# Casey County Schools- 3 rd Grade Math Map

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1 Week(s) Standard I can statement(s) Critical Vocabulary 3.MD.1 (Teach throughout the year) Resources Used throughout the year (math minutes, automaticity) Formative Assessment(s) (this will be left blank for you to fill in as you assess your students in each class) NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. I can round a whole number to the nearest 10 and to the nearest 100. Digits Place value Standard form Word form Expanded form Period Compare Estimate Compatible numbers Round Order Tens Ones Hundreds About how many Resonableness Lessons: 1.1 & & & Ready Common Core Lesson 8 (combine with 2.5) November 2015 Page 1

2 4-5 3.NBT.2 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. I can use strategies and algorithms to fluently add within I can use strategies and algorithms to fluently subtract within Equation Sum Difference Addends Regroup About how many Reasonableness Expanded algorithms Chapter 2/3 (choose topics as needed) Ready Common Core Lesson OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. I can find and interpret products of whole numbers as a total number of objects in a number of groups. Array Equal Groups Fact Family Multiplication Product Factor Lesson 1 November 2015 Page 2

3 OA.9 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. I can identify and explain relationships between numbers in arithmetic patterns. (such as even and odd numbers, patterns in an addition table, patterns in a multiplication table, patterns regarding multiples and sums) I can explain rules for a pattern using properties of operations. (Properties of operations, glossary page 90 Common Core State Standards) Pattern 5.1 & & Lesson NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. I can multiply onedigit whole numbers by multiples of 10 in the range & 5.6 Lesson 10 3.OA.4 Determine the unknown whole number in a multiplication or I can Multiply within 100. November 2015 Page 3

4 division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 X? = 48, 5 = 3, 6 X 6 =? A.3 Use multiplication and division within 100 to solve word problems in situations 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. Solve to find the unknown whole number in a multiplication equation. I can solve word problems in situations involving equal groups, arrays, and measurement quantities. I can multiply within 100. I can represent a word problem using a picture and an equation with a symbol for the unknown number. Symbol Word Problem Multiples Lesson 11, 12, and 13 (pullout multiplication) 13 3.OA.5 Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 4 = 24 is I can apply properties of operations to multiply. Commutative Prop Distributive Prop Associative Prop November 2015 Page 4

5 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.) I can find the product of multiple groups of objects Identity Prop Zero Prop (REVIEW) Review all necessary standards OA.2 Interpret wholenumber 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. For example, describe a context in which a number of I can explain what division means and how it relates to equal shares. I can interpret quotients as the number of shares or the number of groups when a set of objects is divided equally. Review all vocabulary used up to this point. Division Quotient Dividend Divisor Shares = Groups Lesson 4 November 2015 Page 5

6 shares or a number of groups can be expressed as OA.6 Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. I can identify the multiplication problem related to the division problem. I can identify the unknown factor in the related multiplication problem. Fact Family Lesson 5 I can use multiplication to solve division problems. I can explain the relationship between multiplication and division. November 2015 Page 6

7 OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 X? = 48, 5 = 3, 6 X 6 =?. 3.OA.5 Apply properties of operations as strategies to multiply and divide.2 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.) I can divide within 100. Solve to find the unknown whole number in a division equation. I can determine which operations (multiplication and division) is needed to determine the unknown whole number November 2015 Page 7

8 3.0A.3 Use multiplication and division within 100 to solve word problems in situations 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. I can solve word problems in situations involving equal groups, arrays, and measurement quantities. I can divide within 100. I can represent a word problem using a picture and an equation with a symbol for the unknown number OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from I can fluently multiply and divide within November 2015 Page 8

9 memory all products of two one-digit numbers 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 3 This standard is limited to problems posed with whole numbers and having I can use the order of operations (without parentheses). I can construct an equation with a letter standing for the unknown quantity. I can solve two-step word problems using the four operations. I can justify my answer using various estimation strategies. Reasonableness Lesson 12 Lesson 13 November 2015 Page 9

10 whole-number answers; student should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 21 Review all necessary standards NF.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. I can identify the equal parts of a whole region. I can name the equal parts of a region as a fraction. I can express a fraction as the number of unit fractions. I can use unit fractions to represent numbers equal to, less than and greater than one (1/3 and 1/3 is 2/3; 1/3, 1/3, 1/3, and 1/3 is 4/3). Review all vocabulary used up to this point. Halves Thirds Fourths Fifths Sixths Eighths Fraction Unit fraction Numerator Denominator Benchmark fraction 9.1 & Lesson 14 November 2015 Page 10

11 23 3.NF.2a Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. 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 on 0 locates the number 1/b on the number line. I can define the interval from 0 to 1 on a number line as the whole. I can divide a whole on a number line into equal parts. I can recognize that the equal parts between 0 and 1 have a fractional representation. I can represent each equal part on a number line with a fraction. Interval Chapters Lesson 15 I can explain that the end of each equal part is represented by a fraction (1/the number of equal parts). 3.NF.2b Understand a fraction as a number on the number line; represent fractions on a number line diagram. I can define the interval from 0 to 1 on a number line as the whole. November 2015 Page 11

12 b. 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. I can divide a whole on a number line into equal parts. I can represent each equal part on a number line with a fraction. I can name an endpoint NF.3ab Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. 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. I can describe and recognize simple equivalent fractions. I can compare fractions. I can recognize whole numbers written in fractional parts on a number line. Equivalent fraction Lesson 16 & 17 3.NF.3c Explain equivalence of fractions in I can recognize the difference in a whole Mixed number 10.7 November 2015 Page 12

13 special cases, and compare fractions by reasoning about their size. c. 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. 3.NF.3d Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. d. 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. number and a fraction. I can explain how a fraction is equivalent to a whole number. I can explain what the numerator and what the denominator in a fraction represents and its location. I can determine if comparisons of fractions can be made (if they refer to the same size). I can compare two fractions with the Lesson 18 &19 November 2015 Page 13

14 same numerator by reasoning about their size. I can compare two fractions with the same denominator by reasoning about their size 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 that do not belong to any of these subcategories. I can define a polygon. I can identify and define rhombuses, rectangles, and squares as examples of quadrilaterals based on their attributes. I can describe, analyze, and compare properties of twodimensional shapes. I can compare and classify shapes by attributes, sides and angles. I can group shapes with shared attributes to define a larger Lesson 31 & 32 November 2015 Page 14

15 category (e.g., quadrilaterals). 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 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape. I can draw examples of quadrilaterals that do and do not belong to any of the subcategories. I know that shapes can be partitioned into equal areas. I can describe the area of each part as a fractional part of the whole. I can relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole. (See 3rd grade introduction). Lesson 33 November 2015 Page 15

16 28 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 different perimeters. I can define perimeter. I can find the perimeter when given the length of sides. I can find the perimeter when there is an unknown side length. Perimeter Lesson 30 I can exhibit (design, create, draw, model, etc.) rectangles with the same perimeter and different areas. Teach this after area. November 2015 Page 16

17 29 3.MD.5ab Recognize area as an attribute of plane figures and understand concepts of area measurement. a. 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. b. 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. I can exhibit rectangles with the same area and different perimeters. I can define unit square. I can define area. I can relate the number (n) of unit squares to the area of a plane figure. I can cover the area of a plane figure with unit squares without gaps or overlaps. Area Square unit Plane figure Chapter Lesson 27 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). I can measure areas by counting unit squares. I can use unit squares of cm, m, in, ft, and other sizes of unit squares to measure area. November 2015 Page 17

18 3.MD.7a Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. 3.MD.7b Relate area to the operations of multiplication and addition. b. 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. I can find the area of a rectangle by tiling it in unit squares. I can find the side lengths of a rectangle in units. I can compare the area found by tiling a rectangle to the area found by multiplying the side lengths. I can multiply side lengths to find areas of rectangles. I can solve real world and mathematical area problems by multiplying side lengths of rectangles. I can use rectangular arrays to represent whole-number products in multiplication problems. 3.MD.7c Relate area to the operations of November 2015 Page 18

19 multiplication and addition. c. 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. I can multiply using an area model (array). I can relate area of a rectangle to multiplication and addition by modeling the distributive property. Area of a Rectangle 3 x (5+2) = 3x5 + 3x2 3.MD.7d Relate area to the operations of multiplication and addition. d. 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. I can find areas of rectangles. I can add areas of rectangles. I can recognize that areas of each rectangle in a rectilinear (straight line) figure can be added together to find the area of the figure. I can use the technique of decomposing rectilinear figures to November 2015 Page 19

20 find the area of each rectangle to solve real world problems. I can decompose rectilinear figures into non-overlapping rectangles ( Teach time throughout the year) 3.MD.1 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. I can recognize minutes on analog clocks and on digital clocks I can write and tell time to the minute. I can compare an analog clock face with a number line diagram. Hour Minute O clock Half-hour Quarter hour Elapsed time I can use a number line diagram to add and subtract time intervals in minutes. I can solve word problems involving addition and subtraction of time intervals in minutes. November 2015 Page 20

21 3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step 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.7 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 ; see Glossary, Table 2). I can explain how to measure liquid volume in liters. I can explain how to measure mass in grams and kilograms. I can add, subtract, multiply and divide units of liters, grams, and kilograms. I can use strategies to represent a word problem involving liquid volume or mass. I can solve one step word problems involving masses given in the same units. I can solve one step word problems involving liquid volume given in the same units. Capacity Cup (c) Pint (pt) Quart (qt) Gallon (gal) Milliliter (ml) Liter (L) Mass Gram (g) Kilogram (kg) Weight Ounce (oz) Pound (lb) Ton (T) November 2015 Page 21

22 I can measure liquid volumes using standard units of liters. I can measure mass of objects using standard units of grams (g), and kilograms (kg). 3.MD.3 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. I can explain the scale of a graph with a scale greater than one. I can identify the scale of a graph with a scale greater than one. I can analyze a graph with a scale greater than one. I can choose a proper scale for a bar graph or picture graph. I can interpret a bar/picture graph to solve one or two step Bar graph Scale Pictograph Key November 2015 Page 22

23 problems asking how many more and how many less. I can create a scaled picture graph to show data. I can create a scaled bar graph to show data. I can define horizontal axis. 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. I can identify each plot on the line as data or a number of objects. I can analyze data from a line plot. I can determine appropriate unit of measurement. I can determine appropriate scale for line plot. I can generate measurement data by measuring lengths Horizontal Vertical Line plot November 2015 Page 23

24 using rulers marked with halves and fourths of an inch. I can create a line plot where the horizontal scale is marked off in appropriate unitswhole numbers, halves, or quarters. November 2015 Page 24

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