Unit 1: The Number System
In this unit students will explore the number system. Initially, they will learn that factors break a number down evenly. They will explore and develop their understanding of the fact that certain numbers have many factors (composite numbers), while others only have 2 factors (prime numbers). Students will identify the greatest common factor of 2 or more whole numbers. Students will learn that multiples are the products that result from multiplying a given number or numbers by other whole numbers. Students will determine the least common multiple of 2 or more whole numbers. Students will apply their knowledge of factors and multiples to solve real world problems. Students will utilize the distributive property to create equivalent numerical expressions. Students will build on their current understanding of number lines to include the ordering of integers and rational numbers. Students will understand how to compare rational numbers, as well as how to relate rational numbers to real life situations.
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Learning Target |
NYS Standard |
Engage NY |
Textbook Resources |
1: I can determine the GCF of two or more whole numbers. |
6.NS.2 6.NS.4 |
CMP3 Prime Time Go Math 2.1 |
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2: I can determine the LCM of two or more whole numbers. |
6.NS.4 |
CMP3 Prime Time Go Math 2.2 |
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3: I can recognize situations where GCF or LCM is required. |
6.NS.4 MP.1 |
CMP3 Prime Time Go Math Module 2 |
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4: I can generate equivalent numerical expressions according to the distributive property. |
6.NS.4 |
CMP3 Prime Time Go Math 10.3 |
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5: I can compare and order integers. |
6.NS.5 6.NS.6 6.NS.7 |
Go Math Module 1 |
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6: I can compare and order decimals. |
6.NS.6 |
Go Math 3.3 |
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7: I can compare and order fractions. |
6.NS.6 |
Go Math 3.3 |
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8: I can convert between fractions and decimals |
Value |
Go Math 3.3 |
Learning Target 1: I can determine the GCF of 2 or more whole numbers.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.1.A: I can identify factor pairs of a whole number. |
(1) Students may make division errors therefore determining an incorrect factor. |
(1) Finding Factor Pairs using a t-chart; Video (2) Finding Factors of a whole number; Video (3) Factor Rainbows; Skill Practice sheet |
(1) Fact Fluency; Powerpoint Jeopardy Game (2) Factor Pair Game; Word doc (3)(SPED) bllblogs.typepad.com/files/factorracegamepdf.pdf |
1.1.B: I can distinguish between prime and composite numbers. |
(1) Students may not recognize that 2 as a prime number because it is even. However, 2 is prime since it's only factors are 1 and itself. (2) Students may assume that all odd numbers are prime numbers, but many odd numbers are composite. EX: 9 is odd and has factors 1, 3, and 9. |
(1) Recognizing Prime v. Composite Numbers; Video (2) Prime v. Composite Notes; Word Doc/ PDF (2) Identifying Prime & Composite; Skill Practice Sheet (3) Prime v. Composite; Entrance or Exit Ticket |
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1.1.C: I can find the prime factorization of a whole number in exponential form. |
(1) Students may fail to break down the number to solely prime factors. (2) Students may use exponents incorrectly. |
(1) Finding the Prime Factorization of a number; Notes sheet w/ examples |
(1(SPED) primefactorizationmaze.pdf(1) |
1.1 I can determine the GCF of 2 or more whole numbers. |
(1) Students may fail to identify a factor that evenly divides all of the numbers identified, therefore only selecting a number that divides one of the numbers given. (2) Students may fail to identify the largest factor that two or more numbers share and, instead, only identify a common factor. Students must understand that a common factor evenly goes into all of the numbers listed. |
(1) Finding the GCF of 2 or more numbers; Notes sheet with examples using 3 different strategies (2) Finding the GCF of 2 or more numbers; Notes sheet (3) Finding the GCF using Birthday Cake Method; Video (4) Finding the GCF using the Rainbow method; Video (5) Finding the GCF using Rainbow method; Practice problems (6) Finding the GCF using t-charts; Practice problems (7) Finding the GCF by listing factors; Practice problems (8) Identify the GCF; Entrance or Exit Ticket |
Learning Target 2: I can determine the LCM of 2 or more whole numbers.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.2.A: I can list the multiples of a whole number. |
(1) Students may make multiplication errors therefore determining an incorrect multiple. |
(1) Relating Factors & Multiples; Learn Zillion Video |
(1)SPED freemultiplesbingo.pdf |
1.2: I can determine the LCM of 2 or more whole numbers. |
(1) Students may find a multiple that only works for one number and not the other(s). (2) Students may assume that multiplying the two given numbers together will always result in the LCM. EX: LCM of 6 and 8 is 24, but 6 x 8 = 48. 48 is a common multiple but not the least common multiple. |
(1) Find the LCM of two numbers; Learn Zillion Video (2) Finding the LCM of two numbers; Notes sheet with examples (3) LCM Skill; Practice Problems (4) Looking for LCM Flipchart; matches Learning Activity #3 |
(1) Rolling Multiples; Dice Activity (2)SPED factorsandmultiplespuzzlesfreebie__1_.pdf (3) Looking for LCM Connect 4 Game; Word Doc/ PDF |
Learning Target 3: I can recognize situations where the GCF or LCM is required.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.3.A: I can apply GCF to real life situations. |
(1) Students may make errors based on reading comprehension. |
(1) GCF Problem Set Flipchart; matches Learning Activity #2 |
(1) Bewildering Brownies; Problem Set (2) GCF Problem Set with pictures to represent problems; Word Doc/ PDF |
1.3.B: I can apply LCM to real life situations. |
(1) Students may make errors based on reading comprehension |
(1) LCM Problem Set with pictures Flipchart; matches Learning Activity #1 |
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1.3: I can recognize when GCF or LCM is required. |
(1) Students will incorrectly identify whether GCF (the breaking down of a set of numbers) vs. LCM (a situation that requiring the repetition of numbers) is required in a real life situation. |
(1) Identifying Problems as GCF or LCM; Powerpoint Slides (2) Identifying GCF & LCM Word Problems; Khan Academy Video (3) GCF & LCM Word problems; Notes Sheet |
Unit 1 Mastery Quiz 1: see assessment tabs
Learning Target 4: I can generate equivalent numerical expressions according to the distributive property.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.4.A: I can evaluate numerical expressions using the order of operations. |
(1) Students believe that you must add before you subtract and multiply before you divided because of the acronym "PEMDAS" |
(1) Evaluate Expressions Using Order of Operations; Rap Video |
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1.4.B: I can simplify expressions using the distributive property. |
(1) Students may only multiply the factor outside the parentheses by the first addend inside parentheses, neglecting the second addend inside parentheses. |
(1) Distributive Property; Virtual Nerd Video (2) Distributive Property over Addition; Khan Academy Video (3) Distributive Property over Subtraction; Khan Academy Video (4) Simplifying Expressions Using the Distributive Property; Practice Problems |
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1.4.C: I can factor whole number expressions. |
(1) Students may factor an expression using a common factor, but not the GCF. (2) Students may correctly factor the GCF outside parentheses, but write original numbers inside parentheses instead of matching number to complete factor pair, making expressions not equivalent. |
(1) Factoring Numerical Expressions Using the GCF; Learn Zillion Video (2) Factor Whole Number Expressions; Practice Problems |
Value |
1.4: I can generate equivalent expressions according to the distributive property. |
Students may fail to understand that expressions are equivalent because they will yield the same value when simplified. |
(1) Using the Distributive Property; AvtivInspire Slides (2) Creating Equivalent Expressions Using Distributive Property; Relating expressions to area of a rectangle |
(1) Distributive Property; Real World Application Problem |
Learning Target 5: I can compare and order integers.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.5.A: I can identify an integer. |
Students must recognize positive and negative whole numbers and zero as integers. |
(1) What's an integer?: Virtual Nerd Video |
(1) |
1.5.B: I can determine the absolute value of an integer. |
(1) Students may confuse a number's absolute value with a number's opposite. Students must recognize absolute value as a number's distance from zero, therefore this value is always given as a positive value since it does not involve direction from zero. |
(1) Find the Absolute Value; Learn Zillion Video (2) Absolute Value Notes; Definition with practice problems |
(1) Opposite v. Absolute Value Number Line Activity; Word doc/ PDF |
1.5.C: I can compare two integers using <, > or =. |
(1) Students may assume the number with the larger absolute value automatically is the larger number. EX: |-9| >|-2|, but -9 < -2 |
(1) Comparing Integers; Practice Problems |
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1.5.D: I can order a set of integers. |
(1) Students may fail to recognize that as a number is placed further to the left of zero on a number line, the value of the number is getting smaller |
(1) Compare & Order Integers; Learn Zillion Video (2) Ordering Integers on a Number Line; Notes sheet with examples (3) Ordering Integers on a number line; Notes sheet (4) Ordering Integers on a Number line; Notes sheet with exit ticket |
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1.5.E: I can apply integers to real world situations. |
(1) Students may make errors based on reading comprehension and/or positive/negative vocabulary terms. |
(1) Key Words; Notes sheet (2) Representing Real World Situations w/ Integers; Virtual nerd video (3) Relating Integers to Real World Situation; Exit Ticket |
(1) Rolling Integers; Dice Activity (2) Creating Real World Problems from a Number Sentence; Application Activity |
1.5: I can compare and order integers |
(1) Students may fail to recognize that as a number is placed further to the left of zero on a number line, the value of the number is getting smaller |
(1) Comparing & Ordering Integers; Problem Set |
Learning Target 6: I can compare and order decimals.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.6.A: I can identify place values. |
(1) Students may not recognize embedded zeros as affecting place value and placeholder zeros as not affecting place value of other digits |
(1) |
(1) |
1.6.B: I can compare two decimals using <, > =. |
(1) Students may assume that a number with more digits automatically indicates that number has a larger value. EX: 7.021 has more digits than 7.1, but since both numbers have a 7 in the ones place, students must look to the next place value to the right, the tenths place. Since 7.021 has a 0 in the tenths place and 7.1 has a 1 in the tenths place, 7.1 has a larger value even though it has less digits. |
(1) Comparing Decimals Using Place Value; Learn Zillion Video |
(1) SPED comparingdecimalswarcardgame.pdf |
1.6.C: I can order a set of decimals. |
(1) Students may assume that a number with more digits automatically indicates that number has a larger value. EX: 7.021 has more digits than 7.1, but since both numbers have a 7 in the ones place, students must look to the next place value to the right, the tenths place. Since 7.021 has a 0 in the tenths place and 7.1 has a 1 in the tenths place, 7.1 has a larger value even though it has less digits. |
(1) Ordering Decimals; Khan Academy Video |
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1.6.D: I can apply decimals to a real world situation. |
(1) Students may make errors based on reading comprehension |
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1.6: I can compare and order decimals. |
Value |
Unit 1 Mastery Quiz 2: see assessment tab
Learning Target 7: I can compare and order fractions.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.7.A: I can identify the parts of a fraction. |
Students must recognize the numerator represents the part, going on top of fraction bar and the denominator represents the whole, going on bottom of fraction bar. |
(1) Writing a Fraction; Learn Zillion Video |
(1) |
1.7.B: I can create equivalent fractions. |
(1) Students may neglect to multiply/divide both the numerator and denominator by the same number in order to form fraction with equivalent value. Students must recognize equivalent fractions as fractions that are written in the same simplest form. Equivalent fractions can be determined by multiplying or dividing the fraction by a form of 1 whole. |
(1) Creating Equivalent Fractions; Practice problems |
Value |
1.7.C: I can find the least common denominator of two or more fractions. |
Value |
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1.7.D: I can compare two fractions using <, > or =. |
(1) Students may fail to find a common denominator and convert fractions to equivalent fractions using common denominator before comparing values. Students must recognize that you cannot compare sizes of two fractions unless these fractions have a common denominator (whole) to then compare value of numerators (part). |
(1) Comparing Fractions; Guided notes with examples (2) Comparing + and - fractions using <, > or =; Practice problems with visuals |
(1) Comparing Fraction; Card Game |
1.7.E: I can order a set of fractions. |
(1) Students may fail to find a common denominator and convert fractions to equivalent fractions using common denominator before comparing values. Students must recognize that you cannot compare sizes of two fractions unless these fractions have a common denominator (whole) to then compare value of numerators (part). |
(1) Ordering Fractions; Dice Activity |
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1.7.F: I can apply fractions to real world situations. |
(1) Students may make errors based on reading comprehension |
(1) Comparing Fractions in Real World Situations; Learn Zillion Video |
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1.7: I can compare and order fractions. |
Value |
Learning Target 8: I can convert between fractions and decimals.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
1.8.A: I can use long division to convert a fraction to a decimal. |
(1) Students may not properly set up long division Students must recognize numerator as dividend (inside long division) and denominator as divisor (outside long division) (2) Students may neglect to place decimal point and zeros as placeholders to continue dividing if there is a remainder |
(1) Converting Fractions to Decimals; Video |
(1) |
1.8.B: I can use place values to convert a decimal to a fraction in simplest form. |
(1) Students may not correctly identify place value, therefore converting to fraction with incorrect denominator |
(1) Converting Decimals to Fractions; Powerpoint Slides (2) Converting Decimals to Fractions; Video (3) Converting Decimals to Fractions; notes sheet with place value chart |
(1) |
1.8.C: I can solve real world problems involving fractions and decimals. |
(1) Students may make errors based on reading comprehension (2) Students may attempt to solve real world problems without converting fractions and decimals to same form. |
(1) |
(1) |
1.8: I can convert between fractions and decimals. |
Students must recognize both fractions and decimals can be used to represent part of a whole |
(1) |
(1) |