Math Grade Four Unit 1 - Naming and Construction Geometric Figures

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1 Time Frame: Week 1 through Week 3 Math Grade Four Unit 1 - Naming and Construction Geometric Figures Description: - Introduce students to the Student Reference Book and practice using geometry tools. - To classify quadrangles, explore and identify polygons, and review and practice addition and subtraction fact extensions. Enduring Understandings: *Points, lines and planes are the foundation of geometry. *Angles are geometric shapes that are formed when two rays share a common point. *Geometric shapes can be analyzed and classified based on their properties. *Two dimensional objects can be described, classified, and analyzed by their attributes. Essential Questions: *How are 1 and 2 dimensional shapes related? *How are geometric properties used to construct geometric figures? Standards Topics Activities Resources Assessments.NBT.2. 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. *Intro. Student Reference Book 1.1.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. *Points, Line Segments, Lines, and Rays *Parallelograms

2 .MD.5. 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. An angle that turns through n one-degree angles is said to have an angle measure of n degrees *Angles, Triangles, and Quadrangles 1.3.G.2. 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. *Angles, Triangles, and Quadrangles *Polygons *Polygon-Pair-Up *Define Geometric Figures Geometry Race ** Geometry Race, Standards Solution, LLC Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

3 Math Grade Four Unit 2 - Using Numbers to Organize Data Time Frame: Weeks 3 through Week 5 Description: - Examine different uses and equivalent names for numbers and review the base-ten place value system. - Review procedures for addition and subtraction of multidigit whole numbers. - Reintroduce and extend ideas about data collection, organization, display, and analysis. Enduring Understandings: *Place value is based on groups of ten. *Addition and Subtraction are essential skills that we use everyday. Essential Questions: *How can counting, measuring, or labeling help us make sense of the world around us? *How can we decide which algorithm to use in a particular situation? *How can the collection, organization, interpretation, and display of data be used to answer questions? Standards Topics Activities Resources Assessments.NBT.2. 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. *Place Value in Whole Numbers *Place Value with a calculator NBT.. Fluently add and subtract multi-digit whole numbers using the standard algorithm. *Addition of Multi digit Numbers *Subtraction of Multi digit numbers MD.. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. *Median *Making a Line Plot of the Data

4 .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. *Addition Number Stories (enrichment examples) *Subtraction Number Stories 2.7 (enrichment) 2.9 (enrichment) 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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. *Addition Number Stories (enrichment examples) *Subtraction Number Stories (enrichment examples) 2.7 (enrichment) 2.9 (enrichment) 1 Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

5 Time Frame: Weeks 5-8 Math Grade Four Unit 3 - Multiplication and Division; Number Sentences and Algebra Description: - Review strategies for both solving and maintaining automaticity with multiplication facts. - Practice measuring length and using a map scale. - Introduce and practice solving number stories. - Practice with number sentences and open sentences. Enduring Understandings: *Mathematical expressions represent relationships. *Multiplication is adding quickly and division is subtracting rapidly. Essential Questions: *Why is it important to learn multiplication. and division basic facts? *How can we decide which algorithm to use in a particular situation? *What are some ways to represent, describe, and analyze patterns? Standards Topics Activities Resources Assessments.OA.5. 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. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way *What s My Rule 3.1.OA.. 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. *Multiplication Facts *Prime and Composite Numbers OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement *Multiplication and Division 3.5

6 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..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. *Solving Elapsed-Time Problems *Finding Air Distance MD.. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. *Solving Number Stories 3.8.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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding..nbt.2. 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. *Number Models with and unknown or variable *Open Sentences *True or False Number Stories Operations and Algebraic Thinking Learning Center ** 3.8 Operations and Algebraic Thinking Learning Center, Standards Solution, LLC 3.9 Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

7 Math Grade Four Unit - Decimals and Their Uses Time Frame: Weeks 5-11 Description: Extend place value system to decimals. Review and extend basic concepts, notation, and applications for decimals. Extend whole number addition and subtraction to decimals. Review relationships among metric units of length. Enduring Understandings: *Decimals express a relationship between two numbers. *Decimals use the same base ten place value system as whole numbers except we add ths to the word. Essential Questions: *How can we decide which algorithm to use in a particular situation? *Why do we need decimals when describing and measuring data? *How can counting, measuring, or labeling help us make sense of the world around us? Standards Topics Activities Resources Assessments.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. *Decimal Place Value *Review of Basic Decimal Concepts.2.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. *Review of Basic Decimal Concepts *Thousandths.2.7.NF.7. 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. *Comparing and Ordering Decimals *Thousandths.3.7

8 .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. *Estimating with Decimals *Decimal Addition and Subtraction *Decimals in Money..5.6.MD.1. 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. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a ft snake as 8 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 2), (3, 36), *Metric Units of Length *Personal Reference for Metric Length *Measuring in Millimeters Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

9 Math Grade Four Unit 5 - Big Numbers, Estimation, and Computation Time Frame: Weeks 11-1 Description: - Extend basic multiplication facts and review multiplication of multidigit numbers. - Practice estimating and decide when estimation is appropriate. - Review partial-products algorithm for multiplication, and practice multistep x number stories. - Practice reading, writing, and comparing large numbers. Enduring Understandings: *Estimation is a way to get an approximate answer. *Computation involves taking apart and combining numbers using a variety of approaches. *Flexible methods of computation involve grouping numbers in strategic ways. *Proficiency with basic facts aids estimations and computation of larger and smaller numbers. Essential Questions: *Why is it important to learn multiplication and division basic facts? *How can we decide which algorithm to use in a particular situation? *What makes an estimate reasonable? Standards Topics Activities Resources Assessments.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. *Extended Multiplication Facts *Multiplications Wrestling District Made Grade NBT Mini Unit ** NBT Mini Unit, Standards Solution, LLC.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit 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. *Extended Multiplication Fact *Multiplication Wrestling *Estimating Products *Partial Products Multiplication District Made Grade

10 .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. *Representing Measurement Quantities Using Number Line Diagrams *Representing intervals of time on an open number line *Estimating Sums *Partial Products District Made Grade *Multistep Multiplication Number Stories (enrichment) NBT Mini Unit ** Patterns in Place Value Rounding Games What s My Number? Check Mate The Perfect (Division) Game NBT Mini Unit, Standards Solution, LLC.NBT.2. 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. *Big Numbers 5.8 District Made Grade.NBT.3. Use place value understanding to round multi-digit whole numbers to any place. *Estimating Sums *Estimating Products *Rounding and Reporting Large Numbers District Made Grade

11 .MD.1. 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. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a ft snake as 8 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 2), (3, 36),.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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. *Partial Products (part two) *Multistep Multiplication Number Stories (enrichment) *Solving Addition and Subtraction Number Stories 5.5 District Made Grade 1.6 (enrichment ) 5.11 District Made Grade Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

12 Math Grade Four Unit 6 - Division; Map Reference Frames; Measures of Angles Time Frame: Weeks 1-17 Description: - Practice multiplication and division number stories. - Introduce partial quotient division algorithm and the concept of remainders as fractions/decimals. - Practice the drawing, measuring, and naming angles using half-circle protractors. Enduring Understandings: *Division is an essential skill that we use every day. *Division is rapid subtraction and multiplication is rapid addition. *Remainders are leftovers. You must decide if you should use it or throw it away. Essential Questions: *Why is it important to learn multiplication and division basic facts? *How can we decide which algorithm to use in a particular situation? *Is the remainder/integer relevant in finding the solution? Standards Topics Activities Resources Assessments.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. (see Table 2) *Multiplication and Division Number Stories 6.1 2

13 .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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. *Multistep Word Problems (enrichment) *Strategies for Division writing a number model with an unknown variable and then writing a summary number model NBT.6. 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. *Strategies for Division *Partial-Quotients Division Algorithm (part 1 and 2) *Expressing and Interpreting Remainders MD.5a. 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. *Rotations and Angles Protractor and Angles ** Angles in a Circle ** Protractor and Angles, Standards Solution, LLC Angles in a Circle, Standards Solution, LLC 6.5 2

14 .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. *Solving Elapsed- Time Problems MD.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. *Half-Circle Protractor *Partial Quotients MD.7. Recognize angle measure as additive. When an angle is decomposed into nonoverlapping 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. *Adding and Subtracting to find missing angle measures Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.

15 Math Grade Four Unit 7 - Fractions and Their Uses Time Frame: Weeks Description: - Review fractions as parts of a whole, fractions on number line, and uses of fraction. - Order fractions and find fractional parts of sets. - Practice identifying equivalent fractions. Enduring Understandings: *Fractions express a relationship between two numbers. *Fractions/ Decimals are used to measure a multitude of things ranging from length, money, to probability. They help us make sense of what precedes or is between whole numbers. *Fraction rules are the opposite of whole numbers. The larger the fractions denominator the smaller the fraction. *Fractions should be rounded to three benchmarks 0,1/2., or 1. When trying to determine their relationships to whole numbers. *Fractions have an infinite number of equivalent possibilities. Essential Questions: *How can we decide which algorithm to use in a particular situation? *Why do we need fractions /decimals when describing and measuring data? *How are fractions and decimals related?

16 Standards Topics Activities Resources Assessments.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and 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 one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8=1/8+1/8+1/8 ; 3/8=1/8+2/8; 2 1/8= /8=8/8+8/8 +1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. *Review of Basic Fraction Concepts *Pattern Block Fractions *Writing Fraction and Mixed Number Addition Number Stories (enrichment) *Fraction and Mixed Number Addition and Subtraction *Decomposing Fractions *Plotting Data on a Line Plot *Solving Fractions Number Stories District Made Grade.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 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. *Equivalent Fractions *Comparing Fractions *Rename Fractions as Percents District Made Grade.NF.2. 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 1/2. 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 fraction model. *Equivalent Fractions *Comparing Fractions *The One for Fractions District Made Grade

17 .NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. *Fractions and Decimals 7.8 District Made Grade.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. For example, express 3/10 as 30/100, and add 3/10 + /100 = 3/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.).md.. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. *Add Fractions with denominator 10 as an equivalent fractions with denominator 100 (MMR) *Plotting Data on a Line Plot 7.9 District Made Grade 7.10 District Made Grade

18 .NF.. 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. For example, use a visual fraction model to represent 5/ as the product 5 (1/), recording the conclusion by the equation 5/ = 5 (1/). 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. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b)=(n a)/b.) 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. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? *Multiplying Fractions by Whole Numbers 7.10 District Made Grade Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Time Frame: Weeks Description: - Review perimeter and area concepts. Math Grade Four Unit 8 - Perimeter and Area

19 - Develop formula as models for the area of a rectangle. - Multiply a fraction by a whole number. Enduring Understandings: *Fractions/ Decimals are used to measure a multitude of things ranging from area, money, to probability. They help us make sense of what precedes or is between whole numbers. *Fractions should be rounded to three benchmarks 0, 1/2, or 1. When trying to determine their relationships to whole numbers, and comparing. *Measurement is a crucial skill that is used every day. For example measurement is used when driving a car, designing clothing, or decorating and building a home. *Mathematical formulas make measurement faster and easier. Essential Questions: *How can we decide which algorithm to use in a particular situation? *Why do we need fractions /decimals when describing and measuring data? *How are fractions and decimals related? Standards Topics Activities Resources Assessments.NF.2. 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 1/2. 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 fraction model. *Fraction Match Game 8.1 District Made Grade.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8=1/8+1/8+1/8 ; 3/8=1/8+2/8; 2 1/8= /8=8/8+8/8 +1/8. *Multiplying a Fraction by a Whole Number 8.2 District Made Grade

20 .MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. *Area *Formula for area of a rectangle 8.5 District Made Grade.MD.1. 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. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a ft snake as 8 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 2), (3, 36), *Find the area of your skin 8. District Made Grade Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Math Grade Four Unit 9 - Fractions, Decimals, and Percents

21 Time Frame: Weeks Description: - Name equivalencies among fractions, decimals, and percents. - Use a calculator to rename fractions to decimals. - Adding tenths and hundredths. - Solving number stories with multiplication and division. Enduring Understandings: *Fractions, decimals, and percents are used to measure a multitude of things ranging from measurement, money, to discounts. *Decimals use the same base-ten place value system as whole numbers except we add ths to the word. Example hundreds (whole numbers) and hundredths (decimals). *Decimals, fractions, and percents are interchangeable. They are all varying ways to represent the same number. *Multiplication and Division are essential skills that we use every day when dealing with money, measurement, or data collection. *Calculators are important tools to process algorithms quickly and accurately. They also assist in converting numbers quickly from decimals, fractions, and percents. Essential Questions: *How can we decide which algorithm to use in a particular situation? *Why do we need fractions /decimals when describing and measuring data? *How are fractions, decimals, and percents relate Standards Topics Activities Resources Assessments.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. *Fractions, Decimals, and Percents *Using a calculator to convert fractions to decimals 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. For example, express 3/10 as 30/100, and add 3/10 + /100 = 3/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with *Adding Tenths and Hundredths 9.2 3

22 unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.).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, e.g., by using an equation with a symbol for the unknown angle measure. *Angle Addition and Subtraction 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. *Solving Number Stories with Multiplication and 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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. *Solving Number Stories with Multiplication and Division 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 *Multiplication of Decimals (partial products) 9.8 3

23 place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models..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 *Multiplication of Decimals (partial products) *Division of Decimals 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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. *Division of Decimals NBT.6. 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. *Division of Decimals 9.9 3

24 Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Math Grade Four

25 Unit 10 - Reflections and Symmetry Time Frame: Weeks 23-2 Description: - Discover and practice lines of symmetry. - Use coin values to add hundredths. - Explore growing patterns. - Multiply a fraction by a whole number. Enduring Understandings: *Geometry is the fundamental structure of matter created in nature and created by man. *Symmetry brings beauty and balance to nature, architecture, and design. *Plane figures can be described, classified, and analyzed by their attributes. *Plane figures can be transformed in an infinite number of ways. *Decimals, fractions, and percents are interchangeable. They are all varying ways to represent the same number. Essential Questions: *How are geometric properties used to construct geometric figures? *What situations can be analyzed using transformations? *How can we decide which algorithm to use in a particular situation? Standards Topics Activities Resources Assessments.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. For example, express 3/10 as 30/100, and add 3/10 + /100 = 3/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) *Using Coin Values to Add Hundredths *Fraction Addition Problem tenths to hundredths (MMR) NF.. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a multiple of a/b as a multiple of 1/b, and use this *Multiplying a Fractions by a Whole Number 10. 3

26 understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b)=(n a)/b.) b. 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. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?.oa.5. 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. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way *Growing Patterns G.3. Recognize a line of symmetry for a twodimensional 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. *Line Symmetry Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Math Grade Four

27 Unit 11 - Weight Time Frame: Weeks 2-25 Description: - Review grams and ounces as units of weight and mass. - Measure liquid volumes of capacity. - Plotting heights in fractions of an inch on a line plot. Enduring Understandings: *Measurement is a crucial skill that is used every day. Measurement is used when driving a car, designing clothing, cooking a meal, or decorating and building a home. *Mathematical formulas make measurement faster and easier. Essential Questions: *How can we decide which algorithm to use in a particular situation? *Why do we need fractions /decimals when describing and measuring data? *How can counting, measuring, or labeling help us make sense of the world around us? *What makes an estimate reasonable? Standards Topics Activities Resources Assessments.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. *Grams and ounces as units of weight and mass *Measuring Capacity (liquid volumes only) NF.. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 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. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, *Multiplying a Fraction by a whole number (MMR)

28 n (a/b)=(n a)/b.).md.. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. *Plotting heights in fractions of an inch on Line Plot MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor *Area of a rectangle Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards. Math Grade Four

29 Unit 12 - Units of Measure Time Frame: Week 25 Description: - Converting units of measure. - Investigate liters and milliliters. Enduring Understandings: *Measurement is a crucial skill that is used every day. Measurement is used when driving a car, designing clothing, cooking a meal, or building a home. *Mathematical formulas make measurement faster and easier. *Multiplication and Division are essential skills that we use every day when dealing with money, measurement, or data collection. *Addition and Subtraction are essential skills that we use every day when dealing with money, measurement, or data collection. Essential Questions: *How can we decide which algorithm to use in a particular situation? *How can counting, measuring, or labeling help us make sense of the world around us? *What makes an estimate reasonable? Standards Topics Activities Resources Assessments.MD.1. 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. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a ft snake as 8 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 2), (3, 36), *Converting units of measure *Investigating Liters and Milliliters District Made Grade Assessment 3

30 .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. *Investigating Liters and Milliliters District Made Grade Assessment 3 Additional Resources/Activities: Everyday Math Games, Study Guides, Differentiation Options, and resources from are also available to help meet the standards.