# The School District of Palm Beach County 3 rd Grade Mathematics Scope st Trimester

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1 1 st Trimester Measurement and Data (MD) MD.2.3 MD.2.4 Represent and interpret data. 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. 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. 1: Represent and Interpret Data 7 days: August 24 -September 1 Organize data in tables and solve problems using the strategy make a table. Read, interpret, and draw a scaled picture graph. Read, interpret, and draw a scaled picture graph. Solve one- and two-step compare problems using data represented in scaled bar graphs. Read, interpret, and draw a line plot. Organize Data Use and Make Picture Graphs Use and Make Bar Graphs Solve Problems Using Data Use and Make Line Plots bar graph data frequency table horizontal bar graph key line plot picture graph scale skip count survey tally table vertical bar graph

2 1 st Trimester Operations and Algebraic Thinking (OA) OA.1.1 OA.1.3 Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Understand properties of multiplication and the relationship between multiplication and division. OA.2.5 OA.3.7 Apply properties of operations as strategies to multiply and divide. Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 2: Understand 13 days: September 2 September 22 Model and skip count objects in equal groups to find how many there are. Write an addition sentence and a multiplication sentence for a model. Model and skip count on a number line to find how many there are. Use arrays to model products and factors. Model the Commutative Property of and use it to find products. Draw a picture or count by 2s to multiply with 2. Use skip counting or a number line to multiply with 10. Use skip counting or a number line to multiply with 5. Model multiplication with the factors 1 and 0. Count Equal Groups Relate Addition and Skip Count on a Number Line Model with Arrays Commutative Property of Multiply with 2 Multiply with 10 Multiply with 5 Multiply with 1 and 0 array Commutative Property of equal groups factor Identity Property of multiply multiple product Zero Property of

3 1 st Trimester Operations and Algebraic Thinking (OA) OA.1.2 OA.1.3 Represent and solve problems involving multiplication and division. Interpret whole- number 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. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Understand properties of multiplication and the relationship between multiplication and division. OA.2.6 OA.3.7 Understand division as an unknown factor problem. Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 3: Understand Division 9 days: September 24 October 6 Solve division problems by using the strategy act it out. Use models to explore the meaning of partitive (sharing) division. Use models to explore the meaning of quotative (measurement) division. Use repeated subtraction and a number line to relate subtraction to division. Model division by using arrays. Use bar models and arrays to relate multiplication and division and write related multiplication and division facts. Model Division Size of Equal Groups Number of Equal Groups Relate Subtraction and Division Model with Arrays Relate and Division divide dividend divisor inverse operations quotient

4 1 st Trimester Number and Operations Fractions (NF) Develop understanding of fractions as numbers. NF.1.1 NF.1.2 NF.1.2a NF.1.2b NF.1.3 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. 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. 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. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 4: Understand Fractions 13 days: October 7 October 26 Explore and identify equal parts of a whole. Use a fraction to name one part of a whole that is divided into equal parts. Read, write, and model fractions that represent more than one part of a whole that is divided into equal parts. Represent and locate unit fractions on a number line. Represent and locate fractions on a number line. Represent and model fractions greater than one. Relate fractions and whole numbers by expressing whole numbers as fractions and recognizing fractions that are equivalent to whole numbers. Divide models to make equal shares. Equal Parts of a Whole Fractions of a Whole Fractions of a Whole Fractions on a Number Lines Fractions on a Number Line Model Fractions Greater than One using a Number Line or an Area Model Relate Fractions and Whole Numbers Equal Shares denominator eighths equal parts fourths fraction fraction greater than 1 halves numerator sixths thirds unit fraction whole NF.1.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

5 1 st Trimester Measurement and Data (MD) Geometric Measurement: understand concepts of area and relate area to multiplication and addition. MD.3.5 MD.3.5a MD.3.5b MD.3.6 MD.3.7 MD.3.7a 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. 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. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Relate area to the operations of multiplication and 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. 5: Understand Area 6 days: October 27 November 3 Explore area as an attribute of polygons. Estimate and measure area of plane shapes by counting unit squares. Relate area to addition and multiplication by using area models. Connect area to the operations of multiplication and division. Understand Area Measure Area Use Area Models Connect Area to and Division area square unit unit square MD.3.7b 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 whole-number products as rectangular areas in mathematical reasoning. End of Trimester: November 13, 2015

6 2 nd Trimester Geometry (G) Number and Operations - Fractions G.1.1 G.1.2 Reason with shapes and their attributes. Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Develop understanding of fractions as numbers. NF.1.1 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. 6: Two-Dimensional Shapes 11 days: November 4 November 20 Identify and describe attributes of plane shapes and polygons. Describe and identify angles and types of lines. Describe, classify, and compare quadrilaterals based on their sides and angles. Draw quadrilaterals. Solve problems by using the strategy draw a diagram to classify plane shapes. Partition shapes into parts with equal areas and express the area as a unit fraction of the whole. Using pattern block shapes, identify fractions when the whole (region) and a part of the region are given. Identify fractions represented by various pattern blocks when whole is defined in different ways. Describe Plane Shapes and Identify Polygons Identify Angles and Sides of Polygons Classify Quadrilaterals Draw Quadrilaterals Classify Plane Shapes Relate Shapes, Fractions, and Area Region Relationships 2 Region Relationships 3 2-D shape angle closed shape hexagon line segment octagon open shape parallel lines pentagon plane shape polygon quadrilateral quadrilateral rectangle rhombus right angle side square trapezoid triangle Venn Diagram Vertex

7 2 nd Trimester Operations and Algebraic Thinking (OA) OA.1.3 OA.1.4 Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Understand properties of multiplication and the relationship between multiplication and division. OA.2.5 Apply properties of operations as strategies to multiply and divide. Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve problems involving the four operations, and identify and explain the patterns in arithmetic. OA.3.7 OA.4.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. 7: and Division Facts and Strategies 17 days: November 23 December 18 Draw a picture or count by 3s to multiply with 3. Draw a picture or use doubles to multiply with 4. Model using the Distributive Property to find products by breaking apart arrays. Write equations to match a broken apart array using the Distributive Property. Draw a picture, use 5s facts and addition, or doubles to multiply with 6. Identify and explain patterns, including patterns for the factors of 9, on the multiplication table. Use the Associative Property of to multiply by 8 or multiply with 3 factors. Use the Commutative or Distributive Property or known facts to multiply with the factor 7. Write related multiplication and division facts. Use an array or division to find an unknown factor. Use different strategies to divide. Divide using the rules for 1 and 0. Multiply with 3 Multiply with 4 Modeling the Distributive Property Distributive Property Multiply with 6 Multiply with 9 and Patterns on the Table Associative Property of and Multiply with 8 Multiply with 7 Write Related Facts Find Unknown Factors Division Strategies Division Rules with 1 and 0 Associative Property of Distributive Property of equation related facts

8 2 nd Trimester Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Understand properties of multiplication and the relationship between multiplication and division. OA.2.5 Apply properties of operations as strategies to multiply and divide. Understand properties of multiplication and the relationship between multiplication and division. OA.4.8 OA.4.9 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. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Use place value understanding and properties of operations to perform multi-digit arithmetic. NBT.1.3 Multiply one-digit whole numbers by multiples of 10 in the range using strategies based on place value and properties of operations. 8: Patterns and Two-Step Problems 9 days: January 5 January 15 Identify and describe whole number patterns and solve problems. Identify and describe a number pattern shown in a function table. Solve multiplication problems by using the strategy draw a diagram. Use base-ten blocks, a number line, or place value to model and record multiplication with multiples of 10. Use the Distributive Property to multiply with bigger numbers. Solve two-step problems by using the strategy act it out. Write equations that represent twostep problems. Number Patterns Describe Patterns Use the Distributive Property Strategies with Multiples of 10 Multiply with Bigger Numbers Two-Step Problems Write equations for Two-Step Problems Commutative Property of Addition Identity Property of Addition pattern

9 2 nd Trimester Number and Operations Fractions (NF) Develop understanding of fractions as numbers. NF.1.3 NF.1.3a NF.1.3b NF.1.3d 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. Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent. 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. 9: Compare Fractions 13 days: January 19 February 4 Solve comparison problems by using the strategy act it out. Compare unit fractions by using models and reasoning strategies. Compare fractions with the same denominator by using models and reasoning strategies. Compare fractions with the same numerator by using models and reasoning strategies. Model equivalent fractions by folding paper, using area models, and using number lines. Generate equivalent fractions by using models. Identify the fractions represented by various pattern blocks when whole is defined in different ways. End of Trimester: February 12, 2016 Compare Fractions Compare Fractions Compare Fractions with the Same Denominator Compare Fractions with the Same Numerator Model Equivalent Fractions Equivalent Fractions Region Relationships 4 equivalent fractions greater than (>) less than (<)

11 Scope rd Trimester Measurement and Data (MD) Geometric Measurement: understand concepts of area and relate area to multiplication and addition. MD.3.7 MD.3.7c MD.3.7d Relate area to the operations of multiplication and 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. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Geometric Measurement: Recognize perimeter as an attribute of plane figures and distinguish between area and linear models. MD : Area and Perimeter 7 days: March 2 March 10 Explore perimeter of polygons by counting units on grid paper. Estimate and measure perimeter of polygons using inch and centimeter rulers. Find the unknown length of a side of a polygon when you know its perimeter. Apply the Distributive Property to area models and to find the area of combined rectangles. Compare areas of rectangles that have the same perimeter and perimeters of rectangles that have the same area. 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. Spring Break: March 18 25, 2016 Florida Standards Assessment (FSA): March 29 April 8, 2016 Finalizing Mastery of 3rd Grade MAFS: April 11 June 2, 2016 Last Day of School: June 2, 2016 Model Perimeter Find Perimeter Find Unknown Side Lengths Area of Combined Rectangles Same Perimeter, Different Areas and Vice Versa perimeter

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