alignment of the formative assessment lessons … · alignment of the formative assessment lessons...

ALIGNMENT OF THE FORMATIVE ASSESSMENT LESSONS TO THE CCSS

DEVELOPED BY ANN SHANNON & ASSOCIATES FOR THE BILL & MELINDA GATES FOUNDATION

SEPTEMBER 2012

Formative Assessment Alignment to CCSS page 1

OVERVIEW OF MIDDLE SCHOOL COURSE OUTLINES Green indicates a major cluster, yellow indicates an additional cluster, and blue indicates a supporting cluster, as given in the Cluster Emphases from the PARCC and Smarter Balanced Consortia.

Grade 6 Grade 7 Grade 8 6.RP Understand ratio concepts and use ratio reasoning to solve problems.

7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems.

8.NS Know that there are numbers that are not rational, and approximate them by rational numbers.

6.NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

8.EE Work with radicals and integer exponents.

6.NS Compute fluently with multi-digit numbers and find common factors and multiples.

7.EE Use properties of operations to generate equivalent expressions.

8.EE Understand the connections between proportional relationships, lines, and linear equations.

6. NS Apply and extend previous understandings of numbers to the system of rational numbers.

7.EE Solve real-life and mathematical problems using numerical and algebraic equations

8.EE Analyze and solve linear equations and pairs of simultaneous linear equations.

6.EE Apply and extend previous understandings of arithmetic to algebraic expressions.

7.G Draw, construct, and describe geometrical figures and describe the relationships between them.

8.F Define, evaluate, and compare functions.

6.EE Reason about and solve one-variable equations and inequalities.

7.G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

8.F Use functions to model relationships between quantities.

6.EE Represent and analyze quantitative relationships between dependent and independent variables.

7.SP Use random sampling to draw inferences about a population.

8.G Understand congruence and similarity using physical models, transparencies, or geometry software.

6.G Solve real-world and mathematical problems involving area, surface area, and volume.

7.SP Draw informal comparative inferences about two populations.

8.G Understand and apply the Pythagorean theorem.

6.SP Develop understanding of statistical variability.

7.SP Investigate chance processes and develop, use, and evaluate probability models.

8.G Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

6.SP Summarize and describe distributions.

8.SP Investigate patterns of association in bivariate data.

Mathematical Practices

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.


GRADE 6-8 UNIT OVERVIEW The colored bars reflect the weighting of the standards within each unit based on the Cluster Emphases given by the PARCC and Smarter Balanced Consortia.

Grade 6 Grade 7 Grade 8 Unit 6.0 Introduction: Mathematical Investigations

Unit 7.0 Introduction: Mathematical Investigations

Unit 8.0 Introduction: Mathematical Investigations

Unit 6.1 Ratio and Proportional Relationships


Unit 8.1 Numerical Expressions White Space

Unit 6.2 Critical Area 1 White Space White Space

Unit 7.2 Critical Area 1 White Space White Space

Unit 8.2 Proportional Relationships, Lines, and Equations

Unit 6.3 Rational Number System White Space

Unit 7.3 The Number System White Space

Unit 8.3 Linear Equations and Systems of Linear Equations

Unit 6.4 Division of Fractions by Fractions

Unit 7.4 Complex problem solving White Space

Unit 8.4 Bivariate Data White Space White Space

Unit 6.5 Critical Areas 1 & 2

Unit 7.5 Expressions

Unit 8.5 Critical Area 1


Unit 7.6 Equations

Unit 8.6 Functions

Unit 6.7 Equations and Inequalities



Unit 6.8 Quantitative Relationships White Space

Unit 7.8 Geometric Figures White Space White Space

Unit 8.8 Rational and Irrational Numbers

Unit 6.9 Critical Areas 1, 2, & 3

Unit 7.9 Geometric Measurement

Unit 8.9 Transformations

Unit 6.10 Statistics


Unit 8.10 Pythagorean Theorem

Unit 6.11 Geometry White Space White Space

Unit 7.11 Statistics White Space White Space

Unit 8.11 Volume of Cones, Cylinders, and Spheres

Unit 6.12 Critical Areas 1, 2, 3, & 4

Unit 7.12 Probability




CCSS TOOLS: PROGRESSIONS Source: http://ime.math.arizona.edu/progressions/

GRADE 6 GRADE 7 GRADE 8 6.RP Understand ratio concepts and use ratio reasoning to solve problems.

7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems.

8.EE Understand the connections between proportional relationships, lines, and linear equations.

6.EE Represent and analyze quantitative relationships between dependent and independent variables.

8.F Define, evaluate, and compare functions.

8.F Use functions to model relationships between quantities.

6.EE Apply and extend previous understandings of arithmetic to algebraic expressions.

7.EE Use properties of operations to generate equivalent expressions.

8.EE Work with radicals and integer exponents.

6.EE Reason about and solve one-variable equations and inequalities.

7.EE Solve real-life and mathematical problems using numerical and algebraic equations.

8.EE Analyze and solve linear equations and pairs of simultaneous linear equations.

6.NS Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

8.NS Know that there are numbers that are not rational, and approximate them by rational numbers.

6.NS Compute fluently with multi-digit numbers and find common factors and multiples.

6.G Solve real-world and mathematical problems involving area, surface area, and volume.

7.G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G Draw, construct, and describe geometrical figures and describe the relationships between them.

8.G Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G Understand and apply the Pythagorean theorem.

6.SP Develop understanding of statistical variability. 6.SP Summarize and describe distributions.

7.SP Use random sampling to draw inferences about a population. 7.SP Draw informal comparative inferences about two populations. 7.SP Investigate chance processes and develop, use, and evaluate probability models.

8.SP Investigate patterns of association in bivariate data.


FORMATIVE ASSESSMENT LESSON OVERVIEW

GRADE 6 GRADE 7 GRADE 8

Sharing Gasoline*

Optimizing: Security Cameras*

Laws of Arithmetic*

Mean, Median, Mode, and Range*

Design a Candy Carton*

Developing a Sense of Scale

Proportion and Non-proportion Situations*

Using Positive and Negative Numbers in Context

Drawing to Scale: Designing a Garden*

Steps to Solving Equations

Increasing and Decreasing Quantities by a Percent

Using Dimensions: Designing a Sports Bag

Maximizing Area: Gold Rush

Applying Angle Theorems

Estimations and Approximations: The Money Munchers

Estimating: Counting Trees

Evaluating Statements about Probability

Estimating Length Using Scientific Notation

The Difference of Two Squares*

Lines and Linear Equations

Solving Linear Equations in One Variable

Classifying Solutions to Systems of Equations

Solving Real-Life Problems: Baseball Jerseys

Interpreting Distance-Time Graphs

Modeling Situations with Linear Equations

Repeating Decimals

Identifying Similar Triangles*

The Pythagorean Theorem: Square Areas

Modeling: Making Matchsticks

Most of the Formative Assessment Lessons are available at http://map.mathshell.org/materials/lessons.php

For Alpha Formative Assessment Lessons marked with an * please contact your district leader

Formative Assessment Lesson Alignment to CCSS page 5

GRADE 6 COURSE OUTLINE The colored bars reflect the weighting of the standards within each unit based on the Cluster Emphases given by the PARCC and Smarter Balanced Consortia.

CONTENT AREA FORMATIVE ASSESSMENT LESSONS # OF DAYS

Unit 6.0 Introduction: Mathematical Investigations 5


Sharing Gasoline* Optimizing: Security Cameras*

10


5

Unit 6.3 Rational Number System

10

Unit 6.4 Division of Fractions by Fractions

10


13


Laws of Arithmetic* 10

Unit 6.7 Equations and Inequalities

10

Unit 6.8 Quantitative Relationships

10


18


Mean, Median, Mode, and Range* 10

Unit 6.11 Geometry

Design a Candy Carton* 9


24

Total Days 144





Content Area FORMATIVE ASSESSMENT LESSONS # OF DAYS



Developing a Sense of Scale Proportion and Non-proportion Situations*

10


5

Unit 7.3 The Number System

Using Positive and Negative Numbers in Context

10

Unit 7.4 Complex problem solving

10


Drawing to Scale: Designing a Garden* 10

Unit 7.6 Equations

Steps to Solving Equations 10


Increasing and Decreasing Quantities by a Percent

14

Unit 7.8 Geometric Figures

10

Unit 7.9 Geometric Measurement

Using Dimensions: Designing a Sports Bag Maximizing Area: Gold Rush

10


Applying Angle Theorems Estimations and Approximations: The Money Munchers

17


5

Unit 7.12 Probability

5


Estimating: Counting Trees

Evaluating Statements about Probability

23

Total Days 144





CONTENT AREA FORMATIVE ASSESSMENT LESSONS # OF DAYS


Unit 8.1 Numerical Expressions

Estimating Length Using Scientific Notation The Difference of Two Squares*

10

Unit 8.2 Proportional Relationships, Lines, and Equations

Lines and Linear Equations 10

Unit 8.3 Linear Equations and Systems of Linear Equations

Solving Linear Equations in One Variable Classifying Solutions to Systems of Equations

10

Unit 8.4 Bivariate Data

10


Solving Real-Life Problems: Baseball Jerseys

11

Unit 8.6 Functions

Interpreting Distance-Time Graphs 15


Modeling Situations with Linear Equations

15

Unit 8.8 Rational and Irrational Numbers

Repeating Decimals 10

Unit 8.9 Transformations

Identifying Similar Triangles* 10

Unit 8.10 Pythagorean Theorem

The Pythagorean Theorem: Square Areas

10

Unit 8.11 Volume of Cones, Cylinders, and Spheres

Modeling: Making Matchsticks 10


18

Total Days 144 Most of the Formative Assessment Lessons are available at http://map.mathshell.org/materials/lessons.php



OVERVIEW OF HIGH SCHOOL COURSE OUTLINES

ALGEBRA 1 GEOMETRY ALGEBRA 2

A0 Introduction G0 Introduction and Construction

A0 Introduction

A1 Modeling With Functions G1 Basic Definitions and Rigid Motion

A1 Exponential Functions

A2 Linear Functions G2 Geometric Relationships and Properties

A2 Trigonometric Functions

A3 Linear Equations & Inequalities in One Variable

G3 Similarity A3 Functions

Modeling Unit 1 M1 Geometric Modeling 1 Modeling Unit 1

A4 Linear Equations & Inequalities in Two Variables

G4 Coordinate Geometry A4 Rational and Polynomial Expressions

A5 Quadratic Functions G5 Circles and Conics P1 Probability

A6 Quadratic Equations G6 Geometric Measurements and Dimensions

S2 Statistics

S1 Statistics G7 Trigonometric Ratios Modeling Unit 2

Modeling Unit 2 M2 Geometric Modeling 2

MATHEMATICAL PRACTICES

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.


ALGEBRA 1 COURSE OUTLINE

Content Area Formative Assessment Lessons # of Days

A0 Introduction: Mathematical Investigations 5

A1 MODELING WITH FUNCTIONS N-Q Quantities 1, 2, 3. F-IF Interpreting Functions 1, 2, 3, 4, 5, 9 F-LE Linear, Quadratic and Exponential Models 1, 1a, 1b, 3, 5

Functions and Everyday Situations Modeling: Having Kittens

15

A2 LINEAR FUNCTIONS F-IF Interpreting Functions 6, 7a, 9 F-BF Building Functions 1, 1a, 2, 4a F-LE Linear, Quadratic and Exponential Models 1, 1a, 1b

Comparing Investments Generalizing Patterns: Table Tiles

16

A3 LINEAR EQUATIONS & INEQUALITIES IN ONE VARIABLE A-REI Reasoning with Equations and Inequalities 1, 3, 11 A-CED Creating Equations 1, 3, 4

Interpreting Algebraic Expressions Sorting Equations and Identities Creating and Solving Equations

16

A4 LINEAR EQUATIONS & INEQUALITIES IN TWO VARIABLES A-CED Creating Equations 2, 3, 4 A-REI Reasoning with Equations and Inequalities 5, 6, 10, 12

Solving Linear Equations in Two Variables Optimization Problems: Boomerangs Defining Regions Using Inequalities

16

A5 QUADRATIC FUNCTIONS F-IF Interpreting Functions 4, 5, 6, 7, 7a, 8, 8a, 9 F-BF Building Functions 1, 1a, 1b, 3

Forming Quadratics 20

A6 QUADRATIC EQUATIONS N-CN The Complex Number System 7 A-SSE Seeing Structure in Expressions 3a, 3b A-REI Reasoning with Equations and Inequalities 4, 4a, 4b, 7

Solving Quadratic Equations: Cutting Corners

26

S1 STATISTICS S-ID Interpreting Categorical and Quantitative Data 1, 2, 3, 5, 6, 6a, 6b, 6c, 7, 8, 9

Representing Data 1: Using Frequency Graphs Representing Data 2: Using Box Plots Interpreting Statistics: A Case of Muddying the Waters Devising a Measure for Correlation

30

Total days 144

The Formative Assessment Lessons are available at http://map.mathshell.org/materials/lessons.php


GEOMETRY COURSE OUTLINE

Content Area Formative Assessment Lessons

# of Days

G0 INTRO AND CONSTRUCTION G-CO Congruence 12, 13

12

G1 BASIC DEFINITIONS AND RIGID MOTION G-CO Congruence 1, 2, 3, 4, 5, 6, 7, 8

Representing and Combining Transformations Analyzing Congruency Proofs

20

G2 GEOMETRIC RELATIONSHIPS AND PROPERTIES G-CO Congruence 9, 10, 11 G-C Circles 3

Evaluating Statements About Length and Area Inscribing and Circumscribing Right Triangles

15

G3 SIMILARITY G-SRT Similarity, Right Triangles, and Trigonometry 1, 2, 3, 4, 5

Geometry Problems: Circles and Triangles Proofs of the Pythagorean Theorem

20

M1 GEOMETRIC MODELING 1 G-MG Modeling with Geometry 1, 2, 3

Solving Geometry Problems: Floodlights

7

G4 COORDINATE GEOMETRY G-GPE Expressing Geometric Properties with Equations 4, 5, 6, 7

Finding Equations of Parallel and Perpendicular Lines

15

G5 CIRCLES AND CONICS G-C Circles 1, 2, 5 G-GPE Expressing Geometric Properties with Equations 1, 2

Equations of Circles 1 Equations of Circles 2 Sectors of Circles

15

G6 GEOMETRIC MEASUREMENTS AND DIMENSIONS G-GMD 1, 3, 4

Evaluating Statements About Enlargements (2D & 3D) 2D Representations of 3D Objects

15

G7 TRIONOMETRIC RATIOS G-SRT Similarity, Right Triangles, and Trigonometry 6, 7, 8

Calculating Volumes of Compound Objects

15

M2 GEOMETRIC MODELING 2 G-MG Modeling with Geometry 1, 2, 3

Modeling: Rolling Cups 10

Total days: 144



ALGEBRA 2 COURSE OUTLINE

Content Area Formative Assessment Lessons

# of Days

A0 Introduction: Mathematical Investigations 8

A1 EXPONENTIAL FUNCTIONS N-RN The Real Number System 1, 2, 3 A-SSE Seeing Structure in Expressions 3, 4 F-IF Interpreting Functions 3, 7e, 8b F-LE Linear, Quadratic, and Exponential Models 1a, 1b, 1c, 2, 3, 4, 5 F-BF Building Functions 2, 4a

Rational and Irrational Numbers 1 Rational and Irrational Numbers 2

25

A2 TRIGONOMETRIC FUNCTIONS F-TF Trigonometric Functions 1, 2, 5, 8 F-IF Interpreting Functions 7e

Ferris Wheel 15

A3 FUNCTIONS F-BF Building Functions 1a, 1b, 3 F-LE Linear, Quadratic, and Exponential Models 2, 3, 5 F-IF Interpreting Functions 4, 7b, 7c

26

A4 RATIONAL AND POLYNOMIAL EXPRESSIONS A-SSE Seeing Structure in Expressions 1, 1a, 1b, 2 A-APR Arithmetic with Polynomials and Rational Expressions 1, 2, 3, 4, 6 A-REI Reasoning with Equations and Inequalities 2

Representing Polynomials Manipulating Polynomials Manipulating Radicals

15

P1 PROBABILITY S-CP Conditional Probability and the Rules of Probability 1, 2, 3, 4, 5, 6, 7

Modeling Conditional Probabilities 1: Lucky Dip Modeling Conditional Probabilities 2 Medical Testing

28

S2 STATISTICS S-IC Making Inferences and Justifying Conclusions 1, 2, 3, 4, 5, 6 S-ID Interpreting Categorical and Quantitative Data 4

27

Total days: 138



FORMATIVE ASSESSMENT LESSON OVERVIEW

ALGEBRA 1 GEOMETRY ALGEBRA 2

Functions and Everyday Situations

Modeling: Having Kittens

Comparing Investments

Generalizing Patterns: Table Tiles

Interpreting Algebraic Expressions

Sorting Equations and Identities

Creating and Solving Equations

Solving Linear Equations in Two Variables

Optimization Problems: Boomerangs

Defining Regions Using Inequalities

Forming Quadratics

Solving Quadratic Equations: Cutting Corners

Representing Data 1: Using Frequency Graphs

Representing Data 2: Using Box Plots

Interpreting Statistics: A Case of Muddying the Waters

Devising a Measure for Correlation

Representing and Combining Transformations

Analyzing Congruency Proofs

Evaluating Statements About Length and Area

Inscribing and Circumscribing Right Triangles

Geometry Problems: Circles and Triangles

Proofs of the Pythagorean Theorem

Solving Geometry Problems: Floodlights

Finding Equations of Parallel and Perpendicular Lines

Equations of Circles 1

Equations of Circles 2

Sectors of Circles

Evaluating Statements About Enlargements (2D & 3D)

2D Representations of 3D Objects

Calculating Volumes of Compound Objects

Modeling: Rolling Cups

Rational and Irrational Numbers 1

Rational and Irrational Numbers 2

Ferris Wheel

Representing Polynomials

Manipulating Polynomials

Manipulating Radicals

Modeling Conditional Probabilities 1: Lucky Dip

Modeling Conditional Probabilities 2

Medical Testing

alignment of the formative assessment lessons … · alignment of the formative assessment lessons...

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