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| In this unit, students apply their understanding of place value to multiply and divide decimals by powers of 10. They investigate how patterns in powers of 10 can be used to convert measurements in metric units, learn how line plots can be used to organize and analyze measurement data, and explore a method of finding volumes of figures that are not rectangular prisms. Students also extend whole number methods to multiply and divide decimals. The following big ideas will be covered in this unit: - A line plot displays a data set of measurements in fractions of a unit (1/2, ¼, 1/8). - The data from the line plot can be used to identify a typical measurement. - Rules for multiplication and division of whole numbers apply to decimals.
- The placement of the decimal is determined by multiplying or dividing a number by 10 or a multiple of 10.
- Multiplication and division of two numbers will produce the same digits, regardless of the positions of the decimal point. Multiplication with decimals can be performed as whole numbers with the decimal placed by way of estimation. |
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| Number & Operations in Base Ten 5.NBT.A. Understand the place value system. 5.NBT.A.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.A.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. 5.NBT.A.3. Read, write, and compare decimals to thousandths. 5.NBT.B. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.B.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 5.NBT.B.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 5.MD.B. Represent and interpret data. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. 5.MD.C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.C.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.C.5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 5.MD.C.5a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. 5.MD.C.5b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. | Students will have opportunities to: - Explain their mathematical thinking clearly and precisely (MP. 6)
- Use an appropriate level of precision for their problems (MP. 6)
- Use clear labels units and mathematical language (MP. 6)
- Think about accuracy and efficiency when they count, measure, and calculate (MP. 6)
- Look for mathematical structures such as categories, patterns and properties (MP. 7)
- Use structures to solve problems and answer questions (MP. 7)
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| - Addition and subtraction with decimals are based on the fundamental concept of adding and subtracting the numbers in like position values.
- The base-ten place value system extends infinitely in two directions: to tiny values as well as to large values, the 10 to 1 ratio remains the same. - 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. - The algorithm for multiplication is an efficient strategy when computing larger numbers. - The partial quotients and area model can be used to divide 4-digit numbers by 2-digit divisors. | - Multiplication and division can be used to convert and relate units. - Unit conversions can be interpreted as proportional relationships. |
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| base, calibrate, data point, data set, equivalent problem, exponent, exponential notation , line plot, metric system, power of ten, reaction time, scale , centimeter, millimeter, measure, metric unit, kilograms, grams , shift, convert, product, factor, quotient, dividend, divisor, decimal, tenths, hundredths, thousandths, estimate 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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