# 7 Days: August 17 August 27. Unit 1: Two-Dimensional Figures

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1 1 st Trimester Operations and Algebraic Thinking (OA) Geometry (G) OA.3.5 G.1.1 G.1.2 G.1.3 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. DOK 2 Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. DOK 1 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. DOK 2 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. DOK 2 1: Two-Dimensional Figures 7 Days: August 17 August 27 The student will: identify and draw geometry terms. sort and classify quadrilaterals based on properties. identify and draw lines of symmetry. recognize and classify triangles based on side length and angles. generate a shape pattern given a rule. identify features in the pattern not stated in the rule. Lines, Rays, and Angles Parallel and Perpendicular Lines, Classifying Quadrilaterals Line Symmetry Classify Triangles Shape Patterns angle hexagon line line segment parallel lines parallelogram perpendicular lines point quadrilateral ray rectangle regular polygon rhombus right angle square straight angle trapezoid diagonal horizontal line of symmetry line symmetry vertical acute triangle equilateral triangle isosceles triangle obtuse triangle right triangle scalene triangle equiangular triangle MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others. For example, when classifying shapes, students should be able to construct a viable argument as to why the specific shape is located in a specific group. MAFS.K12.MP.4.1: Model with mathematics. For example, students will analyze patterns and draw conclusions based on relationships. MAFS.K12.MP.6.1: Attend to Precision. In this unit, students are introduced to the definitions of many geometric terms. In order to communicate accurately mathematically, students must understand and practice using precise definitions. MAFS.K12.7.1: Look for and make sure of structure. In order to classify quadrilaterals, students must understand the structure of geometric figures. This analysis deepens students understanding of properties of two-dimensional figures and how they are related.

3 1 st Trimester Gain familiarity with factors and multiples. The student will: Factors and Divisibility array Operations and Algebraic Thinking (OA) OA.3.5 OA.2.4c OA.2.4b OA.2.4a OA.2.4 Investigate factors and multiples: DOK 2 Find all factor pairs for a whole number in the range DOK 2 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. DOK 2 Determine whether a given whole number in the range is prime or composite. DOK 2 Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. DOK 2 3: Factors, Multiples, and Patterns 7 Days: September 18 September 27 find all the factor pairs of a number. determine if a number is prime or composite. identify common factors. understand how multiples and factors are related. generate a number pattern given a rule. identify features in the pattern not stated in the rule. Factor Pairs / Prime and Composite Common Factors Factors and Multiples Number Patterns common factor common composite multiple divisible factor multiple number pattern prime number product term MAFS.K12.MP. 6.1: Attend to precision. Students connect the concept of factors and multiples. Precision of language is vital. MAFS.K12. MP. 7.1: Look for and make use of structure. ly proficient students look closely to discern a pattern or structure. For example, when examining factors of square numbers (e.g. 4, 9, 16) students will begin to notice that there will always be one factor repeated so that it does not have a partner like all of the other factors of the square number.

4 1 st Trimester Suggeste d Student Targets Lessons from GO MATH! Book Vocabulary Operations and Algebraic Thinking (OA) Number and Operations in Base OA.1.1 OA.1.2 OA.1.3 OA.1.a NBT.2.5 Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 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. DOK 1 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. DOK 2 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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. DOK 2 Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine whether the equation 60+24=57+27 is true or false. DOK 3 Use place value understanding and properties of operations to perform multi-digit arithmetic. 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. DOK 2 4: Multiply by 1-Digit Numbers 11 Days: September 28 October 12 The student will: interpret a multiplication equation as a comparison. solve multiplication comparisons word problems. select and use appropriate multi-digit by 1 digit multiplication strategies. assess reasonableness of products using mental math strategies. solve multi-step word problems involving multiplication. Multiplication Comparisons Multi-Digit Multiplication Patterns Multiply Using Expanded Form Multiply Using Partial Products Multiply Using Comparative Relational Thinking Multiply Using the Distributive Property Use Estimation to Determine Reasonableness One-Step Multiplication Word Problems Multi-Step Word Problems Associative Property of Multiplication Distributive Property estimate expanded form factor multiply number line partial product place value product MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them. For example, students show understanding of multiplication by estimating the product and comparing the estimation to their answer to determine reasonableness. MAFS.K12.MP.4.1: Model with mathematics. For example, student use the visual model of a rectangular array or area model to show understanding of multiplication. round

5 1 st Trimester Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Use the four operations with whole numbers to solve problems. OA.1.3 NBT.2.6 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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. DOK 2 Use place value understanding and properties of operations to perform multi-digit arithmetic. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. DOK 2 5: Divide by 1 Digit Numbers 13 Days: October 15 November 1 Students will be able to: understand the relationship between multiplication and division. select and use appropriate multi-digit by 1 digit division strategies. assess reasonableness of quotients using mental math strategies. correctly interpret the remainder. solve multi-step word problems involving division. Relate Multiplication and Division Investigate and Interpret Remainders Divide Using Base-Ten Blocks Divide using Repeated Subtraction and Partial Quotients Divide with Area Model and Partial Quotients Divide with Distributive Property and Partial Quotients Real-World Division with Zeros Real-World with Interpreting Remainders Real-World Multi-Step Division MAFS.K12.MP.2.1: Reason abstractly and quantitatively. For example, students show understanding of division by estimating the quotient and comparing the estimation to their answer to determine reasonableness. MAFS.K12.MP.4.1: Model with mathematics. Students use the visual model of a rectangular array or area model to show understanding of division. MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning. Students in fourth grade should notice repetitive actions in computation to make generalizations. Students use models to explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms. compatible numbers Distributive Property divide dividend division divisor quotient partial quotient remainder

7 2 nd Trimester Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Use the four operations with whole numbers to solve problems. OA.1.3 NBT.2.5 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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. DOK 2 Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a onedigit 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. DOK 2 6: Multiply by 2-Digit Numbers 8 Days: November 2 November 14 Students will be able to: select and use appropriate double digit multiplication strategies. assess reasonableness of products using mental math strategies. solve multi-step word problems involving multiplication. Multiply by 10s Multiply two 2-Digit Numbers Using the Area Model Multiply Using Partial Products Estimate to Determine Reasonableness Double-Digit Word Problems Associative Property of Multiplication factor product estimate round partial product Commutative Property of Multiplication MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them. For example, students show understanding of multiplication by estimating the product and comparing the estimation to their answer to determine reasonableness. MAFS.K12.MP.4.1: Model with mathematics. For example, students us the visual model of a rectangular array or area model to show understanding of multiplication. MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning. Students in fourth grade should notice repetitive actions in computation to make generalizations. Students use models to explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms.

8 2 nd Trimester Measurement and Data (MD) Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. MD.1.1 MD.1.2 MD.1.3 MD.2.4 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr., min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. DOK 1 Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models. (Computational fluency with fractions and decimals is not the goal for students at this grade level.) DOK 2 Apply the area and perimeter formulas for rectangles in real world and mathematical problems..) DOK 2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. DOK 2 7: Length, Area, and Perimeter 15 Days: November 15 December 13 The Student will be able to: understand the relative size of length units. convert length measurements. measure and record lengths utilizing a line plot. solve real-world word problems involving lengths. use a formula to find an unknown variable find the area of a rectangle find the perimeter of a rectangle find the unknown measure of a side of a rectangle find the area of combined rectangles Relative Size of Length s Conversions: Metric Lengths Conversions: Customary Lengths Lengths on a Line Plot Word Problems Involving Length How to Use Formulas Area Perimeter Find an Unknown Measurement (two days) Combined Rectangles (two days) Area/Perimeter Word Problems (two days) kilometer meter centimeter mile yard foot inch line plot MAFS.K12.MP.4.1: Model with mathematics. For example, students use the visual model of a rectangular array or area model to show understanding of multiplication to determine the area of rectangles. MAFS.K12.MP.6.1: Attend to precision. Students will be precise when determining the length of an unknown measurements. Students will also attend to precision when solving real-world problems for area and/or perimeter. MAFS.K12.MP.7.1: Look for and make sure of structure. Once students have been introduced to the concept perimeter for squares, they should consider the similarity between squares and rectangles that are not squares. When students begin to discover measurement attributes such as perimeter and area of common polygons, students should see structure or patterns.

9 2 nd Trimester Number and Operations Fractions (NF) NF.1.1 NF.1.2 Extend understanding of fraction equivalence and ordering. 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 and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. DOK 3 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. DOK 2 8: Fraction Equivalence and Comparison 11 Days: December 14- January 14 Students will be able to: recognize equivalent fractions. generate equivalent fractions. compare fractions using appropriate strategies, and justify their conclusions. Review Understanding Fractions (GR3) Equivalent Fractions with Models Generate Equivalent Fractions with Multiplication Generate Equivalent Fractions with Division Comparing Fractions Using Benchmarks Common Denominators Comparing Fractions: Comparing Fractions Greater than 1/Mixed Numbers equivalent fractions denominator fraction numerator simplest form common factor denominator equivalent fractions factor common denominator common multiple multiple benchmark common numerator MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them. For example, students show understanding of multiplication by estimating the product and comparing the estimation to their answer to determine reasonableness. MAFS.K12.MP.6.1: Attend to precision. Students try to communicate precisely to others. They explain the meaning of symbols they choose, including using the greater than, less than, and equal sign symbols when comparing fractions. MAFS.K12.MP7.1: Look for and make use of structure. When students have a solid foundation in the patterns found in multiplication facts, this allows them to quickly discern if two fractions are equivalent. They can see if two fractions are equivalent by using a familiar pattern, such as all numbers multiplied by 2 are even or all numbers multiplied by 5 end in 0 or 5.

12 2 nd /3 rd Trimester Number and Operations Fractions (NF) Measurement and Data (MD) Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 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 1/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, e.g., by using visual fraction models and equations to represent the problem. DOK 2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. DOK 2 NF.2.4 MD : Multiply fractions by Whole Numbers 10 Days: February 4 February 18 Students will be able to: understand multiples of fractions. multiply a fraction by a whole number. solve real-world measurement word problems with fractions. Multiples of Fractions Multiples of Fractions Multiply Fractions and Whole Numbers Multiply Fractions by Double Digit Whole Numbers Multiply Fractions by Mixed Numbers Multiplicative Comparison with Fractions Measurement Problems with Fractions multiple product Identity Property of Multiplication MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them. ly proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. MAFS.K12.MP.4.1: Model with mathematics. For example, students use the visual models of a fraction area model to show understanding of multiplication. MAFS. K12. MP.6.1: Attend to precision. Students are introduced to definitions of geometric terms, they must distinguish between meanings of endpoints and arrows to identify and describe lines, line segments, and rays. They learn that an angle is formed by two rays or line segments, etc. Students will be better equipped to communicate their mathematical reasoning clearly to others by understanding and using precise definitions.

13 3 rd Trimester Number and Operations Fractions (NF) Measurement and Data (MD) NF.3.5 NF.3.6 NF.3.7 Understand decimal notation for fractions, and compare decimal fractions. 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. DOK 1 Use decimal notation for fractions with denominators 10 or 100. DOK 1 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. DOK 2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. MD.1.2 Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models. (Computational fluency with fractions and decimals is not the goal for students at this grade level.) DOK 2 11: Relate Fractions to Decimals 8 Days: February 19 February 28 The student will be able to: convert fractions into decimals. add fractions with tenths and hundredths. compare decimals. solve real-world situations involving decimals. Relate Tenths and Hundredths to Decimals Relate Decimals, Fractions, and Money Equivalent Fractions and Decimals Add Fractional Parts of 10 and 100 Compare Decimals Word Problems with Money decimal tenth compare fraction place value whole hundredth equivalent decimal point MAFS.K12.MP. 7.1: Look for and make use of structure. ly proficient students look closely to discern a pattern or structure. MAFS.K12. MP.8.1: Look for and express regularity and repeated reasoning. ly proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.

14 3 rd Trimester Measurement and Data (MD) Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. MD.1.1 MD.1.2 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. DOK 1 Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models. (Computational fluency with fractions and decimals is not the goal for students at this grade level.) DOK 2 12: Relative Size of Measurements 8 Days: March 1 March 12 The student will be able to: know the relative size of a unit within one system of units (weight, liquid volume, time). Convert and record measurements in a twocolumn table. represent fractional quantities of time on a linear model. solve measurement word problems using four operations. Weight Liquid Volume Measuring Time Elapsed Time Measurement Word Problems weight ounce pound ton cup fluid ounce gallon pint quart second day hour minute month week year A.M. elapsed time P.M. MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them. ly proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. MAFS.K12.MP.4.1: Model with mathematics. For example, students use the visual model of a fraction area model to show understanding of multiplication.

15 3 rd Trimester Measurement and Data (MD) Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two 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 two 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. DOK 1 MD.3.5 MD.3.6 MD.3.7 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure DOK 2 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, e.g., by using an equation with a symbol for the unknown angle measure. DOK 2 13: Angles 7 Days: March 13 March 29 The student will be able to: understand concepts of angle measurements. measure and draw angles. solve addition and subtraction word problems with an unknown angle measure. Angles and Degrees Measure and Draw Angles Join and Separate Angles Word Problems with Unknown Angles angle circle ray vertex degree acute angle obtuse angle right angle straight angle reflex angle protractor MAFS.K12.MP.2.1: Reason abstractly and quantitatively. Using a protractor to measure angles calls for students to reason abstractly and quantitatively. Students need to choose between the two scales on the protractor, in order to make the correct choice they must think about the definitions of acute and obtuse angles. MAFS.K12.MP. 5.1: Use appropriate tools strategically. ly proficient students must consider the available tools when solving a mathematical problem, such as, using a protractor to measure angles.

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