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