curriculum & grade 4: mathematics pacing · pdf fileinto all areas of k -12 education. ......

Grade 4: Mathematics

Curriculum & Pacing Guide

TVaughan

Curriculum & Pacing Guide

Martinsville City Public Schools

Revised Summer 2011

Updated Summer 2012 TJV

Grade 7: Pre-Algebra

Martinsville City Public Schools’ Instructional Plan of Action

The Martinsville City Public Schools Curriculum Guide was developed using the Standards of Learning for Virginia Public Schools and the State Curriculum Framework. Also, an emphasis was placed on the integration of 21st Century Skills into all areas of K-12 education. Martinsville City Public Schools believes that to compete in a global community, all children must develop lifelong independent skills that demonstrate initiative, self direction, and the ability to problem-solve, innovate and create, and communicate by writing and speaking effectively. To provide an avenue for students to develop these important qualifications and provide a more rigorous learning environment, Martinsville City Public Schools encourages problem-based learning in all classrooms. The collaboration between students in this type of learning environment develops skills in leadership, accountability, social, and cross-cultural understanding as they communicate and think critically to problem-solve real world applications of the curriculum. Martinsville City Public Schools’ Core curriculum prepares students to achieve these 21st

Century skills through competent cross- curricular activities that apply knowledge of concepts learned in other areas of study and in the community.

Standard benchmark assessments along with project-based assessments and end of year SOL tests are administered to ensure mastery of the concepts. PALS assessments are used to ensure proficiency in Reading for grades Pre-K through Eight. To further ensure that all students learn to the best of their abilities, a Response to Intervention (RtI) system, using STAR Math and STAR Reading, is in place to guide classroom instruction, screen and progress monitor students so that intervention and enrichment activities are scheduled based on the students individual needs throughout the year.

The Martinsville City Public Schools’ Curriculum Guide is designed to provide a reference document for each subject and grade level that indicates The Curriculum’s Big Ideas, Instructional Strategies, Model lessons, & Assessment Instruments and suggested time frames to be used as a Guide for classroom instruction. In addition, Learning Targets at a Glance contains an overview of the curriculum taught for each grading period for each subject and grade level. 21

Curriculum Guide OVERVIEW

st

This symbol is used through to denote a 21

Century Internet Safety procedures are listed, and for Grades Three through Twelve, an SOL Testing Blueprint Target is included to give insight to the strands that will receive the most focus on the SOL Assessments. Two symbols will be used to denote the 21st Century Focus:

st

This symbol is used throughout to denote a 21

Century skill.

st

Century Global Connection.

Curriculum Big Ideas Instructional Strategies & Model Lessons Assessment Items

The organizing topics, big ideas, or strands under which student learning is organized and the Essential Understandings, Knowledge and Skills students must develop in order to master these concepts (typically from the standards found in the VDOE curriculum framework). Essential Understandings—what we want students to understand about this idea, topic, or concept Essential Knowledge—What students must know in order to develop this understanding Essential Skills—What students must be able to do in order to demonstrate that understanding

Standards of Learning that meet the criteria for 21st

Standards of Learning that meet the 21st Century Learning of Global Connections will be designated with this symbol

Century skills will be identified by this symbol

Resources, strategies, and models for delivery of the curriculum. Includes suggested teaching strategies, links to model lesson plans links to frequently referenced online sites, and suggested teacher resources and where to find them (online and hard copy, such as texts, primary source documents, etc.)

Examples of formative and summative assessments for measuring student mastery of the curriculum. Includes essential questions, writing prompts, sample test items, benchmark test links, model performance-based assessments, and other assessment resources.

The Seventh Grade student will be provided many opportunities to engage in experiences involving problem solving, data collection and analysis, and algebraic thinking. The Virginia Standards of Learning provide the foundation for seventh grade mathematics. The standards are organized into 6 strands:

Learning Overview

Number/Number Sense: The focus of instruction allows students to investigate and develop an understanding of number sense by modeling numbers, using different representations. Students should develop strategies for reading, writing, and judging the size of numbers, fractions and decimals by comparing them, using a variety of models and benchmarks as ferments. Computation and Estimation: The focus of instruction allows students to develop fluency in multiplication and division with whole numbers and decimals, using models, explanation, and proficiency with basic facts and algorithms. Measurement: The focus of instruction allows students to be actively involved in measurement activities that focus on measuring objects and estimating measurements while interacting with their environment. Geometry: The focus of instruction allows students to develop and understanding about how geometric figures relate to each other and begin to use mathematical reasoning to analyze and justify properties and relationships among figures. Probability and Statistics: The focus of instructions allows students to deepen their understanding of concepts of probability by offering opportunities to set up models simulating practical events, engage students in activities to enhance understanding fairness, and activities that instill a spirit of investigation and exploration through use of manipulatives.

Learning Targets at a Glance – 7th Grade Pre-Algebra

First Quarter 8/13-10/15

Second Quarter 10/16-12/21

Third Quarter 1/8-3/13

Fourth Quarter 3/14-5/22

7.3 Integers 7.16a,b,d Properties of Operations -Real Numbers 7.1 a-d Rational Numbers 7.12 Tables, Graphs, Rules and words

7.13a Algebraic Expressions 7.2 Variable Expressions 7.13b Algebraic Expressions 7.14 Linear Equations 7.15 Inequalities 7.16 Properties of Operations

7.8 Transformations 7.7 Quadrilaterals 7.5a Volume/Surface Cylinders 7.5b Volume/Surface Rec. Prisms & Cylinders 7.4 Proportional Reasoning 7.6 Plane Figures 7.5c Rectangular Prism-change attributes

7.10 Fundamental Counting Principle 7.9 Probability(experimental/theoretical) 7.11 Histograms

Grade 7 Mathematics Test Blueprint Summary Table

50 question test

Number/Number Sense

Computation/Estimation

Measurement/Geometry Probability, Statistics, Patterns, Functions and Algebra

16 13 21

10 minutes

0%

30 minutes

20 minutes

Suggested Time Allocation for a 60 Minute Math Block

Bellringer Skill Lesson Practice/Small Group Instruction

21st

1. Teachers should review all internet sites and links prior to using them in the classroom. During this review, teachers need to ensure the Century Internet Safety Procedures

appropriateness of the content on the site. Checking for broken links and paying attention to inappropriate pop-ups or solicitations of information. 2. Teachers should circulate throughout the classroom while students are on the internet to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their MCPS webpage. 4. Teachers should assure that the use of these websites correlate with the objectives of the lesson and provide students with the appropriate challenges.

Content: Mathematics Grade Level: 6

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Essential Vocabulary

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1st

Grading period

SOL 7.3 The student will

a.) Model addition, subtraction, multiplication and division of integers

b.) Add, subtract, multiply and divide integers.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Model addition, subtraction, multiplication and division of integers using pictorial representations of concrete manipulatives.

• Add, subtract, multiply and divide integers.

• Simplify numerical expressions involving addition, subtraction, multiplication and division of integers using order of operations.

• Solve practical problems involving addition, subtraction, multiplication, and division with integers.

Integers

VDOE Word Wall Voc

Dinah Zikes Foldables

Numberline Two-color counters Algeblocks Calculators

Compass Learning Study Island Smartboard Powerpoints JLab IXL Math Math’school Module 3 Algebra’school Module 1.2 NLVM -Rectangle Multiplication of Intergers -Color chips

VDOE ESS: 7.3 -Integers: Multiplication/Division -Integers: Addition/Subtraction Glencoe ARI Companion: 7.3 Integers Reteaching: VA. SOL Coach and Buckle Down

STAR Math ARDT (target date Jan. 2012) Benchmarks Teacher made assessments Flanagan Tests SOL 7.3


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SOL 7.16 The student will apply the following properties of operations with real numbers:

a.) the commutative and associative properties for addition and multiplication

b.) the distributive property c.) the additive and multiplicative identity

properties d.) the additive and multiplicative inverse

properties e.) the multiplicative property of zero


• Identity properties of operations used in simplifying expressions

• Apply the properties of operations to simplify expressions

Zero

Commutative Property

Associative Property

Multiplicative Identity Properties

Multiplicative Inverse Property

Property of Zero

Distributive Property

VDOE Word Wall Voc


Compass Learning Study Island Smartboard Powerpoints JLab IXL Math Math’school Module 1.3, 1.4 Algebra’school Module 2.3

VDOE ESS: 7.16 Properties Glencoe ARI Companion: 7.16 Order of Operations and Properties Reteaching: VA. SOL Coach and Buckle Down



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a.) Investigate and describe the concept of negative exponents for powers of ten

b.) Determine scientific notation for numbers greater than zero

c.) Compare and order fractions, decimals, percents and numbers written in scientific notation

d.) Determine square roots e.) Identify and describe absolute value for

rational numbers The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Recognize powers of 10 with negative exponents by examining patterns

• Write a power of 10 with a negative exponent in fraction and decimal form

• Write a number greater than 0 in scientific notation

• Compare and determine equivalent relationships between numbers larger than 0 written in scientific notation

• Represent a number in a fraction, decimal, and percent forms.

• Compare, order, and determine equivalent relationships among fractions, decimals, and percents. Decimals are limited to the thousandths place, and percents are limited to the tenths place. Ordering is limited to no more than 4 numbers.

• Order no more than 3 numbers greater than 0 written in scientific notation

• Determine the square root of a perfect square less than or equal to 400.

Exponential Notations

Base

Exponent

Power

Perfect Square

Natural Numbers

VDOE Word Wall Voc


Fraction Bars Base-10 Blocks Fraction Circles Graph Paper Numberlines Calculators

Compass Learning Study Island Smartboard Powerpoints JLab IXL Math Math’school Module 5.6, 3.1 Algebra’school Module 1.4, 6.1

VDOE ESS: 7.1 -Powers of Ten -Scientific Notation -Ordering Fractions -Square Roots -Absolute Value Glencoe ARI Companion: 7.1c Comparing and Ordering 7.1b Whole Numbers Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.12 The student will represent relationships with tables, graphs, rules, and words The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Describe and represent relations and functions, using tables, graphs, rules, and words, Given on representation, students will be able to represent the relation in another form.

Table

Graph

Rule

VDOE Word Wall Voc


Compass Learning Study Island Smartboard Powerpoints JLab IXL Math

VDOE ESS: 7.12 Relationships Round Table Glencoe N/A ARI Companion: 7.12 Patterns, Functions, Algebra Reteaching: VA. SOL Coach and Buckle Down



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a.) Write verbal expressions as algebraic expressions and sentences as equations and vice versa

b.) Evaluate algebraic expressions for given replacement values of the variables


• Write verbal expressions as algebraic expressions. Expressions will be limited to no more than 2 operations

• Write verbal sentences as algebraic equations. Equations will contain no more than 1 variable term.

• Translate algebraic expressions and equations to verbal expressions and sentences. Expressions will be limited to no more than 2 operations.

• Identify examples of expressions and equations.

• Apply the order of operations to evaluate expressions for given replacement values of the variables. Limit the number of replacements to no more than 3 per expression.

Verbal Expression

Algebraic Expression

VDOE Word Wall Voc



VDOE ESS: 7.13 Translate and Evaluate Glencoe N/A ARI Companion: 7.13 Patterns, Function, Algebra Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.2 The student will describe and represent arithmetic and geometric sequences using variable expressions


• Analyze arithmetic and geometric sequences to discover a variety of patterns

• Identify the common differences in a n arithmetic sequence

• Identify the common ration in a geometric sequence

• Given an arithmetic or geometric sequence, write a variable expression to describe the relationship between two consecutive terms in the sequence

Common ration

Common differences

Sequences

Numeric patterns

Geometric sequences

VDOE Word Wall Voc



VDOE ESS: 7.2 Arithmetic and Geometric Sequences Glencoe ARI Companion: 7.2 Pattern, Functions, Algebra Reteaching: VA. SOL Coach and Buckle Down



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2nd Grading period


a.) Write verbal expressions as algebraic expressions and sentences as equations and vice versa

b.) Evaluate algebraic expressions for given replacement values of the variables


• Write verbal expressions as algebraic expressions. Expressions will be limited to no more than 2 operations

• Write verbal sentences as algebraic equations. Equations will contain no more than 1 variable term.

• Translate algebraic expressions and equations to verbal expressions and sentences. Expressions will be limited to no more than 2 operations.

• Identify examples of expressions and equations.

• Apply the order of operations to evaluate expressions for given replacement values of the variables. Limit the number of replacements to no more than 3 per expression.

Verbal Expression

Algebraic Expression

VDOE Word Wall Voc



VDOE ESS: 7.13 Translate and Evaluate Glencoe N/A ARI Companion: 7.13 Patterns, Function, Algebra Reteaching: VA. SOL Coach and Buckle Down



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b.) the distributive property c.) the additive and multiplicative

identity properties d.) the additive and multiplicative inverse





Zero





Property of Zero


VDOE Word Wall Voc






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a.) Solve one-and two-step linear equations in one variable

b.) Solve practical problems requiring the solution of one-and two-step linear equations


• Represent and demonstrate steps for solving one-and two-step equations in one variable using concrete materials, pictorial representations and algebraic sentences

• Solve one-and two-step linear equations in one variable

• Solve practical problems that require the solution of a one- or two-step linear equation

Linear Equation

VDOE Word Wall Voc



VDOE ESS: 7.14 Equations Glencoe N/A ARI Companion: 7.14 Patterns, Function, Algebra Reteaching: VA. SOL Coach and Buckle Down



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a.) Solve one-step inequalities in one variable

b.) Graph solutions to inequalities on the numberline

c.) The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Represent and demonstrate steps in solving inequlaities in one variable using concrete materials, pictorial representations and algebraic sentences

• Graph solutions to inequalities on the number line.

• Identify a numerical value that satisfies the inequality

Inequalities

VDOE Word Wall Voc



VDOE ESS: 7.15 Inequalities Glencoe N/A ARI Companion: 7.15 Reteaching: VA. SOL Coach and Buckle Down



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b.) the distributive property c.) the additive and multiplicative identity

properties d.) the additive and multiplicative inverse





Zero





Property of Zero


VDOE Word Wall Voc






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3rd

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SOL 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflection, dilations, rotations. And translations) by graphing in the coordinate plane. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Identify the coordinates of the image of a right triangle or rectangle that has been translated either vertically, horizontally, or a combination of a vertical and horizontal translation

• Identify the coordinates of the image of a right triangle or rectangle that has been rotated 90º or 180º about the origin

• Identify the coordinates of the image of a right triangle or rectangle that has been reflected over the x- or y- axis

• Sketch the image of a right triangle or rectangle translated vertically or horizontally

• Sketch the image of a right triangle or rectangle that has been rotated 90º or 180º about the origin

• Sketch the image of a right triangle or rectangle that has been reflected over the x- or y-axis

• Sketch the image of a dilation of a right triangle or rectangle limited to a scale factor of ¼,½, 2,3,or 4

Transformations

Reflections

Dilations

Rotations

Translations

Right triangle

Rectangle

VDOE Word Wall Voc



VDOE ESS: 7.8 -Rotation -Dilation -Translation and Reflection Glencoe ARI Companion: 7.8 Polygons Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Compare and contrast attributes of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid

• Identify the classification(s) to which a quadrilateral belongs, using deductive reasoning and inferences.

Quadrilaterals

Parallelograms

Rectangles

Trapezoids

Rhombi

Squares

VDOE Word Wall Voc



VDOE ESS: 7.7 Quadrilateral Sort Glencoe ARI Companion: 7.7 Polygons Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.5 The student will a.) Describe volume and surface area of cylinders b.) Solve practical problems involving the volume and

surface area of rectangular prisms and cylinders c.) Describe how changing one measured attribute of

a rectangle prism affects its volume and surface area


• Determine if a practical problem involving a rectangular prism or cylinder represents the application of volume or surface area

• Find the surface area of a rectangular prism • Solve practical problems that require finding

the surface area of a rectangular prism. • Find the surface area of a cylinder • Solve practical problems that require finding

the surface area of a cylinder • Find the volume of a rectangular prism • Solve practical problems that require finding

the volume of a rectangular prism • Find the volume of a cylinder • Solve practical problems that require finding

the volume of a cylinder • Describe how the volume of a rectangular

prism is affected when one measured attribute is multiplied by a scald factor. Problems will be limited to changing attributes by scale factors only

• Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to changing attributes by scale factors only.

Surface Area

Volume

Rectangular Prism

VDOE Word Wall Voc



VDOE ESS: 7.5 -Surface Area and Volume of a Cylinder -Volume of a Rectangular Prism -Surface Area of a Rectangular Prism -Attributes of a Rectangular Prism Glencoe ARI Companion: 7.5 3-D Geometry Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.4 The student will solve single-step and multistep practical problems, using proportional reasoning. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Write proportions that represent equivalent relationships between two sets.

• Solve a proportion to find a missing term.

• Apply proportions to convert units of measurement between the U.S. Customary System and the metric system. Calculators may be used.

• Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and decimals no less than tenths. Calculators may be used.

• Using 10% as a benchmark, mentally compute 5%, 10%, 15%, or 20% in a practical situation such as tips, tax, and discounts.

• Solve problems involving tips, tax, and discounts. Limit problems to only one percent computation per problem.

Proportions

Equality

ratios

Tips

Tax

Discounts

VDOE Word Wall Voc



VDOE ESS: 7.4 -Sales Tax and Tip -Proportions Glencoe ARI Companion: 7.4 Percents Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.6 The student will determine whether plane figures-quadrilaterals and triangles- are similar and write proportions to express the relationships between corresponding sides of similar figures The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representation to

• Identify corresponding sides and corresponding and congruent angles of similar figures using the traditional notation of curved lines for the angles.

• Write proportions to express the relationships between the lengths of corresponding sides of similar figures.

• Determine if quadrilaterals or triangles are similar by examining congruence of corresponding angles and proportionality of corresponding sides.

• Given two similar figures, write similarity statements using symbols such as ΔABC~ΔDEF, ∠A corresponding to ∠D, and AB corresponds to DE

Quadrilaterals

Triangles

Proportions

Corresponding

Congruent

Curved lines

VDOE Word Wall Voc



VDOE ESS: 7.6 Similar Figures Glencoe ARI Companion: 7.6 Ratio/Proportions Reteaching: VA. SOL Coach and Buckle Down



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4th

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SOL 7.10 The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle


• Compute the number of possible outcomes by using the Fundamental (Basic) Counting Principle

• Determine the probability of a compound event containing no more than 2 events

Fundamental Counting Principle

VDOE Word Wall Voc



VDOE ESS: 7.10 The Real Meal Deal Glencoe ARI Companion: 7.10 Probability Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.9 The student will investigate and describe the difference between the experimental probability and theoretical probability of an event.


• Determine the theoretical probability of an event

• Determine the experimental probability of an event

• Describe changes in the experimental probability as the number of trials increases

• Investigate and describe the differences between the probability of an event found through experiment or simulation versus the theoretical probability of that same event

Experimental Probability

Theoretical Probability

VDOE Word Wall Voc



VDOE ESS: 7.9 What are the Chances? Glencoe ARI Companion: 7.9 Probability Reteaching: VA. SOL Coach and Buckle Down



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SOL 7.11 The student given data in a practical situation, will

a.) Construct and analyze histograms b.) Compare and contrast histograms with

other types of graphs presenting information from the same data


• Collect, analyze, display, and interpret a data set using histograms. For collection and display of raw data, limit the data to 20 items

• Determine patterns and relationships within data sets (e.g., trends)

• Make inferences, conjectures, and predictions based on analysis of a set of data

• Compare and contrast histograms with line plots, circle graphs, stem-and-leaf plots presenting information from the same data set

Circle graph

VDOE Word Wall Voc



VDOE ESS: 7.11 Numbers in a Name Glencoe N/A ARI Companion: 7.11 Statistics Reteaching: VA. SOL Coach and Buckle Down


curriculum & grade 4: mathematics pacing · pdf fileinto all areas of k -12 education. ......

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