GRADE 7 MATHEMATICSCURRICULUM GUIDE

DRAFT - 2012-2013Please Note: The Mathematics Office is still vetting and editing this document for typos and errors. The sequencing and general pacing will not change.

Loudoun County Public Schools

Complete scope, sequence, pacing and resources are available on the CD and will be available on the LCPS Intranet.

INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE

This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s teachers concerning the implementation of these standards. In many instances the local expectations for achievement exceed state requirements. The GUIDE is the lead document for planning, assessment and curriculum work. It is a summarized reference to the entire program that remains relatively unchanged over several student generations. Other documents, called RESOURCES, are updated more frequently. These are published separately but teachers can combine them with the GUIDE for ease in lesson planning.

Mathematics Internet Safety Procedures1. Teachers should review all Internet sites and links prior to using it in the classroom.

During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to anyinappropriate pop-ups or solicitation of information.

2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites.Teachers should periodically check and update any web addresses that they have on their LCPS web pages.

3. Teachers should assure that the use of websites correlate with the objectives of lesson and provide students with the appropriate challenge.

4. Teachers should assure that the use of websites correlate with the objectives of the lesson and provide students with the appropriate challenge.

Grade 7 Mathematics Nine Weeks Overview

1st Quarter 2nd Quarter 3rd Quarter 4th QuarterIntegers 7.3 7.16 a, b, d 7.1 e

Rational Numbers 7.1 a, b, c, d

Algebra and Functions 7.12

Algebra and Functions, con’t 7.13 a 7.2 7.13 b

Equations 7.14 7.15 7.16

Transformations 7.8

Geometry 7.7 7.5 a, b

Proportional Reasoning 7.4 7.6 7.5 c

Probability 7.10 7.9

Statistics 7.11

Grade 7 Quarter 1

Number of

Blocks

Topics, Essential Questions, and Essential Understandings

(Students should be able to answer essential questions.)

Standard(s) of Learning Essential Knowledge and Skills

Additional Instructional Resources/Comments

10 blocks

IntegersComputation

7.3 Essential Questions and Understandings Model computation with integers using

Algeblocks™, pictorial, and numerical representations.

How can you use the additive identity to model subtracting negative integers?

The sums, differences, products and quotients of integers are either positive, zero, or negative. How can this be demonstrated? This can be demonstrated through the use of patterns and models.

-------------------------------------------------------------Properties of Real Numbers

7.16 a, b, d Essential Questions and Understandings Why are the commutative and associative

properties limited to addition and

SOL 7.3 The student willa) model addition, subtraction, multiplication, and division of integers; andb) add, subtract, multiply, and divide integers.

7.3 Essential Knowledge and Skills Add, subtract, multiply, and divide integers,

using the laws of arithmetic. Model addition, subtraction, multiplication

and division of integers using pictorial representations of concrete manipulatives.

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number.

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.

------------------------------------------------------7.16 a, b, d The student will apply the following properties of operations with real numbers:a) the commutative and associative properties of addition and multiplication; b) the distributive property; …

Algeblocks™Math’scool Module 3Algebra’scool Module 1.2

NLVM – Rectangle multiplication of integers

NLVM – Color chips addition

NLVM – Color chips subtraction

---------------------------------Math’scool Module 1.3, 1.4Algebra’scool Module 2.3

Grade 7 Quarter 1

multiplication? Justify your answer. How can the commutative, associative and

additive inverse properties be used to allow you to compute integers mentally?

How does distributing a negative number affect the expression value?

------------------------------------------------------------Absolute Value

7.1 e Essential Questions and Understanding Why is the absolute value of a number

always positive? The absolute value of a number represents distance from zero on a number line regardless of direction. Distance is positive.

Describe real life situation revolving around absolute value.

d) the multiplicative property of zero.

7.16 a, b, d Essential Knowledge and Skills Apply commutative, associative, distributive,

and additive inverse properties with the modeling and computing of integers

Continue to use the addition and multiplication identities, the multiplication inverse.

Identify properties of operations used in simplifying expressions.

Apply the properties of operations to simplify expressions.

Generate equivalent expressions from a given expression using the laws of arithmetic and conventions of algebraic notation.

-----------------------------------------------------SOL 7.1 e The student will …e) identify and describe absolute value for rational numbers.

7.1 e Essential Knowledge and Skills Demonstrate absolute value using a number

line. Determine the absolute value of a rational

number. Show that the distance between two rational

numbers on the number line is the absolute value of their difference, and apply this principle to solve practical problems.†

-------------------------------------Math’scool- Module 3.1Algebra’scoo l -Module 6.1

Rational Numbers

7.1 a, b, c, dNegative exponents for powers of ten What does a negative exponent mean when the

SOL 7.1 a, b, c, d The student willa) investigate and describe the concept of negative exponents for powers of ten;

Mission Mathematics

Math’scool – Module 5.6Algebra’scool – Module 1.4

Grade 7 Quarter 1

10 blocks

base is ten? What relationship occurs with negative

exponents? Describe the relationship with trend as an

exponent decreases.

----------------------------------------------------------Scientific notation for numbers greater than zero When should scientific notation be used? What is the difference between scientific

notation and standard form? In which situation would you use either?

----------------------------------------------------------Compare and order fractions, decimals, percents, and scientific notation How are fractions, decimals, and percents

related? When can this knowledge be helpful for

understanding numerical relationships?

------------------------------------------------------------Square roots How is taking the square root different from

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

7.1 Essential Knowledge and Skills 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. Recognize a number greater than 0 in

scientific notation. Order no more than 3 numbers greater than 0

written in scientific notation. Compare and determine equivalent

relationships between numbers larger than 0 written in scientific notation.

---------------------------------------------------- Represent a number in fraction, decimal, and

percent forms. Compare, order, and determine equivalent

relationships among fractions, decimals, and percents.

------------------------------------------------------------- Determine the square root of a perfect square

---------------------------------Math’scool –Module 5.7Algebra’scool – Module 11.2

----------------------------------Math’scool- Modules 4.1, 4.2, 5.2

NLVM - Percentages

------------------------------------Math’scool- Module 7.1

Grade 7 Quarter 1

squaring a number? Describe the subsets of the real number system How do exponents relate to the factors of the

base? How can one number be classified in more

than one subset group? Generate negative numbers that are not

classified as integers. What is the difference between a rational and

irrational number?

less than or equal to 400.

Understand informally that every number on a number line has a decimal expansion, which can be found for rational numbers using long division.

Understand that rational numbers are those with repeating decimal expansions (this includes finite decimals which have an expansion that ends in a sequence of zeros).

Informally explain why is irrational. Use rational approximations (including those

obtained from truncating decimal expansions) to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., π2). For example, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Algebra’scool- Module 1.1

2 blocks

Algebra and Functions

7.12 Essential Questions and UnderstandingsWhat are the different ways to represent the relationship between two sets of numbers?Rules that relate elements in two sets can be represented by word sentences, equations, tables of values, graphs or illustrated pictorially.

SOL7.12 The student will represent relationships with tables, graphs, rules, and words.

7.12 Essential Knowledge and SkillsDescribe and represent relations and functions, using tables, graphs, rules, and words. Given one representation, students will be able to represent the relation in another form.

3 blocksEnrichment, Assessment, and Remediation

Grade 7 Quarter 2

Number of

Blocks

Topics, Essential Questions, andEssential Understandings

(Students should be able to answer essential questions.)

Standard(s) of Learning Essential Knowledge and Skills

Additional Instructional Resources/Comments

10 blocks

Algebra and Functions, con’tTranslating verbal phrases into mathematic expressions and vice-versa

7.13 a Essential Questions and Understandings What do variables represent in an expression? Why do we use a variable(s) in an expression? Generate a real life problem and represent it

using a mathematical expression. What is a variable expression? How can it be

used to represent a mathematical sequence?

7.13 The student willa) write verbal expressions as algebraic expressions and sentences as equations and vice versa;…

7.13 Essential Knowledge and Skills Use the following terms appropriately:

expressions, equations, and inequalities 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.

Algebra’scool - Module 2.1,4.1

Sequences

7.2 Essential Questions and UnderstandingsWhen are variable expressions used?Variable expressions can express the relationship between two consecutive terms in a sequence.

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

7.2 Essential Knowledge and Skills Analyze arithmetic and geometric sequences to

discover a variety of patterns. Identify the common difference in an

arithmetic sequence. Identify the common ratio in a geometric

Grade 7 Quarter 2

sequence. Given an arithmetic or geometric sequence,

write a variable expression to describe the relationship between two consecutive terms in the sequence.

Writing expressions and equations: properties

7.13b Essential Questions and Understandings Evaluate numerical expressions using order of

operations Evaluate algebraic expressions given

replacement values How can algebraic expressions and equations be

written? Why do we need to know the identity and

inverse properties in order to understand how to balance an equation?

How can the multiplicative property of zero be used to balance an equation?

Generate equivalent expressions from a given expression using the laws of arithmetic and conventions of algebraic notation.

Apply the properties of operations to simplify expressions

SOL 7.13 b

7.13 Essential Knowledge and Skills

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, P + 0.05P = 1.05P means that “increased by 5%” is the same as “multiplied by 1.05”.

Identify examples of expressions and equations.Understand that an expression records operations with numbers or with letters standing for numbers.Understand that applying the laws of arithmetic to an expression results in an equivalent expression. 3 (2 + x) = 6 + 3x

8 blocks

Equations and Inequalities

7.14 Essential Questions and Understandings What is equality? Why is it important in

equations? How do performing identical operations on each

side of the equation maintain equality? How can the solution to an equation be

graphed?

SOL 7.14 The student willa) solve one- and two-step linear equations in one

variable; andb) solve practical problems requiring the solution

of one- and two-step linear equations.

7.14 Essential Knowledge and Skills Choose variables to represent quantities in a

word problem, and construct simple

Algebra’scool- Module 3.3

NLVM- Function MachineNLVM- Algebra Balance ScalesNLVM- Algebra Balance

Grade 7 Quarter 2

When solving an equation, why is it important to perform identical operations on each side of the equal sign?

Inequalities

7.15 Essential Questions and Understandings How are the procedures for solving equations

and inequalities similar and different? How is the solution to an inequality different

from that of a linear equation? How is the solution to an inequality graphed? What is the difference between the graph of a

solution to an equation and an inequality? How do mathematical properties apply to solving

multi-step equations and inequalities? How can you use properties to justify the

accuracy of your solution?

equations to solve the problem by reasoning about the quantities.

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

Solve word problems arithmetically, by using a sequence of operations on the given n umbers, and algebraically by using a variable to stand for the unknown quantity.

Understand that a linear equation in one variable might have one solution, infinitely many solutions, or no solutions.

Understand that a linear equation in one variable might have one solution, infinitely many solutions, or no solutions.

Solve linear equations with rational number coefficients, including equations that require expanding expressions using the distributive law and collecting like terms.

SOL 7.15

7.15 Essential Knowledge and Skills

Represent and demonstrate steps in solving inequalities 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

Scales- Negatives

Algebra’scool- Module 3.4

Multi-step optional-Algebra’scool- Module 3.5

Pythagorean Theorem optional:Math’scool- 8.7, 10.3NLVM- Pythagorean Theorem PuzzleIlluminations- Proof without wordsAlgebra blocksNLVM- Function MachineNLVM- Algebra Balance ScalesNLVM- Algebra Balance Scales - NegativesIlluminations (NCTM)- Chairs

Grade 7 Quarter 2

Using properties to justify equation and inequality solutions

Use properties of real numbers to justify equation and inequality solutions.

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; ande) the multiplicative property of zero.

Use properties of real numbers to justify equation and inequality solutions.

2 blocks Enrichment, Assessment, and Remediation

Grade 7 Quarter 3

Number of

Blocks

Topics, Essential Questions, andEssential Understandings

(Students should be able to answer essential questions.)

Standard(s) of Learning Essential Knowledge and Skills

Additional Instructional Resources/Comments

5 blocks

Transformations

7.8 Essential Questions and Understandings Identify and sketch translations, reflections,

rotation, and dilations of right triangles of rectangles

-How does the size/shape/ and position change with each type of transformation (translation, rotation, reflection, and dilation)?

-How do transformations affect the graph of a functional relationship? (explore a variety of functions – linear, quadratic, cubic, absolute value etc)

-Where can are transformations displayed in real life?

SOL 7.8

7.8 Essential Knowledge and Skills 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 90° or 180° about the origin.

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

Identify the coordinates of a right triangle or rectangle that has been dilated. The center of the dilation will be the origin.

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 90° or 180° 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 , , 2, 3 or 4.

Math’scool- Module 11

Sketchpad

NLVM – TranslationsNLVM – RotationsNLVM – Reflection

Illuminations- Algebraic Transformations

Grade 7 Quarter 3

5 blocks

GeometryComparing quadrilaterals

7.7 Essential Questions and Understandings

Why can some quadrilaterals be classified in more than one category?

How is deductive reasoning used to classify quadrilaterals?

SOL 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.

7.7 Essential Knowledge and Skills 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 inference.

Understand that properties belonging to a category of plane figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Math’scool- Module 9.2

Illuminations- Shape Sorter

Volume and surface area How are volume and surface area related? How are area of the base and the volume of

the solid related?

SOL 7.5 a, b 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; and ….

7.5 a, b Essential Knowledge and Skills 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.

Math’scool- Modules 10.4, 10.5Math’scool- Modules13.4, 13.5, 13.6, and 13.7

NLVM- Constructing 3-D ShapesNLVM- How High? (volume)

Grade 7 Quarter 3

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.

10 blocks

Proportional ReasoningProportions

7.4 Essential Questions and Understandings7.47.4 – proportional reasoningSolve practical problems using proportions

-How are comparison used in proportional reasoning?

- What makes two quantities proportional?

SOL 7.4 The student will solve single-step and multistep practical problems, using proportional reasoning.

7.4 Essential Knowledge and Skills 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.

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.

Math’scool- Module 7

Illuminations- Bagel AlgebraIlluminations- Mixtures

Sketchpad

Similar figures

7.6 Essential Questions and Understandings How do polygons that are similar compare

to polygons that are congruent? What makes something proportional? How can proportions be solved for a

missing value? How are proportional relationships relevant

to real-life situations?

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.

7.6 Essential Knowledge and Skills Identify corresponding sides and corresponding

and congruent angles of similar figures using the traditional notation of curved lines for the angles.

Math’scool- Module 8.6 and Module 9.4

Grade 7 Quarter 3

What is the difference between congruent and similar figure?

How can you prove two figures are similar? How can proportions be used to solve the

unknown side length?

Effect of changing the measure of one attribute of a 3-dimensional figureHow does the volume of a rectangular prism change when one of the attributes is increased? There is a direct relationship between the volume of a rectangular prism increasing when the length of one of the attributes of the prism is changed by a scale factor.

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 , A corresponds to D, and corresponds to .

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~SOL 7.5 c The student will …

c) describe how changing one measured attribute of a rectangular prism affects its volume and surface area.

7.5 c Essential Knowledge and Skills Describe how the volume of a rectangular prism

is affected when one measured attribute is multiplied by a scale factor.

Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor.

4 blocks Enrichment, Assessment and Remediation

Grade 7 Quarter 4

Number of

Blocks

Topics, Essential Questions, andEssential Understandings

(Students should be able to answer essential questions.)

Standard(s) of Learning Essential Knowledge and Skills Additional Instructional

Resources/Comments

10blocks

Probability

7.10 Essential Questions and Understandings How do the Fundamental Counting Principle and

Tree Diagrams relate to probability? What is the role of the Fundamental Counting

Principle in determining the probability of compound events?

------------------------------------------------------------7.9 Essential Questions and Understandings What is the difference between experimental and

theoretical probability? How is the probability of an event determined and

described? How do you analyze and test the fairness of games? We say nothing is impossible, so why are some

events considered impossible? How can the probability of an event be represented

visually? What is the difference between chance and choice?

How can an understanding of probability affect my choices?

What careers use probability every day? How is probability applied to real-life situations?

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

7.10 Essential Knowledge and Skills 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.

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

7.9 Essential Knowledge and Skills 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 difference between

the probability of an event found through experiment or simulation versus the theoretical probability of that same event.

Algebra’scool- Module 20.1, 20.3

-----------------------------------------Algebra’scool- Module 20.2

Illuminations- Random DrawingIlluminations- The Game of Skunk

Statistics

7.11 Essential Questions and Understandings How can you display experimental probability in a

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

Algebra’scool- Module 19.3NLVM- HistogramsNLVM- Histogram Tool

Grade 7 Quarter 4

8 blocks

histogram? What is the difference between a histogram and a

bar graph?

a) construct and analyze histograms; andb) compare and contrast histograms with other types of graphs presenting information from the same data set.

7.11 Essential Knowledge and Skills Collect, analyze, display, and interpret a data set

using histograms. 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, and stem-and-leaf plots presenting information from the same data set.

3 blocks Enrichment, Assessment, and Remediation