Unit 1: The Number System
Important Documents
Unit 1 Outline
Unit 1 Student Clear Expectations
Unit 1 Parent Clear Expectations
Unit 1 Portfolio Cover Sheet
Unit 1 Data Sheet
Unit 1 Student Clear Expectations
Unit 1 Parent Clear Expectations
Unit 1 Portfolio Cover Sheet
Unit 1 Data Sheet
Learning Target 1: I can determine the GCF of 2 or more whole numbers.
Misconceptions:
(1) Students mistakenly find a factor of one number that does not work with the other number.
ex) GCF of 15 and 20 is 10 because 2 x 10 = 20, however, the GCF is actually equal to 5
(2) Students mistakenly find a common factor of 2 or more numbers, instead of the greatest common factor.
ex) The GCF of 10 and 20 is 5 because 5 evenly divides both numbers, however the GCF is actually 10
Student Outcomes:
(1) Students will independently find the biggest factor that a set of numbers share.
(1) Students mistakenly find a factor of one number that does not work with the other number.
ex) GCF of 15 and 20 is 10 because 2 x 10 = 20, however, the GCF is actually equal to 5
(2) Students mistakenly find a common factor of 2 or more numbers, instead of the greatest common factor.
ex) The GCF of 10 and 20 is 5 because 5 evenly divides both numbers, however the GCF is actually 10
Student Outcomes:
(1) Students will independently find the biggest factor that a set of numbers share.
Objective A: I can identify factor pairs of a whole number.
Via:
(1) Identify factor pairs using a t-chart; Video
(2) Finding factors ; Video
(3) Fact Fluency; Jeopardy Game
Skill Practice:
(1) Identifying Factor pairs of a whole number using the Rainbow method; L, M & H
Learning Activities:
(1) Factor Pair Game Activity; L, M, or H
Via:
(1) Identify factor pairs using a t-chart; Video
(2) Finding factors ; Video
(3) Fact Fluency; Jeopardy Game
Skill Practice:
(1) Identifying Factor pairs of a whole number using the Rainbow method; L, M & H
Learning Activities:
(1) Factor Pair Game Activity; L, M, or H
Objective B: I can distinguish between prime and composite numbers.
Via:
(1) Recognizing Prime and Composite Numbers; Video
(2) Factors and Multiples; Powerpoint slides
Skill Practice:
(1) Identifying Prime or Composite Numbers
Learning Activities:
(1)
Via:
(1) Recognizing Prime and Composite Numbers; Video
(2) Factors and Multiples; Powerpoint slides
Skill Practice:
(1) Identifying Prime or Composite Numbers
Learning Activities:
(1)
Objective C: I can find the prime factorization of a whole number in exponential form.
Via:
(1) Finding the GCF using prime factorization; Video
(2) Finding the GCF & LCM using prime factorization; Video
(3) Finding the prime factorization of a whole number using the factor tree method and birthday cake method; Active Inspire Slides
(4) Finding the GCF & LCM using prime factorization; Active Inspire Slides
Skill Practice:
(1) Prime Factorization Skill Sheet
Learning Activities:
(1)
Via:
(1) Finding the GCF using prime factorization; Video
(2) Finding the GCF & LCM using prime factorization; Video
(3) Finding the prime factorization of a whole number using the factor tree method and birthday cake method; Active Inspire Slides
(4) Finding the GCF & LCM using prime factorization; Active Inspire Slides
Skill Practice:
(1) Prime Factorization Skill Sheet
Learning Activities:
(1)
Objective D: I can determine the GCF of 2 or more whole numbers.
Via:
(1) Find the greatest common factor of two numbers; Video
(2) Find the GCF of two or more whole numbers; Notes sheet with examples
(3) Factor Rainbow ; Video
(4) Finding the GCF using the birthday cake method; Video
(5) Finding the GCF; Notes sheet with examples
Skill Practice:
(1) Determine the GCF of 2 or more whole numbers using the rainbow method skill
(2) Determine the GCF of 2 or more whole numbers using the t- chart method skill
(3) Determine the GCF of 2 or more whole numbers using the listing method skill
Learning Activities:
(1) Bewildering Brownies GCF Activity; L, M & H
(2) GCF Snatch Game
Learning Target 2: I can determine the LCM of 2 or more whole numbers.
Misconceptions:
(1) Students mistakenly find a multiple that only works for one number and not the other(s)
ex) The LCM of 5 and 8 is 24 because 8 x 3 = 24, the LCM is actually equal to 40
(2) Students assume that multiplying the 2 given numbers together will always result in the LCM.
ex) The LCM of 6 and 8 is 48 because 6 x 8 = 48; the LCM is actually equal to 24
Student Outcomes:
(1) Students will independently find the smallest multiple that two or more whole numbers share.
(1) Students mistakenly find a multiple that only works for one number and not the other(s)
ex) The LCM of 5 and 8 is 24 because 8 x 3 = 24, the LCM is actually equal to 40
(2) Students assume that multiplying the 2 given numbers together will always result in the LCM.
ex) The LCM of 6 and 8 is 48 because 6 x 8 = 48; the LCM is actually equal to 24
Student Outcomes:
(1) Students will independently find the smallest multiple that two or more whole numbers share.
Objective A: I can list the multiples of a whole number.
Via:
(1) Multiples of a whole number; Video
(2) Identifying multiples of a whole number; Notes sheet with examples
(3)
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Multiples of a whole number; Video
(2) Identifying multiples of a whole number; Notes sheet with examples
(3)
Skill Practice:
(1)
Learning Activities:
(1)
Objective B: I can determine the LCM of 2 or more whole numbers.
Via:
(1) Find the LCM of two numbers; Video
(2) Find the LCM ; Video
Skill Practice:
(1) LCM Skill Sheet
Learning Activities:
(1) LCM Dice Activity; L, M or H
(2) "Rolling Multiples" LCM Dice Activity- varied rounds; L, M or H
Via:
(1) Find the LCM of two numbers; Video
(2) Find the LCM ; Video
Skill Practice:
(1) LCM Skill Sheet
Learning Activities:
(1) LCM Dice Activity; L, M or H
(2) "Rolling Multiples" LCM Dice Activity- varied rounds; L, M or H
Learning Target 3: I can recognize situations where the GCF or LCM is required.
Misconceptions:
(1) Confusing a GCF situation for a LCM situation and vice versa
Student Outcomes:
(1) Students will independently solve GCF and LCM word problems correctly.
(1) Confusing a GCF situation for a LCM situation and vice versa
Student Outcomes:
(1) Students will independently solve GCF and LCM word problems correctly.
Objective A: I can apply GCF to real life situations.
Via:
(1) Apply GCF to real life situations; Active Inspire
(2) Apply GCF to real life situations; Video
Skill Practice:
(1)
Learning Activities:
(1) Real Life Situation applying GCF Task L
(2) Real Life Situation applying GCF Task; L
Via:
(1) Apply GCF to real life situations; Active Inspire
(2) Apply GCF to real life situations; Video
Skill Practice:
(1)
Learning Activities:
(1) Real Life Situation applying GCF Task L
(2) Real Life Situation applying GCF Task; L
Objective B: I can apply LCM to real life situations.
Via:
(1) Apply LCM to real life situations; Video
(2) Applying LCM to Real life situations; Active Inspire
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Apply LCM to real life situations; Video
(2) Applying LCM to Real life situations; Active Inspire
Skill Practice:
(1)
Learning Activities:
(1)
Objective C: I can recognize when GCF or LCM is required.
Via:
(1) Recognize when GCF or LCM is required; Powerpoint slides
(2) Distinguishing between GCF & LCM word problems; Video
(3) Distinguishing between GCF & LCM word problems; Notes sheet
(4) Recognize when GCF or LCM is required in word problems; Active Inspire
Skill Practice:
(1)
Learning Activities:
(1) Recognize where GCF & LCM are Required Task; H
(2) Recognize where GCF & LCM are Required Task; M
(3) Recognize where GCF & LCM are Required Task; L
(4) Recognize where GCF & LCM are Required Task Cards
Via:
(1) Recognize when GCF or LCM is required; Powerpoint slides
(2) Distinguishing between GCF & LCM word problems; Video
(3) Distinguishing between GCF & LCM word problems; Notes sheet
(4) Recognize when GCF or LCM is required in word problems; Active Inspire
Skill Practice:
(1)
Learning Activities:
(1) Recognize where GCF & LCM are Required Task; H
(2) Recognize where GCF & LCM are Required Task; M
(3) Recognize where GCF & LCM are Required Task; L
(4) Recognize where GCF & LCM are Required Task Cards
Mastery Quiz 1
High, Medium, Low
Learning Target 4: I can generate equivalent numerical expressions according to the distributive property.
Misconceptions:
(1) Students mistakenly multiply the number outside the parentheses by only the first number inside the parentheses.
ex) 5(2 + 3) = 10 + 3 + 13; the correct answer is 5(2 + 3) = 10 + 15 = 25
(2) Students will factor an expression using a common factor, but not the GCF.
ex) 20 + 30 = 2(10 + 15) when they should factor 20 + 30 using 10 the GCF to result in 10(2 + 3)
Student Outcomes:
(1) Students will independently distribute a number outside the parentheses to both numbers inside the parentheses.
(2) Students will independently factor a pair of numbers to create an equivalent expression according to the distributive property.
(1) Students mistakenly multiply the number outside the parentheses by only the first number inside the parentheses.
ex) 5(2 + 3) = 10 + 3 + 13; the correct answer is 5(2 + 3) = 10 + 15 = 25
(2) Students will factor an expression using a common factor, but not the GCF.
ex) 20 + 30 = 2(10 + 15) when they should factor 20 + 30 using 10 the GCF to result in 10(2 + 3)
Student Outcomes:
(1) Students will independently distribute a number outside the parentheses to both numbers inside the parentheses.
(2) Students will independently factor a pair of numbers to create an equivalent expression according to the distributive property.
Objective A: I can evaluate numerical expressions using the order of operations.
Via:
(1) Evaluate numerical expressions using the order of operations; Video
(2) Order of operations; Activinspire
(3) Evaluate numerical expressions using the order of operations; Active Inspire
(4) Evaluate numerical expressions using the order of operations; Video
Skill Practice:
(1)
Learning Activities:
(1) Order of Operations BINGO; L, M or H
(2) Order of Operations Footloose Game
(3) Order of Operations Maze
Via:
(1) Evaluate numerical expressions using the order of operations; Video
(2) Order of operations; Activinspire
(3) Evaluate numerical expressions using the order of operations; Active Inspire
(4) Evaluate numerical expressions using the order of operations; Video
Skill Practice:
(1)
Learning Activities:
(1) Order of Operations BINGO; L, M or H
(2) Order of Operations Footloose Game
(3) Order of Operations Maze
Objective B: I can simplify expressions using the distributive property.
Via:
(1) Distributive property over addition; video
(2) Distributive property; video
(3) Distributive property over subtraction; video
(4) Distributive property; Powerpoint slides
(5) Distributive Property and GCF; video
Skill Practice:
(1) Simplify expressions using the distributive property skill
Learning Activities:
(1) Distributive Property Problem Set M
Via:
(1) Distributive property over addition; video
(2) Distributive property; video
(3) Distributive property over subtraction; video
(4) Distributive property; Powerpoint slides
(5) Distributive Property and GCF; video
Skill Practice:
(1) Simplify expressions using the distributive property skill
Learning Activities:
(1) Distributive Property Problem Set M
Objective C: I can factor whole number expressions.
Via:
(1) Factor an expression; Video
(2) Factor an expression; Video
(3)
Skill Practice:
(1) Factor using the distributive property skill
Learning Activities:
(1)
Via:
(1) Factor an expression; Video
(2) Factor an expression; Video
(3)
Skill Practice:
(1) Factor using the distributive property skill
Learning Activities:
(1)
Learning Target 5: I can compare and order integers.
Misconceptions:
(1) Students fail to recognize that moving to the left of zero means the numbers are getting smaller, which is opposite of positive numbers.
ex) -7 > -5 when in reality -7 < -5
Student Outcomes:
(1) Students will be able to order integers correctly.
(1) Students fail to recognize that moving to the left of zero means the numbers are getting smaller, which is opposite of positive numbers.
ex) -7 > -5 when in reality -7 < -5
Student Outcomes:
(1) Students will be able to order integers correctly.
Objective A: I can identify an integer.
Via:
(1) What's an integer; Video
(2) Integers; Activinspire
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) What's an integer; Video
(2) Integers; Activinspire
Skill Practice:
(1)
Learning Activities:
(1)
Objective B: I can determine the absolute value of an integer.
Via:
(1) Determine the absolute value of an integer; Video
(2) Find the Absolute Value of an integer; Notes sheet with examples
(3) Absolute Value; Activinspire
(4) Determine the absolute value of an integer; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Determine the absolute value of an integer; Video
(2) Find the Absolute Value of an integer; Notes sheet with examples
(3) Absolute Value; Activinspire
(4) Determine the absolute value of an integer; Video
Skill Practice:
(1)
Learning Activities:
(1)
Objective C: I can compare two integers using <, > or =.
Via:
(1) Compare and order integers; Video
(2) Compare Integers using a Number Line: PowerPoint Slides
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Compare and order integers; Video
(2) Compare Integers using a Number Line: PowerPoint Slides
Skill Practice:
(1)
Learning Activities:
(1)
Objective D: I can order a set of integers.
Via:
(1) Ordering Integers on a Number Line; notes sheet with examples
(2) Ordering Integers on a Number line; video
(3) Ordering Integers; Powerpoint Slides
(4) Ordering Integers on a Number line; Active Inspire
(5) Ordering Integers on a Number Line; note sheet with examples
Skill Practice:
(1)
Learning Activities:
(1) Ordering Integers on a Number Line; H
(2) Ordering Integers on a Number Line; L
Via:
(1) Ordering Integers on a Number Line; notes sheet with examples
(2) Ordering Integers on a Number line; video
(3) Ordering Integers; Powerpoint Slides
(4) Ordering Integers on a Number line; Active Inspire
(5) Ordering Integers on a Number Line; note sheet with examples
Skill Practice:
(1)
Learning Activities:
(1) Ordering Integers on a Number Line; H
(2) Ordering Integers on a Number Line; L
Objective E: I can apply integers to real world situations.
Via:
(1) Table with Key Words for Positive & Negative Numbers; Handout
(2) Apply integers to real world situations; Video
(3) Apply integers to real world situations; Powerpoint Slides
(4) Applying integers to real world situations; Video
Skill Practice:
(1) Relating Integers to Real World Situations; Exit Ticket
Learning Activities:
(1) Relating Integers to Real World Situations; Problem Set - M
(2) Integer Task Question; Banking
Via:
(1) Table with Key Words for Positive & Negative Numbers; Handout
(2) Apply integers to real world situations; Video
(3) Apply integers to real world situations; Powerpoint Slides
(4) Applying integers to real world situations; Video
Skill Practice:
(1) Relating Integers to Real World Situations; Exit Ticket
Learning Activities:
(1) Relating Integers to Real World Situations; Problem Set - M
(2) Integer Task Question; Banking
Learning Target 6: I can compare and order decimals.
Misconceptions:
(1) Failing to recognize that moving to the left of zero means the numbers are getting smaller, which is opposite of positive numbers
ex) -5.2 < -5.3; when in reality -5.2>-5.3
Student Outcomes:
(1) Students will correctly order decimals independently.
(1) Failing to recognize that moving to the left of zero means the numbers are getting smaller, which is opposite of positive numbers
ex) -5.2 < -5.3; when in reality -5.2>-5.3
Student Outcomes:
(1) Students will correctly order decimals independently.
Objective A: I can identify place values.
Via:
(1) Identify decimal place values; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Identify decimal place values; Video
Skill Practice:
(1)
Learning Activities:
(1)
Objective B: I can compare two decimals using <, > =.
Via:
(1) Comparing and ordering decimals; Video
(2) Comparing and ordering decimals; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Comparing and ordering decimals; Video
(2) Comparing and ordering decimals; Video
Skill Practice:
(1)
Learning Activities:
(1)
Objective C: I can order a set of decimals.
Via:
(1) Ordering a set of decimals; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Ordering a set of decimals; Video
Skill Practice:
(1)
Learning Activities:
(1)
Objective D: I can apply decimals to a real world situation.
Via:
(1)Adding and Subtracting Decimals Real-Life; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1)Adding and Subtracting Decimals Real-Life; Video
Skill Practice:
(1)
Learning Activities:
(1)
Mastery Quiz 2
High, Medium, Low
Learning Target 7: I can compare and order fractions.
Misconceptions:
(1) Students fail to find a common denominator in order to compare fraction.
ex) 5/6 < 5/8 because 6 is smaller than 8, meanwhile 5/6 > 5/8 because 5/6 = 20/24 and 5/8 = 15/24
(2) Students fail to recognize that moving to the left of zero means the numbers are getting smaller, which is opposite of positive numbers
ex) -3/4 > -1/4, meanwhile -3/4 < -1/4
Student Outcomes:
(1) Students will correctly order fractions
(1) Students fail to find a common denominator in order to compare fraction.
ex) 5/6 < 5/8 because 6 is smaller than 8, meanwhile 5/6 > 5/8 because 5/6 = 20/24 and 5/8 = 15/24
(2) Students fail to recognize that moving to the left of zero means the numbers are getting smaller, which is opposite of positive numbers
ex) -3/4 > -1/4, meanwhile -3/4 < -1/4
Student Outcomes:
(1) Students will correctly order fractions
Objective A: I can identify the parts of a fraction.
Via:
(1) Identifying the parts of a fraction; Video
(2) Fractions; Activinspire
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Identifying the parts of a fraction; Video
(2) Fractions; Activinspire
Skill Practice:
(1)
Learning Activities:
(1)
Objective B: I can create equivalent fractions.
Via:
(1) Create an equivalent fraction; Video
Skill Practice:
(1) Finding the missing number to create an equivalent fraction; skilled based sheet
Learning Activities:
(1)
Via:
(1) Create an equivalent fraction; Video
Skill Practice:
(1) Finding the missing number to create an equivalent fraction; skilled based sheet
Learning Activities:
(1)
Objective C: I can find the least common denominator of two or more fractions.
Via:
(1) Finding the least common denominator of two or more fractions; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Finding the least common denominator of two or more fractions; Video
Skill Practice:
(1)
Learning Activities:
(1)
Objective D: I can compare two fractions using <, > or =.
Via:
(1) Compare two fractions using <,> or =; Video
(2) Comparing and ordering fractions; Video
(3) Comparing fractions; Powerpoint Slides
(4) Comparing Positive & Negative Fractions: ActivInspire Slides
Skill Practice:
(1) Comparing Positive & Negative Fractions: Notes Sheet & Practice: M - matches "via #4"
Learning Activities:
(1) Comparing and Ordering Fractions; Task Cards
Via:
(1) Compare two fractions using <,> or =; Video
(2) Comparing and ordering fractions; Video
(3) Comparing fractions; Powerpoint Slides
(4) Comparing Positive & Negative Fractions: ActivInspire Slides
Skill Practice:
(1) Comparing Positive & Negative Fractions: Notes Sheet & Practice: M - matches "via #4"
Learning Activities:
(1) Comparing and Ordering Fractions; Task Cards
Objective E: I can order a set of fractions.
Via:
(1) Ordering fractions; Video
Skill Practice:
(1)
Learning Activities:
(1) Fraction Card Games
Via:
(1) Ordering fractions; Video
Skill Practice:
(1)
Learning Activities:
(1) Fraction Card Games
Objective F: I can apply fractions to real world situations.
Via:
(1) Applying fractions to real world situations; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Applying fractions to real world situations; Video
Skill Practice:
(1)
Learning Activities:
(1)
Learning Target 8: I can convert between fractions and decimals.
Misconceptions:
(1) Students incorrectly setting up a division equation to convert a a fraction to a decimal; putting the numerator as the divisor instead of the dividend. Students want to put the bigger number as the dividend.
ex) 1/4 = 4 because 4 divided by 1 = 4, instead of 1/4 = 0.25 because 1 divided by 4 = 0.25
(2) Students fail to reduce a fraction
Student Outcomes:
(1) Students will be able to solve problems involving decimals and fractions by converting fractions to decimals or decimals to fractions.
(1) Students incorrectly setting up a division equation to convert a a fraction to a decimal; putting the numerator as the divisor instead of the dividend. Students want to put the bigger number as the dividend.
ex) 1/4 = 4 because 4 divided by 1 = 4, instead of 1/4 = 0.25 because 1 divided by 4 = 0.25
(2) Students fail to reduce a fraction
Student Outcomes:
(1) Students will be able to solve problems involving decimals and fractions by converting fractions to decimals or decimals to fractions.
Objective A: I can use long division to convert a fraction to a decimal.
Via:
(1) Convert a fraction to a decimal; Video
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Convert a fraction to a decimal; Video
Skill Practice:
(1)
Learning Activities:
(1)
Objective B: I can use place value to convert a decimal to a fraction in simplest form.
Via:
(1) Convert Decimal to Fraction; Powerpoint Slides
(2) Convert Fraction to Decimal; Video
(3) Converting Fractions & Decimals; Notes Sheet
Skill Practice:
(1)
Learning Activities:
(1)
Via:
(1) Convert Decimal to Fraction; Powerpoint Slides
(2) Convert Fraction to Decimal; Video
(3) Converting Fractions & Decimals; Notes Sheet
Skill Practice:
(1)
Learning Activities:
(1)
Objective C: I can solve real world problems involving fractions and decimals.
Via:
(1) Solve real world problems using addition, subtraction, multiplication and division; Video
Skill Practice:
(1)
Learning Activities:
(1) Stock Exchange Task Question; M
Via:
(1) Solve real world problems using addition, subtraction, multiplication and division; Video
Skill Practice:
(1)
Learning Activities:
(1) Stock Exchange Task Question; M
