Operations and Algebraic Thinking
 
Represent and solve problems involving multiplication and division.
 

1 ) Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] Example: Describe a context in which a total number of objects can be expressed as 5 x 7. NAEP Framework
Alabama Alternate Achievement Standards



2 ) Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] Example: Describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. NAEP Framework
Alabama Alternate Achievement Standards



3 ) Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3OA3] NAEP Framework



4 ) Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] NAEP Framework


Understand properties of multiplication and the relationship between multiplication and division.
 

5 ) Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property) NAEP Framework



6 ) Understand division as an unknownfactor problem. [3OA6] Example: Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. NAEP Framework


Multiply and divide within 100.
 

7 ) Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. [3OA7] NAEP Framework
Alabama Alternate Achievement Standards


Solve problems involving the four operations, and identify and explain patterns in arithmetic.
 

8 ) Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] NAEP Framework
Alabama Alternate Achievement Standards



9 ) Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] Example: Observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. NAEP Framework
Alabama Alternate Achievement Standards


Number and Operations in Base Ten
 
Use place value understanding and properties of operations to perform multidigit arithmetic. (A range of algorithms may be used.)
 

10 ) Use place value understanding to round whole numbers to the nearest 10 or 100. [3NBT1] NAEP Framework
Alabama Alternate Achievement Standards



11 ) 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. [3NBT2] NAEP Framework
Alabama Alternate Achievement Standards



12 ) Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] NAEP Framework
Alabama Alternate Achievement Standards


Number and Operations — Fractions
(Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)  
Develop understanding of fractions as numbers.
 

13 ) 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 and size ^{1}/_{b}. [3NF1] NAEP Framework
Alabama Alternate Achievement Standards



14 ) Understand a fraction as a number on the number line; represent fractions on a number line diagram. [3NF2] a. 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.
[3NF2a] b. 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. [3NF2b] NAEP Framework
Alabama Alternate Achievement Standards



15 ) Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] a. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. [3NF3a] b. Recognize and generate simple equivalent fractions, e.g., ^{1}/_{2} = ^{2}/_{4}, ^{4}/_{6} = ^{2}/_{3}. Explain why the fractions are equivalent, e.g., by using a visual fraction model. [3NF3b] c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. [3NF3c] Examples: Express 3 in the form 3 = ^{3}/_{1}; recognize that ^{6}/_{1} = 6; locate ^{4}/_{4} and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [3NF3d] NAEP Framework
Alabama Alternate Achievement Standards


Measurement and Data
 
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
 

16 ) 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, e.g., by representing the problem on a number line diagram. [3MD1] Alabama Alternate Achievement Standards



17 ) Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] NAEP Framework
Alabama Alternate Achievement Standards


Represent and interpret data.
 

18 ) Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] Example: Draw a bar graph in which each square in the bar graph might represent 5 pets. Alabama Alternate Achievement Standards



19 ) 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. [3MD4] Alabama Alternate Achievement Standards


Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
 

20 ) Recognize area as an attribute of plane figures, and understand concepts of area measurement. [3MD5] a. A square with side length 1 unit called "a unit square," is said to have "one square unit" of area and can be used to measure area. [3MD5a] 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. [3MD5b] NAEP Framework
Alabama Alternate Achievement Standards



21 ) Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] NAEP Framework



22 ) Relate area to the operations of multiplication and addition. [3MD7] a. Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. [3MD7a] b. Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving realworld and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. [3MD7b] c. Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. [3MD7c] d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve realworld problems. [3MD7d] NAEP Framework
Alabama Alternate Achievement Standards


Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
 

23 ) Solve realworld 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. [3MD8] NAEP Framework
Alabama Alternate Achievement Standards


Geometry
 
Reason with shapes and their attributes.
 

24 ) Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and 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. [3G1] NAEP Framework
Alabama Alternate Achievement Standards



25 ) Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] Example: Partition a shape into 4 parts with equal area, and describe the area of each part as ^{1}/_{4} of the area of the shape. 