Post on 03-Sep-2018
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:
5.NBT.1-2.2, 2-3, 2-10, 7-2 5.NBT.2-1-1, 1-2, 1-5, 1-6, 1-8, 1-9, 2-1, 2-8, 2-9, 3-2, 3-5,3-8, 3-9, 4-1, 7-1, 7-2, 7-4, 7-7, 10-1, 10-3, 11-6 5.NBT.5-7-10, 9-2, 5.NBT.6-4-1, 4-2, 4-4, 4-6, 7-10 5.NBT.7-2.2, 2-3, 2-4, 2-5, 2-7, 2-8, 2-9, 4-5, 4-6, 5-11, 6-5, 6-7, 7-10, 9-8, 9-10, 10-6, 12-2, 5.OA.1 - 5.OA.2 - Additional Resources: Unpacked standards from North Carolina http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf k-5 Math Teaching Resources – Activities listed by Common Core Standard http://www.k-5mathteachingresources.com/5th-grade-number-activities.html
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
Grade 5 Unit 2
Initial Performance Task: Betty’s Bakery
Name_______________________ Date___________
1. Betty’s Bake Shop makes 15 dozen sugar cookies and 288 chocolate chip cookies each day.
For a – c, use any method to show your mathematical thinking. (1 dozen = 12 cookies)
a. How many sugar cookies are made each day?
b. How many sugar cookies are made in 2 weeks?
c. How many dozen chocolate chip cookies are made each day?
2. Use the price table to answer questions. Use any method to prove your answers.
Price List
Red Velvet Cupcakes
$6.75 per box
Peanut butter chip cookies
$4.80 per box
Pumpkin pie
$12.35 per pie
a. A group of five friends order 2 boxes of cupcakes and 1 pumpkin pie for a party. The five
friends will each pay an equal amount. How much will each friend pay?
b. Sal wants to buy a box of peanut butter chip cookies, but he only has dimes! How many
dimes will he need to pay for 1 box?
c. The local supermarket placed a big Thanksgiving order for 10 boxes of cupcakes and 100
pumpkin pies. How much will the order cost?
3. Describe how the expression “double five and then add 26” is related to “10 + 26”
4. (5.OA.1) Alex and James evaluated the following equation: 9 + 2 x (10 - 4) = ?
Alex thinks the solution is 21. James thinks the solution is 66. Who do you agree with? Why?
Explain your thinking with words and numbers.
Show your math thinking here:
Grade 5: Initial Task
Betty’s Bakery Scoring Guide
Betty’s Bakery Scoring Guide Rubric
The core elements of the performance required by this task are:
Understand place value of whole numbers and decimal numbers to multiply and divide
Represent their mathematical thinking through pictures, words and number models
Points
Section Points
1. (5NBT5, 5NBT6) a. Student uses any method to find correct answer of 180 sugar cookies
(15 x 12) b. Student uses any method to find correct answer of 2, 520 sugar cookies
(15 x 12 x 14) c. Student uses any method to find correct answer 24 dozen chocolate chip
cookies (288 ÷ 12)
1
1
1
3
2. (5NBT1, 5NBT2, 5NBT7) a. Student uses any viable method to find the correct answer of $5.17 per
person. $6.75 x 2 = $13.50 $13.50 + 12.35 = $25.85 $25.85 ÷ 5 = $5.17
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
1 2
3
Total Points 12
12
Novice Apprentice Practitioner Expert
0 - 3 4 - 7 8 - 10 11- 12
Grade 5 Unit 2
Final Performance Task: Thanksgiving Dinner
Name: __________________________ Date: _______________
The teachers at PS 276 are planning a Thanksgiving meal for their students. Use the price chart to
answer the following questions. Use any method to show your mathematical thinking.
Grocery Store Price List
Potatoes Turkey Cranberries Stuffing String Beans
.89 per
pound
.75 per pound $2. 39 per bag $1.25 per
box
$ 1.66 per pound
1. The teachers buy 14 pounds of potatoes and 4 bags of cranberries. What is the total cost?
2. The teachers have $21 for a turkey. What is the heaviest turkey they can buy (in pounds)?
3. The 5th grade teachers buy 3 boxes of stuffing and 4 pounds of string beans. The 4th grade
teachers buy 2 boxes of stuffing and 3 pounds of string beans. How much more did the 5th
grade teachers spend than the 4th grade teachers?
The local supermarket places orders with the farm. Use the chart to answer the following
questions. Use any method to show your mathematical thinking.
Apples Walnuts Pumpkins
$14 per crate $156 per crate ? per crate
4. The supermarket orders 12 crates of pumpkins. The farm charges $456. What is the price per
crate?
5. The supermarket spends a total of $650 on a combination of apples and walnuts. They order
13 crates of apples. How many crates of walnuts did they order?
6. Evaluate the following expressions. Show all steps.
a. 3 + 104 ÷ 10 x (32 ÷ 8) =
b. 42 + 7 x 5 + (70 x 800) =
7. Write an expression that means “triple the sum of twelve and seventeen”. How is it different
from the expression “the sum of three times twelve and seventeen”?
Grade 5: Final Task
Thanksgiving Dinner Scoring Guide
Thanksgiving Dinner Scoring Guide Rubric
The core elements of the performance required by this task are:
Understand place value of whole numbers and decimal numbers to multiply and divide
Represent their mathematical thinking through pictures, words and number models
Points
Section
Points
1. (5.NBT.7)
Student correctly answers $22.02 using any method to show their work such as:
( 14 x $.89) + (2 x $2.39) = $22.02
2
2
2. (5.NBT.7)
Student correctly answers 28 pounds and uses any viable method to prove the
answer such as using algorithm, drawing a diagram or recording in a t-chart
1 1
3. (5.NBT.7)
Student correctly answers “the 5th grade teachers spend $2.91 more” OR “the
4th grade teachers spend $2.91 less” using any viable solution method. Note:
the most efficient method is to add 1 box of stuffing to 1 pound of string beans
since this is the difference between the two orders.
2
2
4. (5.NBT.6)
Student correctly answers $38. Student may choose any method to show their
thinking.
1 1
5. (5.NBT.5, 5.NBT.6)
Student correctly answers “3 crates of pumpkins” and shows correct work such
as algorithm, diagram or chart.
$650 – 13($14) = $ on walnuts
$650 - $182 = $468 on walnuts
$468 ÷ $156 = 3 crates
2 2
6. (5.OA.1)
a) Student correctly evaluates expression and follows correct order of operations
3 + 104 ÷ 10 x (32 ÷ 8)
3 + 104 ÷ 10 x (4)
3 + 10,000 ÷ 10 x (4)
3 + 10,000 ÷ 10 x (4)
3 + 1,000 x 4
3 + 4,000
4,003
b) Student correctly evaluates expression and follows correct order of operations
42 + 7 x 5 + (70 x 800)
42 + 7 x 5 + 56,000
42 + 35 + 56,000
77 + 56,000
56,077
2
2
4
7. (5.OA.2)
Student correctly translates the verbal expression into a numerical expression
Student is able to explain the difference between the two expressions and articulate
how the order of the operations is different. In the first expression, 12 is added to
17 first: 3(12 + 17) then multiplied by 3. But in the second expression the 3 and 12
are multiplied first then added to 17 ie: (3 x 12) + 17
1
2
3
Total Points 15 15
Novice Apprentice Practitioner Expert
0 - 3 4 - 7 9 - 12 13- 15