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1 Unit 1: Place Value and Multi-Digit Addition and Subtraction Place value drawings to represent numbers. Place value drawings to add and subtract whole numbers. Different methods to add and subtract whole numbers. Pacing 20 days (September) Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value. In a multi-digit whole number, a digit in one place represents ten times what if would represent in the place immediately to its right. Place value can be used to compare and order numbers. Rounding whole numbers is a process for finding the multiple of 10, 100, and so on closest to a given number. Representing numbers and numerical expressions in equivalent forms can make some calculations easy to do mentally. There is more than one way to do a mental calculation. The standard addition and subtraction algorithms for multi-digit numbers break the calculation into simpler calculations using place value starting with the ones, then the tens, and so on. There is more than one way to estimate a sum or difference. Use place value drawings to conceptualize numbers and understand the relative sizes of place values. Use different methods to add and subtract whole numbers. Read and write whole numbers to one million. Use place value to round whole numbers to any place. 4.NBT Number and Operations in Base Ten How are greater numbers read and written? How can whole numbers be compared and ordered? How can sums and differences of whole numbers be estimated? What are standard procedures for adding and subtracting whole numbers? Generalize place value understanding for multi-digit whole numbers less than or equal to 1,000,000.

2 o o o Recognize that in a multi-digit whole number, a digit in any place represents 10 times as much as it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. Use place value understanding and properties of operations to perform multi-digit arithmetic on whole numbers less than or equal to 1,000,000. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Place value drawings Dot array Digit Standard form Word form Expanded form Greater than > Less than < Sum Difference Inverse operations (2) forms resources (Print Resources; Digital Resources); differentiated Instruction Quick Quizzes (after each Big Idea section) Unit Tests (Open Response; Multiple Choice; Performance Task)

3 Unit 2: Multiplication with Whole Numbers Pacing 21 days (Oct/Nov) 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 will be able to use the commutative, associative, identity, What are the properties of multiplication? and distributive properties to solve multiplication What are multiplication patterns? problems. How can I solve division problems? I will use area models and rectangular arrays to solve multiplication and division problems. How can multiplication help me to divide? Students will use addition, subtraction, multiplication and division to compute answers to solve real world problems. They will review and apply multiplication and division facts and strategies for mentally computing products and quotients. They will also use variables to solve multiplication and division problems. Students will apply these skills to solve real world problems by using manipulatives and word problem challenges. NBT.A.1: Recognize in a multi-digit whole number, a digit in one place represents 10 times what it represented in the place to its right. NBT.A.5: Multiply a whole number of up to 4 digits by a one-digit whole number, & multiply 2 two-digit numbers, using strategies based on place value & the properties of operations. Illustrate & explain the calculation by using equations, rectangle arrays, and/or area model. OA.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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. Know multiplication facts and related division facts through 12 x MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. array area (2) forms resources (Print Resources; Digital (4) Quick Quizzes (after each Big Idea section)

4 area model square unit factor product estimate rounding Place Value Sections Methods Expanded Notation Method Distributive Property partial products Algebraic Notation Method Shortcut Method Resources); differentiated Instruction (3) Unit Tests (Open Response; Multiple Choice; Performance Task)

5 Unit 3: Division with Whole Numbers Pacing: 17 Days (Nov./Dec.) use arrays and area models to represent multiplication and division use concrete materials or diagrams to count all of the quantities involved in a multiplication or division. use drawings and equations to solve word problems. use properties of operations to multiply and divide. Estimating and rounding can be used to see if an answer is reasonable. How can we use estimation to see if an answer is reasonable? Area models can be used to solve division problems. What methods can be used to solve division problems? Remainders can be interpreted in different ways. What does a remainder represent in a division problem? Draw visual array and rectangle diagrams to represent multiplication Reason repeatedly about the connection between math drawings and written numerical work See that division algorithms are summaries of their reasoning about quantities NBT.3 Use place value understanding to round multi-digit whole numbers to any place. NBT.6 Find whole-number quotients & remainders with up to 4-digit dividends & 1-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication & division. OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equation with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. divisor quotient dividend situation equation solution equation (2) Quick Quizzes (1) Unit Review Assessment (1) Unit Test (choice of 2 forms: open response; multiple choice) (1) District Developed Assessment 2 forms (Print & Digital resources)

6 Unit 4: Equations and Word Problems Pacing 17 Days (Jan.) Use arrays and area models to represent multiplication and division Use concrete materials or diagrams to count all of the quantities involved in a multiplication or division. Use drawings and equations to solve word problems. Use properties of operations to multiply and divide. There are types of word problems that have similar What strategies can be used to solve word problems? characteristics. What determines if a number is prime or composite? Word problems may involve a combination of addition, subtraction, multiplication, and division. What is a number pattern? Numbers are prime or composite. Number patterns follow rules. Write equations to solve problems using any of the four operations. Solve multistep word problems. Identify numerical, repeating, and growing patterns Evaluate expressions with parentheses NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. NBT.6 Find whole-number quotients & remainders with up to 4-digit dividends & 1-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication & division. MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

7 OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 1 OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equation with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. OA.4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. divisor quotient dividend situation equation solution equation 2 forms (Print & Digital resources) (2) Quick Quizzes (1) Unit Review Assessment (1) Unit Test (choice of 3 forms: open response; multiple choice; performance)

8 Unit 5: Measurement Pacing: 13 Days (Jan./Feb.) Represent problems involving addition and subtraction of time using a number line diagram. Use drawings to represent a measurement problem. Use tiles and square unites to represent an area problem Decompose a rectilinear figure into non-overlapping rectangle Measurement units can be converted within a single system of measurement. How can the four operations help solve word problems with measurement? Converting measurements in the metric system involves What is the customary system of measurement? multiplication and division by ten or factors of ten. What are the metric units for measuring length, capacity, Data sets can be organized in a variety of ways, including line plots. weight/mass? Know relative sizes of measurement units within one system of measurement. Express measurements in a larger unit in terms of a smaller unit. Use the four operations to solve word problems with measurement. Use formulas to solve area and perimeter problems. MD.1: Know relative sizes of measurement units within 1 system of units & express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a 2-column table. MD.2: Use all 4 basic operations to solve word problems involving distances, interval of times, liquid volume, masses of objects, money (fractions or decimals), and using MD.1. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. MD.3: Apply the area & perimeter formulas for rectangles in real world & mathematical problems. MD.4: Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition & subtraction of fractions by using information presented in line plots. millimeter (mm) square unit 2 forms (Print & Digital resources) (2) Quick Quizzes centimeter (cm) area (1) Unit Review Assessment decimeter (dm.) meter (M) (1) Unit Test (choice of 3 forms: open kilometer (km.) liquid volume response; multiple choice; performance) metric system mass liter (L) gram (g) kiloliter (kl.) kilogram (kg)

9 milliliter (ml) line plot foot (ft.) mile (mi) ounce (oz.) cup (c) quart (qt.) gallon (gal.) length formula milligram (mg) inch (in) yard (yd.) pound (lb.) ton (T) fluid ounce pint (pt.) perimeter width

10 Unit 6: Fraction Concepts and Operations Pacing: 16 Days (Feb./Mar.) *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. *represent fractions on a number line Improper fractions and mixed numbers express the same value. A product of a fraction and a whole number can be written as a multiple of a unit fraction. Why do we need like denominators to add or subtract fractions? What models can be used to represent the addition and subtraction of fractions? Express a fraction as a sum of other fractions Express a fraction as a product of whole number and a unit fraction. Add and subtraction fractions with like denominators. Multiply unit and non-unit fractions by a whole number. Solve real-world problem involving line plots. NF.3: Understand a fraction a/b with a >1 as a sum of fractions 1/b. a: Understand addition & subtraction of fractions as joining and separating parts referring to the same whole. b: Decompose a fraction into a sum of fractions with the same denominator in more than 1 way, recording each decomposition by an equation. Justify decomposition. c: Add and subtract mixed numbers with like denominators. d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. NF.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a: Understand a fraction a/b as a multiple of 1/b. b: Understand a multiple of a/b as a multiple of a/b, and use this understanding to multiply a fraction by a whole number. c: Solve word problems involving multiplication of a fraction by a whole number (using visual fraction models and equations to represent the problem). MD.4: Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition & subtraction of fractions by using information presented in line plots. unit fraction fraction 2 forms (Print & Digital resources) (2) Quick Quizzes

11 numerator denominator mixed number (1) Unit Review Assessment (1) Unit Test (choice of 3 forms: open response; multiple choice; performance)

12 Unit 7: Fractions and Decimals Pacing: 19 Days (Mar.) Use number lines to determine if two fractions are equivalent Use visual models to explain why fractions are equivalent Recognize that comparisons are valid only when they refer to the same whole. Use the symbols >, <, or = to compare fractions and justify conclusions using a visual model. Fractions can be compared by reasoning about the size of the numerator and the denominator. How does finding equivalent fractions help you compare? Decimal notation is another way to represent a fraction. How are decimals and fractions related? Fractions with denominators of 10 can be expressed as an equivalent fraction with a denominator of 100. Fractions with denominators of 10 or 100 can be expressed as decimals. Explain why fraction a/b is equivalent to fraction n x a/n x b. Compare two fractions with different denominators. Add two fractions with denominators of 10 or 100. Use decimal notation for fractions with denominators 10 or 100. Compare two decimals to hundredths. NF.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number & size of the parts differ even though the 2 fractions themselves are the same size. Use this principle to recognize & generate equivalent fractions NF.2: Compare 2 fractions with different numerators & different denominators (ex. By creating common denominators or numerators or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the 2 fractions refer to the same whole. Record the results of comparisons with symbols >, <, =, and justify the conclusion by using visual model. NF.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. NF.7: Compare 2 decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the 2 decimals refer to the same whole. Record the results of comparisons with the symbols >, <, or = & justify the conclusions by using visual model. MD.4: Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition & subtraction of fractions by using information presented in line plots.

13 equivalent fractions tenths 2 forms (Print & Digital resources) (3) Quick Quizzes simplify hundredths (1) Unit Review Assessment common denominator decimal number (1) Unit Test (choice of 3 forms: open response; multiple choice; performance)

14 Unit 8: Geometry Pacing: 19 Days (Apr./May) Sorting quadrilaterals by shared attributes. Lines, rays, and angles are used to identify 2- dimensional figures. How are parallel and perpendicular lines used to classify two-dimensional figures? Two-dimensional figures are classified by the type of lines (parallel or perpendicular) and size of angles. How can lines, angles, and shapes be described, analyzed, and classified? Angles are composed of smaller angles. Why do some shapes have more than one line of symmetry? Measure angles in whole number degrees Solve problems to find unknown angles Draw and identify two-dimensional figures. Classify 2-D figures using attributes including parallel and perpendicular sides and angle size Recognize and draw lines of symmetry for 2-D figures G.1: draw points, lines (perpendicular and parallel), line segments, rays, angles (right, acute, obtuse). Identify these in 2- dimenstional figures. G.2.: classify 2-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of a specified size. G.3: recognize a line of symmetry for a 2-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify and draw line-symmetric figures. MD.5: recognize angles as geometric shapes that are formed wherever 2 rays share a common endpoint, and understand concepts of angle measurement. a. an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the 2 rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles. b: an angle that turns through n one-degree angles is said to have an angle measure of n degrees. MD.6: measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. MD.7: recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. point vertex 2 forms (Print & Digital resources) (4) Quick Quizzes

15 line line segment endpoint angle ray straight angle circle triangle right triangle obtuse triangle congruent triangle adjacent angle decompose perpendicular adjacent trapezoid rhombus square polygon line of symmetry right angle acute angle obtuse angle straight angle degree protractor reflex angle isosceles triangle scalene triangle acute triangle equilateral compose parallel quadrilateral opposite parallelogram rectangle diagonal line symmetry (1) Unit Review Assessment (1) Unit Test (choice of 3 forms: open response; multiple choice; performance)

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