Unit 3: Fraction Operations
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In this unit students will be exploring all four operations with fractions, and mixed numbers. Students should have already worked on these skills in 5th grade; specifically, addition, subtraction and multiplication. Students will need to understand and apply the correct steps for completing each operation. A common denominator is required when adding or subtracting fractions, therefore students need to apply their knowledge of multiples from Unit 1. For all operations, it is important the answer is in simplest form. This will require students to utilize their knowledge of common factors for Unit 1. Throughout the unit, students will be applying their understanding of the operations with fractions to solve real world word problems.
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Unit 3 Portfolio Cover Sheet
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Learning Target |
NYS Standard |
Engage NY |
Textbook Resources |
1: I can add and subtract fractions. |
5.NF.1 |
CMP3: Let's Be Rational |
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2: I can add and subtract mixed numbers. |
5.NF.1 |
CMP3: Let's Be Rational |
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3: I can multiply fractions and mixed numbers. |
5.NF.4 |
CMP3: Let's Be Rational Go Math 4.1 |
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4: I can divide a fraction by a fraction. |
6.NS.1 |
CMP3: Let's Be Rational Go Math 4.2 |
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5: I can divide a mixed or whole number by a fraction. |
6.NS.1 |
CMP3: Let's Be Rational Go Math 4.3 |
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6: I can divide a fraction by a mixed or whole number. |
6.NS.1 |
CMP3: Let's Be Rational Go Math 4.3 |
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7: I can solve real world problems involving fractions. |
5.NF.2 5.NF.3 6.NS.1 MP.1 MP.4 |
CMP3: Let's Be Rational Go Math 4.4 |
Learning Target 1: I can add and subtract fractions.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
3.1.A: I can use common multiples of whole numbers in order to create equivalent fractions. |
(1) |
(1) Listing Multiples to Create an Equivalent Fraction; Active Inspire Slides (2) Listing Multiples to Create Equivalent Fractions; Practice Sheet (3) Creating an Equivalent Fraction using Multiplication; Practice Sheet (4) Common multiples of whole numbers; Practice Sheet |
(1) |
3.1.B: I can determine a least common denominator of two or more fractions. |
(1)Students may find a common multiple but not the least common multiple. This error leads to more frequent errors when the student reduces the fraction. |
(1) (1) Determine a least common denominator of two or more fractions; video (2) Finding a common denominator; Notes sheet (3) Least common denominator of two or more fractions; Notes Sheet |
(1) |
3.1.C: I can identify common factors of whole numbers. |
(1) |
(1) Common factors of whole numbers; Notes Sheet |
(1) |
3.1.D: I can simplify fractions using the greatest common factor. |
(1)Students may find a common factor but not the greatest common factor. This leads to errors when reducing fractions. Although the fraction may be reduced it would not be in simplest form. |
(1) Simplifying Fractions; Activinspire (2) Simplifying Fractions using GCF; Powerpoint Slides (3) Simplifying Fractions; Notes sheet (4) Simplify fractions using the greatest common factor; Notes Sheet |
(1) |
3.1.E: I can add two or more fractions with unlike denominators following the standard algorithm. |
(1)Students add straight across or fail to list the multiples of the numerator as well Students have to list the multiples of the numerators and denominators and then add the two fractions that have the common denominator |
(1) Adding Fractions with two or more fractions with unlike denominators; Slides (2) Adding and Subtracting Fractions with unlike denominators; Activinspire (3) Adding Fractions with two or more fractions with unlike denominators; Powerpoint Slides (4) Adding Fractions with unlike denominators by creating an area model; Video (5) Adding Fractions with unlike denominators; Video (6) Adding Fractions with unlike denominators using fraction bars; Video (7) Add two or more fractions; Notes Sheet |
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3.1.F: I can subtract two or more fractions with unlike denominators following the standard algorithm. |
(1)Students subtract straight across or fail to list the multiples of the numerator as well Students have to list the multiples of the numerators and denominators and then subtract the two fractions that have the common denominator |
(1) Adding & Subtracting Fractions with Unlike Denominators; Notes sheet (2) Subtracting Fractions with unlike denominators; Powerpoint Slides (3) Subtracting Fractions with unlike denominators; Video (4) Adding & Subtracting Fractions with Unlike Denominators; Practice Sheet (5) Subtracting Fractions with Unlike Denominators; Practice Sheet |
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3.1: I can add and subtract fractions. |
(1) Adding & Subtracting Fractions with Unlike Denominators; 5 skill, 2 word problems (2) Adding & Subtracting Fractions with Unlike Denominators; HW assignment with steps (3) Identify the operation; Practice Sheet |
Learning Target 2: I can add and subtract mixed numbers.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
3.2.A: I can convert between mixed numbers and improper fractions. |
(1)Students mess up the steps Multiply the denominator by the whole number and then add that product to the numerator. Denominator stays the same |
(1) Convert between mixed numbers and improper fractions; Powerpoint Slides (2) Convert an improper fraction into a mixed number; Video (3) Convert a mixed number into an improper fraction; Video (4) Converting mixed numbers and improper fractions; Notes sheet (5) Convert between mixed numbers and improper fractions; Practice Sheet |
(1) |
3.2.B: I can add two or more mixed numbers following the standard algorithm. |
(1) Students may mess up the steps to convert the mixed numbers into improper fractions or just add across Students need to memorize the steps for converting a mixed number to an improper fraction. Students can also find the LCD by listing the multiples of the numerators and denominators and then adding. |
Value |
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3.2.C: I can subtract two or more mixed numbers following the standard algorithm. |
(1)Students may fail to convert the mixed numbers into improper fractions. Failing to do this would lead to an incorrect difference if the fraction part of the mixed number of the subtrahend is greater than the fraction part of the mixed number of the minuend. |
(1) Subtracting Mixed Number Introduction; Video (2) Adding & Subtracting Mixed Numbers; Notes sheet (3) Subtracting Mixed Numbers (with regrouping); ActivInspire Slides (4) Adding & Subtracting Mixed Numbers; Practice Sheet |
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3.2.D: I can explain why the sum or difference is correct. |
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3.2: I can add and subtract mixed numbers. |
Learning Target 3: I can multiply fractions and mixed numbers.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
3.3.A: I can multiply two more fractions following the standard algorithm. |
(1)Students forget to simplify or use a common factor to simplify and not the GCF Products must be in simplest form by finding the GCF of the numerator and denominator |
(1) Multiplying a Fraction by a Fraction; Notes sheet (2) Multiplying Fractions; PowerPoint Slides (3) Multiply Fractions; Video (4) Multiply Fractions; Practice Sheet |
(1) |
3.3.B: I can multiply two or more mixed numbers following the standard algorithm. |
(1)Students may fail to convert the mixed number to an improper fraction when multiplying mixed numbers. Instead they may multiply the whole numbers, then multiply the fractions, and add the products. Students need to recognize that mixed numbers are values between whole numbers greater than 1. When multiplied the product is a greater value. When students break up the mixed number and multiply the fractions separately the product is a lesser value because they are multiplying numbers that are less than 1. For example : Correct: 12 ¼ x 10 ½ -> 49/4 x 21/2 = 128 ⅝ Incorrect: 12 x 10 = 120, ¼ x ½ = ⅛, 120 + ⅛ = 120 ⅛ |
(1) Multiplying Mixed Numbers; Powerpoint Slides (2) Multiplying 2 or more mixed numbers; Video (3) Multiplying fractions & Mixed numbers; Notes sheet (4) Multiplying Fractions; Practice Sheet (5) Multiply 2 or more mixed numbers; Practice Sheet |
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3.3.C: I can explain why multiplying a fraction by a fraction or by a whole number results in a smaller answer. |
(1) |
(1) |
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3.3: I can multiply fractions and mixed numbers. |
Unit 3 Mastery Quiz 1: see assessment tabs
Learning Target 4: I can divide a fraction by a fraction.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
3.4.A: I can divide a fraction by a fraction following the standard algorithm. |
(1)Students forget to flip the second fraction or flip the first fraction Keep the first fraction, change division to multiplication, and flip the second fraction |
(1) Divide a fraction by a fraction using models; video (2) Dividing a fraction by a fraction; slides (3) Divide a fraction by a fraction; Notes sheet with examples |
(1) |
3.4.B: I can explain the quotient when I divide a fraction by a fraction. |
(1) |
(1) Dividing a Whole/Mixed Number by a Fraction; Powerpoint slides- includes steps & conceptual understanding |
Value |
3.4: I can divide a fraction by a fraction. |
(1) |
Learning Target 5: I can divide a mixed or whole number by a fraction.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
3.5.A: I can divide a mixed or whole number by a fraction following the standard algorithm. |
(1)Failing to convert the mixed number to improper Students must convert a mixed number to an improper fraction before completing the steps to dividing |
(1) |
(1) |
3.5.B: I can explain the quotient when I divide a mixed or whole number by a fraction. |
(1) |
(1) |
Value |
3.5: I can divide a mixed or whole number by a fraction. |
(1) |
Unit 3 Mastery Quiz 2: see assessment tab
Learning Target 6: I can divide a fraction by a mixed or whole number.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
3.6.A: I can divide a fraction by a mixed or whole number following the standard algorithm. |
(1)Once the mixed number is converted to an improper fraction or the whole number is placed over 1, forgetting to flip it Keep the first fraction, change the division to multiplication, and flip the second fraction |
(1) Divide a fraction by a whole or mixed number; video (2) Divide a fraction by a whole or mixed number; Notes sheet with examples |
(1) |
3.6.B: I can explain the quotient when I divide a mixed or whole number by a fraction. |
(1) |
(1) |
Value |
3.6: I can divide a fraction by a mixed or whole number. |
(1) |
Learning Target 7: I can solve real world problems involving fractions.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
3.7.A: I can correctly identify and solve problems that involving adding or subtracting fractions. |
(1)Students choose the incorrect operation for the word problem Students must recognize the key words for all four operations and understand what the question is asking |
(1) SPED |
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3.7.B: I can correctly identify and solve problems that involving multiplying or dividing fractions. **including area of a rectangle |
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(1) |
Value |
3.7: I can solve real world problems involving fractions. |
(1) |
Value |
