linear and area measurement are fundamentally different and require different units of measure
- 3.4.2.a Use concepts of area and relate area to multiplication and to addition.
- 3.4.2.a.i Recognize area as an attribute of plane figures and understand concepts of area measurement.
- 3.4.2.a.ii Find area of rectangles with whole number side lengths using a variety of methods.
- 3.4.2.a.iii Relate area to the operations of multiplication and addition and recognize area as additive.

- 3.4.2.b Describe perimeter as an attribute of plane figures and distinguish between linear and area measures.
- 3.4.2.c Solve real world and mathematical problems involving perimeters of polygons.
- 3.4.2.c.i Find the perimeter given the side lengths.
- 3.4.2.c.ii Find an unknown side length given the perimeter.
- 3.4.2.c.iii Find rectangles with the same perimeter and different areas or with the same area and different perimeters.

- 3.4.2.a Use concepts of area and relate area to multiplication and to addition.
- 3.4.3 Time and attributes of objects can be measured with appropriate tools
- 3.4.3.a Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
- 3.4.3.a.i Tell and write time to the nearest minute.
- 3.4.3.a.ii Measure time intervals in minutes.
- 3.4.3.a.iii Solve word problems involving addition and subtraction of time intervals in minutes using a number line diagram.
- 3.4.3.a.iv Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
- 3.4.3.a.v Use models to add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units.

- 3.4.3.a Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.