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