Unit%1:%Order%of%Operations%&%Algebraic% … APS...

* Standards in green bold font are major work of 5th grade. 2015 – 2016 Pacing Calendar * Standards in purple bold font are major work of 6th grade. Office of K – 5 Mathematics

5th Grade Advanced Mathematics Pacing Calendar

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

Atlanta Public Schools

August 2015

Sun Mon Tue Wed Thu Fri Sat

4 5 First Day of School

9 10 11

12 13 14

18 19 20 21 22

23 24 25 26 27

Unit 1: Order of Operations & Algebraic Expressions

Unit 1

September 2015

6 7 Labor day

8 9 10 11 12

13 14 15 16 17 18 19

21 22 23 24 25 26

27 28 29 30

Fall CAAS SLO (Grades 1 – 3)

** Unit 2 – Decimal Operations is a combination of Grade 5 Math Units 2 & 3; when pulling resources, teachers will need to look at the Georgia Frameworks, accordingly. In Unit 2 students will: • Solve problems by understanding that like with whole numbers, the location of a digit in a

decimal number determines the value of a digit. • Understand that rounding decimals should be “sensible” for the context of the problem. • Understand that decimal numbers can be represented with models. • 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.

Unit 2 Standards: MGSE.5.NBT.1 MGSE.5.NBT.3 MGSE.5.NBT.4 MGSE.5.NBT.7 MGSE.5.NBT.2 MGSE.6.NS.3

Unit 2: Decimal Operations

Unit 1: Order of Operations & Algebraic Expressions

** 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

October 2015

4 5 6 7 8 Professional Learning Day

9 Fall Break

12 Fall Break

Columbus Day

13 14 15 16 17

20 21 22 23 24

25 26 27 28 29 30 31 Halloween

Unit 3: Fraction Operations

** 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)

November 2015 Sun Mon Tue Wed Thu Fri Sat

1 2 3 4 5 6 7

10 11 Veterans Day 12 13 14

16 17 18 19 20 21

23 24 25 26

Unit 4: Ratios and Proportional Reasoning

Unit 4

Unit 3: Fraction Operations

Thanksgiving Break

December 2015

8 9 10 11 12

13 14 15 16 17 18 19

21 22 23 24 25 26

27 28 29 30 31

Semester Break

Unit 4: Ratios and Proportional Reasoning

January 2016

Sun Mon Tue Wed Thu Fri Sat 1 2

3 4 5 Professional Learning Day

6 7 8 9

12 13 14 15 16

17 18 M L King

19 20 21 22 23

24 25 26 27 28 29 30

** 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…

• 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

Semester Break

Unit 5: The Number System & Algebraic Reasoning

February 2016

2 3 4 5 6

7 8 9 10 11 12 13

16 17 18 19 20

22 23 24 25

** 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

Winter Break

Unit 6: Volume, Measurement & 2D Figures

Unit 6

5th Grade Advanced Mathematics Pacing Calendar Atlanta Public Schools

March 2016 Sun Mon Tue Wed Thu Fri Sat

8 9 10 11 12

13 14 15 16 17 18 Professional Learning Day

21 22 23 24 25 26

27 28 29 30 31

** 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

Unit 7: Geometry and the Coordinate Plane

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

April 2016

3 4 5 6 7 8 9

12 13 14 15 16

19 20 21 22 23

24 25 26 27 28 29 30

Metro Area Spring Break

Unit 7

Unit 8: Show What We Know

May 2016

1 2 3 4 5 6 7

12 13 14

16 17 18 19 20 21

23 24 25 Last Day of School

29 30 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)

Unit 8: Quantitative Relationships

Year Wrap-‐Up

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

Unit%1:%Order%of%Operations%&%Algebraic% … APS...

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