Publisher: Pearson Scott Foresman & Prentice Hall
Program Title: enVisionMATH California Common Core Edition, Grade 3
Components: Student Edition (SE); Teacher’s Edition (TE)
Standards Map for a Basic Grade Level Program
2014 Mathematics Primary Adoption
enVisionMATH CaliforniaCommon Core
©2015
CommonCoreState Standards with California Additions
Grade 3 – Mathematics
CommonCoreState Standards with California Additions[1]
Standards Map for a Basic GradeLevel Program
Grade Three – Mathematics
Publisher Citations / Meets Standard / For Reviewer Use OnlyStandard No. / Standard Language / Primary Citations / Supporting Citations / Y / N / Reviewer Notes
Operations and Algebraic Thinking
Represent and solve problems involving multiplication and division.
3.OA 1. / Interpret products of whole numbers, e.g., interpret 5 × 7 as the totalnumber of objects in 5 groups of 7 objects eachor 7 groups of 5 objects each. For example, describea context in which a total number of objects can be expressed as
5 × 7. / SE/TE: 9899, 102103
TE: 98A99B, 102A103B / SE/TE: 100101, 104105
TE: 100A101B, 104A105B
3.OA 2. / Interpret wholenumber quotients of whole numbers, e.g., interpret56 ÷ 8 as the number of objects in each share when 56 objects arepartitioned equally into 8 shares, or as a number of shares when
56 objects are partitioned into equal shares of 8 objects each. Forexample, describe a context in which a number of shares or a number ofgroups can be expressed as 56 ÷ 8. / SE/TE: 170171, 172173
TE: 170A171B, 172A173B
3.OA 3. / Use multiplication and division within 100 to solve word problems insituations 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. / SE/TE: 100101, 104105, 176177, 178179, 208211, 336337
TE: 100A101B, 104A105B, 176A177B, 178A179B, 208A211B, 336A337B / SE/TE: 102103, 154155, 170171, 200201
TE: 102A103B, 154A155B, 170A171B, 200A201B
3.OA 4. / Determine the unknown whole number in a multiplication or divisionequation relating three whole numbers. For example, determine theunknown number that makes the equation true in each of the equations 8
× ? = 48, 5 = ÷ 3, 6 × 6 =?. / SE/TE: 174175, 176177
TE: 174A175B, 176A177B / SE/TE: 190191, 200201, 202203, 206207
TE: 190A191B, 200A201B, 202A203B, 206A207B
Understand properties of multiplication and the relationship between multiplication and division.
3.OA 5. / Apply properties of operations as strategies to multiply anddivide.[2]Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
(Commutative property of multiplication.) 3 × 5 × 2 can be found by 3× 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associativeproperty of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, onecan find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributiveproperty.) / SE/TE: 102103, 140141, 152153
TE: 102A103B, 140A141B, 152A153B / SE/TE: 122123, 204205
TE: 122A123B, 204A205B
3.OA 6. / Understand division as an unknownfactor problem. For example, find32 ÷ 8 by finding the number that makes 32 when multiplied by 8. / SE/TE: 174175, 190191, 206207
TE: 174A175B, 190A191B, 206A207B
Multiply and divide within 100.
3.OA 7. / Fluently multiply and divide within 100, using strategies such as therelationship between multiplication and division (e.g., knowing that 8 ×5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the endof Grade 3, know from memory all products of two onedigit numbers. / SE/TE: 190191, 192195, 196197, 198199, 204205
TE: 190A191B, 192A195B, 196A197B, 198A199B, 204A205B / SE/TE: 122123, 206207
TE: 122A123B, 206A207B
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA 8. / Solve twostep word problems using the four operations. Representthese problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mentalcomputation and estimation strategies including rounding.[3] / SE/TE: 130131, 158161, 200201
TE: 130A131B, 158A161B, 200A201B / SE/TE: 4849
TE: 48A49B
3.OA 9. / Identify arithmetic patterns (including patterns in the addition table ormultiplication table), and explain them using properties of operations.For example, observe that 4 times a number is always even, and explainwhy 4 times a number can be decomposed into two equal addends. / SE/TE: 116119, 120121, 122123, 124125, 126127
TE: 116A119B, 120A121B, 122A123B, 124A125B, 126A127B / SE/TE: 106107, 174175
TE: 106A107B, 174A175B
Number and Operations in Base Ten
Use place value understanding and properties of operations toperform multidigit arithmetic.[4]
3.NBT 1. / Use place value understanding to round whole numbers to the nearest10 or 100. / SE/TE: 1417, 1819
TE: 14A17B, 18A19B / SE/TE: 21, 4043, 4447
TE: 40A43B, 44A47B
3.NBT 2. / Fluently add and subtract within 1000 using strategies and algorithmsbased on place value, properties of operations, and/or the relationshipbetween addition and subtraction. / SE/TE: 3031, 5859, 6063, 7071, 7477, 8485
TE: 30A31B, 58A59B, 60A63B, 70A71B, 74A77B, 84A85B / SE/TE: 6465, 6667, 7273, 7879
TE: 64A65B, 66A67B, 72A73B, 78A79B
3.NBT 3. / Multiply onedigit whole numbers by multiples of 10 in the range10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value andproperties of operations. / SE/TE: 128129
TE: 128A129B / SE/TE: 126127, 132133 Sets D and E
TE: 126A127B
Number and Operations—Fractions[5]
Develop understanding of fractions as numbers.
3.NF 1. / Understand a fraction 1/b as the quantity formed by 1 part when awhole is partitioned into b equal parts; understand a fraction a/b asthe quantity formed by a parts of size 1/b. / SE/TE: 222223, 234235
TE: 222A223B, 234A235B / SE/TE: 224225, 226227
TE: 224A225B, 226A227B
3.NF 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 theinterval from 0 to 1 as the whole and partitioning it into b equalparts. Recognize that each part has size 1/b and that the endpointof the part based at 0 locates the number 1/b on the number line. / SE/TE: 228229, 230231
TE: 228A229B, 230A231B / SE/TE: 260261, 236237 Sets C and D
TE: 260A261B
3.NF 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. / SE/TE: 228229
TE: 228A229B / SE/TE: 230231, 232233, 236237 Set C
TE: 230A231B, 232A233B
3.NF 3a. / 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. / SE/TE: 248249, 252255, 256257
TE: 248A249B, 252A255B, 256A257B / SE/TE: 244245, 246247, 250251
TE: 244A245B, 246A247B, 250A251B
3.NF 3b. / 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., byusing a visual fraction model. / SE/TE: 250251, 252255
TE: 250A251B, 252A255B / SE/TE: 256257
TE: 256A257B
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 thatare equivalent to whole numbers. Examples: Express 3 in the form3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same pointof a number line diagram. / SE/TE: 256257, 258259
TE: 256A257B, 258A259B / SE/TE: 228229
TE: 228A229B
3.NF 3d. / 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. / SE/TE: 244245, 246247, 248249, 250251
TE: 244A245B, 246A247B, 248A249B, 250A251B
Measurement and Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
3.MD 1. / Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtractionof time intervals in minutes, e.g., by representing the problem on a number line diagram. / SE/TE: 296297, 298299, 300301
TE: 296A297B, 298A299B, 300A301B / SE/TE: 292295
TE: 292A295B
3.MD 2. / Measure and estimate liquid volumes and masses of objects usingstandard units of grams (g), kilograms (kg), and liters (l).[6]Add,subtract, multiply, or divide to solve onestep word problems involvingmasses or volumes that are given in the same units, e.g., by usingdrawings (such as a beaker with a measurement scale) to represent the problem.[7] / SE/TE: 364365, 366367, 368369, 370371, 372373
TE: 364A365B, 366A367B, 368A369B, 370A371B, 372A373B
Represent and interpret data.
3.MD 3. / Draw a scaled picture graph and a scaled bar graph to represent adata set with several categories. Solve one and twostep “how manymore” and “how many less” problems using information presented inscaled bar graphs. For example, draw a bar graph in which each square inthe bar graph might represent 5 pets. / SE/TE: 386A389, 390391, 392393, 394395
TE: 386A389B, 390A391B, 392A393B, 394A395B
3.MD 4. / 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. / SE/TE: 384385
TE: 384A385B / SE: 382383, 396397 Set B
TE: 382A383B
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
3.MD 5a. / 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. / SE/TE: 330331, 332333, 334335
TE: 330A331B, 332A333B, 334A335B / SE/TE: 340341
TE: 340A341B
3.MD 5b. / 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. / SE/TE: 332333
TE: 332A333B / SE/TE: 334335
TE: 334A335B
3.MD 6. / Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). / SE/TE: 330331, 334335
TE: 330A331B, 334A335B / SE/TE: 332333, 340341
TE: 332A333B, 340A341B
3.MD 7a. / Relate area to the operations of multiplication and addition.Find the area of a rectangle with wholenumber side lengths bytiling it, and show that the area is the same as would be found bymultiplying the side lengths. / SE/TE: 336337
TE: 336A337B / SE/TE: 338339, 340341
TE: 338A339B, 340A341B
3.MD 7b. / Relate area to the operations of multiplication and addition. Multiply side lengths to find areas of rectangles with wholenumberside lengths in the context of solving real world andmathematical problems, and represent wholenumber products asrectangular areas in mathematical reasoning. / SE/TE: 346347, 348349
TE: 346A347B, 348A349B / SE/TE: 336337, 338339
TE: 336A337B, 338A339B
3.MD 7c. / Relate area to the operations of multiplication and addition.Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths aand b + c is the sum of a × b and a × c. Use area models to represent the distributiveproperty in mathematical reasoning. / SE/TE: 338339
TE: 338A339B / SE/TE: 354355 Set D
3.MD 7d. / Relate area to the operations of multiplication and addition.Recognize area as additive. Find areas of rectilinear figures bydecomposing them into nonoverlapping rectangles and addingthe areas of the nonoverlapping parts, applying this technique tosolve real world problems. / SE/TE: 340341, 342344
TE: 340A341B, 342A345B / SE/TE: 282283
TE: 282A283B
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
3.MD 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 differentperimeters. / SE/TE: 310311, 314315, 316317, 346347, 348349
TE: 310A311B, 314A315B, 316A317B, 346A347B, 348A349B / SE/TE: 312313, 318321
TE: 312A313B, 318A321B
Geometry
Reason with shapes and their attributes.
3.G 1. / 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 thatdo not belong to any of these subcategories. / SE/TE: 276277, 278279, 280281
TE: 276A277B, 278A279B, 280A281B / SE/TE: 272275
TE: 272A275B
3.G 2. / 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 4parts with equal area, and describe the area of each part as 1/4 of the area of the shape. / SE/TE: 220221, 350351
TE: 220A221B, 350A351B / SE/TE: 356357 Set H
MATHEMATICAL PRACTICES
MP 1. / Make sense of problems and persevere insolving them. / SE: xviii, xix, xxvii
TE: 2A, 2B, 2F
MP 2. / Reason abstractly and quantitatively. / SE: xviii, xx, xxvii
TE: 2A, 2B, 2F
MP 3. / Construct viable arguments and critiquethe reasoning of others. / SE: xviii, xxi, xxvii
TE: 2A, 2C, 2F
MP 4. / Model with mathematics. / SE: xviii, xxii, xxvii
TE: 2A, 2C, 2F
MP 5. / Use appropriate tools strategically. / SE: xviii, xxiii, xxvii
TE: 2A, 2D, 2F
MP 6. / Attend to precision. / SE: xviii, xxiv, xxvii
TE: 2A, 2D, 2F
MP 7. / Look for and make use of structure. / SE: xviii, xxv, xxvii;
TE: 2A, 2E, 2F
MP 8. / Look for and express regularity in repeated reasoning. / SE: xviii, xxvi, xxvii
TE: 2A, 2E, 2F
Appendix
California Department of Education
Posted February 2013
© California Department of EducationCommonCoreState Standards MapJanuary 16, 2013
Page 1
[1]These standards were originally produced by the Common Core State Standards Initiative, a stateled effort coordinated by the NationalGovernorsAssociationCenter for Best Practices and the Council of Chief State School Officers. California additions were made by the State Board of Education when it adopted the Common Core on August 2, 2010 and modified pursuant to Senate Bill 1200 located at on January 16, 2013. Additions are marked in bold and underlined.
[2]Students need not use formal terms for these properties.
[3]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).
[4]A range of algorithms may be used.
[5]Grade 3 expectations in this domain are limited to fractions with denominators 2, 3,4, 6, and 8.
[6]Excludes compound units such as cm3 and finding the geometric volume of a container.
[7] Excludes multiplicative comparison problems (problems involving notions of “times as much”).