The standards are taught in the following sequence.

Transcription

1 B L U E V A L L E Y D I S T R I C T C U R R I C U L U M MATHEMATICS Third Grade In grade 3, instructinal time shuld fcus n fur critical areas: (1) develping understanding f multiplicatin and divisin and strategies fr multiplicatin and divisin within 100; (2) develping understanding f fractins, especially unit fractins (fractins with numeratr 1); (3) develping understanding f the structure f rectangular arrays and f area; and (4) describing and analyzing tw-dimensinal shapes. Nt all f the cntent in a given grade is emphasized equally in the standards. Sme clusters require greater emphasis than thers based n the depth f ideas, the time that they take t master, and/r their imprtance t future mathematics r the demands f cllege and career readiness. In additin, an intense fcus n the mst critical material at each grade level allws depth and learning, which is carried ut thrugh the Standards fr Mathematical Practice which are: 1. Make sense f prblems and persevere in slving them. 2. Reasn abstractly and quantitatively. 3. Cnstruct viable arguments and critique the reasning f thers. 4. Mdel with mathematics. 5. Use apprpriate tls strategically. 6. Attend t precisin. 7. Lk fr and make use f structure. (Deductive Reasning) 8. Lk fr and express regularity in repeated reasning. (Inductive Reasning) The standards are taught in the fllwing sequence.

2 Number and Operatins-Base 10 Tpic 1 Tpic 2 Tpic 3 NBT.1 Use place value understanding t rund whle numbers t the nearest 10 r 100. NBT.2 Fluently add and subtract within 1000 using strategies and algrithms based n place value, prperties f peratins, and/r the relatinship between additin and subtractin. NBT.3 Multiply ne-digit whle numbers by multiples f 10 in the range (e.g. 9 x 80, 5 x 60) using strategies based n place value and prperties f peratins. Use place value understanding and prperties f peratins t perfrm multidigit arithmetic.

3 Operatins and Algebraic Thinking Tpic 4 Tpic 5 Tpic 6 Tpic 7 Tpic 8 Represent and slve prblems invlving multiplicatin and divisin. OA.1 Interpret prducts f whle numbers (e.g. interpret 5 x 7 as the ttal number f bjects in 5 grups f 7 bjects each. Fr example, describe a cntext in which a ttal number f bjects can be expresses ad 5 x 7). OA.2 Interpret whle-number qutients f whle numbers, (e.g. interpret 56 8 as the number f bjects in each share when 56 bjects are partitined equally int 8 shares, r as a number f shares when 56 bjects are partitined int equal shares f 8 bjects. Fr example, describe a cntext in which a number f shares r a number f grups can be expressed as 56 8). OA.3 Use multiplicatin and divisin within 100 t slve wrd prblems in situatins invlving equal grups, arrays, and measurement quantities, (e.g. by using drawings and equatins with a symbl fr the unknwn number t represent the prblem). OA.4 Determine the unknwn whle number in a multiplicatin r divisin equatin relating three whle numbers. Understand prperties f multiplicatin and the relatinship between multiplicatin and divisin. OA.5 Apply prperties f peratins as strategies t multiply and divide. (Examples: If 6 x 4 = 24 is knwn, then 4 x 6 = 24 is als knwn - Cmmutative Prperty f Multiplicatin. 3 x 5 x 2 can be fund by 3 x 5 = 15, then 15 x 2 = 30, r by 5 x 2 = 10, then 3 x 10 = 30 - Assciative Prperty f Multiplicatin. Knwing that 8 x 5 = 4 and 8 x 2 = 16, ne can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = = 56 - Distributive Prperty). OA.6 Understand divisin as an unknwn-factr prblem. (Fr example, find 32 8 by finding the number that makes 32 when multiplied by 8).

4 Multiply and divide within 100. OA.7 Fluently multiply and divide within 100, using strategies such as the relatinship between multiplicatin and divisin (e.g., knwing that 8 x 5 = 40, ne knws 40 5 = 8) r prperties f peratins. By the end f Grade 3, knw frm memry all prducts f tw ne-digit numbers. Slve prblems invlving the fur peratins, and identify and explain patterns in arithmetic. OA.8 Slve tw-step wrd prblems using the fur peratins. Represent these prblems using equatins with a letter standing fr the unknwn quantity. Assess the reasnableness f answers using mental cmputatin and estimatin strategies including runding. OA. 9 Identify arithmetic patterns (including patterns in the additin table r multiplicatin table), and explain them using prperties f peratins. (Fr example, bserve that 4 times a number is always even, and explain why 4 times a number can be decmpsed int tw equal addends). Numbers and Operatins - Fractins Tpic 9 Tpic 10 Develp understanding f fractins as numbers. NF.1 Understand a fractin 1/b as the quantity frmed by 1 part when a whle is partitined int b equal parts; understand a fractin a/b as the quantity frmed by a parts f size 1/b. NF.2 Understand a fractin as a number n the number line; represent fractins n a number line diagram. NF.2a-Represent a fractin 1/b n a number line diagram by defining the interval frm 0 t 1 as the whle and partitining it int b equal parts. Recgnize that each part has size 1/b and that the endpint f the part based at 0 lcates the number

5 1/b n the number line. NF.2b -Represent a fractin a/b n a number line diagram by marking ff a lengths 1/b frm 0. Recgnize that the resulting interval has size a/b and that its endpint lcates the number a/b n the number line. NF.3 Explain equivalence f fractins in special cases, and cmpare fractins by reasning abut their size. NF.3a-Understand tw fractins are equivalent (equal) if they are the same size, r the same pint n the number line. NF.3b-Recgnize and generate simple equivalent fractins, (e.g., ½ = 2/4, 4/6 = 2/3). Explain why the fractins are equivalent, (e.g., by using visual fractins mdels). NF.3c- Express whle numbers as fractins, and recgnize fractins that are equivalent t whle numbers. (Examples: Express 3 in the frm 3 = 3/1; recgnize that 6/1 = 6; lcate 4/4 and 1 at the same pint n a number line diagram). NF.3d-Cmpare tw fractins with the same numeratr r the same denminatr by reasning abut their size. Recgnize that cmparisns are valid nly when the tw fractins refer t the same whle. Recrd the results f cmparisns with the symbls >, =, <, and justify the cnclusins, (e.g., by using a visual fractin mdel).

6 Gemetry Tpic 11 Reasn with shapes and their attributes. Measurement and Data Tpic 12 Tpic 13 Tpic 14 Tpic 15 Tpic 16 G.1 Understand that shapes in different categries (e.g., rhmbuses, rectangles, and thers) may share attributes (e.g.,having fur sides), and that the shared attributes can define a larger categry (e.g., quadrilaterals). Recgnize rhmbuses, rectangles, and squares as examples f quadrilaterals, and draw examples f quadrilaterals that d nt belng t any f these subcategries. G.2 Partitin shapes int parts with equal areas. Express the area f each part as a unit fractin f the whle. (Fr example, partitin a shape int 4 parts with equal area, and describe the area f each part as ¼ f the area f the shape). Slve prblems invlving measurement and estimatin f intervals f time, liquid vlumes, and masses f bjects. MD.1 Tell and write time t the nearest minute and measure time intervals in minutes. Slve wrd prblems invlving additin and subtractin f time intervals in minutes, (e.g., by representing the prblem n a number line diagram). MD.2 Measure and estimate liquid vlumes and masses f bjects using standard units f grams (g), kilgrams (kg), and liters (l). Add, subtract, multiply r divide t slve ne-step wrd prblems invlving masses r vlumes that are given in the same units, (e.g., by using drawings, such as a beaker with a measurement scale, t represent the prblem).

7 Represent and interpret data. MD.3 Draw a scaled picture graph and a scaled bar graph t represent a data set with several categries. Slve ne- and tw-step hw many mre and hw many less prblems using infrmatin presented in scaled bar graphs. (Fr example, draw a bar graph in which each square in the bar graph might represent 5 pets). MD.4 Generate measurement data by measuring lengths using rulers marked with halves and furths f an inch. Shw the data by making a line plt, where the hrizntal scale is marked ff in apprpriate units whle numbers, halves, and quarters. Gemetric measurement: understand cncepts f area and relate area t multiplicatin and t additin. MD. 5 Recgnize area as an attribute f plane figures and understands cncepts f area measurement. MD.5a-A square with side length 1 unit, called a unit square, is said t have ne square unit f area, and can be used t measure area. MD.5b- A plane figure which can be cvered withut gaps r verlaps by n unit squares is said t have an area f n square units. MD.6 Measure areas by cunting the unit squares (square cm, square m, square in, square ft, and imprvised units), MD.7 Relate area t the peratins f multiplicatin and additin. MD.7a-Find the area f a rectangle with whle-number side lengths by tiling it, and shw that the area is the same as wuld be fund by multiplying the side lengths. MD.7b-Multiply side lengths t find areas f rectangles with whle-number side lengths in the cntext f slving real wrld and mathematical prblems, and represent whle-number

8 prducts as rectangular areas in mathematical reasning. MD.7c-Use tiling t shw in a cncrete case that the area f a rectangle with whle-number side lengths a and b + c is the sum f a b and a c. Use the area mdels t represent the distributive prperty in mathematical reasning. MD.7d- Recgnize area as additive. Find areas f rectilinear figures by decmpsing them int nn-verlapping rectangles and adding the areas f the nn-verlapping parts, applying this technique t slve real wrld prblems. Gemetric measurement: recgnize perimeter as an attribute f plane figures and distinguish between linear and area measures. MD.8 Slve real wrld and mathematical prblems invlving perimeters f plygns, including finding the perimeter given the side lengths, finding an unknwn side length, and exhibiting rectangles with the same perimeter and different areas r with the same area and different perimeters. Resurces: EnVisins Teacher Prgram Overview-Grade 3 pp 8,9,10-11 Pacing Guide referenced: p.14