CCSS 5th Grade Operations and Algebraic Thinking 2.0Write 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.Lesson to be used by EDI-trained teachers only.
READY TO TEACHSM EDI® Lessons©2013 All rights reserved.
What are we going to do?What are we going to do?
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Students, you already know how to write simple expressions. Now, we will write more complex numerical expressions.
Students, you already know how to write simple expressions. Now, we will write more complex numerical expressions.
Make ConnectionMake Connection
We will write numerical expressions. Learning Objective
Learning Objective
Activate Prior Knowledge
Activate Prior Knowledge
Match the words to the expression.
1. The sum of six and eight. 6 8
8× 5
9 3
9 32. The product of eight and five.
3. The quotient of nine and three.
4. The difference of nine and three.
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
On your whiteboards, write an example of a numerical expression. How do you know it is a numerical expression?
Which numerical expression below would be read as: “the difference of nine and five, multiplied by three.”
A 9 – 5 × 3
B (9 – 5) × 3In your own words, what is a numerical expression?A numerical expression is ____.
On your whiteboards, write an example of a numerical expression. How do you know it is a numerical expression?
Which numerical expression below would be read as: “the difference of nine and five, multiplied by three.”
A 9 – 5 × 3
B (9 – 5) × 3In your own words, what is a numerical expression?A numerical expression is ____.
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Writing Numerical Expressions
Concept DevelopmentConcept Development
A numerical expression is made up of numbers connected by operations (+, –, , ).•Grouping symbols are used to group operations and numbers.•The words sum, difference, product, and quotient declare1 a group of operations.
( )parentheses
[ ]brackets
{ }braces
Grouping Symbols
“Six plus eight times five.”
“The sum of six and eight, multiplied by five.”
“Add six and eight, then multiply by five.”
1 say1 say
VocabularyVocabulary
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Read the description of the expression.Identify2 numbers (underline) and operations (circle).
Write the numerical expression.
Write numerical expressions.1
2a
2 find2 find
VocabularyVocabulary
How did I/you identify numbers and operations?How did I/you write the numerical expression?
How did I/you identify numbers and operations?How did I/you write the numerical expression?
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2
1a
Skill Development/Guided Practice
Skill Development/Guided PracticeA numerical expression is made up of numbers connected by operations (+, –, , ).•Grouping symbols are used to group operations and numbers.•The words sum, difference, product, and quotient declare a group of operations.
1. Twenty-one divided by seven plus four.
2. Five times eight minus nine.
3. Eighteen minus five times three.
4. Three plus sixteen divided by two.
5. Add nine and one, then multiply by seven.
6. Subtract eleven and two, then divide by three.
21 7 +4 5 × 8 9
Application
18 – 5 × 3 3 + 16 2
(9 + 1) × 7 (11 – 2) 3
Interpret the numerical expressions.
T: (105 – 9) × 4 ________________________________________________________
S: (54 + 36) × 3 ________________________________________________________
is four times the difference of 105 and 9.
is three times the sum of 54 and 36.
( )parentheses
[ ]brackets
{ }braces
Grouping Symbols
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Skill Development/Guided Practice (continued)
Skill Development/Guided Practice (continued)
7. The difference of twenty-one and three, divided by nine.
8. The sum of twelve and six, times seventeen.
9. Half of the difference between eight and four.
10. Triple the sum of six and nine.
Application
(21 – 3) 9 (12 + 6) × 17
× (8 – 4) 1 2 3 × (6 + 9)
Interpret the numerical expressions.
T: (95 – 74) 3 ________________________________________________________
S: (45 + 29) 2 ________________________________________________________
is one-third of the difference between 95 and 74.
is half of the sum of 45 and 29.
Read the description of the expression.Identify numbers (underline) and operations (circle).
Write the numerical expression.
Write numerical expressions.1
2a
How did I/you identify numbers and operations?How did I/you write the numerical expression?
How did I/you identify numbers and operations?How did I/you write the numerical expression?
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2
1a
A numerical expression is made up of numbers connected by operations (+, –, , ).•Grouping symbols are used to group operations and numbers.•The words sum, difference, product, and quotient declare a group of operations.
( )parentheses
[ ]brackets
{ }braces
Grouping Symbols
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Writing numerical expressions will help you understand mathematical expressions in the real world.
Writing numerical expressions will help you do well on tests.
1
Does anyone else have another reason why it is relevant to write numerical expressions? (Pair-Share) Why is it relevant to write numerical expressions? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?
Does anyone else have another reason why it is relevant to write numerical expressions? (Pair-Share) Why is it relevant to write numerical expressions? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?
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2Sample Test Question:
32. Which expression shows fifteen minus eight times three?
A 15 8 3 B (15 8) 3 C 8 15 3 D (8 15) 3
RelevanceRelevance
A numerical expression is made up of numbers connected by operations (+, –, , ).•Grouping symbols are used to group operations and numbers.•The words sum, difference, product, and quotient declare a group of operations.
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Read the description of the expression.Identify numbers (underline) and operations (circle).
Write the numerical expression.
Write numerical expressions.1
2a
What did you learn today about writing numerical expressions? (Pair-Share)Use words from the word bank.
Skill ClosureSkill Closure
Access Common CoreAccess Common Core
Summary ClosureSummary Closure
Word Bank
numericalexpressionsoperationsgroupingsymbols
Describe and correct the error in writing the numerical expression.
The sum of seven and eight, divided by three.
1. Three plus eleven times two. 2. The difference of seven and six, times twelve.
3 + 11 × 2 (7 – 6) × 12
( )parentheses
[ ]brackets
{ }braces
Grouping Symbols
A numerical expression is made up of numbers connected by operations (+, –, , ).•Grouping symbols are used to group operations and numbers.•The words sum, difference, product, and quotient declare a group of operations.
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Independent PracticeIndependent Practice
1. Twenty-seven divided by three times seven.
2. Sixteen minus eight plus four.
3. Six times eight plus four. 4. Add twenty and four, then divide by six.
5. The sum of nineteen and six, divided by five.
6. Twice the difference of thirteen and three.
Application
27 3 7 16 8 +4
6 × 8 + 4 (20 + 4) 6
(19 + 6) 5 2 × (13 – 3)
Interpret the numerical expressions.
S: (15 + 9) × 3 ________________________________________________________
S: (45 + 29) 2 _______________________________________________________
is three times the sum of 15 and 9.
is half the sum of 45 and 29.
Read the description of the expression.Identify numbers (underline) and operations (circle).
Write the numerical expression.
Write numerical expressions.1
2a
A numerical expression is made up of numbers connected by operations (+, –, , ).•Grouping symbols are used to group operations and numbers.•The words sum, difference, product, and quotient declare a group of operations.
( )parentheses
[ ]brackets
{ }braces
Grouping Symbols
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Periodic Review 1Periodic Review 1
Access Common CoreAccess Common Core
1. Twelve divided by six plus nine.
2. Twenty-four divided by eight minus one.
3. Forty-six plus four times three. 4. Forty-eight plus nine divided by three.
5. Add twenty-five and three, then divide by seven.
6. Add twenty-two and two, then divide by six.
12 6 + 9 24 8 – 1
46 + 4 × 3 48 + 9 3
(25 + 3) 7 (22 + 2) 6
Interpret each numerical expression.
1. 2 (24 14)
2. (19 6) 4
3. (36 9) 3
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Periodic Review 2Periodic Review 2
Access Common CoreAccess Common Core
1. Subtract forty-nine and thirty-three, then divide by four.
2. Thirty-two divided by four plus twenty-six.
3. The sum of thirty-seven and three, divided by five.
4. Twelve plus forty-four divided by eleven.
Match each expression to its written description.
2 (16 13)
(22 3) 4
40 25 3
22 3 4
(40 25) 3
2 16 13
Forty minus twenty-five divided by three.
Twenty-two plus three times four.
Two times sixteen minus thirteen.
Add twenty-two and three, then multiply by four.
Twice the difference of sixteen minus thirteen.
The difference between forty and twenty-five, divided by three.
(49 – 33) 4 32 4 + 26
(37 + 3) 5 12 + 44 11
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
Periodic Review 3Periodic Review 3
Access Common CoreAccess Common Core
1. Five plus thirty-four divided by two.
2. Ten times the sum of six and three.
1. Choose Yes or No to indicate whether each expression correctly matches the written description.
A 10 3 22
B 2 (44 16)
C (23 13) 5
Ten times three minus twenty-two.
Two times forty-four minus sixteen.
Subtract twenty-three and thirteen, then divide by five.
O Yes O No
O Yes O No
O Yes O No
2. Choose Yes or No to indicate whether each expression correctly matches the written description.
A 3 (4 6)
B (14 7) 7
C 7 4 2
Triple the sum of four and six.
Fourteen minus seven divided by seven.
Subtract four from seven, then multiply by two.
O Yes O No
O Yes O No
O Yes O No
3. Choose Yes or No to indicate whether each expression correctly matches the written description.
A 10 2 3
B 6 (5 1)
C (48 24) 6
Ten divided by two plus three.
Six times the sum of five and one.
The difference of forty-eight and twenty-four, divided by six.
O Yes O No
O Yes O No
O Yes O No
5 + 34 2 10 × (6 + 3)
CCSS 5th Grade Operations and Algebraic Thinking 2.0Write numerical expressions.
Lesson to be used by EDI-trained teachers only. ©2013 All rights reserved.
EDI – Cognitive, Teaching, and English Learner Strategies
Learning Objective: We will write numerical expressions.
Elaboration
Targeted Vocabulary
Academic declare, identify
Content numerical expression
Support
Demonstration
VocabularyStrategy
Multiple-Meaning
Synonym declares, identifyDefinition numerical expression
Homophone
Internal Context Clue
Listen, Speak Similar Sounds
Write Writing
Read Tracked Reading
Comprehensible Input
Cognates
Contextual Clues
Graphic Organizer
Contextualized Definitions
Pictures
Language Strategies
Cognitive Strategies Teaching Strategies
Content Access Strategies