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| In this unit, students deepen their understanding of fractions and develop strategies for adding and subtracting fractions and mixed numbers with unlike denominators. They also connect fraction-of thinking to multiplication and generalize a fraction multiplication algorithm.The following big ideas will be covered in this unit: - An equivalent fraction can be made by multiplying the numerator and denominator of a fraction by a fraction equivalent to 1 to get an equivalent fraction. - Previous understandings of multiplication can be applied to multiply a fraction by a fraction. - Multiplication is an operation by which one factor scales the second up or down. - If the first factor is greater than 1, then the product is greater than the second factor. - If the first factor is less than 1, then the product is less than the second factor. - If the first factor is equal to 1, then the number remains unchanged. - There are two meanings for division of fractions: partition and measurement. |
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| Number & Operations—Fractions 5.NF.A. Use equivalent fractions as a strategy to add and subtract fractions. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. 5.NF.B. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 5.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) 5.NF.B.4b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5.NF.B.5. Interpret multiplication as scaling (resizing), by: 5.NF.B.5a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5.NF.B.5b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. 5.NF.B.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. | Students will have opportunities to: - Make mathematical conjectures and arguments. (MP. 3)
- Make sense of others’ mathematical thinking. (MP. 3)
- Model real -world situations using graphs, drawings, tables, symbols, numbers, diagrams, and other representations. (MP. 4)
- Use mathematical models to solve real world problems and answer questions. (MP. 4)
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| - The meanings of the operations on fractions are the same as the meanings for the operations on whole numbers. - A mental image or awareness of the size of a fraction helps assess for reasonableness of the answer. - A fraction is another representation for division. - Fractions may represent division with a quotient less than one. - Equivalent fractions can be used to add and subtract fractions with unlike denominators. - Previous understandings of multiplication can be applied to multiply a fraction with a whole number. | - Fractional side lengths can be multiplied to find the area of a rectangle. - Previous understandings of multiplication can be applied to multiply a fraction by a fraction. (mixed numbers) - A line plot displays a data set of measurements in fractions of a unit (1/2, ¼, 1/8). |
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| algorithm, factor pair, product, area model, horizontal, common denominator, dimensions, multiple, quotient, dividend, divisor, represent, unit fraction, equivalent fraction, multiplicative identity property, vertical, factor, unknown, dividend, quotient, numerator, denominator, estimate, reasonableness, renaming, converting, Commutative Property Bold Font: Listed in teacher's EDM4 edition
Normal Font: not listed in teacher’s edition as a vocabulary word but will be helpful for students in explanations |
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| The following lesson plan sequence is obtained from Everyday Mathematics 4. Each lesson is aligned with a learning objective to inform the teachers on what students should be able to at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day. |
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| The following language supports are for English Language Learners but could also be used to support any struggling learner in mathematics. The strategies are obtained from the SIOP model. The language objectives will support students' academic language development. The sentence stems and starters provides the support many students need to be able to participate in discussions and writing about mathematics. |
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