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### 3.OA Operations and Algebraic Thinking

- 3.OA.A Represent and solve problems involving multiplication and division.
- 3.OA.A.1 Interpret a product of whole numbers as a grouping of sets, e.g., 5 × 7 as five groups of seven objects each.
- 3.OA.A.2 Interpret a quotient of whole numbers as equal sharing, e.g., 56 ÷ 8 as the number in each share when 56 objects are split into 8 equal shares, or as the number of shares when 56 objects are split into equal shares of 8 objects each.
- 3.OA.A.3 Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurements by using visual and symbolic representations, with a symbol for an unknown number.
- 3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

- 3.OA.B Understand properties of multiplication and the relationship between multiplication and division.
- 3.OA.B.5 Apply the properties of operations to multiply and divide.
- 3.OA.B.6 Understand division as determining an unknown factor in a multiplication problem.

- 3.OA.C Multiply and divide within 100.
- 3.OA.C.7 Demonstrate fluency for multiplication within 100.
- 3.OA.C.7.a Demonstrate understanding of strategies that make use of the relationship between multiplication and division or properties of operations.
- 3.OA.C.7.b Know from memory all products of two single-digit numbers and related division facts.

- 3.OA.C.7 Demonstrate fluency for multiplication within 100.
- 3.OA.D Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- 3.OA.D.8 Solve two-step word problems involving whole numbers using the four operations.
- 3.OA.D.8.a Represent these problems using equations with a letter standing for the unknown quantity.
- 3.OA.D.8.b Assess the reasonableness of answers using mental computation and estimation strategies, including rounding.

- 3.OA.D.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

- 3.OA.D.8 Solve two-step word problems involving whole numbers using the four operations.

### 3.NBT Number and Operations in Base Ten

- 3.NBT.A Use place value understanding and properties of operations to perform multi-digit arithmetic.
- 3.NBT.A.1 Round a whole number to the tens or hundreds place, using place value understanding or a visual representation.
- 3.NBT.A.2 Fluently add and subtract whole numbers within 1,000 using understanding of place value and properties of operations.
- 3.NBT.A.3 Multiply one-digit whole numbers by multiples of ten in the range 110 – 90 using understanding of place value and properties of operations.

### 3.NF Number and Operations – Fractions

- 3.NF.A Develop understanding of fractions as numbers.
- 3.NF.A.1 Understand a fraction
^{1}/_{b}as the quantity formed by one part when a whole (a single unit) is partitioned into*b*equal parts; understand^{a}/_{b}as the quantity formed by*a*parts of size^{1}/_{b}. - 3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 3.NF.A.2.a Represent a unit fraction
^{1}/_{b}on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into*b*equal parts. Recognize that each part has size^{1}/_{b}and that the fraction^{1}/_{b}is located^{1}/_{b}of a whole unit from 0 on the number line. - 3.NF.A.2.b Represent a fraction
^{a}/_{b}on a number line diagram by marking off a length^{1}/_{b}from 0. Recognize that the resulting interval has size^{a}/_{b}and that its endpoint locates the number^{a}/_{b}on the number line.

- 3.NF.A.2.a Represent a unit fraction
- 3.NF.A.3 Explain equivalence of fractions and compare fractions by reasoning about their size, in limited cases.
- 3.NF.A.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- 3.NF.A.3.b Recognize and generate simple equivalent fractions, and explain why the fractions are equivalent, such as by using a visual fraction model.
- 3.NF.A.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
- 3.NF.A.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize the comparisons are valid only when the two fractions refer to the same whole. Record the results of the comparisons with the symbols >, = , and <, and justify the conclusion using visual representations and/or verbal reasoning.

- 3.NF.A.1 Understand a fraction

### 3.MD Measurement and Data

- 3.MD.A Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
- 3.MD.A.1 Tell and write time to the nearest minute within the same hour and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes.
- 3.MD.A.2 Identify and use the appropriate tools and units of measurement, both customary and metric, to solve one-step word problems using the four operations involving weight, mass, liquid volume, and capacity (within the same system and unit).

- 3.MD.B Represent and interpret data.
- 3.MD.B.3 Draw a scaled picture graph and scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.
- 3.MD.B.4 Generate measurement data by measuring lengths of objects using rulers marked with halves and fourths of an inch. Record and show the data by making a line plot (dot plot), where the horizontal scale is marked off in appropriate units — whole numbers, halves, or fourths.

- 3.MD.C Geometric measurement: Understand concepts of area and relate area to multiplication and to addition.
- 3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
- 3.MD.C.5.a A square with side length one unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
- 3.MD.C.5.b A plane figure which can be covered without gaps or overlaps by
*n*unit squares is said to have an area of*n*square units.

- 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and nonstandard units).
- 3.MD.C.7 Relate area to the operations of multiplication and addition.
- 3.MD.C.7.a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
- 3.MD.C.7.b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
- 3.MD.C.7.c Use tiling to show in a concrete case that the area of a rectangle with whole number side lengths
*a*and*b*+*c*is the sum of*a*×*b*and*a*×*c*. Use area models to represent the distributive property in mathematical reasoning. - 3.MD.C.7.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

- 3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
- 3.MD.D Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
- 3.MD.D.8 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

### 3.G Geometry

- 3.G.A Reason with shapes and their attributes.
- 3.G.A.1 Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Compare and classify shapes by their sides and angles. Recognize rhombi, rectangles, squares, and trapezoids as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
- 3.G.A.2 Partition two-dimensional figures into equal areas, and express the area of each part as a unit fraction of the whole.