BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

*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: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

Grade 7: Unit 1

Fractions, Decimals, Percents


TIME FRAME 3 to 4 days / PREREQUISITE SKILLS
Equivalent Forms of Rational Numbers(extension) /
  • Long Division
  • Place Value of Decimals
  • Compare Decimals

VSC OBJECTIVE
8.6.A.1b. 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
Decimal
Fraction
Proper Fraction
Improper Fraction
Convert
Percent
Ratio
Integer
Rational Number
Equivalent Form
Annex
Terminating Decimal
Repeating Decimal
Numerator
Denominator
Fraction Bar
Positive
Negative
Absolute Value
Teacher Definitions
Student Vocabulary
Word Wall Vocabulary
Total Vocabulary Matrix / ENDURING UNDERSTANDINGS
  • Rational numbers are numbers that can be written as a fraction.
  • Fractions, decimals, and percents can represent the same quantity in different forms.
ESSENTIAL QUESTIONS
  • How can you compare different forms of rational numbers?
CONCEPT KNOWLEDGE
  • To compare rational numbers, they can be written in the same form that will help to compare numbers.
  • To change a fraction to a decimal, divide the numerator by the denominator and annex zeros. Some decimals are terminal, meaning they end with a strand of zeros. Other decimals are repeating, having one or more digits that repeat.
  • Integers are the set of whole numbers and their opposites. Absolute value is a number’s distance from zero.

ERROR INTERVENTION
Students invert numerator and denominator when converting fractions to decimals using thedivision method / Use logic – a fraction that is less than one should have a decimal equivalent that is less than one.
Suggested Learning Plan / Learning Activities and Strategies
Activity / Description / Materials
Game / BINGO / Teacher calls out a fraction. Students convert fraction to decimal and locate decimal on BINGO chart. /
  • Blank BINGO chart
  • Colored Chips

Cooperative Learning / Fall In Line / Each student is given a fraction, decimal, or percent. Students order themselves from least to greatest. /
  • Fraction/Decimal/Percent Cards

Game / War / Students use a deck of fraction, decimal, and percent cards to play a game similar to war. /
  • Fraction/Decimal/Percent Playing Cards

Social / Scavenger Hunt / Students use converting skills to answer clues and spell out a message. /
  • Clues
  • Prizes

DIFFERENTIATION
Accommodations* G.A.T.E./Enrichment [See Connected Mathematics I]
Resources
Sub-Skills / Math Works Teaching Skill / Connected Mathematics 1 / Other
Equivalent Forms – Comparing and Ordering /
  • 1SKILL Equivalent Forms
  • 2SKILL Comparing and Ordering
/
  • CMP 1: Bits and Pieces 1Investigation 6.3 (p 75)
  • Fractions and Decimals
  • Comparing and Ordering Decimals
  • Fractions, Decimals, Percents
/
  • MSA Coach Gr. 7 p 174, 180
  • MSA Finish Line Gr. 7 p 120, 124
  • MSA Grand Slam Gr. 7 p 12, 14
  • MSA Coach Gr. 8 p 183
  • MSA Finish Line Gr. 8 p 144
  • MSA Grand Slam Gr. 8 p 10, 12
  • Fraction Converter Calculator
  • Notes on Converting
  • Fraction Decimal Concentration
  • Fraction, Decimal,Percent Fill-in

CONCEPT ASSESSMENT / CONCEPT TRACKINGSHEET / BCR’s

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

TIME FRAME 2 to 3 days / PREREQUISITE SKILLS
Locate Rational Numbers on a Number Line(review) /
  • Equivalent Forms
  • IdentifyIntegers on a Number Line

VSC OBJECTIVE
7.1.C.1a Represent rational numbers on a number line
ASSESSMENT LIMIT: Use rational numbers (-100 to 100)
VOCABULARY
Decimal
Fraction
Percent
Integer
Rational Number
Positive
Negative
Absolute Value*
Opposite
*First Formal Introduction
Teacher Definitions
Student Vocabulary
Word Wall Vocabulary
Total Vocabulary Matrix / ENDURING UNDERSTANDINGS
  • A number line consists of positive numbers to the right [above]of zero and negative numbers to the left [below] of zero.
ESSENTIAL QUESTIONS
  • What is important to remember about a number line with positive and negative numbers?
CONCEPT KNOWLEDGE
  • To locate rational numbers on a number line, convert benchmarks and numbers to equivalent forms.

ERROR INTERVENTION
Students have difficulty plotting negative rational numbers / Have them fold a number line in half and plot the positve value and unfold.

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

Suggested Learning Plan / Learning Activities and Strategies
Activity / Description / Materials
Kinesthetic / Human Number Line / Students represent fraction benchmarks. Another student is given a rational number and then stands in the correct spot between the fraction benchmarks /
  • Fraction Benchmark Cards
  • Rational Number Cards

Technology / Find Granny / Students enter fractional distances on a number line. /
  • Computer Lab or Projector or Promethean Board

/ Online game from the UK - interactive
Social / Give Me One Greater / Students are given one benchmark on a number line. They then must provide a rational number that is larger.
Concrete/ Hands On / Where Would It Be / Students move clothespins along a hand-made number line to find a given rational number. /
  • Number Lines
  • Clothespins

DIFFERENTIATION
Accommodations* G.A.T.E./Enrichment [See Connected Mathematics I]
Resources
Sub-Skills / Math Works Teaching Skill / Connected Mathematics 1 / Other
Locating Rational Numbers on a Number Line /
  • 1SKILL Rational Numbers on a Number Line
/
  • CMP 1: Bits and Pieces (p 81 #21-25)
  • CMP 1: Bits and Pieces 1 (p 85 #2)
/
  • MSA Coach Gr. 7 p 29
  • MSA Finish Line Gr. 7 p 28
  • Comparing Two Numbers on a Number Line

CONCEPT ASSESSMENT / CONCEPTTRACKINGSHEET / BCR’s

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

TIME FRAME 1 to 2 days / PREREQUISITE SKILLS
Divide a Decimal Dividend by a Decimal Divisor (new) /
  • Division of a Decimal bya Whole Number

VSC OBJECTIVE
6.6.C.1d. Divide decimals
NOT ASSESSED ON MSA but is needed for the Terra Nova in 8th grade. Divisor is a decimal up to hundredths place value
VOCABULARY
Divide
Dividend
Divisor
Quotient
Decimal
Place Value
Teacher Definitions
Student Vocabulary
Word Wall Vocabulary
Total Vocabulary Matrix / ENDURING UNDERSTANDINGS
  • Division and multiplication are connected. Division is the opposite of multiplication.
ESSENTIAL QUESTIONS
  • How do you use estimation skills to check that the answer makes sense?
  • How is dividing by a decimal different from dividing by a whole number?
CONCEPT KNOWLEDGE
  • Estimate the answer before dealing with decimals.
  • Make the divisor into a whole number by moving the decimal point to the right of the one’s place. Move the decimal point in the dividend the same number of places. This is the same as multiplying the dividend and divisor by powers of ten.

21.3
0.08 ) 1.704
ERROR INTERVENTION
Students forget to write zeros when the dividend does not have enough digits / Have students make loops representing place values moved and fill in empty loops with zeros.
Students try to move their decimal point in their quotient / Students should complete Why It Works activity.
Suggested Learning Plan / Learning Activities and Strategies
Activity / Description / Materials
Logical / Why It Works* / Students use calculators to explore related division expressions to justify why the algorithm works. /
  • Calculators

Real World / Money Magic / Students use play money to simplify division expressions. /
  • Play Money

Cooperative Learning / BoardRaces / Teams of students compete against each other to solve problems on the board. Each student on the team has a job.
Visual / Drawing Division* / Students use hundredths grids to represent division of decimal problems. They should begin to understand why their quotient is larger than their divisor or dividend. /
  • Hundredths Grids
  • Colored Pencils
  • Place value boards & rods

DIFFERENTIATION
Accommodations* G.A.T.E./Enrichment
Resources
Sub-Skills / Math Works Teaching Skill / Connected Mathematics 1 / Other
Dividing a Decimal by a Decimal /
  • 1SKILL Dividing Decimals.decimal dividend
  • 2SKILL Dividing Decimals.whole number dividend
  • 3SKILL Dividing Decimals.mixed review
  • 1EXIT TICKET Dividing Decimals
/
  • Dividing Decimals Tutorial with Practice
  • Dividing Decimals Using Base Ten Blocks
  • Great Introduction PowerPoint

CONCEPT ASSESSMENT / CONCEPT TRACKINGSHEET / BCR’s

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

TIME FRAME 2 to 3 days / PREREQUISITE SKILLS
Divide Fractions and Mixed Numbers (new) /
  • Change Mixed Numbers to Improper Fractions
  • Multiply Fractions (with and without Canceling Method)
  • Simplify to Lowest Terms
  • Change Improper Fractions to Mixed Numbers

VSC OBJECTIVE
7.6.C.1c. Divide fractions and mixed numbers
NO ASSESSMENT LIMIT ON VSC. Not tested on MSA. However students need this skill on the Terra Nova [High School Entrance test] Divisor and dividend can be fractions, whole, or mixed numbers.
VOCABULARY
Divide
Quotient
Fraction
Numerator
Denominator
Mixed Number
Improper Fraction
Proper Fraction
Reciprocal
Multiply
Simplify
Inverse
Teacher Definitions
Student Vocabulary
Word Wall Vocabulary
Total Vocabulary Matrix / ENDURING UNDERSTANDINGS
  • Division is the process of making equal groups.
ESSENTIAL QUESTION
  • What is one method that could be used to show division of fractions?
CONCEPT KNOWLEDGE
  • Dividing by a fraction or mixed number is the same as multiplying by its reciprocal. In this way, an expression with dividing fractions will become a multiplication problem. Therefore, once you have found the reciprocal of the second fraction, you will follow the same rules for multiplying fractions
  • Reciprocals are numbers whose numerators and denominators have been switched. The product of a number and its reciprocal is 1.
  • Quotients can be simplified if possible.
  • Fraction bar implies division

ERROR INTERVENTION
Students attempt to solve the problem by finding the LCD / Have students write the problem horizontally.
Students proceed without changing mixed numbers to improper fractions / Students should circle any mixed number/whole number to remind them to convert to improper fractions.

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

Suggested Learning Plan / Learning Activities and Strategies
Activity / Description / Materials
Concrete/ Hands On / Fraction Foods* / Students can explore the process of dividing fractions using bags of food and measuring cups. /
  • Bags of Food
  • Measuring Cups
  • Record Sheet

Technology / Dividing Fractions Tutorial / Students are able to visualize the process of dividing fractions by viewing division as splitting a quantity. /
  • Computer Lab

Kinesthetic / Post-It Products* / Students can physically change division expressions to multiplication expressions by moving post-its to represent reciprocals. /
  • Post-It Notes of Varying Sizes/Colors

Social / Pass-a-Problem / Students start with two fraction cards and find the quotient. Each student then passes one card to the right. A new problem is formed and dividend becomes divisor. /
  • Fraction cards

DIFFERENTIATION
Accommodations* G.A.T.E./Enrichment [See Connected Mathematics I]
Resources
Sub-Skills / Math Works Teaching Skill / Connected Mathematics 1 / Other
Finding Reciprocals /
  • 1WARM UP Reciprocals

Dividing Proper Fractions /
  • 1SKILL Dividing Fractions.proper
/
  • CMP 1: Bits and Pieces 2 Investigation 7 (p 77)
  • Dividing Fractions

Dividing Mixed Numbers /
  • 1SKILL Dividing Fractions.fraction by a whole number
  • 2SKILL Dividing Fractions.mixed number by a whole number
  • 3SKILL Dividing Fractions.fraction by mixed number
  • 4SKILL Dividing Fractions.mixed number by mixed number
/
  • CMP 1: Bits and Pieces 2Investigation 7 (p 77)
  • Dividing Mixed Numbers
/
  • DividingMixed Numbers
  • Dividing Mixed Numbers
  • Area Model for Division
  • Common Denominator Model for Division
  • Dividing Mixed Numbers Video

CONCEPT ASSESSMENT / CONCEPT TRACKING SHEET / BCR’s

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

Grade 7: Unit 2

Integers

TIME FRAME 2 to 3 days / PREREQUISITE SKILLS
Add Integers (extension) /
  • Addition of Whole Numbers
  • Subtraction of Whole Numbers

VSC OBJECTIVE
8.6.C.1a. Add, subtract, multiply, and divide integers
ASSESSMENT LIMIT: Use one operation (-1,000 to 1,000)
VOCABULARY
Sum
Integer
Absolute Value*
Zero Pair
Additive Inverse
Sign
*First Formal Introduction
Teacher Definitions
Student Vocabulary
Word Wall Vocabulary
Total Vocabulary Matrix / ENDURING UNDERSTANDINGS
  • Integers add to whole numbers the ideas of opposite and absolute value.
ESSENTIAL QUESTIONS
  • What is a method that can be used to show addition of integers?
  • How is adding and subtracting integers different from multiplying and dividing them?
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 (one pos. and one neg.) means you will subtract the amounts
  • The sum of any 2 numbers, positive or negative is decided by which number has a higher absolute value.

ERROR INTERVENTION
Students have difficulty deciding which sign their answer should have / Have students work problems on a number line; Review absolute value and compare.

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

Suggested Learning Plan / Learning Activities and Strategies
Activity / Description / Materials
Game / Adding Integers War / Students (one representing positive answers and the other negative answers) use playing cards to add integers. /
  • Deck of playing cards per 2 students
  • Scrap Paper

Game / Who Has? / Each student has an index card with a value and an addition expression. Teacher calls out an expression and student with the value stands and reads his/her expression. The game loops back to the teacher. /
  • Who Has? Activity Cards
  • Index Cards
  • Glue

Visual / Adding integer Placecards* / Students use two different colored chips to solve addition expressions by making zero pairs. Cards are then passed around the classroom. /
  • Adding Integers Placecards
  • Positive Colored Chips (20 per student)
  • Negative Colored Chips (20 per student)

Kinesthetic / Human Number Line / Students construct human number line. Two students are selected to show the answer to an addition expression on the number line. /
  • Construction Paper Numbered -20 to 20

DIFFERENTIATION
Accommodations* G.A.T.E./Enrichment [See Connected Mathematics I]
Resources
Sub-Skills / Math Works Teaching Skill / Connected Mathematics 1 / Other
Adding Integers /
  • 1SKILL Adding Integers
  • 1Adding Integers on a Number Line
  • 2Adding Integers on a Number Line
  • Adding Integers
/
  • CMP 1: Accentuate the NegativeInvestigation 2.2 (p 21)
  • Addition of Integers
/
  • MSA Coach Gr. 7, p 189
  • MSA Finish Line Gr. 7, p128
  • MSA Grand Slam Gr. 7, p 30
  • MSA Coach Gr. 8, p 187
  • MSA Finish Line Gr. 8, p 148
  • MSA Grand Slam Gr. 8, p 16
  • Adding Integers Virtual Manipulatives
  • Narrated Step-by-Step Tutorials
  • Online Flashcards

CONCEPT ASSESSMENT / CONCEPT TRACKING SHEET / BCR’s

BCPSS Office of Math: ril 2008 DRAFT

Quarter 4 Curriculum: GRADE 7 Page 1

TIME FRAME2 to 4 days / PREREQUISITE SKILLS
Subtract Integers (extension) /
  • Addition of Whole Numbers
  • Subtraction of Whole Numbers

VSC OBJECTIVE
8.6.C.1a. Add, subtract, multiply, and divide integers
ASSESSMENT LIMIT: Use one operation (-1,000 to 1,000)
VOCABULARY
Difference
Integer
Absolute Value
Zero Pair
Opposite
Sign
Debits [negative]*
Credit [positive]*
*First Formal Introduction
Relate “real world” terminology to math instruction. How are positive and negative numbers used in the world of banking, economics, and accounting?
Teacher Definitions
Student Vocabulary
Word Wall Vocabulary
Total Vocabulary Matrix / ENDURING UNDERSTANDINGS
  • Integers add to whole numbers the ideas of opposite and absolute value.
ESSENTIAL QUESTION
  • What is a method that can be used to show how to subtract integers?
CONCEPT KNOWLEDGE
  • To subtract is to add the opposite.

ERROR INTERVENTION
Students may not write the equivalent addition expression / Have students rewrite the addition expression below the subtraction expression
Students have difficulty deciding which sign their answer should have / Have students work problems on a number line
Students forget the concept / Use Keep Change CHANGE. This changes the subtraction to an addition problem. This works because addition and subtraction are inverse operations. When you change the subtraction sign to an addition sign and change the sign of the second integer, you are adding the opposite. Now you can use the rules for addition.
Suggested Learning Plan / Learning Activities and Strategies
Activity / Description / Materials
Visual / Subtracting integer Placecards* / Students use two different colored chips to solve subtraction expressions by making zero pairs. Cards are then passed around the classroom. /
  • Subtracting Integers Placecards
  • Positive Colored Chips (20 per student)
  • Negative Colored Chips (20 per student)

Game / Concentration / Students must match the subtraction expression with its equivalent addition expression. Students get an extra point for solving the expression. /
  • Concentration Game Cards

Technology / Integer Subtraction - What's the Difference? / Students use a number line to explore subtraction of integers and justify the rules they develop. /
  • Graphing Calculators

Game / BINGO / Students solve integer subtraction expressions and locate their answer on their BINGO card. /
  • Blank BINGO card
  • Colored Chips

DIFFERENTIATION
Accommodations* G.A.T.E./Enrichment [See Connected Mathematics I]
Resources
Sub-Skills / Math Works Teaching Skill / Connected Mathematics 1 / Other
Subtracting Integers /
  • 2SKILL Subtracting Integers
  • Subtracting Integers
/
  • CMP 1: Accentuate the NegativeInvestigation 3.1 (p 35)
  • Subtraction of Integers
/
  • MSA Coach Gr. 7, p 189
  • MSA Finish Line Gr. 7, p 128
  • MSA Grand Slam Gr. 7, p 30
  • MSA Coach Gr. 8, p 187
  • MSA Finish Line Gr. 8, p 148
  • MSA Grand Slam Gr. 8, p 16
  • Subtracting Integers Virtual Manipulatives
  • Narrated Step-by-Step Tutorials
  • Online Flashcards

CONCEPT ASSESSMENT / CONCEPTTRACKING SHEET / BCR’s

BCPSS Office of Math: ril 2008 DRAFT