5 th Grade Unit 2: Multi-Digit Whole Number and Decimal Fraction Operations (7 Weeks) Stage 1 – Desired Results Established Goals Unit Description Students will have a chance to practice and hone their skills at multiplying and dividing (decimal) numbers by 1-digit whole numbers. They will be able to generalize the 1-digit algorithms to the multi-digit whole number versions. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices. Common Core Learning Standards 5.NBT.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.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.5: Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.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.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.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product Common Core Standards of Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ESL Language Standards Standard 1: Students will listen, speak, read, and write in English for information and understanding. 1.1. Identify and use reading and listening strategies to make text comprehensible and meaningful. 1.3 Select information appropriate to the purpose of the investigation, relate ideas from one written or spoken source to another, and exclude nonessential information. 1.5 Formulate, ask, and respond to various question forms to obtain, clarify, and extend information and meaning. 1.7 Present information clearly in a variety of oral and written forms for different audiences and purposes related to all academic content areas.
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Grade Unit 2: Multi-Digit Whole Number and Decimal Fraction Operations (7 Weeks) · 2013-12-01 · ... Multi-Digit Whole Number and Decimal Fraction ... decimal is multiplied or divided
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5th Grade Unit 2: Multi-Digit Whole Number and Decimal Fraction Operations (7 Weeks) Stage 1 – Desired Results
Established Goals Unit Description
Students will have a chance to practice and hone their skills at multiplying and dividing (decimal) numbers by 1-digit whole numbers. They will be able to generalize the 1-digit algorithms to the multi-digit whole number versions. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Common Core Learning Standards
5.NBT.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.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.5: Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.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.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.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product Common Core Standards of Mathematical Practice
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
ESL Language Standards
Standard 1: Students will listen, speak, read, and write in English for information and understanding. 1.1. Identify and use reading and listening strategies to make text comprehensible and meaningful. 1.3 Select information appropriate to the purpose of the investigation, relate ideas from one written or spoken source to another, and exclude nonessential information. 1.5 Formulate, ask, and respond to various question forms to obtain, clarify, and extend information and meaning. 1.7 Present information clearly in a variety of oral and written forms for different audiences and purposes related to all academic content areas.
1.9 Convey and organize information, using facts, details, illustrative examples, and a variety of patterns and structures. 1.16 Apply learning strategies to acquire information and make texts comprehensible and meaningful.
Big Ideas 1. Basic facts and algorithms for operations with rational
numbers use notions of equivalence to transform calculations into simpler ones.
2. The same number sentence can be associated with different concrete or real-world situations, AND different number sentences can be associated with the same concrete or real-world situation.
Essential Questions 1. Numbers can be named in equivalent ways using place
value
1. Decimal numbers can be named in an infinite number of
equivalent but different forms
2. The real world actions for addition and subtraction of
whole numbers are the same for operations with fractions
and decimals
2. Some real world problems involving joining groups,
separating equal groups, comparison or combinations can
be solved using multiplication, others can be solved with
division
2. Different real world interpretations can be associated
with multiplication and division calculations involving
decimals
Content (Students will know….) A. A digit in one place represents ten times as much
as it represents in the place to right and 1/10 of what it represents in the place to its left (5.NBT.1)
B. There is a pattern in the number of zeros when multiplying or dividing by powers of ten. This is directly related to the base ten system (5.NBT.2)
C. Standard algorithm for multiplying multi digit whole numbers (5.NBT.5)
D. Division of whole numbers with up to four digit dividends by two digit divisors (5.NBT.6)
Skills (Students will be able to…) A1. Determine the value of digits in a whole number and decimal number to the thousandths B1. Explain the patterns in the number of zeros when multiplying by powers of 10 B2. Explain the patterns in the decimal point when multiplying or dividing by powers of 10. B3. Use the understanding of the patterns above to efficiently multiply and divide by powers of 10. B4. Create equivalent expressions for multiples of 10 using exponents. For example: 36 x 10 = 36 x 101 = 360 36 x 10 x 10= 36 x 102 =3600 C1. Fluently (accurately, efficiently, and flexibly) multiply multi-digit whole numbers using the standard algorithm Note: should not exceed a two digit factor by three digit factor C2. Use alternative strategies such as partial products or an area model to build conceptual understanding of multiplication D1. Find whole number quotients of whole numbers by whole numbers D2. Use strategies to find quotients based on place value, properties of operations, and the relationship between multiplication and division. D3. Illustrate and explain division by using equations, arrays and/or area model
E. Operations with decimals to the hundredths
(5.NBT.7)
F. Numerical expressions (5.OA.1)
G. Numerical expressions (5.OA.2)
E1. Add, subtract, multiply (factors to hundredths) and divide decimals (quotients to thousandths) based on whole number operations E2. Use concrete models, drawings, and strategies based on place value, properties and/or the relationship between addition and subtraction E3. Relate the strategy chosen to a written method and explain the reasoning used F1. Evaluate numerical expressions, including powers of ten, with parentheses ( ), brackets [ ] and braces { } using the conventional order of operations:
1. Grouping symbols: parentheses, then brackets then braces
2. Addition or subtraction (left to right) 3. Multiplication or division (left to right)
G1. Write simple numerical expressions given a verbal expression G2. Interpret numerical expressions without evaluating them G3. Describe the relationship between expressions without evaluating them
Terms/ Vocabulary: place value, digit, decimal number, decimal point, tenths, hundredths, thousandths, power of ten, multiple, factor, product, divisor, dividend, quotient, algorithm, array, area model, decompose, compose, partition
Stage 2 – Assessment Evidence
Initial Task: Betty’s Bakery Final Performance Task: Thanksgiving Dinner
Other Evidence Teacher observation, conferencing, teacher designed assessment pieces, student work, exit slips, journal entries
Stage 3 – Learning Plan
Everyday Mathematics /Impact Mathematic Lessons – The following lessons may support some of the CCLS & essential questions outlined in this unit map:
Adding and subtracting decimal tasks from Georgia Department of Education (5.NBT.1, 5.NBT.7) https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit2FrameworkSE.pdf Multiplying and dividing decimal tasks from Georgia Department of Education (5.NBT.2, 5.NBT.7) https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit3FrameworkSE.pdf Operations with Whole Numbers from Georgia Department of Education 95.NBT.1, 5.NBT.2, 5.NBT.5, 5.NBT.6) https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit1FrameworkSE.pdf Additional Performance Task Assessment (5.NBT.5, 5.NBT.6) http://insidemathematics.org/common-core-math-tasks/5th-grade/5-2004%20Fruits%20&%20Vegetables.pdf
b. Student correctly answers “48 dimes” using any viable method c. Student correctly answers $1,302 using any viable method
( $6.75 x 10) + ($12.35 x 100)
2
1 1
4
3. (5OA2) Student is able to explain that the two expressions are equivalent because “doubling 5” is the same as 10 AND “+ 26” remains the same in both expressions“. Note: Student may evaluate both expressions but it is not required in this standard to evaluate
2
2
4. (5OA1) Student earns 1 point for correct mathematical answer and 2 points for either of following correct explanation: Alex is correct because he follows the order of operations correctly: 9 + 2 x (10 – 4) 9 + 2 x 6 9 + 12 21 James is incorrect because he evaluates from left to right without regard to the order of operations: 9 + 2 x (10 – 4) 11 x (10 – 4) 11 x 6 66