Download 5 Grade Unit 2: Multi-Digit Whole Number and Decimal Fraction

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.
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 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.
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
Skills (Students will be able to…)
A1. Determine the value of digits in a whole number and
decimal number to the thousandths
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)
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
C. Standard algorithm for multiplying multi digit
whole numbers (5.NBT.5)
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
D. Division of whole numbers with up to four digit
dividends by two digit divisors (5.NBT.6)
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)
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
F. Numerical expressions (5.OA.1)
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)
G. Numerical expressions (5.OA.2)
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/CommonCore/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/CommonCore/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/CommonCore/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.
Red Velvet Cupcakes
$6.75 per box
a.
Price List
Peanut butter chip cookies
$4.80 per box
Pumpkin pie
$12.35 per pie
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
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
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)
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)
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
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+2x6
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
Total Points
Novice
0-3
Apprentice
4-7
Practitioner
8 - 10
Rubric
Points
Section
Points
1
3
1
1
2
4
1
1
2
2
1
2
3
12
12
Expert
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.
Potatoes
.89 per
pound
Grocery Store Price List
Turkey
Cranberries
Stuffing
.75 per pound $2. 39 per bag $1.25 per
box
String Beans
$ 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
$14 per crate
Walnuts
$156 per crate
Pumpkins
? 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
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
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. (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
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.
4. (5.NBT.6)
Student correctly answers $38. Student may choose any method to show their
thinking.
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
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
Rubric
Points
Section
Points
2
2
1
1
2
2
1
1
2
2
2
4
2
7. (5.OA.2)
Student correctly translates the verbal expression into a numerical expression
1
3
Student is able to explain the difference between the two expressions and articulate 2
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
Total Points
15
Novice
0-3
Apprentice
4-7
Practitioner
9 - 12
Expert
13- 15
15