MCSD Math Curriculum Map ~ 5 th Grade

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1 MCSD Math Curriculum Map ~ 5 th Grade Common Core State Standard PA Core Standard CC B.1 Apply place value concepts to show an understanding 5.NBT.1, 5.NBT.2, 5.NBT.3, 5.NBT.4 of operations and rounding as they pertain to whole numbers and decimals. Taught in Unit(s) Harcourt textbook lessons: 1.1, 1.2, 7.1, 10.1, 11.1, 2.1, 1.4, 2.2, 2.3, 3.1, 3.2 PA Core Coach Grade 5: Domain 2 Lessons 4 7 VMath Live Module 1 Explanation/Example of Standard Demonstrate understanding of place value of whole numbers to the millions period and decimals to the thousandths, and compare quantities and magnitudes of numbers. Common Misconceptions The more digits in a number with a decimal, the greater the value of the number. As you move to the right of the decimal point, the number increases in value. A comma within a number should be read as and. There are commas after a decimal. There is a place value called oneths. Hundreds and hundredths are the same value. An exponent of 10³ means 10 x 3. Big Idea(s) Essential Question(s) Our place value system is based on powers of How does place value change the value of a ten. digit? Every time you move a column to the left you How does identifying powers of ten in are multiplying by 10. multiplication and division correlate to the Every time you move a column to the right product/quotient? you are multiplying by 1/10 (dividing by 10). How do you represent whole numbers and A decimal can be converted to a fraction by decimals in standard, word, and expanded turning the digits to the right of the decimal forms? into the numerator and naming the How do you identify and create equivalent denominator by the place value of the decimals? decimal. (example 2.3 is converted to 2 ଷ ) How do you compare whole numbers and/or ଵ decimals from the millions to the Equivalent decimals can be made by adding or taking away a 0 from the end of the number. Numbers need to be vertically aligned by place value if making comparisons. Assessments PSSA Math Test (required Spring) MAP Math Test (required 3x/year) Combination of Chapter tests from Harcourt Chapter 1, 2, 3, 7, 10, 11 VMath Module 1 Commoncoresheets.com thousandths? How do you round whole numbers and decimals from the millions to the thousandths? Concepts Skills (what students need to know) (what students must be able to do) Read, write, and model whole and decimal Eligible Content numbers from the millions period through Demonstrate an understanding that the thousandths. M05.Ain a multi digit number, a digit in Model and identify equivalent decimals. T one place represents 1/10 of what it

2 M05.A T M05.A T represents in the place to its left. Example: Recognize that in the number 770, the 7 in the tens place is 1/10 the 7 in the hundreds place. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. Example 1: 4 x 102 = 400 Example 2: = Read and write decimals to thousandths using base ten numerals, word form, and expanded form. Example: = = 3 x X x x (0.1) + 9 x (0.01) + 2 x (0.001) Compare two decimals to M05.A thousandths based on meanings of T the digits in each place using >, =, and < symbols. Round decimals to any place (limit M05.A T rounding to ones, tenths, hundredths, or thousandths place). Vocabulary: Place value Greater than, Less than, Equal to Equivalent Whole numbers values: ones, tens, hundreds, thousands, ten thousands, hundredthousands, millions, ten millions, hundredmillions. Decimal values: tenths, hundredths, thousandths Standard Form Word Form Expanded Form Exponents Powers of 10: example 10¹, 10², 10³ Base ten Round Magnitude Quantity Period Understand and apply the shift patterns when multiplying and dividing by 10, 100, or 1,000. Understand and apply shift patterns when multiplying and dividing by 0.1, 0.01, or Compare whole numbers and decimals from the millions period through the thousandths. Round whole numbers and decimals from the millions period through the thousandths.

3 I Can Statements 1. I can understand and explain the value of digits in a number. 2. I can explain patterns of zeroes in an answer when multiplying a number by powers of I can explain patterns of decimal placement when a decimal is multiplied or divided by a power of I can use whole number exponents to show powers of I can identify and create equivalent decimals. 6. I can read, write and compare whole numbers to the millions period through decimals to thousandths. 7. I can read and write decimals to thousandths using base ten numbers, number names, and expanded form. 8. I can compare two decimals to thousandths using the >, <, = symbols correctly. 9. I can compare two whole numbers to the millions period using the >, <, = symbols correctly. 10. I can round a whole number or decimal to the designated place value column. 11. I can use place value understanding to round decimals or whole numbers to any place. Reflections

4 Common Core State Standard 5.NBT.5, 5.NBT.6, 5.NBT.7 MCSD Math Curriculum Map ~ 5 th Grade PA Core Standard CC B.2 Extend an understanding of operations with whole numbers to perform operations including decimals. Taught in Unit(s) Harcourt textbook lessons 7.2, 7.3, 7.4, 12.6, 9.2, 9.3, 9.4, 10.3, 10.5, 3.5, 3.6, 8.1, 8.2, 8.3, 8.4, 8.5, 11.2, 11.3 PA Core Coach Grade 5: Domain 2 Lessons 8-12 VMath Live Modules 2, 3, and 4 Explanation/Example of Standard Add, subtract, multiply, and divide whole numbers and decimals (straight computation or word problems). Common Misconceptions When adding/subtracting, numbers should be aligned by the first digit. For example, may be written in this manner: ,215 Instead of regrouping during addition, both digits of a two-digit sum should be written below the equal sign. For example: ,414 Instead of regouping/borrowing during subtraction, the smaller digit can be subtracted from the larger digit. For example: To compute the sum or difference of decimals, line up the right hand digits as they would be when adding/subtracting whole numbers. For example, , students may be written in this manner: Multiplication problems should be solved in the same manner as addition problems. For example: 34 x When multiplying decimals, align the decimal points. When multiplying decimals, the decimal should be brought straight down as it is done in an addition/subtraction problem. When dividing multi-digit whole numbers and decimals, the dividend and divisor can be written vertically. Placing the decimal in the answer is the same for all operations. Big Idea(s) When adding/subtracting whole numbers or decimals, digits of the same place value must be aligned. When multiplying multi-digit numbers, digits do not need to be aligned according to place value. When solving word problems, key words and phrases give clues about which operation is needed to solve a problem. Essential Question(s) How do you solve problems involving addition and subtraction of decimals? What is the process for multiplying multidigit numbers (up to three-digit by threedigit)? What steps are necessary to multiply decimal numbers? How do you solve real world problems with whole numbers and decimals?

5 Arrays or models can be used to solve What key words/phrases are associated with multiplication and division problems. each of the four operations (addition, Compatible numbers can be used to estimate subtraction, multiplication, division)? a product or quotient. How do you divide multi-digit whole numbers by one- and two-digit whole numbers in cases with and without remainders? How do you divide whole numbers and decimals by decimals to the hundredths? How can you interpret the remainder of a whole number division problem in a way that makes sense in the context of the problem? How can estimation be used in computation? Why should estimation be used? Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) Combination of Chapter tests from Harcourt Chapter 3, 7, 8, 9, 10, 11, 12 VMath Modules 2, 3, and 4 Commoncoresheets.com Concepts Skills (what students need to know) (what students must be able to do) M05.A- T Eligible Content Multiply multi-digit whole numbers (not to exceed three-digit by threedigit). Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). M05.A- T M05.A- T Place value of whole numbers and decimals Addition of whole numbers Subtraction of whole numbers Multiplication/Division facts Vocabulary: Addition Subtraction Multiplication Division Whole number Decimal Addend Sum Subtrahend Difference Factor Product Add whole numbers and decimals from millions to hundredths. Subtract whole numbers and decimals from millions to hundredths. Multiply whole numbers up to three-digit by three-digit. Multiply decimals to the hundredths place. Divide whole numbers up to four-digit by two-digit, with or without a remainder. Divide decimals with whole number divisors and dividends to the hundredths place. Multiply and divide decimals to hundredths. Use estimation to validate answers. Illustrate and explain the quotient in a division problem. Interpret the remainder of a division problem. Explain method used to solve word problems in addition, subtraction, multiplication, and division problems. Identify key words or phrases in a word problem.

6 Dividend Divisor Quotient Compatible numbers Remainder Estimation I Can Statements 1. I can add and subtract whole numbers to millions. 2. I can multiply multi-digit numbers up to three-digit by three-digit. 3. I can multiply decimals to the hundredths place. 4. I can divide up to a 4-digit dividend by a one- or two- digit divisor to find a quotient with or without a remainder. 5. I can divide whole number divisors and dividends to the hundredths place. 6. I can illustrate and explain division problems. 7. I can add, subtract, multiply, and divide decimals to hundredths. 8. I can explain the reasoning used to solve decimal problems in written form. 9. I can interpret and explain remainders. 10. I can relate the strategies I used to add, subtract, multiply, and divide decimals to hundredths to word problems and explain why I chose a specific strategy to help me solve the problem. 11. I can estimate answers to addition, subtraction, multiplication, and division problems. 12. I can identify key words and phrases. Reflections

7 Common Core State Standard 5.NF.1, 5.NF.2 MCSD Math Curriculum Map ~ 5 th Grade PA Core Standard CC C.1 Use the understanding of equivalency to add and subtract fractions. Taught in Unit(s) Harcourt textbook lessons: 11.5,13.1, 13.2, 13.3, 15.1, 15.2, 15.3, 15.4, 16.1, 16.2, 16.4, 16.5 PA Core Coach Grade 5: Domain 3 Lessons 13, 14, 15 VMath Live Module 5-6 Lessons 1-5 Explanation/Example of Standard Solve addition and subtraction problems involving fractions and mixed numbers with unlike denominators (straight computation or word problems). Common Misconceptions Just add or subtract the numerators and denominators as the problem is written. A fraction with a large number as the denominator is more than a fraction with a small number as the denominator. When subtracting mixed numbers, fractions can be switched to more easily compute the answer. Add or subtract to find a like denominator. Big Idea(s) A fraction is part, or a piece, of the whole. A mixed number is more than a whole. A fraction is defined as division of a numerator by a denominator. Every fraction has an equivalent decimal. When fractions and/or mixed numbers have common denominators, they can be added or subtracted as is. To add or subtract fractions and/or mixed numbers, both fractions and/or mixed numbers must have the same denominator. A fraction can be renamed using an equivalent fraction by using multiplication or division. When adding or subtracting fractions and/or mixed numbers the common denominator does not change. A fraction can be reduced into smaller terms, but still be the same amount. A fraction with a numerator larger than the denominator is more than one. A fraction with same numerator and denominator is equal to one. Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3 x/ year) Combination of Chapter tests from Harcourt Chapters 11, 13, 15, 16 VMath Module 6 Lessons 1-5 Commoncoresheets.com Essential Question(s) How do you create equivalent fractions? How do you compare fractions using a variety of strategies? How do you add and subtract fractions and mixed numbers with like and unlike denominators? How do you make reasonable estimates of sums and differences of fractions and mixed numbers? Where are fractions found in real-world situations? How do you estimate a reasonable answer when adding or subtracting fractions and mixed numbers with and without like denominators? How are fractions related to division? How are fractions related to decimals? Concepts (what students need to know) Skills (what students must be able to do)

8 M05.A- F Eligible Content Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Example: 2/3 + 5/4 = 8/ /12 = 23/12 Vocabulary: Fraction Numerator Denominator (like and unlike) Mixed numbers Equivalent fractions Sum Difference Common denominator Improper fraction Least Common Denominator Least Common Multiple Greatest Common Factor Improper Fraction Reduce Simplest Form Rename Borrow Use models to the 16 th to discuss basic fraction and mixed number ideas. Model and explain equivalent fractions. Understand the role of the multiplier in equivalent fractions. Use a variety of strategies to compare fractions. Convert between fractions and mixed numbers when necessary. Convert between fractions and decimals. Reduce an answer when possible. Add and subtract fractions with like and unlike denominators. Add and subtract mixed numbers with like and unlike denominators. Estimate sums and differences of fractions and mixed numbers, and decide whether answers are reasonable. When adding fractions and/or mixed numbers, rename an improper fraction answer to a proper fraction and regroup the whole number when necessary. When subtracting mixed numbers, borrow from the whole number of the first mixed number if necessary. I Can Statements 1. I can model fractions and mixed numbers to the 16 th. 2. I can create equivalent fractions. 3. I can convert between improper fractions and mixed numbers. 4. I can find a common denominator. 5. I can add and subtract fractions and mixed numbers with unlike denominators. 6. I can reduce an answer when adding and subtracting fractions and mixed numbers. 7. I can borrow when necessary when subtracting mixed numbers. 8. I can solve word problems that involve addition and subtraction of fractions and mixed numbers. 9. I can determine which operation to use when solving word problems involving fractions and mixed numbers. 10. I can use number sense and fractions that I know to estimate the reasonableness of answers to fraction problems. 11. I relate fractions to division and decimals. Reflections

9 MCSD Math Curriculum Map ~ 5 th Grade Common Core State Standard PA Core Standard CC C.2 Apply and extend previous understandings of 5.NF.3, 5.NF.4, 5.NF.5, 5.NF.6, 5.NF.7 multiplication and division to multiply and divide fractions. Taught in Unit(s) Harcourt textbook lessons: 17.1, 17.2, 17.3, 17.4, 18.1, 18.2, 18.3, 18.4, 19.1, 19.2, 19.3, 19.4, 19.5 PA Core Coach Grade 5: Domain 3 Lessons VMath Live Module 6 Lessons 6-8 Explanation/Example of Standard Solve multiplication and division problems involving fractions, mixed numbers, and whole numbers (straight computation or word problems). Common Misconceptions Multiplication always results in a larger number. Division always results in a smaller number. You need to find a common denominator before solving multiplication and division problems with fractions. You can multiply and divide mixed numbers without turning them into improper fractions. Big Idea(s) Essential Question(s) The product of two fractions will be What strategies can be used to multiply and divide less than the fractions that were fractions? multiplied because a fraction is part How do you multiply a fraction, whole number, or of a whole. mixed number by a fraction or mixed number? When multiplying a given number by How do you predict how a product will compare to a fraction greater than 1, the result one factor based on the size of the other factor? will be a product greater than the How do you solve real world problems with given number. fractions? When multiplying a given number by How do you divide a whole number by a whole a fraction less than 1 the result will number in cases where the quotient is a fraction or a be a product smaller than the given number. mixed number? Division is the inverse of How do you divide a unit fraction (proper fraction) multiplication. by a whole number or a whole number by a unit Since division is the inverse of fraction? multiplication, when dividing fractions the quotient can be more than the fractions. Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) Combination of Chapter tests from Harcourt Chapters 17, 18, 19 VMath Module 6 Lessons 6-8 Commoncoresheets.com Concepts Skills (what students need to know) (what students must be able to do) Determine whether solving a word problem requires Eligible Content multiplication or division. Solve word problems Solve division word problems of whole numbers and involving division of whole M05.Anumbers leading to answers interpret the remainder when the remainder is a F fraction or mixed number. in the form of fractions (including mixed numbers).

10 M05.A- F M05.A- F M05.A- F Multiply a fraction (including mixed numbers) by a fraction. Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing the size of a product to the size of one factor on the basis of the size of the other factor without performing the indicated multiplication. Example 2: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Divide unit fractions by whole numbers and whole numbers by fractions. Multiply any two fractions and reduce and/or rename to a proper fraction when necessary. Multiply a whole number by a fraction to produce a fraction. Multiply with mixed numbers and rename/reduce when necessary. Predict the size of a product relative to the size of one factor based on the size of the other factor (resizing). Connect dividing a fraction to multiplying by the inverse (reciprocal). Interpret the product fraction and whole number as a q x q as a x or (a x q) b. b b Interpret the product of two fractions as a x c = ac b d bd Divide fractions by fractions, unit fractions by a whole number, and whole numbers by fractions. Multiply and divide fractions to solve word problems. Vocabulary: Unit fraction Proper fraction Improper fraction Rename Reduce/Simplify Resizing Scaling Reciprocal Inverse I Can Statements 1. I can understand that fractions are really the division of a numerator by the denominator. 2. I can solve word problems where I need to divide whole numbers leading to answers that are fractions or mixed numbers. 3. I can interpret the quotient and remainder in a division problem. 4. I can multiply a fraction or whole number by a fraction. 5. I can think of multiplication as the scaling of a number (similar to a scale on a map). 6. I can mentally compare the size of a product to the size of one of the factors by thinking about the other factor in the problem. 7. I can explain why multiplying a number by a fraction greater than 1 will result in a bigger number than the number I started with. 8. I can explain why multiplying a number by a fraction less than 1 will result in a smaller number than the number I started with. 9. I can solve real world problems that involve multiplication of fractions and mixed numbers. 10. I can divide fractions by whole numbers and whole numbers by fractions. 11. I can solve real world problems that involve division of fractions.

11 Reflections

12 Common Core State Standard 5.OA.1, 5.OA.2 MCSD Math Curriculum Map ~ 5 th Grade PA Core Standard CC A.1 Interpret and evaluate numerical expressions using order of operations. Taught in Unit(s) Harcourt textbook lessons: 4.1, 12.1, 12.2 PA Core Coach Grade 5: Domain 1 Lessons 1-2 VMath Live Module 9 Lesson 1 Explanation/Example of Standard Analyze and complete calculations by applying the order of operations. Including brackets, parenthesis, exponents, multiplication, division, addition, subtraction. Common Misconceptions Problems should be solved in the order they appear when reading the expression from left to right. Multiplication must be completed before division. Addition must be completed before subtraction. An exponent of 10³ means 10 x 3. When translating a word problem to an expression, the numbers must stay in the same order as they appear in the problem. Big Idea(s) When evaluating an expression, the order of operations must be followed (brackets, parenthesis, exponents, multiplication and division as they appear from left to right, addition and subtraction as they appear from left to right). Key words should be used to correctly write an expression based on a word problem. The Commutative Property allows the multiplication of factors in any order. The Associative Property allows factors to be grouped differently to make multiplication easier. Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) Combination of Chapter tests from Harcourt Chapter 4, 12 VMath Module 9 Lesson 1 Commoncoresheets.com M05.B- O M05.B- O Essential Question(s) What is an expression? What is the order of operations for evaluating expressions? What are grouping symbols in an expression and what do they mean? How do verbal phrases relate to numerical expressions? Concepts Skills (what students need to know) (what students must be able to do) Eligible Content Follow order of operations to read and write Use multiple grouping symbols expressions. (parentheses, brackets, or braces) in Follow order of operations to simplify numerical expressions and evaluate numerical expressions. expressions containing these Write and/or evaluate expressions that symbols. contain variables. Write simple expressions that Translate verbal expressions or word model calculations with numbers problems to numerical expressions.

13 and interpret numerical expressions without evaluating them. Example 1: Express the calculation add 8 and 7, then multiply by 2 as 2 x (8+7). Example 2: Recognize that 3 x (18, ) is three times as large as 18, without having to calculate the indicated sum or product. Evaluate exponents Apply Commutative and Associative properties for addition and multiplication. Recognize patterns in multiplication and division to increase number sense. Vocabulary: Expression Evaluate Parenthesis Bracket Simplify Variable Number sentence Exponent Grouping Symbols Commutative Property Associative Property I Can Statements 1. I can write and solve expressions that have parenthesis and brackets (grouping symbols), multiple operations, and exponents. 2. I can correctly follow the order of operations to write or solve an expression. 3. I can correctly use mathematical symbols in an expression. 4. I can use key words to write an expression when solving a word problem. Reflections

14 Common Core State Standard 5.OA.3 Harcourt textbook lesson 12.3 PA Core Coach Grade 5: Domain 1 Lesson 3 VMath Live Module 9 Lesson 3 Explanation/Example of Standard Create, extend, and analyze patterns. Common Misconceptions All patterns must begin with zero. All patterns must follow the same rule. Big Idea(s) MCSD Math Curriculum Map ~ 5 th Grade PA Core Standard CC A.4 Analyze patterns and relationships using two rules. Taught in Unit(s) Essential Question(s) Patterns can be created or extended by How do you generate numerical patterns, identifying and following a rule. given rules? Patterns continue infinitely based on their rules. How can two patterns, with two different Patterns do not all begin at zero. rules, be compared? Rules for numerical patterns may require What methods can be used to display a addition, subtraction, multiplication, or division. pattern? Patterns may have multi-step rules. How can patterns be written as ordered Patterns with different rules may have a common pairs? relationship. Corresponding terms of two patterns can be used to generate and graph ordered pairs. Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) Harcourt test: Chapter 12 VMath Live Module 9 Lesson 3 Commoncoresheets.com Concepts Skills (what students need to know) (what students must be able to do) Generate and extend two numerical patterns Eligible Content with different rules (addition, subtraction, Generate two numerical patterns multiplication, or division) using two given rules. Example: Identify relationships between two numerical Given the rule add 3 and the patterns M05.Bstarting number 0 and given the rule Identify relationships between corresponding O add 6 and the starting number 0, terms generate terms in the resulting Use various methods to display patterns, such as sequences. lists, tables, or coordinate planes Identify apparent relationships Construct a table using two patterns to form between corresponding terms of ordered pairs two patterns with the same starting Use corresponding terms from two patterns to numbers that follow different rules. generate ordered pairs Example: Given two patterns in M05.Bwhich the first pattern follows the Graph ordered pairs on a coordinate plane O Write a rule for a pattern using a variable rule add 8 and the second pattern follows the rule add 2, observe that the terms in the first pattern are 4 times the size of the terms in the second pattern.

15 Use tables to display patterns. Use corresponding terms from two patterns to generate ordered pairs. Vocabulary: Patterns Rules Relationships Terms Corresponding Table Coordinate plane Ordered pair Variable I Can Statements 1. I can generate two number patterns using two different rules. 2. I can identify relationships between two number patterns. 3. I can form ordered pairs using corresponding terms from two patterns and graph them on a coordinate plane. Reflections

16 MCSD Math Curriculum Map ~ 5 th Grade Common Core State PA Core Standard Standard CC A.1 Graph points in the first quadrant on the coordinate plane and 5.G.1, 5.G.2 interpret these points when solving real world and mathematical problems. Taught in Unit(s) Harcourt textbook lessons: 6.2, 23.1 PA Core Coach Grade 5: Domain 5 Lessons 27, 28 VMath Live Module 8 Lessons 1 Explanation/Example of Standard Identify parts of a coordinate plane (x-axis, y-axis, and the origin) and describe or interpret points given an ordered pair (quadrant 1 only). Common Misconceptions The order of the ordered pair is reversible and will lead to the same location on the coordinate plane. The x-axis and y-axis are interchangeable. Points should be in the middle of box on the coordinate plane. Big Idea(s) Essential Question(s) Lines on a coordinate plane are marked at a How do you generate ordered pairs given consistent interval. rules? Two intersecting number lines can be used to What do you need to know in order to locate identify the location of points on a plane. and plot points in Quadrant I of the Ordered pairs tell the distance a point is from coordinate plane? the origin on the x and y axes. How do you solve real world problems The x-coordinate defines the number of units involving algebra, patterns, and the to the right of the origin. coordinate plane? The y-coordinate defines the number of units How do you interpret points on the above the origin. coordinate plane? Real life situations with two sets of related data can be represented through graphs on a coordinate grid. There are four quadrants on the coordinate plane. Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3 x/ year) Combination of Chapter tests from Harcourt Chapters 6 and 23 VMath Module 8 Lessons 1 Commoncoresheets.com Concepts Skills (what students need to know) (what students must be able to do) Generate, extend, and graph numerical Eligible Content patterns and identify relationships of Identify parts of the coordinate corresponding terms. plane (x-axis, y-axis, and the origin) Locate and plot points in the first quadrant of M05.Cand the ordered pair (x-coordinate the coordinate plane. G and y-coordinate). Limit the Name points as ordered pairs in the first coordinate place to quadrant I quadrant of the coordinate plane. Represent real-world and Graph ordered pairs and use them to M05.C- mathematical problems by plotting represent and solve real-world problems. G points in quadrant I of the coordinate plane and interpret

17 coordinate values of points in the context of the situation. Vocabulary: Coordinate Plane Ordered Pairs Quadrant I x-axis y-axis x-coordinate y-coordinate origin interval scale I Can Statements 1. I can understand a coordinate plane and ordered pairs of number coordinates on that plane (Quadrant 1). 2. I can graph and interpret points in the first quadrant of a coordinate plane. 3. I can represent real-world and mathematical problems by graphing points in the first quadrant of a coordinate plane. 4. I can understand coordinate values in the context of a real-world or mathematical problem. Reflections

18 Common Core State Standard 5.G.3, 5.G.4 MCSD Math Curriculum Map ~ 5 th Grade Harcourt textbook lessons 20.3, 20.4, 20.5, 20.6, 21.1, 21.2 PA Core Coach Grade 5: Domain 5 Lesson 29 VMath Live Module 8 Explanation/Example of Standard Use basic properties to classify two-dimensional figures. Common Misconceptions Two-dimensional figures only have one classification. Big Idea(s) Two-dimensional figures can be categorized based on their attributes. Two-dimensional figures can fit into more than one category. Two dimensional figures have more than one name when they can be classified in more than one way. Two-dimensional figures can be organized in a hierarchy to show their relationship to one another. PA Core Standard CC A.2 Classify two-dimensional figures into categories based on an understanding of their properties. Taught in Unit(s) Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) Combination of Chapter tests from Harcourt Chapters 20, 21 VMath Module 8 Commoncoresheets.com Concepts (what students need to know) M05.C- G Eligible Content Classify two-dimensional figures in a hierarchy based on properties. Example 1: All polygons have at least three sides, and pentagons are polygons, so all pentagons have at least three sides. Example 2: A rectangle is a parallelogram, which is a quadrilateral, which is a polygon; so, a rectangle can be classified as a parallelogram, as a quadrilateral, and as a polygon. Attributes of Two-Dimensional Shapes: triangles, quadrilaterals, etc. Vocabulary: Attributes/Properties Congruent Parallel Perpendicular Essential Question(s) What attributes are used to classify twodimensional figures? Skills (what students must be able to do) Identify polygons based on attributes Describe attributes of polygons Categorize polygons according to their attributes Describe polygons as having more than one name if they can be classified in more than one way Classify polygons in a hierarchy based on their attributes Define the subcategories of a quadrilateral

19 Equilateral Isosceles Scalene Polygon Quadrilateral Parallelogram Rhombus Rectangle Square Trapezoid Right angle Acute Obtuse I Can Statements 1. I can understand that attributes of two-dimensional shapes in a category also belong to all subcategories of those shapes. 2. I can classify two-dimensional shapes into categories based on attributes. Reflections

20 MCSD Math Curriculum Map ~ 5 th Grade Common Core State Standard 5.MD.1 PA Core Standard CC A.1 Solve problems using conversions within a given measurement system. Harcourt textbook lessons: 24.3, 24.4, 24.5, 24.6 PA Core Coach Grade 5: Domain 4 Lessons 21 VMath Live Module 7 Lessons 1-6 Explanation/Example of Standard Taught in Unit(s) Solve problems using simple conversions (may include multistep, real-world problems). Common Misconceptions The metric system and the customary measurement system are equally interchangeable. Measurements with different labels can be compared. Common units are not necessary to compute a problem accurately. Big Idea(s) Essential Question(s) PSSA Math Test (required- Spring) MAP Math Test (required- 3 x/ year) Chapter test from Harcourt Chapter 24 VMath Module 7 Lessons 1-6 Commoncoresheets.com Concepts (what students need to know) Skills (what students must be able to do) The metric system is based on powers of ten. How do you multiply or divide to convert Measurements must be converted to the among standard measurement units within a same unit within the system in order to given measurement system? complete any type of operation or How do you use conversions to solve realcomparison. world problems? When changing from a large unit to a small unit, multiply because it takes many small units to make a large. When changing from a small unit to large unit, divide because you need less of the large units. Assessments M05.D- M Convert among metric units of length. Eligible Content Convert among metric units of liquid volume. Convert among metric units of mass. Convert between different-sized Convert among customary units of length. measurement units within a given Convert among customary measures of liquid measurement system. A table of volume. equivalencies will be provided. Convert among customary measures of Example: Convert 5 cm to meters. weight.

21 Solve conversions within a word problem. Some conversions require an answer written Knowledge of the Metric System- Units of in two units or as a decimal or mixed length, liquid volume, mass number. Knowledge of the Customary System- Units o 110 inches = 9 feet 2 inches of Length, liquid, weight o 150 inches = 4 1 yards 6 Some conversions will require multiple steps. I Can Statements 1. I can convert different-sized measurements within the same measurement system. 2. I can use measurement conversions to solve real-world problems. 3. I can convert measurements within a word problem. Reflections

22 Common Core State Standard none MCSD Math Curriculum Map ~ 5 th Grade Harcourt textbook lessons: 1.5, 2.4, 5.1, 5.5, 6.1, 6.3, 6.6 PA Core Coach Grade 5: Domain 4 Lessons 23 VMath Live Module 9 Lesson 4 PA Core Standard CC A.2 Represent and interpret data using appropriate scale. Taught in Unit(s) Explanation/Example of Standard Organize, display, and interpret data in various graph and table formats. Common Misconceptions Data collected becomes the x- or y-axis instead of using an interval. Any graph is acceptable for any data collected. When plotting data points, if the data does not fall on the interval, placing the point between the two closest intervals is close enough. Big Idea(s) Essential Question(s) Creating a graph is a way to collect and What do all graphs have? organize data to make it easier to read and How do you determine which type of graph is interpret. needed? Graphs enable us to compare data. What is appropriate scale? How do you find a reasonable interval? How do you represent and interpret data using an appropriate graph, scale, and interval? Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) Combination of Chapter tests from Harcourt Chapters 1, 2, 5, and 6 VMath Module 9 Lesson 4 Commoncoresheets.com M05D- M Concepts (what students need to know) Eligible Content Display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs. Skills (what students must be able to do) Set up a graph in quadrant I with appropriate scale/interval, labels, and a title. Convert charts and tables to bar graph or a line graph (a grid will be provided). Interpret data that is between two intervals. Compare data within the graph. Vocabulary: Title Label Range Scale Interval Data Tallies Pictograph Bar graph Line graph

23 I Can Statements 1. I can display and read data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs. 2. I can use titles, scales/intervals, and labels on a graph. 3. I can represent and interpret data using appropriate scale. Reflections

24 Common Core State Standard 5.MD.2 MCSD Math Curriculum Map ~ 5 th Grade PA Core Standard CC A.4 Solve problems involving computation of fractions using information provided in a line plot. Taught in Unit(s) PA Core Coach Grade 5: Domain 4 Lesson 22 VMath Live Module 7 Explanation/Example of Standard Organize, display, and answer questions based on data. Common Misconceptions If data does not exist for a fraction in the line plot, the fraction can be omitted. Big Idea(s) A line plot begins as a number line. The Xs show the number of times the value occurs in the set of data. The scale of a line plot is based on the data. It may involve fractions or whole numbers, but must have a consistent interval. Line plots can be used to add, subtract, multiply, and divide fractional data. PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) VMath Live Module 7 Commoncoresheets.com Concepts (what students need to know) M05.D- M Vocabulary: Line plot Fraction Outlier Eligible Content Solve problems involving computation of fractions by using information presented in line plots. Assessments Essential Question(s) How is a line plot used to display information? How is a line plot used to interpret information? How do you solve problems involving fractions using information from a line plot? Skills (what students must be able to do) Use number sense with fractions to create a line plot. Rename fractions to have a common denominator in order to display them on the line plot. Transfer information/data from a problem onto a line plot. Correctly label the line plot. Solve problems using fractions represented in a line plot. Add, subtract, multiply, and divide fractions. I Can Statements 1. I can make a line plot to display data sets of measurements in fractions. 2. I can use fraction operations to solve problems involving information presented on a line plot. Reflections

25 MCSD Math Curriculum Map ~ 5 th Grade Common Core State PA Core Standard Standard CC A.5 Apply concepts of volume to solve problems and relate volume to 5.MD.3, 5.MD.4, 5.MD.5 multiplication and to addition. Taught in Unit(s) Harcourt textbook lessons 27.3, 27.4, 27.5 VMath Live Module 7 Lesson 8 PA Core Coach Grade 5 Domain 4 Lessons Explanation/Example of Standard Use, describe, and develop procedures to solve problems involving volume for one right rectangular prism or two non-overlapping right rectangular prisms. Common Misconceptions Add all sides of the figure Choose two of the given numbers and multiply Volume is the same as area Big Idea(s) Essential Question(s) Volume is a measure of the amount of space How do you use a formula to help you find inside a solid figure. It can be found by filling the volume of a rectangular prism? the figure with cubes. Each cube represents How does volume help me solve problems in one cubic unit with a side length of one. everyday life? Volume is measured in cubic units (Length is How do you calculate the volume of two nonmeasured in linear units and area is overlapping right rectangular prisms measured in square units). (composite solid figures) and get the total Volume is used for three-dimensional figures. volume? Two formulas can be used to calculate volume. o V= l x w x h o V = B x h To find the volume of two non-overlapping right rectangular prisms (composite solids), we can decompose them into right rectangular prisms to find the volume of each part. The Commutative Property allows the multiplication of sides in any order. The Associative Property allows factors to be grouped differently to make multiplication easier. Assessments PSSA Math Test (required- Spring) MAP Math Test (required- 3x/year) Harcourt Chapter 27 test VMath Live Module 7 Lesson 8 Commoncoresheets.com Concepts Skills (what students need to know) (what students must be able to do) Use the appropriate formula to find the volume of a rectangular prism. Eligible Content Compute the volume of a rectangular prism. Apply the formulas V = l x w x h and M05.D- Identify whether a situation involves length, V = B x h for rectangular prisms to M area, or volume. find volumes of right rectangular

26 M05.D- M prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided. Find volumes of solid figures composed of two non-overlapping right rectangular prisms. Find the volume of two non-overlapping right rectangular prisms (composite solid figures). Find the measurement of a missing side. Label answer with appropriate units. Apply properties when solving equations. Cubic Units Relate Length, Area, and Volume Vocabulary: Volume Area Base Height Length Width Right rectangular prism Formula Composite solid figure Commutative Property of Multiplication Associative Property of Multiplication 3-D figures I Can Statements 1. I can recognize volume as a characteristic of solid figures and understand how it can be measured. 2. I can understand a unit cube as a cube with side lengths of one unit and can use it to measure volume. 3. I can measure volume by counting unit cubes. 4. I can understand that a solid figure filled with a number of unit cubes is said to have a volume of that many cubes. 5. I can solve real world problems involving volume of one right rectangular prism or two nonoverlapping right rectangular prisms. 6. I can find the volume of an object using the formulas V = l x w x h or V = B x h. 7. I can determine when to use perimeter, area, and volume to solve a problem. 8. I can calculate the volume of two non-overlapping right rectangular prisms (composite solid figures) and get the total volume. Reflections

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