curriculumoverview · Web viewASSESSMENT LIMIT: Use no more than 4 integers (-100 to 100) or positive rational numbers (0 to 100) using equivalent forms or absolute value. VOCABULARY

Version 1.2Updated May 18, 2008

BCPSS Office of Math: [email protected] April 2008 DRAFTQuarter 4 Curriculum: GRADE 8 Page 1

Quarter 4 Curriculum Overview*

4th Quarter: 43 days

All of the skills acquired during the 4th quarter will better prepare eighth graders for Algebra 1. These skills are part of the Core Learning Goals and will be tested on the HSA.

High school algebra teachers say that students come to high school not prepared with the basic fraction, decimal, and percent concepts. During this quarter, go back and review these skills to make sure that students are prepared for high school.

The June Benchmark will test all of these skills in the 4th quarter as well as the other skills from Quarters 1, 2, and 3.

Unit 1: Integers Time Frame:10 to 18 days

Integer Concepts 1 to 2 days Add Integers 1 to 3 days Subtract Integers 2 to 4 days Multiply & Divide Integers 2 to 3 days Order of Operations 4 to 6 daysUnit 2: Representing the

UnknownTime Frame:8 to 13 days

Numeric & Geometric Patterns 3 to 4 days Write Expressions 3 to 5 days Simplify Expressions 2 to 4 days

Unit 3: Solving & Using Equations Time Frame:15 to 23 days

Write Equations 3 to 5 days Solve Linear Equations 5 to 8 days Use Formulas 2 to 4 days Percent of a Number 5 to 6 days

4th Quarter Curriculum Guide April 2008This 3-part curriculum guide is designed to assist you in helping your students meet the requirements of the Maryland Voluntary State Curriculum (VSC). This curriculum is in paper form, on CD, and on TSS. Updates will continually be made to the curriculum document on TSS and therefore, you are encouraged to download the revised document on a regular basis. We welcome your feedback via email at officeofmath.bcps.k12.md.us. AssessmentsAssessing students’ needs is the key to a successful math program. Unit 1 assessments are included. Other types of assessments will be available online. Requiring students to SHOW WORK on all problems will enable you to see students’ thinking and better analyze errors. All assessments are directly aligned with the MD VSC. The VSC objectives and numbers are also listed in this section. For concepts that are new or are being extended, the VSC objective for the next grade level has been used. The VSC objective number starts with the grade level followed by the standard.

Concept Assessments are provided with an on-line tracking sheet that will allow you to track the progress of each student in order to provide differentiated instruction for students who did not initially master the concept. There are many other ways that you can assess students’ progress. Choose methods that are effective for you and your students. Unit assessments provide evidence of student achievement for the content of each unit. On-line data analysis sheets will help track student progress.

The June Math Benchmark will assess students’ knowledge from the fourth quarter as well as those skills that are essential for the next grade level.

Knowledge and SkillsThis section includes a range of time to teach each concept based on students’ needs. This is a suggested time that it might take for students to master a concept. For that reason a calendar is provided so you can plan your quarter. The sum of the days in the upper range will exceed 43 days. Therefore, adjust your instructional plan accordingly. Prerequisite skills as well as sub-skills are indicated for each concept. Take time to revisit prerequisite skills and add sub-skills as needed.

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New means that this is the first time that the concept has been introduced to students. Review means that it was taught previously but is important to revisit again to make sure that all students have mastered it. Extension means that the skill has been taught previously, but the assessment limit has been extended to the next grade.

Vocabulary words are important in developing an understanding of a concept, but they should be introduced along with the concept and never in isolation. On-line vocabulary links are provided to develop and reinforce the meaning of these words.

Enduring Understandings are the “Big Ideas” that need to be retained for a lifetime. Samples have been included as a starting point; add more as the concept develops. Sample Essential Questions have been included to help frame your daily instruction. Concept Knowledge is the basic information that students need to know in order to understand the concept.

Error Intervention suggestions, also known as “Hot Spots”, help identify the problems students might have and possible ways to prevent them.

The Learning PlanThis section includes various activities and strategies that can be used to motivate the students, and to introduce, teach, or reinforce each concept. On-line links to access additional activities and resources are provided.

The math textbook and Math Works have great ideas, information, and materials, but should not be the only source for your learning plan. You are the key in developing a learning plan to engage all students and ensure that they master the concepts.

. A special thanks to all the teachers, IST’s, and administrators who wrote, revised, and provided feedback for our curriculum.

*The Quarter Overview lists the concepts students must master in the 4th quarter. Suggested time frames are provided; however, each teacher has the responsibility to make choices to adapt the timing and sequence of units based on student needs as identified by data.

BCPSS Office of Math: [email protected] April 2008 DRAFTQuarter 4 Curriculum: GRADE 8 Page 2

Student Name

UNIT 1:Integers

UNIT 2:Representing the

Unknown

UNIT 3:Solving & Using

Equations

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Sim

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Writ

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Solv

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Use

Form

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Quarter 4 Tracking and Progress Matrix*To be used in conjunction with the Quarter 4 Curriculum Overview for long-term lesson planning.

Quarter 4 Planning Calendar*Monday Tuesday Wednesday Thursday Friday

Apri

l

7 8 9Quarter 4 Begins

10 11

14 15 16 17 18

21 22 23 24 25

28 29 30 1 2

May

5 6 7 8 9

12 13 14 15 16

19 20 21 22 23

26MEMORIAL DAY

27 28 29 30

June

2

3 4 5 6

9 10 11 12 13Last Day of School

Parent Conferences

Early Dismissal Early Dismissal Early Dismissal Early Dismissal

Teacher Key

Grade 8: Unit 1Integers

Unit 1 Assessment

TIME FRAME 1 to 2 days

PREREQUISITE SKILLS

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UNIT 1: Concept 1: NUMBER RELATIONSHIPS: Integers Concepts

IF THEN

THENIF

Integer Concepts Compare and order integers Absolute value

Read, write, and represent integers using numbers -100 to 100 Represent integers or numbers on a number line using numbers -10

to 10 VSC OBJECTIVE8.6.A.1.b – Compare, order, and describe rational numbers with and without relational symbols.ASSESSMENT LIMIT: Use no more than 4 integers (-100 to 100) or positive rational numbers (0 to 100) using equivalent forms or absolute value.

VOCABULARY

IntegerPositiveNegativeWhole NumberAbsolute ValueOppositesOriginSign

Teacher DefinitionsStudent VocabularyWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Whole numbers and their opposites are integers. Zero is a whole number so it is an integer (but

called the origin). Comparisons can be absolute or relative. The further a number gets away from 0 on the negative side, the smaller it gets; the further a

number gets away from 0 on the positive side, the larger it gets.ESSENTIAL QUESTIONS How is a number line useful in comparing integers?CONCEPT KNOWLEDGE A number’s absolute value is the distance it is away from zero (it is always positive because it

literally is just counting the spaces away; the direction does not matter). Absolute value is shown with straight bars .

Negative numbers are less than 0 and written with a negative sign (-17). Positive numbers are more than 0 and usually written with no sign (17).

ERROR INTERVENTIONStudents make negative numbers positive and positive numbers negative when finding the absolute value…

Have them draw a numberline and count how many spaces the negative number is away from zero out loud. Point out how when counting we don’t say -1, -2, -3, etc.

Students confuse negative numbers with a larger absolute value as being greater than other negative numbers with a smaller absolute value…

Relate the numbers to real-world contexts like temperature for them to see why numbers like-14 are actually smaller than -2, even though they “appear” bigger.

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LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials

Visual Math Goodies An interactive web site that provides an introduction to integers and on-line or printable practice resources/examples.

Computer with internet

Kinesthetic Thermometer Number Line Creation

Have students create a thermometer to act as a number line that can be used for reference throughout the lesson.

Construction paper

VerbalAuditory

War Card Games

Students play the traditional card game of “war” using cards with positive and negative numbers. To win the round, students must have the higher card and explain why it is higher.

Score sheet and playing cards

ACCOMODATIONSAccommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Identify and describe the difference between positive and negative numbers

1SKILL.Integers (6 th grade) Middle School Math, Course 2 Scott Foresman (p 432)

Compare and order integers

1SKILL.Integers (6 th grade) Middle School Math, Course 2 Scott Foresman (p 437)

Determine absolute value

1SKILL.Integer Absolute Value (8 th grade)

PC Comparing Integers

Middle School Math, Course 2 Scott Foresman (p 434)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 1 : C o n c e p t 1 : N U M B E R R E L A T I O N S H I P S : I n t e g e r C

TIME FRAME 1 to 3 days

PREREQUISITE SKILLS

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UNIT 1: Concept 2: NUMBER RELATIONSHIPS: Add Integers

THENIF

IF THEN

Add Integers Add 2 positive or 2 negative numbers Add 1 negative and 1 positive number Apply the addition of integers to word problems Add with more than 2 addends

Add whole numbers Read, write, represent, and compare integers

VSC OBJECTIVE8.6.C.1.a – Add, subtract, multiply, and divide integersASSESSMENT LIMIT: Use one operation (-1000 to 1000)

VOCABULARY

SumAddendSignPositiveNegativeIntegers

Teacher DefinitionsStudent VocabularyWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Integers add to the concept of number the idea of opposite, so that every number has

both a size relationship and a positive or negative relationship to other numbers.ESSENTIAL QUESTIONS What examples show how adding integers is used every day?CONCEPT KNOWLEDGE Adding integers, unlike whole numbers, can make a number smaller if you are adding a

negative number to another number. Adding numbers with the same sign (pos. or neg.) means you literally will add the amounts

together and the sign will stay the same. Adding numbers with different signs (pos. plus neg.) means you will subtract the amounts.

The sum of any two numbers, positive or negative, is decided by which number has a higher absolute value.

ERROR INTERVENTIONStudents add the numbers no matter what…

Model how adding positives will look on a number line. Next, model by adding two negatives and making real-world connections (i.e. debt, temperature drops), then model a negative number added to a positive number.

If students are assigning the wrong sign to the number…

Have them model the problem using +1 and -1 algebra tiles to see which there are more of when adding to see what sign the answer will have.

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LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials

Visual Auditory Kinesthetic

Thermometer Students make a thermometer from -20 to 20 and use it to represent a variety of word problems.

Construction paper or pre-made thermometers

1 marking item per student

Visual Positive and Negative Number Tile Grouping

Students will represent the number sentences using number tiles.

+1, -1 algebra tiles

Kinesthetic Games

Integer Board Game Students make a game board and are given place cards that have a variety of integer computation problems on them. The answer tells students how many spaces to move to get to the end.

Materials to make a board

Playing pieces Pre-made playing cards

Auditory Integer Song Students can sing the lyrics of this song to “Row Row Row Your Boat” to remember the rules for adding and subtracting integers.

ACCOMMODATIONS Accommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Add 2 positive or 2 negative numbers

1 SKILL.Adding Integers Additional Practice Addition CMP (7 TH grade)

Middle School Math, Course 2 Scott Foresman (pp 450-454) Middle School Math, Course 1 Scott Foresman (pp 472-475)

Add 1 negative and 1 positive number

1 SKILL.Adding Integers Additional Practice Addition CMP (7 TH grade)

Middle School Math, Course 2 Scott Foresman (pp 450-454) Middle School Math, Course 1 Scott Foresman (pp 472-475)

Apply the addition of integers to word problems

1 SKILL.Adding Integers Additional Practice Addition CMP (7 TH grade)

Middle School Math, Course 2 Scott Foresman (pp 450-454) Middle School Math, Course 1 Scott Foresman (pp 472-475)

Add with more than 2 addends

2SKILL.Adding Integers (8 th grade)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 1 : C o n c e p t 2 : N U M B E R R E L A T I O N S H I P S : A d d I n t e g

TIME FRAME 2 to 4 days

PREREQUISITE SKILLS

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UNIT 1: Concept 3: NUMBER RELATIONSHIPS: Subtract Integers

IF THEN

IF THEN

Subtract Integers Subtract a positive number from a positive or negative

number Subtract a negative number from a positive or negative

number Apply the subtraction of integers to word problems

Subtraction of whole numbers Add integers Read, write, and represent integers using numbers

-100 to 100

VSC OBJECTIVE8.6.C.1.a – Add, subtract, multiply, and divide integersASSESSMENT LIMIT: Use one operation (-1000 to 1000)

VOCABULARY

IntegerPositive NegativeOpposite“Adding the Opposite”DifferenceSign

Teacher DefinitionsStudent VocabularyWord WallVocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Integers add to the concept of number the idea of opposite, so that every number has both a

size relationship and a positive or negative relationship to other numbers.ESSENTIAL QUESTIONS What examples can be used to show the meaning of subtracting integers?CONCEPT KNOWLEDGE Subtracting integers, unlike whole numbers, can make a number SMALLER OR BIGGER! Subtracting a positive number means you are taking away more and the number gets smaller. Subtracting a negative number means you have two negative signs that cancel each other out

and become a positive! Subtracting a number is the same as adding its opposite.

ERROR INTERVENTIONStudents are having trouble understanding that subtracting a negative makes a positive…

Discuss a real world example like, “The temperature dropped from -3 to -11 degrees; what is the difference between these two numbers?”

Students are simply subtracting normally (i.e. -9 – 1 = 8)…

Have students ALWAYS rewrite the problem verbally first, with the minus sign translating to “and the opposite of,” and then translating to numbers. Ex.:

-5 - (9)= Negative 5 and the opposite of (9) -5 + (-9) = -14

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LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials

VisualAuditory Kinesthetic

Thermometer Students make a thermometer from -20 to 20. The teacher reads aloud a variety of numbers to be represented on the number line and word problems that can be solved by moving a marker up and down the number line.

Construction paper or pre-made thermometers

1 marking item per student

Kinesthetic Games

Integer Board Game

Students make a game board and are given place cards that have a variety of integer computation problems on them. The answer tells them how many spaces to move to get to the end.

Materials to make a board Playing pieces Pre-made playing cards

Auditory Integer Song Students can sing the lyrics of this song to “Row Row Row Your Boat” to remember the rules for adding and subtracting integers.

VisualKinesthetic

Modeling Subtraction

Students can apply the intuitive notion of subtraction (take away) to model problems involving the subtraction of negative numbers. Students must be aware of the fact that (+1) + (-1) = 0 and that n + 0 = n.

2-color chips or algebra tiles

ACCOMODATIONS Accommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Subtract a positive number from a positive or negative number

2 SKILL.Subtracting Integers Additional Practice Addition CMP (7 TH grade)

Middle School Math, Course 2 Scott Foresman (pp 455-460) Middle School Math, Course 1 Scott Foresman (pp 476-480)

Subtract a negative number from a positive or negative number

2 SKILL.Subtracting Integers Additional Practice Addition CMP (7 TH grade)

Middle School Math, Course 2 Scott Foresman (pp 455-460) Middle School Math, Course 1 Scott Foresman (pp 476-480)

Apply the subtraction of integers to word problems

2 SKILL.Subtracting Integers Additional Practice Addition CMP (7 TH grade)

Middle School Math, Course 2 Scott Foresman (pp 455-460) Middle School Math, Course 1 Scott Foresman (pp 476-480)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 1 : C o n c e p t 3 : N U M B E R R E L A T I O N S H I P S : S u b t r a c t

TIME FRAME 2 to 3 days

PREREQUISITE SKILLS

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UNIT 1: Concept 4: NUMBER RELATIONSHIPS: Multiply & Divide Integers

THENIF

IF THEN

Multiply & Divide Integers Multiply and divide 2 integers Multiply and divide more than 2 integers Apply the multiplication and division of integers to word problems

Multiply whole numbers Divide whole numbers Subtraction of whole numbers Read, write, & represent integers using

numbers VSC OBJECTIVE 8.6.C.1.a – Add, subtract, multiply, and divide integersASSESSMENT LIMIT: Use one operation (-1000 to 1000)

VOCABULARY

ProductQuotientMultiple FactorSignPositiveNegative

Teacher DefinitionsStudent VocabularyWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Mathematically, ideas can be represented numerically or symbolically.ESSENTIAL QUESTIONS What are ways that the multiplication and division of integers can be shown?CONCEPT KNOWLEDGE The product of two numbers is the same as repeating addition

(i.e. -3 5 = -3 + -3 + -3 + -3 + -3). The quotient of two numbers is the same as breaking a number into equal groups

(i.e. -10 / 2 = -5 in one group, -5 in another group). The product or quotient of numbers with the same sign (both positive or both negative) is a

positive result; the product or quotient of numbers with different signs (one positive, one negative) is a negative result.

ERROR INTERVENTIONStudents mistake the sign in the answer but multiply correctly…

Have students make a key that they can keep on their desk with + and – signs showing the rules (+ times - = neg.; - times - = pos.).

Students are having trouble with just mutliplying and dividing normally…

Give students a calculator or give students completed number sentences that don’t have the sign in the answer. Then, have students fill in the sign of the answer.

IF THEN

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LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials

Kinesthetic Games

Integer Board Game Students make a game board and are given place cards that have a variety of integer computation problems on them. The answer tells them how many spaces to move to get to the end.

Materials to make a board Playing pieces Pre-made playing cards

Visual Positive and Negative Number Tile Grouping

Students will represent the number sentences using number tiles.

+1, -1 algebra tiles

ACCOMMODATIONS Accommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Multiply and divide 2 integers

4SKILL.Multiplying Integers 5SKILL.Dividing Integers (7 th

grade)

Middle School Math, Course 2 Scott Foresman (pp 461-469)

Middle School Math, Course 1 Scott Foresman (pp 481-484)

Multiply and divide more than 2 integers

3SKILL.Multiplying & Dividing Integers

Middle School Math, Course 2 Scott Foresman (pp 461-469)

Middle School Math, Course 1 Scott Foresman (pp 481-484)

Apply the multiplication and dividing of integers to word problems

4SKILL.Multiplying Integers 5SKILL.Dividing Integers (7 th

grade)

Middle School Math, Course 2 Scott Foresman (pp 461-469)

Middle School Math, Course 1 Scott Foresman (pp 481-484)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

TIME FRAME 4 to 6 days PREREQUISITE SKILLSOrder of Operations Concept of order of operations (whole numbers and integers to start) Exponents of integer bases Expressions with parenthesis and brackets Absolute value

Computation of whole numbers Computation of integers Computation of rational numbers Computation of decimals

VSC OBJECTIVE 8.1.B.1.c – Evaluate numeric expressions using the order of operationsASSESSMENT LIMIT: Use no more than 4 operations (+, -, x, ÷ with no remainders) with or without up to 2 sets of parentheses, brackets, or a division bar, with whole numbers (0 to 200), fractions with denominators as factors of 100 (0 to 100), or decimals with no more than three decimal places (0 to 100)

VOCABULARY

Order of OperationsSumProductDifferenceQuotientGrouping Symbols Teacher DefinitionsStudent VocabularyWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS The context of a situation determines the order in which calculations are performed. Order of operations is not arbitrary. Order of operations is the order in which an expression should be evaluated.ESSENTIAL QUESTION Show why the order of operation makes a difference in solving a problem.CONCEPT KNOWLEDGE The order of operations can be used with the acronym GEMDAS- Grouping Symbols

(parenthesis, brackets), Exponents, Multiplication/Division and Addition/Subtraction If there are no grouping symbols or exponents, the multiplication and division should be

solved from left to right at the same time. Afterward, addition and subtraction should be solved in the problem from left to right as well.

ERROR INTERVENTIONStudents are having trouble with the computation…

Give students a calculator that is not scientific. OR Give students a numeric expression and just have them list the steps they would do. Use different color chalk to show each step.

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UNIT 1: Concept 5: ALGEBRA: Order of Operations

U N I T 1 : C o n c e p t 4 : N U M B E R R E L A T I O N S H I P S : M u lt i p l y a

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Activity Description MaterialsU N I T 1 : C o n c e p t 5 : A L G E B R A : O r d e r o f O p e r a ti o n s

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Kinesthetic Integer Board Game Students make a game board and are given place cards that have a variety of integer computation problems on them. The answer tells them how many spaces to move to get to the end.

Materials to make a board playing pieces

Pre-made playing cards

KinestheticVisual

Calculator- May I Take Your Order?

Students take or make orders from a menu using a non-scientific and a scientific calculator.

Scientific and non-scientific calculators

ACCOMODATIONS Accommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Concept of order of operations (whole numbers and integers to start)

1SKILL Order of Operations Say It with Symbols TE Investigation 1 (pp 5-19i)

Middle School Math, Course 1 Scott Foresman (pp 99-100)

Middle School Math, Course 2 Scott Foresman (p 60)

Exponents of integer bases

2SKILL Order of Operations Say It with Symbols TE Investigation 1 (pp 5-19i)

Middle School Math, Course 2 Scott Foresman (p 465)

Expressions with parenthesis and brackets

3SKILL Order of Operations Say It with Symbols TE Investigation 1 (pp 5-19i)

http://www.teachnology.com/ teachers/lesson_plans/math/operations/

Absolute value 4SKILL Order of Operations Middle School Math, Course 2 Scott Foresman (p 434)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

Grade 8: Unit 2Representing the

Unknown

Unit 2 Assessment

TIME FRAME 3 to 4 days

PREREQUISITE SKILLS

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UNIT 2: Concept 1: ALGEBRA: Numeric & Geometric Patterns

IF THEN

Identify, Describe, & Extend Numeric Patterns & Geometric Patterns [extension]

Making tables Write rules for sequences Identify arithmetic and geometric sequences

Identify, describe, and extend numeric patterns and functions

Create linear patterns and functions Add, subtract, multiply, and divide rational numbers General knowledge/use of the order of operations with

whole numbers Core Learning Goal HS Indicator 1.1.1 – The student will recognize, describe, and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically. ASSESSMENT LIMITS: The given pattern must represent a relationship of the form y = mx + b (linear), y = x2 + c (simple quadratic), y = x3 + c

(simple cubic), simple arithmetic progression, or simple geometric progression with all exponents being positive. The student will not be asked to draw three-dimensional figures.

VOCABULARY

Recursive RelationshipGrowing PatternRepeating PatternEntry [input]Numeric PatternGeometric PatternRelationship/Rule

Teacher DefinitionsStudent VocabularyWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Patterns exist in the natural world and can be represented numerically and graphically. Patterns reflect the past and forecast the future. Patterns are predictable.ESSENTIAL QUESTION What are different ways that a pattern can be identified?

CONCEPT KNOWLEDGE The description that tells how a pattern changes from any given frame to the next frame is

known as the recursive relationship. Growing, geometric patterns have a visual component and/or a numeric component that

students should analyze using a table. From here, they can figure out the “rule/relationship” to help predict the nth term in a series. (Process Chart)

ERROR INTERVENTIONStudents are able to create a table but unable to see the pattern…

Walk them through the process steps for identifying the rule of a function table.

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LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials

Kinesthetic Create a Pattern

Students should be given plastic connector blocks to create a growing pattern. Have a partner record, in a table, how many blocks total are in the figure after each entry and then both students analyze the table together to see the pattern.

Plastic or wooden blocks

VisualVerbal

Create a Pattern

Students can create a growing pattern on index cards and then pass it to another student who then analyzes the picture/completes a table of information and writes the rule.

Blank paper and/or index cards

Games Guess the Pattern

Have students write a rule for a pattern in a table and keep it a secret. On another piece of paper, the students should show the first 3 entries of the growing pattern using numbers or geometric figures. Students will try to guess the pattern after 3 entries, for 3 points. If an entry has to be added to help, the student earns 2 points. Etc.

Blank paper score sheet

ACCOMODATIONS Accommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Make a table 1SKILL.Identify/Describe Geometric

Growing, Growing, Growing TE Investigation 1,2, & 3 (pp 5-44g)

Clever Counting TE Investigation 4 (pp 36j-46f)

Middle School Math, Course 1 Scott Foresman (p xxiv)

Write rules for sequences

2SKILL.Identify/Describe Numeric

Growing, Growing, Growing TE Investigation 1,2, & 3 (pp 5-44g) Clever Counting TE Investigation 4 (pp 36j-46f)

Middle School Math, Course 2 Scott Foresman (p 490)

Identify arithmetic and geometric sequences

3SKILL.Determining Relationships Geometric/Numeric

Growing, Growing, Growing TE (pp 5-44g) Clever Counting TE Investigation 4 (pp 36j-46f)

Middle School Math, Course 2 Scott Foresman (p 490)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

UNIT 2: Concept 1: ALGEBRA: Numeric Patterns & Geometric Patterns

TIME FRAME 3 to 5 days

PREREQUISITE SKILLS

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UNIT 2: Concept 2: ALGEBRA: Write Expressions

IF THEN

Write Expressions [review] Write two-step expressions from verbal phrases Write two-step expressions from word problems Write three-step expressions from verbal phrases or word

problems

Solve word problems/choose the correct operation to solve a one-step word problem

Write a one-step expression

VSC OBJECTIVE 8.1.B.1.a – Write an algebraic expression to represent unknown quantitiesASSESSMENT LIMIT: Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)

VOCABULARY

CoefficientOperationVariableExpressionQuotientProductSumDifferenceMore ThanLess ThanDecreased ByHalfDoubleSeparated EquallyOne-Third Of

Teacher DefinitionsStudent Vocabulary SheetWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Symbols offer flexibility in dealing with different representations. Symbols offer an efficient way to describe a circumstance or situation.ESSENTIAL QUESTION What are ways that the expression can be written to represent the problem?

CONCEPT KNOWLEDGEAn expression names an amount

Sometimes an expression is just a number, like 5. Sometimes an expression is just a variable, like n. Sometimes an expression is a combination of numbers, variables, and operations

like 2 3 or y – 6.There are two main types of expressions:

Algebraic – which include variables AND numbers. Numeric – which include JUST numbers (Process Chart)

ERROR INTERVENTIONReading comprehension level of student is low and therefore, their comprehension of the initial word problem is low…

Give or make with student a “key word chart” to be used to help identify the correct operation to be used. Have student always draw a visual representation of what is going on in the problem.

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LEARNING ACTIVITIES AND STRATEGIESActivity Description Materials

Auditory Story Translation Read a simple story problem to students, but omit the question and one piece of important information. Their task is to write an expression that means the same thing using a variable or a symbol for the unknown amount.

1 word problem

Visual Story Translation in Reverse

Have students create a story problem based on an expression. Have them create a visual to match the words they wrote.

Paper Drawing utensils

Kinesthetic Show Me with Blocks Give students simple word problems with missing information to start. Have them use the color blocks to represent the problem. Have them use the coin to hold the place of the unknown amount.

Colored blocks/tiles 1 coin

DIFFERENTIATIONAccommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Write two-step expressions from verbal phrases

1SKILL.Writing Expressions Middle School Math, Course 2 Scott Foresman (p 78)

Middle School Math, Course 1 Scott Foresman (p 115)

Math At Hand Great Source Education Group

Write two-step expressions from word problems

2SKILL.Writing Expressions Say It with Symbols, TE Investigation 2 & 5 (pp 19j-33o; 64b-70h)

Write three-step expression from verbal phrases or word problems

3SKILL.Writing Expressions 4SKILL.Writing Expressions

Say It with Symbols, TE Investigation 2 & 5 (pp 19j-33o; 64b-70h)

Algebra I, Cliffs Quick Review Cliffnotes (p 139)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

TIME FRAME 2 to 4 days PREREQUISITE SKILLS

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lsU N I T 2 : C o n c e p t 2 : A L G E B R A : W ri t e E x p r e s s i o n s

UNIT 2: Concept 3: ALGEBRA: Simplify Expressions

THENIF

IF THEN

Simplify Expressions Identify like terms and constants Simplify by combining like terms and constants Simplify using the distributive property

Computation of rational numbers Computation of decimals Concept of a coefficient; understand a coefficient means to

multiply

VSC OBJECTIVE8.6.C.1.d – Use properties of addition and multiplication to simplify expressionsASSESSMENT LIMIT: Use the commutative property of addition or multiplication, associative property of addition or multiplication, additive inverse property, or the identity property for one or zero with integers (-100 to 100)

VOCABULARY

ExpressionTermConstantCoefficientLike TermsVariable

Teacher DefinitionsStudent Vocabulary Word Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS An expression can be written in a variety of equivalent ways.ESSENTIAL QUESTION How can expressions be simplified?

CONCEPT KNOWLEDGESimplifying an expression means to combine terms so that there are less terms in the expression. When simplifying, GEMDAS still should be followed (multiply terms together, before, addition,

etc.). Terms can only be added together if they are like terms (share a common variable set) or are

constants (numbers that don’t vary). To add like terms, you add the coefficients together. Any two terms can be multiplied or divided together (Process Chart).ERROR INTERVENTION

Students multiply the coefficients together when adding like terms instead of adding them…

Have students write out what each term is as repeated addition above the terms(i.e. 4x means x + x + x + x).

Students struggle with the computation of rational numbers…

Give them a calculator; however require them to write down each step for the problems they used the calculator for so that you can see their work.

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LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials

Kinesthetic Visual

Algebra Tile Activity

Students can use printable algebra tiles to represent constants, terms that share the same variable, and terms that share different variables to show which tiles can be “put together” or simplified.

Algebra tiles

Game BINGO Students will simplify algebraic expressions and find the matching, most simplified version of that expression on their bingo card.

Bingo cards Chips to mark cards

Game Card Sort Students are given cards with a variety of terms on them and they try to group the cards based on classifications they come up with.

Cards cut out and mixed up into groups

Sheet to record observations

ACCOMODATIONS Accommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Identify like terms and constants

1SKILL.Simplifying Expressions

Simplify by combining like terms and constants

2SKILL.Simplifying Expressions Say It with Symbols, TE Investigation 2 (pp 19j-33o)

Simplify using the distributive property

3SKILL.Simplifying Expressions Say It with Symbols, TE Investigation 2 (pp19j-33o) Investigation 3 (pp 33p-52q)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 2 : C o n c e p t 3 : A L G E B R A : S i m p li f y E x p r e s s i o n s

Grade 8: Unit 3Solving & Using

EquationsUnit 3 Assessment

TIME FRAME 3-5 days

PREREQUISITE SKILLS

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IF THEN

Write Equations Write one-step equations from verbal translations (all operations) Write two- or three-step equations from verbal translations (all

operations)

Write two-step expressions from verbal phrases and from word problems

Understand the difference between an expression and an equation

VSC OBJECTIVE 8.1.B.2.a – Write equations or inequalities to represent relationshipsASSESSMENT LIMIT: Use a variable, the appropriate relational symbols (>, >, <, <, =), no more than three operational symbols (+, -, , ) on either side, and rational numbers (-1000 to 1000)

VOCABULARY

EquationVariable Zero PairAdditive InverseBalancing the EquationCoefficient (of 1)Reciprocal

Teacher DefinitionsStudent Vocabulary SheetWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Numbers and variables are conceptual images assigned and used to

communicate.ESSENTIAL QUESTION What are the steps that could be used to write equations from word problems?CONCEPT KNOWLEDGE Understand the concept of a variable. Write two-step expressions from verbal phrases and from word problems.(Process Chart – Writing One-Step Equations)(Process Chart – Writing Two- and Three-Step Equations)ERROR INTERVENTION

Students struggling with reading comprehension have trouble thinking critically about what makes sense for the problem

Use highlighters to highlight key words.Have a chart listing common words used in word problems available in their notes and/or on the classroom wall. Also, have them represent the problem pictorially or act it out and ask questions like, “is the amount getting bigger or smaller?”

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LEARNING ACTIVITIES AND STRATEGIESActivity Description Materials

Game Memory After students have successfully completed the writing task in WTA 1 of the 2SKILL.1-Step Equation document below, have them cut out each box to use in a game of Memory. With all cards face down, students can take turns trying to match each phrase with its equation.

Equation cards

Visual Draw a Picture Have students represent a given word problem using a picture.

Drawing paper

DIFFERENTIATIONAccommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math

Concepts 1Other

Write 1-step equations from verbal translations (all operations)

2SKILL.1-Step Equations Middle School Math, Course 1 Scott Foresman (p 118) Math At Hand Great Source Education Group (p 237) Math to Know Great Source Education Group (p 255)

Write 2- or 3-step equations from verbal translations (all operations)

2SKILL.2- to 3-Step Equations

http://www.mathgoodies.com/lessons/vol7/ equations.html

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 3 : C o n c e p t 1 : A L G E B R A : W ri t e E q u a ti o n s

TIME FRAME 5 to 8 days

PREREQUISITE SKILLS

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UNIT 3: Concept 2: ALGEBRA: Solve Linear Equations

Solve Linear Equations One-step equations (all operations) Two- to three-step equations without parenthesis; only integers

and whole numbers Two- to three-step equations with parenthesis and all rational

numbers Two- to three-step equations (simplifying first) Equations whose solution is null set or infinite solution

Computation of whole numbers Computation of integers Computation of other rational numbers Understand addition-subtraction and

multiplication-division are inverse operations Simplify like terms by combining coefficients

VSC OBJECTIVE 8.1.B.2.a – Solve for the unknown in a linear equation ASSESSMENT LIMIT: Use one unknown no more than three times on one side and up to three operations (same or different but only one division) and rational numbers (-2000 to 2000)

VOCABULARY

EquationVariable Zero PairAdditive InverseBalancing the EquationCoefficient (of 1)Reciprocal

Teacher DefinitionsStudent Vocabulary SheetWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Linear functions show a pattern of growth.

ESSENTIAL QUESTION What are ways that you can prove the solution is correct?

CONCEPT KNOWLEDGE To solve an equation means to isolate the variable so that it is “alone” (having a coefficient

of 1). To ISOLATE the variable, you need to “undo” the problem by working backwards to find the

missing variable (Process Charts-Solving One-Step equations ; Two- to Three-step equations).

When solving equations, you must always BALANCE THE EQUATION (you have to do that same operation with the same number to the other side).

To check a solution, substitute the value you found back into the original equation to make sure both sides are equal.

There are some equations that have “no solution” or could have an infinite number of solutions.

ERROR INTERVENTION

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LEARNING ACTIVITIES AND STRATEGIESActivity Description Materials

Kinesthetic Algebra Tile Activity

Represent the equations using number and algebra tiles. Algebra tiles – variables and +1 and -1 tiles

VisualKinesthetic

Tilt or Balance Use a simple two-pan balance to visually represent equations and analyze changes.

Picture or actual two-pan scale

Literature Connection

Anno’s Mysterious Multiplying Jar, by Mitsumasa Anno

It tells an imaginative story of a mysterious jar that contains a sea. On the sea is one island. The island has two mountains. Each mountain has…This story can be used to create word problems and equations. The story can be altered and numbers replaced with variables.

Copy of book

DIFFERENTIATIONAccommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

One-step equations (all operations)

1SKILL.1-Step Equations Say It with Symbols, TE Investigation 4 (pp 52r-64t)

Middle School Math, Course 1 Scott Foresman (p 122)

Math At Hand Great Source Education (pp 242-243)

Two- to three-step equations without parenthesis; only integers and whole numbers

1SKILL.2 – 3-Step Equations

Middle School Math, Course 2 Scott Foresman (pp 191, 524-536)

Two- to three-step equations with parenthesis and all rational numbers

1SKILL.1-Step Equations

Two- to three-step equations (simplifying first)

1SKILL.2 – 3-Step Equations

Equations whose solution is null set or infinite solution

1SKILL.1-Step Equations

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 3 : C o n c e p t 2 : A L G E B R A : S o l v e L i n e a r E q u a ti o n s

TIME FRAME 2 to 4 days

PREREQUISITE SKILLS

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UNIT 3: Concept 3: ALGEBRA: Use Formulas

IF THEN

Use Formulas Distance and average Area and perimeter of a triangle, square, or rectangle Volume

Evaluate algebraic expressions (7 th ) Solve one- and two-step equations (6 th and 7 th )

VSC OBJECTIVE 8.1.B.2.a – Apply given formulas to a problem-solving situation ASSESSMENT LIMIT: Use no more than four variables and up to three operations with rational numbers (-500 to 500)HS Indicator 1.2.5 – The student will apply formulas and/or use matrices to solve real-world problems ASSESSMENT LIMIT:

Formulas will be provided in the problem or on the reference sheet. Formulas may express linear or non-linear relationships. Students will be expected to solve for first-degree variables only.

VOCABULARY

FormulaVariableEquation

Teacher DefinitionsStudent Vocabulary SheetWord Wall VocabularyTotal Vocabulary Matrix

ENDURING UNDERSTANDINGS Formulas organize information. Formulas describe relationships between two or more variables. Formulas produce an output when the input is entered.ESSENTIAL QUESTION What are ways that the formula can be solved?CONCEPT KNOWLEDGE A formula is a rule showing relationships among many quantities and usually includes a

variable. Formulas help to solve problems involving: perimeter, distance, area, and other

geometric concepts (Process Chart).ERROR INTERVENTION

Students read a problem and are subsituting information into the formula for the wrong variable…

Make them write the equation used every time and draw an arrow from the variable they are substituting and/or color-code the information in the problem to match the color-coded variables in the formula.

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LEARNING ACTIVITIES AND STRATEGIESActivity Description Materials

Kinesthetic Classroom Races Students will do an experiment to calculate rate/speed when they measure the distance of the classroom and the time it takes two students to race from one end to the other on their knees.

Stopwatch Experiment sheet

Visual Perimeter and Area Grids

Students will draw a variety of rectangles, squares, and triangles given the perimeter and area. They will find the missing lengths and widths.

Graph paper

VisualAuditory

Poster-Making Presentation

Students will create a poster showing four useful formulas and how they could be used to solve a real-world dilemma.

Poster paper Markers Magazines

DIFFERENTIATIONAccommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Distance and Average 1SKILL.Using Formulas 2SKILL.Using Formulas

Middle School Math, Course 2 Scott Foresman (p 56)

Area and Perimeter of a Triangle, Square, or Rectangle

1SKILL.Using Formulas 2SKILL.Using Formulas

Say It with Symbols Investigation 2 (pp 19j-33o)

Looking for Pythagoras Investigation 2 (pp 16h-26k)

Middle School Math, Course 2 Scott Foresman (pp 56, 233, 248)

VolumeOther Formulas

1SKILL.Using Formulas 2SKILL.Using Formulas

Looking for Pythagoras Investigation 3 (pp 26n-52i)

Investigation 4 (pp 36j-46i)CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 3 : C o n c e p t 3 : A L G E B R A : U s e F o r m u l a s

THENIF

IF THEN

IF THEN

TIME FRAME 5 to 6 days PREREQUISITE SKILLSPercent of a Number Understand percents greater than 100, less than 1 or that include a decimal Find the part Find the total Find the percent Discount, commission, and sales tax

Multiplication of whole numbers Identify parts of a fraction

(part/total) Solve equations Use formulas

VSC OBJECTIVE8.1.B.2.b – Determine or use percents, rates of increase and decrease, discount, commission, sales tax, and imply interest in the context of a problemASSESSMENT LIMIT: Use positive rational numbers (0 to 10,000)

VOCABULARYPercentFractionDecimalRatioProportionPartTotal

Cross MultiplyEquationVariable

Teacher DefinitionsStudent Vocabulary SheetWord Wall Vocabulary Total Vocabulary Matrix

ENDURING UNDERSTANDINGS Percents are per a hundred. Relative comparisons are communicated with fractions, decimals, and percents.ESSENTIAL QUESTION How can problems be set up to determine the percent when parts are missing?CONCEPT KNOWLEDGE A percent is a ratio that describes a part of 100. A fraction can be converted to a percent by setting up two equal ratios (a proportion):

Process Chart)ERROR INTERVENTION

Students have a hard time understanding which is the part, total, or perecent…

Have them draw visual representations of what is going on in the problem.

Students cannot compute the numbers…

give them a calculator.

Students have not yet fully mastered how to solve equation…

give them a process chart for solving one-step equations.

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LEARNING ACTIVITIES AND STRATEGIES Activity Description Materials

VisualKinesthetic

Shopping Spree Students will use real-world applications in learning to find the percent of a number.

Catalog of items

Cooperative Rainforest Report Students will be given a variety of facts about the rainforest and or other topics connecting to content areas. Students will rewrite these facts as percents and present them to the class.

Fact sheets Index cards

VisualGroup Work

Performance Task

This task will be completed in groups that work in stations that include 10 questions, each with two parts. The questions are centered on “percent of a number” questions.

Activity sheets

DIFFERENTIATIONAccommodations G.A.T.E./Enrichment [See Connected Mathematics I]

RESOURCESSub-Skills Math Works Teaching Skill Connected Math Concepts 1 Other

Understand percents greater than 100, less than 1, or that include a decimal

1SKILL Percent (8 th grade) Middle School Math, Course 1 Scott Foresman (pp 550-553)

Find the part 2SKILL Percent of a Whole Number. Using Ratio Box (6 th grade)

6 Skill Percent (7 th grade)

Middle School Math, Course 1 Scott Foresman (pp 563-567)

Find the total 2SKILL Percent (8 th grade) 6 SKILL Percent (7 th grade)

Middle School Math, Course 1 Scott Foresman (pp 563-567)

Find the percent 3 SKILL Percent (8 th grade) Middle School Math, Course 1 Scott Foresman (pp 563-567)

Discount, commission, and sales tax

4SKILL Percent (8 th grade) Thinking with Mathematical Models Investigation 3 (p 47)

CONCEPT ASSESSMENT CONCEPT TRACKING SHEET BCR’s

U N I T 3 : C o n c e p t 4 : A L G E B R A : P e r c e n t o f a N u m b e r