1. me this writing stuff doesn’t involve any kind of poetry!
Please tell
me this writing stuff doesn’t involve any kind of poetry!
CCSS 5.OA.A.2
Writing
and
Interpreting Numerical Expressions
PowerPoint
©Mike’s Math Mall

2. Numerical Expressions
Part 1:
Writing
Numerical Expressions

3. all my brain hears is, “blah-blah-blah, yada-bada
Numerical Expressions
Solving math word problems
can be confusing.
When I
read word problems,
all my brain hears is, “blah-blah-blah, yada-bada
ding-dong!”
This lesson will help
you learn how to create
numerical expressions when
you encounter word problems.
Numerical Expression – a combination
of numbers and operational symbols. (+, −, ×, ÷)
Somehow, Sparky, I’m not
finding that hard to believe!

4. Numerical Expressions
In this lesson, we will:
Quotient
 Review some math vocabulary
Product
𝟒×𝟕 +𝟓
 Write numerical expressions from word phrases
No poetry writing?
 Write word phrases from numerical expressions
“the sum of 9 and 2”
No poetry!

5. Very Vocabulary!
Can you think of some words that are associated with addition? +
plus
sum
increased by
total
more than
altogether −
How about subtraction?
minus
difference
decreased by
fewer than
less than
take away

6. We’re really just getting started!
Writing Numerical Expressions
Can you think of a few words associated with multiplication? ×
times
product
I actually
know most of
these words!
So our
work here is
done, right? by
double
What!
(times by 2)
Rat eggs! ÷
How about division?
divided by
quotient
That’s fantastic!
We’re really just getting started!
half
goes into
Umm, Sparky….!
Rats don’t lay eggs!
(divide by 2)

7. Writing Numerical Expressions
Now that we have reviewed the vocabulary, let’s write some numerical expressions!
1) 8 more than 12
𝟏𝟐+𝟖 or 𝟖+𝟏𝟐
2) 4 fewer than 11
𝟏𝟏−𝟒
3) 7 times 10
𝟕×𝟏𝟎 or 𝟏𝟎×𝟕
4) 20 divided by 5
𝟐𝟎÷𝟓
Why can’t number’s 2 and 4 be turned around?

8. Writing Numerical Expressions
Let’s make sure you have this!
5) The sum of 6 and 9
𝟔+𝟗 or 𝟗+𝟔
6) The difference of 15 and 13
𝟏𝟓−𝟏𝟑
7) The product of 11 and 8
𝟏𝟏×𝟖 or 𝟖×𝟏𝟏
8) The quotient of 36 and 6
𝟑𝟔÷𝟔
Now it’s your turn!

9. Time to Show Your Stuff! 1) 14 minus 9 3) 5 increased by 11
Write a numerical expression for each word phrase.
1) 14 minus 9
3) 5 increased by 11
5) The sum of 7 and 17
7) 21 and 9 altogether
9) 10 by 12
2) 18 divided by 3
4) 2 times 26
6) The product of 9 and 4
8) 15 less than 35
10) The quotient of 24 and 8
𝟏𝟒−𝟗
𝟏𝟖÷𝟑
𝟓+𝟏𝟏
𝟐×𝟐𝟔
𝟕+𝟏𝟕
𝟗×𝟒
𝟐𝟏+𝟗
𝟑𝟓−𝟏𝟓
𝟏𝟎×𝟏𝟐
𝟐𝟒÷𝟖

10. Time to Raise the Bar!
Well, then why don’t we ratchet-up the difficulty level just a tad?
How did you do on the practice problems, Sparky?
I have to
admit that this writing numerical expression junk isn’t so bad
after all!
Middle…
name…beginning to fade…fast!
Confidence
is my new middle
name, sir!
So, you’re feeling pretty confident then?
Come on, Sparkington! You can do this!

11. Numerical Expressions
Part 2:
Writing Multi-Step
Numerical Expressions

12. Whenever you see the following phrases, think “parentheses”!
Writing Numerical Expressions
Now we’ll look at writing some multi-step numerical expressions.
Whenever you see the following phrases, think “parentheses”!
“the sum of”
“the difference of”
“the quotient of”
“the product of”
or “the quantity of”

13. Writing Numerical Expressions
Check this out!
The difference of 14 and 5 divided by 3.
(𝟏𝟒−𝟓)÷𝟑
8 more than the quotient of 24 and 6.
𝟐𝟒÷𝟔 +𝟖
Double the quantity of 11 fewer than 15.
(𝟏𝟓−𝟏𝟏)×𝟐
Half of the product of 4 and 10.
(𝟒×𝟏𝟎)÷𝟐
You try some! →

14. Writing Numerical Expressions
Write a numerical expression for each word phrase.
1) Add 19 and 2 and then multiply by 4.
(𝟏𝟗+𝟐)×𝟒
2) 6 less than the sum of 45 and 7.
𝟒𝟓+𝟕 −𝟔
3) The quantity of 18 divided by 9 increased by 18.
𝟏𝟖÷𝟗 +𝟏𝟖
4) The product of 10 and 3 plus the product of 15 and 5.
𝟏𝟎×𝟏𝟑 +(𝟏𝟓×𝟓)

15. Writing Numerical Expressions
You just created a beautiful piece of math poetry!
Are you still hanging in there,
Mr. Sparkles?
I had a pretty
awesome session with those multi-step expressions!
And this
will remain our little secret?
Suddenly…
can’t…breath!
What’s that!
I’m afraid the cat’s already out of the bag!
Sparky! Do you know what you just did?

16. Numerical Expressions
Part 3:
Interpreting
Numerical Expressions

17. Interpreting Numerical Expressions!
Now that you’ve written numerical expressions from word phrases like this…
The product of 8 and 11
𝟖×𝟏𝟏
...it’s time to write word phrases when given numerical expressions.
𝟑𝟔−𝟏𝟓
15 fewer than 36
Can you think of some other ways we could
have written this expression?

18. Interpreting Numerical Expressions!
Let’s look at some sample problems!
𝟓+𝟐𝟏
5 increased by 21 or The sum of 5 and 21
𝟒𝟐÷𝟕
42 divided by 7 or The quotient of 42 and 7
(𝟏𝟔−𝟖)×𝟗
The difference of 16 and 8 multiplied by 9
𝟐𝟐÷(𝟕+𝟒)
The quotient of 22 and the sum of 7 and 4

19. Show What You Know! Answers may vary 1) 𝟑𝟓−𝟐𝟗 2) 𝟔𝟒÷𝟐 3) 𝟏𝟎×(𝟏𝟒+𝟏𝟏)
Write a word phrase for each numerical expression.
1) 𝟑𝟓−𝟐𝟗
Answers
may vary
29 less than 35
2) 𝟔𝟒÷𝟐
Half of 64
3) 𝟏𝟎×(𝟏𝟒+𝟏𝟏)
10 times the sum of 14 and 11
4) (𝟑𝟑−𝟏𝟑)÷𝟒
The difference of 33 and 13 divided by 4

20. Word Problems and Expressions!
Write a numerical expression that will help you solve the following word problems. Simplify and label your answers.
Marcus ran 4 laps on a track Monday, 6 laps on Wednesday, and 8 laps on Friday. He did this same workout four weeks in a row. How many total laps did Marcus run after four weeks?
𝟒+𝟔+𝟖 ×𝟒= ?
Marcus ran 𝟕𝟐 laps

21. Expressions & Word Problems!
Danielle bought a pair of socks for $3.59 (including tax) and a belt for $9.79 (including tax). She gave the cashier $15 to purchase the items. How much change did she get back?
𝟏𝟓− 𝟑.𝟓𝟗+𝟗.𝟕𝟗 = ?
Danielle received $1.62 in change

22. Expressions & Word Problems!
Five friends went out to dinner. They decided to split the $65 food bill and the $9.75 tip evenly. How much did each person have to pay?
(𝟔𝟓+𝟗.𝟕𝟓)÷𝟓 = ?
Each person paid $14.95

23. Wow! And it would seem your poetry is improving as well!
Numerical Expressions
Wow! And it would seem your poetry is improving as well!
So, how do you think you’ll do with story problems in the future, Sparky?
Sparky and Jill
went up the hill to work out
some story problems. Sparky was up to the test and Jill was so impressed that she treated him to a “buy-one-
get-one-free,” spicy chili
burrito grande!
Just showing
the ladies Spark-o-Rama’s more sensitive side!
Yep! You’re jealous!
I think they see enough of you already!