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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 Represent the concept of multiplication of whole numbers using models including, but not limited to, equal-sized groups (“groups of”), arrays, area models, repeated addition, and equal “jumps” on a number line.
- 3.OA.A.2 Represent the concept of division of whole numbers (resulting in whole number quotients) using models including, but not limited to, partitioning, repeated subtraction, sharing, and inverse of multiplication.
- 3.OA.A.3 Solve multiplication and division word problems within 100 using appropriate modeling strategies and equations.
- 3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient.
- 3.OA.B Understand properties of multiplication and the relationship between multiplication and division.
- 3.OA.B.5 Apply properties of multiplication as strategies to multiply and divide.
- 3.OA.B.6 Understand division as an unknown-factor problem.
- 3.OA.C Multiply and divide within 100.
- 3.OA.C.7 Fluently multiply and divide with factors 1-10 using mental strategies. By end of Grade 3, know automatically all products of one-digit factors based on strategies.
- 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 (limited to the whole number system) using the four basic operations. Students should apply the Order of Operations when there are no parentheses to specify a particular order.
- 3.OA.D.8A Represent these problems using equations with a symbol standing for the unknown quantity.
- 3.OA.D.8B Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 3.OA.D.9 Identify arithmetic patterns and explain the relationships using properties of operations.
- 3.OA.D.8 Solve two-step word problems (limited to the whole number system) using the four basic operations. Students should apply the Order of Operations when there are no parentheses to specify a particular order.
3.NBT Number and Operations in Base Ten
- 3.NBT.E Use place value understanding and properties of operations to perform multi-digit arithmetic (a range of algorithms may be used).
- 3.NBT.E.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
- 3.NBT.E.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of addition, and/or the relationship between addition and subtraction.
- 3.NBT.E.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of multiplication.
3.NF Number and Operations-Fractions
- 3.NF.F Develop understanding of fractions as numbers.
- 3.NF.F.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- 3.NF.F.2 Understand and represent fractions on a number line diagram.
- 3.NF.F.2A Represent a 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 endpoint of the part based at 0 locates the number 1/b on the number line.
- 3.NF.F.2B Represent a fraction a/b on a number line diagram by marking off a lengths 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.F.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- 3.NF.F.3A Understand two fractions as equivalent if they are the same size, or the same point on a number line.
- 3.NF.F.3B Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent.
- 3.NF.F.3C Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
- 3.NF.F.3D Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
3.MD Measurement and Data
- 3.MD.G Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
- 3.MD.G.1 Use analog clocks to tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes.
- 3.MD.G.2 Measure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (L). (Excludes compound units such as cm³ and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units. (Excludes multiplicative comparison problems involving notions of “times as much.”)
- 3.MD.H Represent and interpret data.
- 3.MD.H.3 Draw a scaled picture graph and a 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 graphs.
- 3.MD.H.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Use the data to create a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.
- 3.MD.I Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
- 3.MD.I.5 Understand area as an attribute of plane figures and understand concepts of area measurement, such as square units without gaps or overlaps.
- 3.MD.I.6 Measure areas by counting unit squares (square cm, square m, square in., square ft, and improvised units).
- 3.MD.I.7 Relate area to the operations of multiplication and addition.
- 3.MD.I.7A Find the area of a rectangle with whole-number side lengths (dimensions) by multiplying them. Show that this area is the same as when counting unit squares.
- 3.MD.I.7B 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.I.7C Use area models to represent the distributive property in mathematical reasoning. 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.
- 3.MD.J Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
- 3.MD.J.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 area or with the same area and different perimeter.
3.G Geometry
- 3.G.K Reason with shapes and their attributes.
- 3.G.K.1 Use attributes of quadrilaterals to classify rhombuses, rectangles, and squares. Understand that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
- 3.G.K.2 Partition rectangles, regular polygons, and circles into parts with equal areas. Express the area of each part as a unit fraction of the whole.