# Estimating with Fractions

**NYS Mathematics, Science, and Technology Learning
Standards Addressed
**Standard 1: Students will use mathematical analysis, scientific inquiry, and
engineering

design, as appropriate, to pose questions, seek answers, and develop

solutions .

Standard 3: Students will understand mathematics and
become mathematically confident

by communicating and reasoning mathematically, by applying mathematics

in real -world settings, and by solving problems through the integrated study

of number systems , geometry, algebra, data analysis, probability, and

trigonometry .

Standard 6: Students will understand the relationships and
common themes that connect

mathematics, science, and technology and apply the themes to these and

other areas of learning.

Standard 7: Students will apply the knowledge and thinking
skills of mathematics,

science, and technology to address real-life problems and make informed

decisions.

**Objectives:
**• The student will be able to estimate sums, differences, products, and
quotients involving

fractions and mixed numbers (Knowledge).

• The student will be able to explain the process of estimating fractions and mixed numbers

to someone unfamiliar with the concept (Comprehension).

**Materials:
**• PowerPoint Presentation (“7.1 Estimating with Fractions”)

• Computer with Microsoft PowerPoint (and the ability to project what is on the computer

onto a larger screen).

• One “Estimating Fractions – FAQ” note sheet for each student (20 total).

• One “Estimating Fractions – Homework” sheet for each student (20 total).

**Anticipatory Set:
**When students enter the room, have the first slide of the PowerPoint
Presentation titled “7.1

Estimating with Fractions” (included with this lesson plan) projected onto the front screen. This

slide gives today’s lists today’s Agenda and includes a Far Side comic to lighten the mood at the

beginning of class.

Once everyone is seated, click to the next slide
(“Warm-Up”). This slide instructs the students to

write a short paragraph in their math journals explaining how they would explain
to someone the

process of estimating the numbers 59.6541, 4.302, and 77.77777 to the nearest
tenth. Give

students between 3-5 minutes to complete this task, and then ask, “Can someone
volunteer to

read what he or she has written for the class?” (Responses should explain that
59.6541 would be

rounded to 59.7, because the digit in the hundredths place is a 5, and the rule
for rounding

numbers is to round up if this digit is 5 or higher and round down otherwise.
Using this

reasoning, 4.302 would be rounded to 4.3 and 77.77777 would be rounded to 77.8.)

Say, “Today, we are going to devise a rule somewhat
similar to this for estimating fractions and

mixed numbers.”

**Lesson Body:**

Hand out one “Estimating Fractions – FAQ” note sheet to
each student. Ask everyone to fill in

this sheet as we cover today’s lesson. (All answers appear in the PowerPoint
presentation.) Click

the PowerPoint presentation to the next slide (slide 3). The first question from
the note sheet

should appear on the screen, “Why would we want to know how to estimate
fractions?” Give

students a change to suggest an answer of their own, and then click the mouse
button to reveal

the response “to quickly estimate the sum, difference, product , or quotient of
an expression

involving fractions or mixed numbers.” (Throughout this lesson, students should
be writing the

words written in italics on their note sheet.)

Next, pose the question “When am I ever going to need to
estimate fractions?” Click the mouse

button three times to reveal the first three responses (Approximating the amount
of ingredients

needed in a recipe, Estimating the amount of money you will make doing a job,
Estimating the

distance between two locations ). Clicking the mouse button one more time will
reveal “Any

other ideas?” in which the floor should be open to the students for any
additional examples they

may have.

Move on to the next slide by clicking the mouse button.
This slide (4) corresponds with the next

bullet on the note sheet: “To estimate the sum or difference of fractions, round
each fraction

to…” Clicking the mouse button twice will reveal the answer: 0, ½, or 1,
whichever is closest.

After students have had a chance to write this down, click on to slide 5 to
answer the next

question, “How do you decide what to round to?” Clicking the button again
reveals “Drawing

fraction models can help you decide how to round.” Example A illustrates this
technique. Click

the mouse button again to reveal the example of rounding 5/8 that is already
printed on the

students’ note sheets. Show that the white bar is divided into 8 even pieces,
and that five of these

pieces have been filled in blue to represent 5/8. Notice that 0, ½, and 1 are
also clearly marked

on this bar, and ask students, “Is the end of the blue bar closest to 0, ½, or
1?. (Students should

see that 5/8 is closet to ½, and should write this answer in the appropriate
line on their note

sheet.) Clicking the mouse button again also reveals this answer.

Click to the next slide (6), and then click the mouse
button two more times to reveal the

cautionary note: “It is deceiving what to round some fractions to, so if you
ever have any doubt,

draw the fraction models to help you.” Clicking the mouse button three more
times reveals

Example B: “What would you round 1/3 to?” As before, a fraction model has been
drawn on the

PowerPoint screen, (but it has been left for the students to draw in their
notes). Show students

that in this case, although their first instinct may be to round this fraction
to 0, the blue bar is

actually closer to ½ than 0. Click the mouse button again to show the answer:
1/3 should be

rounded to ½.

Click to the next slide (7) for Example C. Explain that
this question, What would you round 2/3

to, is also deceiving. Click the mouse two times to reveal the question. Say,
“Your instinct may

be to round 2/3 to 1, but if we take a look at the fraction model, we find that
this is not the best

answer.” (Click the mouse again to reveal the fraction model). Show students
that this time, the

blue bar is actually closer to ½ than 1. Click the mouse one more time to reveal
the answer: ½.

Move on to slide 8 – “Activity.” Allow students to work
with the person they’re sitting next to

and estimate each of the fractions listed on the screen (which are also printed
on their sheet) to 0,

½, or 1 and place them in the appropriate column in the table on their note
sheet. Give students

between 5 and 10 minutes to complete this, and then go around the class asking
the pairs what

they estimated each fraction to, beginning with 1/5 and proceeding through 5/6.
(Each time, after

a pair gives their answer, click the mouse button once and the fraction will
slide down to its

correct column in the table on the screen.)

Click on to slide 9 – which gives students one more
essential note before bringing the lesson to a

close: “What about Mixed Numbers?” Explain “when we are asked to estimate mixed
numbers,

we use a similar process. The mixed number can either be rounded down the whole
number that

appears in the mixed number, the “½ of the mixed number” or one greater than the
whole

number that appears in the mixed number.” Example D illustrates this: 7 ¼ can
either be rounded

to (a) 7 , (b) 7 ½ , or (c) 8. Ask students “Can anyone tell me why estimating
this mixed number

is especially difficult?” (Students should say that 7 ¼ falls directly between 7
and 7 ½.) Say,

“Numbers like this are somewhat ambiguous to round. In this case, it is
acceptable to either

round down to 7 or round up to 7 ½.”

**Closure:**

The next slide, (10) contains the essential question for
this lesson, which students are again asked

to respond to in a brief paragraph written in their journal. (Allow about 5
minutes for this).

(1) Summarize what you learned about estimating fractions and mixed numbers today.

(Responses should include that fractions can be estimating
by either rounding them to 0, ½, or 1,

and a similar procedure is used when rounding mixed numbers. Mention should also
be made of

using fraction models to help decide which of these the number should be rounded
to. Other

responses are possible as well.)

If time permits, ask a student or two to volunteer what
they have written. Lastly, click to the last

slide (11) which lists the homework assignment. Pass out the sheet labeled
“Homework: 7.1

Estimating with Fractions” to each student.

**Accommodations for IEP:**

Since this lesson is essentially uses a direct teaching
method of instruction , the student with

ADD may have a particularly difficult time focusing. Remind the student before
class that he is

expected to complete all notes and activities that are contained within today’s
lesson, but if he

feels like he needs to get up and stretch once or twice during the period, he
may do so quietly.

**Homework/Assessment**

The homework worksheet (7.1 Estimating with Fractions)
essentially reviews the concepts

presented in the PowerPoint presentation, as well as taking the lesson a step
further. Students are

first asked to round fractions to 0, ½, or 1 (as they did in the class activity)
as well as estimating

the mixed numbers, as shown in the lesson. After this, they are asked to use
this knowledge to

estimate some algebraic expressions by first estimating the fractions and mixed
numbers

contained within them. Finally, students are presented with a real- life
scenario in the form of a

word problem that uses the techniques from today’s lesson.

**Extensions**

If time permits, have students do exercises 16-43 on page
270 of their textbook orally. These

problems ask them to round fractions or estimate expressions involving
fractions. By having

them practice doing these orally, they will gain practice for the homework and
also see the

relevance of estimating with fractions. (It allows them to evaluate otherwise
difficult expressions

quickly.)

**Estimating Fractions - FAQ**

• Why would we want to know how to estimate fractions?

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

• When am I ever going to need to estimate fractions?

1) _____________________________________________________________________

2) _____________________________________________________________________

3) _____________________________________________________________________

4) _____________________________________________________________________

• To estimate the sum or difference of fractions, round each fraction to

____, ____, or ____.

• How do you decide what to round to?

__________________________________________________________________________

__________________________________________________________________________

Example A:

Is 5/8 closest to 0, 1/2, or 1? ________

**Caution!!!**

• It is deceiving what to round some fractions to, so if
you ever have any doubt …

__________________________________________________________________________

Example B:

What would you round 1/3 to? ________

Example C:

What would you round 2/3 to? ________

Activity:

Estimate each of the fractions below to whichever is closest and place them in
the appropriate

column in the table that follows.

Fractions Close to 0 | Fractions Close to 1/2 | Fractions Close to 1 |

**What About Mixed Numbers?**

• We can follow a similar procedure for estimating mixed
numbers.

Example D:

What would you round to?

(a) 7 (b) 7 ½ (c) 8

Round each fraction to 0, 1/2, or 1:

(1) 1/6______ (2) 3/5 ______ (3) 9/10 ______ (4) 3/10 ______

(5) 2/7 ______ (6) 1/4 ______ (7) 7/50 ______ (8) 10/13 ______

Estimate each mixed number:

(9) ______ (10)
_______ (11)_______
(12) ______

Estimate each expression by first estimating
the fractions and then adding the

estimations.

Example:

** Answer the following question:
**Komodo dragons are the largest lizards ever to have lived. A 250-point
komodo dragon can eat

enough in one sitting to increase its weight by 3/4. Estimate 3/4 x 250 to find how much weight a

komodo dragon would gain after eating.

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