5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools August 2015 Sun
Mon
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1
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First Day of School 9
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7
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Unit 1: Order of Operations & Algebraic Expressions 13
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Unit 1: Order of Operations & Algebraic Expressions 16
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Unit 1: Order of Operations & Algebraic Expressions 23
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Unit 1: Order of Operations & Algebraic Expressions 30
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Unit 1 Fall CAAS SLO (Grades 1 – 3) In Unit 1 students will: • Solve problems by representing mathematical relationships between quantities using mathematical expressions and equations. • Use the four whole number operations efficiently, including the application of order of operations. • Write, evaluate, and interpret mathematical expressions with and without using symbols. • Apply strategies for multiplying a 2-­‐ or 3-­‐digit number by a 2-­‐digit number. • Develop paper-­‐and-­‐pencil multiplication algorithms (not limited to the traditional algorithm) for 3-­‐ or 4-­‐digit number multiplied by a 2-­‐ or 3-­‐digit number. • Apply paper-­‐and-­‐pencil strategies for division • Solve problems involving multiplication and division. • Investigate the effects of multiplying whole numbers by powers of 10. • Represent repeated multiplication with exponents. • Evaluate expressions containing exponents to solve mathematical and real world problems. • Translate verbal phrases and situations into algebraic expressions. • Identify the parts of a given expression. • Use the properties to identify equivalent expressions. • Use the properties and mathematical models to generate equivalent expressions. Unit 1 Standards: MGSE.5.OA.1 MGSE.5.OA.2 MGSE.5.NBT.1 MGSE.5.NBT.2 MGSE.5.NBT.5 MGSE.5.NBT.6 MGSE.6.EE.1 MGSE.6.EE.2 MGSE.6.EE.2(a) MGSE.6.EE.2(b) MGSE.6.EE.2(c) MGSE.6.EE.3 MGSE.6.EE.4 * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools September 2015 Sun
Mon
Tue
1
Wed
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Thu
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Fri
Sat
4
5
11
12
Unit 1: Order of Operations & Algebraic Expressions 6
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Labor day
8
9
10
Unit 1: Order of Operations & Algebraic Expressions 13
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25
26
Unit 2: Decimal Operations 20
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Unit 2: Decimal Operations 27
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Unit 2: Decimal Operations Fall CAAS SLO (Grades 1 – 3) ** Unit 2 – Decimal Operations is a combination of Grade 5 Math Units 2 & 3; when pulling Unit 2 Standards: resources, teachers will need to look at the Georgia Frameworks, accordingly. MGSE.5.NBT.1 MGSE.5.NBT.3 In Unit 2 students will: MGSE.5.NBT.4 • Solve problems by understanding that like with whole numbers, the location of a digit in a MGSE.5.NBT.7 decimal number determines the value of a digit. MGSE.5.NBT.2 • Understand that rounding decimals should be “sensible” for the context of the problem. • Understand that decimal numbers can be represented with models. MGSE.6.NS.3 • Understand that addition and subtraction with decimals are based on the fundamental concept of adding and subtracting the numbers in like position values. • Understand how and why the placement of the decimal is determined by multiplying or dividing a number by 10 or a multiple of 10. • Understand that multiplication and division are inverse operations of each other. • Understand that rules for multiplication and division of whole numbers also apply to decimals. • Fluently add, subtract, multiply, and divide multi-­‐digit decimals using the standard algorithm for each operation. * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools October 2015 Sun
Mon
Tue
Wed
Thu
1
Fri
2
Sat
3
Unit 2: Decimal Operations 4
5
6
7
8
Professional Learning Day Unit 2: Decimal Operations 11
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13
14
Fall Break Columbus Day
18
19
15
9
10
Fall Break 16
17
23
24
30
31
Unit 3: Fraction O perations 20
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Unit 3: Fraction O perations 25
26
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28
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Halloween Unit 3: Fraction O perations ** Unit 3 – Fraction Operations is Grade 5 Math Unit 4; when pulling resources, teachers will need to look at the Georgia Frameworks, accordingly. In Unit 3 students will understand: • A fraction is another representation for division. • Fractions are relations – the size or amount of the whole matters. • Fractions may represent division with a quotient less than one. • Equivalent fractions represent the same value. • With unit fractions, the greater the denominator, the smaller the equal share. • Shares don’t have to be congruent in order to be to be equivalent. • Fractions and decimals are different representations for the same amounts and can be used interchangeably. • The meanings of each operation on fractions are consistent with the meanings of the operations on whole numbers. For example: It is possible to divide fractions without multiplying by the inverse or reciprocal of the second fraction. • When dividing by a fraction, there are two ways of thinking about the operation – partition and measurement, which will lead to two different thought processes for division. • When we divide one number by another, we may get a quotient that is bigger than the original number, smaller than the original number, or equal to the original number. Unit 3 Standards: MGSE.5.NF.1 MGSE.5.NF.2 MGSE.5.NF.3 MGSE.5.NF.4 MGSE.5.NF.5 MGSE.5.NF.6 MGSE.5.NF.7 MGSE.5.MD.2 MGSE.6.NS.1 * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools November 2015 Sun
1
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13
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Unit 3: Fraction O perations 8
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Veterans Day
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Unit 3: Fraction Operations 15
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Unit 4: Ratios and Proportional Reasoning 22
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Thanksgiving Break 29
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Unit 4 ** Unit 4 Ratios and Proportional Reasoning is Grade 6 Math Unit 2; when pulling resources, teachers will need to look at the Georgia Frameworks, accordingly. In Unit 4 students will understand: • A ratio is a number that relates two quantities or measures within a given situation in a multiplicative relationship (in contrast to a difference or additive relationship).The relationships and rules that govern whole numbers, govern all rational numbers. • Making explicit the type of relationships that exist between two values will minimize confusion between multiplicative and additive situations. • Ratios can express comparisons of a part to whole, (a/b with b ≠ 0), for example, the ratio of the number of boys in a class to the number of students in the class. • The ratio of the length to the width of a rectangle is a part-­‐to-­‐part relationship. • Understand that fractions are also part-­‐whole ratios, meaning fractions are also ratios. Percentages are ratios and are sometimes used to express ratios. • Both part-­‐to-­‐whole and part-­‐to-­‐part ratios compare two measures of the same type of thing. A ratio can also be a rate. • A rate is a comparison of the measures of two different things or quantities; the measuring unit is different for each value. For example if 4 similar vans carry 36 passengers, then the comparison of 4 vans to 36 passengers is a ratio. • All rates of speed are ratios that compare distance to time, such as driving at 45 miles per hour or jogging at 7 minutes per mile. • Ratios use division to represent relations between two quantities. Unit 4 Standards: MGSE.6.RP.1 MGSE.6.RP.2 MGSE.6.RP.3 MGSE.6.RP.3(a) MGSE.6.RP.3(b) MGSE.6.RP.3(c) MGSE.6.RP.3(d) * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools December 2015 Sun
Mon
Tue
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Wed
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Unit 4: Ratios and Proportional Reasoning 6
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Unit 4: Ratios and Proportional Reasoning 13
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Unit 4: Ratios and Proportional Reasoning 20
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Semester Break 27
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Semester Break * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools January 2016 Sun
Mon
Tue
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1
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Semester Break 3
4
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Semester Break 10
11
6
Professional Learning Day 12
7
8
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Unit 5: The Number System & Algebraic Reasoning 13
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Unit 5: The Number System & Algebraic Reasoning 17
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M L King
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Unit 5: The Number System & Algebraic Reasoning 26
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Unit 5: The Number System & Algebraic Reasoning 31
** Unit 5 – The Number System and Algebraic Reasoning is a combination of Grade 6 Math Units 4 & 7; when pulling resources, teachers will need to look at the Georgia Frameworks, accordingly. In Unit 5, students will… •
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Determine if an equation or inequality is appropriate for a given situation. Solve mathematical and real-­‐world problems with equations. Represent real-­‐world situations as inequalities. Interpret the solutions to equations and inequalities. Represent the solutions to inequalities on a number line. Analyze the relationship between dependent and independent variables through the use of tables, equations and graphs. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself. Find and position integers and other rational numbers on a horizontal or vertical number line diagram. Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-­‐world contexts. Understand the absolute value of a rational number as its distance from 0 on the number line Interpret absolute value as magnitude for a positive or negative quantity in a real-­‐world situation. Distinguish comparisons of absolute value from statements about order. Unit 5 Standards: MGSE.6.NS.5 MGSE.6.NS.6 MGSE.6.NS.6(a) MGSE.6.EE.5 MGSE.6.EE.6 MGSE.6.EE.7 MGSE.6.EE.8 * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools February 2016 Sun
Mon
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12
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Unit 6: Volume, Measurement & 2D Figures 7
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Unit 6: Volume, Measurement & 2D Figures 14
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Winter Break 19
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Unit 6: Volume, Measurement & 2D Figures Winter Break 21
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Unit 6: Volume, Measurement & 2D Figures 28
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Unit 6 ** Unit 6 – Volume, Measurement, & 2D Figures is a combination of Grade 5 Math Units 5 & 6; when pulling resources, teachers will need to look at the Georgia Frameworks, accordingly. In Unit 6 students will: • Change units to related units within the same measurement system by multiplying or dividing using conversion factors. • Use line plots to display a data set of measurements that includes fractions. • Use operations to solve problems based on data displayed in a line plot. • Recognize volume as an attribute of three-­‐dimensional space. • Understand that volume can be measured by finding the total number of same size units of volume required to fill the space without gaps or overlaps. • Understand that a 1-­‐unit by 1-­‐unit by 1-­‐unit cube is the standard unit for measuring volume. • Select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. • Decompose three-­‐dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. • Measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems. • Communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. • Identify similarities and differences among two-­‐dimensional figures. Reason about attributes (properties) of two-­‐
dimensional figures. • Have experiences discussing properties of two-­‐dimensional figures. • Build upon their fourth grade knowledge and create a hierarchy diagram. • Understand that attributes belonging to a category of two-­‐dimensional figures also belong to all subcategories of that category. Unit 6 Standards: MGSE.5.MD.1 MGSE.5.MD.2 MGSE.5.MD.3 MGSE.5.MD.4 MGSE.5.MD.5 MGSE.5.G.3 MGSE.5.G.4 * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools March 2016 Sun
Mon
Tue
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Wed
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Thu
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4
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Unit 6: Volume, Measurement & 2D Figures 6
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Unit 7: Geometry and the Coordinate Plane 13
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Unit 7: Geometry and the Coordinate Plane 20
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Professional Learning Day 25
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Unit 7: Geometry and the Coordinate Plane 27
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Unit 7: Geometry and the Coordinate Plane ** Unit 7 – Geometry and the Coordiante Plane is Grade 6 Math Unit 7; when pulling resources, teachers will need to look at the Georgia Frameworks, accordingly In Unit 7 students will: • Understand that on the coordinate plane, a point represents the two facets of information associated with an ordered pair. • Know that graphical representations can be used to make predictions and interpretations about real world situations. • Given two rules, generate two numerical patterns, and create line graphs from the pattern. This explains a linear function and why straight lines are generated from the pattern. • Solve real-­‐world and mathematical problems by graphing points in all four quadrants of the coordinate plane. • Find and position pairs of integers and other rational numbers on a coordinate plane. • Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. • Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. • Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. Unit 7 Standards: MGSE.5.G.1 MGSE.5.G.2 MGSE.5.OA.3 MGSE.6.NS.6(b) MGSE.6.NS.6(c) MGSE.6.NS.7 MGSE.6.NS.7(a) MGSE.6.NS.7(b) MGSE.6.NS.7(c) MGSE.6.NS.7(d) MGSE.6.NS.8 * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools April 2016 Sun
Mon
Tue
Wed
Thu
Fri
1
Sat
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Unit 7 3
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6
7
8
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15
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29
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Metro Area Spring Break 10
11
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Unit 8: Show What We Know 17
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Unit 8: Show What We Know 24
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Unit 8: Show What We Know Georgia Milestones EOG in Grades 3 – 8 Spring Post Administration SLO Window and CAAS SLO Unit 8: Show What We Know • April 11 – May 25 • Review and Reteach ALL content standards • Apply skills and concepts learned from all units • Engage in problem-­‐based learning • Demonstrate mastery using summative assessments * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools May 2016 Sun
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Unit 8: Quantitative Relationships 8
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Unit 8: Quantitative Relationships 15
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Unit 8: Quantitative Relationships 22
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Year Wrap-­‐Up 29
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Last Day of School 26
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Memorial Day In Unit 8 students will: • Determine if an equation or inequality is appropriate for a given situation. • Solve mathematical and real-­‐world problems with equations. • Represent real-­‐world situations as inequalities. • Interpret the solutions to equations and inequalities. • Analyze the relationship between dependent and independent variables through the use of tables, equations and graphs. • Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. • Relate and compare different forms of representation for a relationship. • Use values from specified sets to make an equation or inequality true. • Use graphs to to represent all of the possible solutions to a given situation. Unit 8 Standards: MGSE.6.EE.9 MGSE.6.EE.9(a) MGSE.6.EE.9(b) * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics 5th Grade Advanced Mathematics Pacing Calendar Units Instruction Window Pre & Post Test Assessment Window Unit 1 Order of Operations and Algebraic Expressions August 5 – September 9, 2015 September 10 – September 11, 2015 Unit 2 Decimal Operations September 14 – October 5, 2015 October 6 – October 7, 2015 Unit 3 Fraction Operations October 13 – November 11, 2015 November 12 – November 13, 2015 Unit 4 Ratios and Proportional Reasoning November 16 – December 16, 2015 December 17 – December 18, 2015 Unit 5 The Number System and Algebraic Reasoning January 6 – January 27, 2016 January 28 – January 29, 2016 Unit 6 Volume, Measurement & 2D Figures February 1 – March 2, 2016 March 3 – March 4, 2016 Unit 7 Geometry and the Coordinate Plane March 7 – March 30, 2016 March 31 – April 1, 2016 Unit 8 Quantitative Relationships May 2 – May 18, 2016 May 19 – May 20, 2016 * Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar th
* Standards in purple bold font are major work of 6 grade. Office of K – 5 Mathematics