Second Quarter Benchmark Expectations for Units 3 and 4. Represent multiplication as equal groups with arrays.

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1 Mastery Expectations For the Third Grade Curriculum In Third Grade, Everyday Mathematics focuses on procedures, concepts, and s in four critical areas: Understanding of division and strategies within 100. Understanding of fractions, especially unit fractions. Understanding of the structure of rectangular arrays and of area. Describing and analyzing two-dimensional shapes. Common Core 3.OA.1 Represent multiplication as equal groups with concrete objects and drawings. Represent multiplication as equal groups with arrays. Interpret multiplication in terms of equal groups. For example, describe a context in which a total number of objects can be expressed as OA.2 Equally share groups of concrete objects. Represent equal shares with drawings. Represent equal shares with drawings and number models. Interpret division in terms of equal shares or equal groups. For example, describe a context in which a number of shares or a number of groups can be expressed as OA.3 Use skip counting, repeated addition, or multiplication to solve number stories involving equal groups. Use multiplication or division to solve number stories involving equal groups or equal shares. Use multiplication and division to solve number stories. Model number stories involving multiplication. Use multiplication and division to solve number stories. Model number stories involving division. 1

2 3.OA.4 Use fact triangles to generate fact families. Determine the unknown product or factor in division equations involving 1s, 2s, 5s, and 10s facts. Determine the unknown product or factor in division equations involving square products, and 0s, 1s, 2s, 3s, 5s, 9s, and 10s facts. Determine the unknown in division equations. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = _ 3, 6 6 =?. 3.OA.5 Illustrate the turn-around rule (Commutative Property of Multiplication) with arrays and facts. Use strategies such as adding/subtracting a group, near squares, and doubling to multiply and divide. Apply properties of operations to multiply or divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = = 56. (Distributive property.) 3.OA.6 Use multiplication to determine the unknown factor in division equations involving 1s, 2s, 5s, and 10s facts. Use multiplication to determine the unknown factor in division equations involving 1s, 2s, 5s, 10s, square products, and 0s, 3s, and 9s facts. Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. 3.OA.7 Know all products of one-digit numbers 1, 2, 5, and 10. Know all square products of one-digit numbers. Know all products of one-digit numbers 0, 1, 2, 3, 5, 9, and 10. Fluently multiply and divide within 100, using strategies such as the relationship between division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 2

3 3.OA.8 Use drawings, diagrams, and estimates to explain why answers to number stories involving addition and subtraction are reasonable. Use pictures, words, or numbers to solve 2-step number stories involving addition and subtraction. Use mental computation and estimation strategies, including rounding, to determine whether answers to addition and subtraction problems are reasonable. Represent problems using equations with a? standing for the unknown quantity. Solve 2-step number stories using two of the four operations. Solve two-step 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. 3.OA.9 Use the multiplication table to help identify whether products of 2 even factors, 2 odd factors, and 1 even and 1 odd factor are even or odd. Use doubling as a strategy to solve multiplication facts. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 3.NBT.1 Use open number lines to round 2-digit numbers to the nearest 10 and 3-digit numbers to the nearest 100. Use place value understanding to round whole numbers to the nearest 10 or NBT.2 Add and subtract within 1000 using tools along with strategies based on place value and/or the relationship between addition and subtraction. Add and subtract within 1000 using partial-sums addition, and countingup and expand-and-trade subtraction, or other strategies. Fluently add within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction; fluently subtract within 1000 using counting up, expand and trade, trade first, or other strategies. 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

4 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. 3.NF.1 Identify and represent given unit (1//b) and nonunit (a//b) fractions using pictures, words, and fraction circles. 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.2; 3NF.2a Understand a fraction as a number on the number line; represent fractions on a number line diagram. 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.2; 3NF.2b Understand a fraction as a number on the number line; represent fractions on a number line diagram. 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. 4

5 3.NF.3; 3.NF.3a Use fraction circle pieces to determine that equivalent fractions are the same size. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 3.NF.3; 3.NF.3b Use fraction circle pieces to generate simple equivalent fractions Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 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. 3.NF.3; 3.NF.3c Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. 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. 5

6 3.NF.3; 3.NF.3d Use tools, such as fraction circle pieces, to justify the conclusions of fraction comparisons. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 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. 3.MD.1 Tell and write time to the nearest 5 minutes. Use an open number line or other tools to add time intervals in minutes. Use open number lines, toolkit clocks, or other strategies to solve problems and number stories involving 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. 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. 3.MD.2 Estimate the mass of objects by comparing benchmark masses to the masses of various items. Use addition and subtraction to solve one-step number stories about mass. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). 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. 6

7 3.MD.3 Use information in a given scaled bar graph to solve one-step how many more and how many less problems. Represent a data set with several categories on a given scaled bar graph and use the information presented in the graph to solve onestep how many more and how many less problems. 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 bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 3.MD.4 Measure lengths to the nearest inch using rulers marked with whole and half inches. Measure lengths to the nearest half-inch using rulers marked with wholes, halves, and fourths of an inch. Represent length data on a line plot where the horizontal scale is marked off in whole numbers and halves. Measure lengths to the nearest half-inch using rulers marked with wholes, halves, and fourths of an inch. Represent length data on a line plot where the horizontal scale is marked off in whole numbers and halves. 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.MD.5; 3.MD.5a Recognize area as an attribute of plane figures. Recognize area as an attribute of plane figures and understand concepts of area measurement. 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. 3.MD.5; 3.MD.5b Recognize area as an attribute of plane figures. Recognize area as an attribute of plane figures and understand concepts of area measurement. 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. 7

8 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7; 3.MD.7a Find the area of a rectangle with whole number side lengths by tiling it. Relate area to the operations of addition. 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.7; 3.MD.7b Multiply side lengths to find areas of rectangles. Relate area to the operations of addition. 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 wholenumber products as rectangular areas in mathematical reasoning. 3.MD.7; 3.MD.7c Explain how a given area model, fully labeled, with a side length decomposed into 2 addends can be used to solve a multiplication problem. Relate area to the operations of addition. 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. 8

9 3.MD.7; 3.MD.7d Relate area to the operations of addition. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. 3.MD.8 Solve problems involving perimeters of polygons. Distinguish between area and perimeter. 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.1 Understand that shapes in different categories may share attributes that can define a larger category. Recognize specified subcategories of quadrilaterals. 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. 9

10 3.G.2 No expectations of Partition rectangles into parts with equal areas. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For 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. 10

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