Curriculum Pacing Guide s1

3rd Grade Math Curriculum Guide 2012-2013

1st six Weeks Grade/Course Grade 3/Math Number and Operations in Base Ten & Operations & Algebraic Thinking

st Vocabulary 1 Six Weeks CCS “I can” Statements Assessments Resources Words Use place value understanding and properties of operations to I can use different ways Teacher created Use place value perform multi-digit arithmetic. to describe whole Discovery CCE, SES, BES: Properties of understanding and 3.NBT1: numbers. Education tests operations properties of  Use place value understanding to round whole numbers to the and probes. Accelerated Math operations to nearest I can round whole Multi-digit perform multi-digit numbers to the nearest Drops in the 10 or 100. arithmetic arithmetic 10 or 100. Bucket 3.NBT.2: Rounding  Fluently add and subtract within 1000 using strategies and algorithms Represent and I can fluently DPP Trailblazers Whole solve problems based on place value, properties of operations, and/or the numbers involving relationship between addition and subtraction. add/subtract within One-to-One series Nearest 10 multiplication and 1000 using different Nearest 100 division. Represent and solve problems involving multiplication and strategies. Education City division. Multiply and divide 3.OA.1: What’s My Place? Base Ten within 1 00. I can use strategies to What’s My Value?  Interpret products of whole numbers, e.g., interpret 5 × 7 as the total multiply one-digit Pack number of objects in 5 groups of 7 objects each. For example, Flats Solve problems numbers by multiples Crosswalk Coach involving the four describe a context in which a total number of objects can be Skinnies operations, and expressed as 5 ×7. of 10 (up to 90). McGraw-Hill Math Bits identify and 3.OA.2: Series explain patterns in  Interpret whole-number quotients of whole numbers, e.g., interpret I can use different Multiply arithmetic. 56 ÷ 8 as the number of objects in each share when 56 objects are strategies for adding Discovery subtracting within 1000. Education Divide partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For Product example, describe a context in which a number of shares or a I can fluently Groundworks: add/subtract within 1000. Factors number of groups can be expressed as 56 ÷ 8. Algebraic Thinking Arrays Multiply and divide within 100. 3.OA.1 Reasoning About Quotient 3.OA.7: I can find the product Measurement Dividend  Fluently multiply and divide within 100, using strategies such as the of multiple groups of Divisor relationship between multiplication and division (e.g., knowing that 8 Reasoning with × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the objects. Digit Data and end of Grade 3, know from memory all products of two one-digit Probability numbers. .3.OA.3 Equations Reasoning with I can multiply and Pattern Geometry Understand properties of multiplication and the relationship divide within 100. Order of Reasoning with between multiplication and division. operation Numbers 3.OA.5: I can solve word Estimation  Apply properties of operations as strategies to multiply anddivide.2 problems using Table Common Core Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. different strategies. Flip chart (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. I can represent a word Problem Solver 3 Associative property of multiplication.) Knowing that 8 × 5 = 40 and problem using 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = pictures or symbols. 40 + 16 = 56. (Distributive CCE: property.) Harcourt Math 3.OA.6: 3.OA.4 Silver Burdett Ginn  I can multiply and Understand division as an unknown-factor problem. For example, find Series 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. divide within 100. Represent and solve problems involving multiplication and Singapore Math division. 3.0A.4 3.OA.4: I can solve to find the Everyday Math  Determine the unknown whole number in a multiplication or division unknown whole equation relating three whole numbers. For example, determine the Buckle Down, unknown number that makes the equation true in each of the number in a Terra Nova & Coach equations 8× ? = 48, 5 = � ÷ 3, 6 × 6 = ?. multiplication or 3.OA.3: division equation.  Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement I can explain how the SES: quantities,e.g., by using drawings and equations with a symbol for the properties of unknown number to represent the problem.1 operations work. Common Core Solve problems involving the four operations, and identify and Clinics explain patterns in arithmetic. 3.OA.9: I can apply properties  Identify arithmetic patterns (including patterns in the addition table or of operations as multiplication table), and explain them using properties of operations. strategies to multiply For example, observe that 4 times a number is always even, and and divide. explain why 4 times a number can be decomposed into two equal addends.

3.OA.8:  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 Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.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 operations. 3rd Grade Math Curriculum 2012-2013 2nd Six Weeks

Grade/Course Grade 3/Math Numbers and Operations: Fractions & Geometry

Vocabulary 2nd Six Weeks CCS “I can” Assessments Resources Words Statements Fractions: Develop Develop understanding of fractions as numbers. I can recognize and Teacher created understanding of 3.NF.1: identify a unit fraction formative CCE, SES, BES: Adding fractions as  Understand a fraction 1/b as the quantity formed by 1 part when a when the whole is Assessments Comparing numbers. whole is partitioned into b equal parts; understand a fraction a/b as partitioned into equal Accelerated Math Ordering the quantity formed by a parts of size 1/b. parts. Teacher created Equivalent Reason with Discovery Drops in the Part of a whole shapes and their 3.NF.2: I can use fractions to Education tests Bucket Part of a group attributes. Understand a fraction as a number on the number line; represent fractions represent numbers equal and probes. Simplest form on a number line diagram. to, less than, and greater DPP Trailblazers Numerator Develop  a. Represent a fraction 1/b on a number line diagram by defining the than one. Denominator understanding of interval from 0 to 1 as the whole and partitioning it into b equal parts. One-to-One Number line fractions as Recognize that each part has size 1/b and that the endpoint of the I can define the interval series Subtracting numbers. part based at 0 locates the number 1/b on the number line. from 0 to 1 on a number  b. Represent a fraction a/b on a number line diagram by marking off line as the whole. Education City a lengths 1/b from 0. Recognize that the resulting interval has size I can recognize that the What’s My Place? a/b and that its endpoint locates the number a/b on the number line. equal parts between 0 to What’s My Reason with shapes and their attributes. 1 have a fractional Value? 3.G.2: representation.  Partition shapes into parts with equal areas. Express the area of each Crosswalk Coach part as a unit fraction of the whole. For example, partition a shape I can explain that the end into 4 parts with equal area, and describe the area of each part as 1/4 of each equal part is McGraw-Hill of the area of the shape. represented by a fraction. Math Series Develop understanding of fractions as numbers. 3.NF.3: I can describe and Discovery Explain equivalence of fractions in special cases, and compare fractions recognize simple Education by reasoning about their size. equivalent fractions.  a .Understand two fractions as equivalent (equal) if they are the same I can compare fractions Groundworks: size, or the same point on a number line. by looking at their size to Algebraic  b. Recognize and generate simple equivalent fractions, e.g., 1/2 = determine equivalence. Thinking 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. I can use number lines, Reasoning About  c. Express whole numbers as fractions, and recognize fractions that size, visual fraction Measurement models, etc. to find are equivalent to whole numbers. Examples: Express 3 in the form 3 equivalent fractions. Reasoning with = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a Data and number line diagram. Probability  d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that Reasoning with comparisons are valid only when the two fractions refer to the same Geometry whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Reasoning with Numbers

Common Core Flip chart

Problem Solver 3

CCE: Harcourt Math

Silver Burdett Ginn Series

Singapore Math

Everyday Math

Buckle Down, Terra Nova & Coach

Common Core Clinics

3rd Six Weeks Grade/Course Grade 3/Math Measurement & Data (Review-operations & algebraic thinking)

Vocabulary Words 3rd Six Weeks CCS “I can” Assessments Resources Statements Solve problems I can recognize minute Teacher created involving Solve problems involving measurement and estimation of intervals marks on an analog formative CCE, SES, BES: measurement and of time, liquid volumes, and masses of objects. clock face and the Assessments estimation of minute position on a Accelerated Math Analog intervals of time, digital clock face. Teacher created Digital liquid volumes, and 3.MD.1: Discovery Drops in the Minute masses of objects.  Tell and write time to the nearest minute and measure time intervals in I can write and tell time Education tests Bucket Intervals minutes. Solve word problems involving addition and subtraction of to the nearest minute. and probes. Number line time intervals in minutes, e.g., by representing the problem on a DPP Trailblazers diagram Represent and number line diagram. I can compare an analog Compare interpret data. 3.MD.2: clock face with a number One-to-One Minute marks  Measure and estimate liquid volumes and masses of objects using line diagram. series Recognize I can use a number line standard units of grams (g), kilograms (kg), and liters (l).6 Add, Minute Position to add and subtract time Education City Addition subtract, multiply, or divide to solve one-step word problems involving intervals in minutes. Subtraction masses or volumes that are given in the same units, e.g., by using What’s My Place? drawings (such as a beaker with a measurement scale) to represent the I can solve word What’s My problem.7 problems involving Value? Represent and interpret data. addition and subtraction of time intervals in Crosswalk Coach 3.MD.3: minutes. McGraw-Hill  Draw a scaled picture graph and a scaled bar graph to represent a data 3.MD.2 Math Series set with several categories. Solve one- and two-step “how many more” I can explain how to and “how many less” problems using information presented in scaled measure liquid volume in Discovery bar graphs. For example, draw a bar graph in which each square in the liters. Education bar graph might represent 5 pets. I can explain how to Groundworks: 3.MD.4: measure mass in grams Algebraic  Generate measurement data by measuring lengths using rulers marked and kilograms. Thinking with halves and fourths of an inch. Show the data by making a line I can add, subtract, Reasoning About plot, where the horizontal scale is marked off in appropriate units— multiply and divide units Measurement whole numbers, halves, or quarters. of liters, grams, and kilograms. Reasoning with Data and I can use various Probability strategies represent a word problem involving Reasoning with liquid volume or mass. Geometry

3.MD.2 Reasoning with I can solve one step Numbers word problems involving masses given in the Common Core same units. Flip chart

I can solve one step Problem Solver 3 word problems involving liquid volume given in the same units. CCE: Harcourt Math I can measure liquid volumes using standard Silver Burdett units of liters. Ginn Series

I can measure mass of Singapore Math objects using standard units of grams (g), and Everyday Math kilograms (kg). Buckle Down, I can define horizontal Terra Nova & axis. Coach

I can identify each plot Problem Solver 3 on the line as data or a number of objects. SES: I can analyze data from a line plot. Common Core Clinics I can determine appropriate unit of measurement.

I can determine appropriate scale for a line plot.

I can generate measurement data by using rulers marked with halves and fourths of an inch.

3rd Grade Math Curriculum Guide 2012-2013 th Grade/Course Grade 3/Math 4 Six Weeks Measurement and Data (Review operations & algebraic thinking)

Vocabulary 4th Six Weeks CCS “I can” Assessments Resources Words Statements Geometric I can define horizontal Teacher created Plane figure measurement: Geometric measurement: understand concepts of area and relate axis. formative CCE, SES, BES: Square understand area to multiplication and to addition. Assessments Measurement concepts of area 3.MD.5: I can identify each plot Accelerated Math Rectangle and relate area to Recognize area as an attribute of plane figures and understand concepts on the line as data or a Teacher created Area multiplication and of area measurement. number of objects. Discovery Drops in the Tiling to addition. Education tests Bucket  Polygon a. A square with side length 1 unit, called “a unit square,” is said to I can analyze data from and probes. have “one square unit” of area, and can be used to measure area. Perimeter Geometric a line plot. DPP Trailblazers  Length measurement b. A plane figure which can be covered without gaps or overlaps by Side recognize n unit squares is said to have an area of n square units. I can determine One-to-One perimeter as an 3.MD.6: appropriate unit of series attribute of plane  Measure areas by counting unit squares (square cm, square m, measurement. figures and square in, square ft, and improvised units). Education City distinguish 3.MD.7: I can determine between linear and Relate area to the operations of multiplication and addition. appropriate scale for a What’s My Place? line plot. What’s My area measures.  a. Find the area of a rectangle with whole-number side lengths by Value? tiling it, and show that the area is the same as would be found by 3.MD.5 multiplying the side lengths. I can define area. Crosswalk Coach  b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and I can define a “unit McGraw-Hill mathematical problems, and represent whole-number products as square”. Math Series rectangular areas in mathematical reasoning.  c. Use tiling to show in a concrete case that the area of a rectangle I can relate the number Discovery with whole-number side lengths a and b + c is the sum of a × b and a (n) of unit squares to Education the area of a plane × c. Use area models to represent the distributive property in figure. Groundworks: mathematical reasoning. Algebraic  d. Recognize area as additive. Find areas of rectilinear figures by I can cover the area of a Thinking decomposing them into non-overlapping rectangles and adding the plane figure with unit areas of the non-overlapping parts, applying this technique to solve squares without gaps or Reasoning About real world problems. overlaps. Measurement

3.MD.6 Reasoning with Geometric measurement: recognize perimeter as an attribute of I can measure area by Data and plane figures and distinguish between linear and area measures. counting unit squares. Probability 3.MD.8: I can use unit squares Reasoning with  Solve real world and mathematical problems involving perimeters of cm, m, in, ft, and other Geometry polygons, including finding the perimeter given the side lengths, sizes of unit squares to finding an unknown side length, and exhibiting rectangles with the measure the area. Reasoning with same perimeter and different areas or with the same area and Numbers different perimeters. 3.MD.7a I can find the area of a Common Core rectangle by tiling it in Flip chart unit squares. Problem Solver 3 I can find the side lengths of a rectangle in CCE: units. Harcourt Math

3.MD.7b Silver Burdett I can multiply side Ginn Series lengths to find areas of rectangles. Singapore Math

I can use rectangular Everyday Math arrays to represent whole-number products Buckle Down, in multiplication Terra Nova & problems. Coach

3.MD.8 Problem Solver 3 I can define a polygon.

I can define perimeter. SES:

I can find perimeter Common Core when given the length of Clinics sides and when there is an unknown side.

I can exhibit rectangles with the same area and different perimeters.

5th Six Weeks Grade/Course Grade 3/Math Geometry (Review-operations & algebraic Thinking)

Vocabulary 5th Six Weeks CCS “I can” Assessments Resources Words Statements I can identify and define Teacher created CCE, SES, BES: Reason with rhombuses, rectangles, formative 2D figure shapes and their and squares as examples Assessments Accelerated Math Square attributes. of quadrilaterals based Rectangle Reason with shapes and their attributes. on their attributes. Teacher created Drops in the Triangle 3.G.1: Discovery Bucket Circle  Understand that shapes in different categories (e.g., rhombuses, rectangles, and I can describe, analyze, Education tests others) may share attributes (e.g., having four sides), and compare properties and probes. DPP Trailblazers 3D figure and that the shared attributes can define a larger category (e.g., quadrilaterals). of two-dimensional Rectangular Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and shapes. One-to-One prism draw examples of quadrilaterals that series Cylinder do not belong to any of these subcategories. I can compare and Cube classify shapes by Education City Cone attributes, sides, and Pyramid angles. What’s My Place? Sphere What’s My Base I can group shapes with Value? Vertex shared attributes to Face define a larger category. Crosswalk Coach Edge Net I can define a polygon. McGraw-Hill Math Series Ray I can define perimeter. Angle Discovery Parts of a line: I can partition shapes Education Line into equal areas. Line Segment Groundworks: Endpoint I can describe the area Algebraic Intersecting of each part as a Thinking lines fractional part of a Parallel lines whole. Reasoning About Measurement Parts of a circle: Diameter I can identify, describe, Reasoning with radius and classify polygons. Data and Probability I can identify attributes of triangles & Reasoning with quadrilaterals. Geometry

Reasoning with Numbers

Common Core Flip chart

Problem Solver 3 CCE: Harcourt Math

Silver Burdett Ginn Series

Singapore Math

Everyday Math

Buckle Down, Terra Nova & Coach

Common Core Clinics

th Grade/Course Grade 3/Math 6 Six Weeks Review 3rd Grade content based on Discovery Benchmark 3 results

Vocabulary 6th Six Weeks CCS “I can” Assessments Resources Words Statements Focus based on the Review 3rd Grade content based on Discovery Benchmark 3 Results. Teacher created 3rd Discovery formative Assessment Assessments

Teacher created Discovery Education tests and probes.