Estimating and Finding
Exact Costs
Objective To provide experiences with estimating costs
and then calculating exact costs.
a
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Calculate exact money amounts and
share solution strategies. [Operations and Computation Goal 2]
• Solve money number stories using
a calculator. [Operations and Computation Goal 2]
• Estimate money amounts. [Operations and Computation Goal 3]
Key Activities
Children estimate the total cost of grocery
items and use a calculator to find the exact
total cost.
Ongoing Assessment:
Informing Instruction See page 751.
Materials
Math Journal 2, pp. 230 and 243
Home Link 10 4
Math Masters, p. 441
transparency of Math Masters, p. 441
(optional) slate calculator
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Displaying Shoe Length Data
on a Line Plot
My Reference Book, pp. 41, 45, and 46
stick-on notes tape measures
Children measure their shoe lengths
and display the data on a line plot.
Math Boxes 10 5
Math Journal 2, p. 244
Children practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 3. Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Rounding Numbers
Math Masters, p. 308; p. 418 (optional)
Children practice rounding numbers to
the nearest multiple of 10.
ENRICHMENT
Solving Tic-Tac-Toe Addition Problems
Math Masters, p. 309
Children apply their knowledge of
estimating and finding exact amounts by
solving Tic-Tac-Toe Addition problems.
ELL SUPPORT
[Patterns, Functions, and Algebra Goal 1]
Building a Math Word Bank
Home Link 10 5
Differentiation Handbook, p. 142
Children add the terms exact and estimate
to their Math Word Banks.
Math Masters, p. 307
Children practice and maintain skills
through Home Link activities.
Advance Preparation
For the Part 1 activities that involve the Good Buys Poster, you may want to make copies or use an overhead
transparency of Math Masters, page 441. By doing this, children won’t have to flip back to the journal page
to see the poster.
For a mathematics and literacy connection, obtain a copy of Betcha! by Stuart J. Murphy (Scholastic Inc., 1997).
Teacher’s Reference Manual, Grades 1– 3 pp. 186–190
748
Unit 10
Decimals and Place Value
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Getting Started
Mental Math and Reflexes
Math Message
Write a money amount on the board. Ask a volunteer to read
it aloud. Have the class draw coin and bill symbols (P, N, D,
Q, $1) on their slates to represent the amount. Suggestions:
90 + 110 = 200
230 = 140 + 90
240 = 180 + 60
$1.25 ‰ ‰ ‰ ‰ ‰
$1.15 ‰ ‰ ‰ ‰ Í Â
30 + 100 + 70 = 200
Home Link 10 4 Follow-Up
$0.23 Í Í Î Î Î
$0.67 ‰ ‰ Í Â Î Î
Children share then-and-now stories from
home. Children share solution strategies for
1 practice problem.
$1.05 ‰ ‰ ‰ ‰ Â
$0.07 Â Î Î
Answers vary. Sample answers show amounts using the least number
of bills and coins.
1 Teaching the Lesson
Adjusting the Activity
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Check responses to assess children’s ability to add multiples of 10
up to 200. This skill will aid children in making estimates.
Estimating and Finding
Exact Costs
Take a few minutes to share
strategies for solving these problems. For
90 + 110, encourage children to think about
9 + 11; for 180 + 60, think 18 + 6, or 8 + 6,
if necessary. You might want to begin with
numbers less than 100.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
WHOLE-CLASS
ACTIVITY
ELL
(Math Journal 2, p. 230; Math Masters, p. 441)
If possible, display an overhead transparency of Math Masters,
page 441, the Good Buys Poster. Ask children to describe what
they notice about the items and their prices on the Good Buys
Poster. Sample answers: The items are grouped according to kinds
of foods. All the numbers are close to “nice” numbers, or numbers
that end in 0. Both the price and the quantity of an item that can
be bought at that price are shown. All but one of the prices end in
9. Ask: Why do advertised prices often end in 9? Sample answer: If
people look at the dollars, or the large number, first, they may
think that the item costs less than it actually does. Ask: Why is it
useful to estimate total cost when shopping in the store? Sample
answer: It makes it easier to add to help in deciding if you have
enough money to pay for the items. An estimate can also be used
to check if the cashier has made a mistake.
Student Page
Date
Time
LESSON
Good Buys Poster
10 1
Fruit/Vegetables Group
Carrots
Seedless Grapes
Pork & Beans
1-lb bag
99¢ lb
Oranges
$1.49 lb
Bananas
59¢ lb
Peanut Butter
16 oz
3/$1.00
Plums
69¢ lb
Meat Group
18-oz jar
2/89¢
$1.29
Chunk Light
Ground Beef
$1.99 lb
Tuna
Lunch Meat
6.5 oz
1-lb package
69¢
$1.39
Milk Group
Celery
Watermelons
$2.99 ea.
59¢ lb
Grain Group
Gallon
Milk
$2.39
Wheat Bread
99¢
1 lb
69¢
8 oz
$1.49
6-pack
Yogurt
$2.09
Miscellaneous Items
16 oz
Saltines
American
Cheese
Hamburger Buns
16 oz
69¢
Mayonnaise
32 oz
$1.99
Catsup
32 oz
$1.09
Grape Jelly
2-lb jar
$1.69
Math Journal 2, p. 230
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Lesson 10 5
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Pose the following problem: Estimate the total amount to buy one
pound of grapes (99¢) and one jar of peanut butter ($1.29).
(Pretend that there is no sales tax on grocery items.) If you had two
$1 bills would you have enough to buy these two items? no How do
you know?
Emphasize that it is not necessary to find the exact total cost. An
estimate is good enough to tell whether you have enough money.
To support English language learners, discuss the meaning of the
word estimate. Have children share their estimation strategies.
When estimating the cost of several items, it helps to think of
prices to the nearest 10 cents. (While you need not mention it at
this time, keep in mind that for larger prices, one might estimate
with amounts to the nearest dollar, 10 dollars, 100 dollars, or
whatever other amounts are appropriate.) One possible strategy
using the problem above about the grapes and peanut butter is: 99
cents is closer to $1.00 and $1.29 is closer to $1.30, so one can
think 100 + 130 = 230 or $1.00 + $1.30 = $2.30. Discuss the
children’s different estimation strategies. Ask: Is one strategy
better than another? no Why or why not? Sample answer: An
estimate of 90 cents and $1.20 is as good an estimate as $1.00
and $1.30 to answer the question.
Adjusting the Activity
Have children purchase multiple
pounds of fruit and vegetables and estimate
the cost. For example, 3 pounds of oranges
at $1.49 a pound is about $4.50.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
Have children use their calculators to find the exact costs. If
necessary, review how to enter dollars-and-cents amounts into the
calculator using the decimal point. Mention that in this situation
their calculators are like a cash register. Both find the exact cost.
Refer back to the question: If I had two $1 bills, would I have
enough to buy these two items? no If I had $3.00? yes
NOTE Help children see that there are good
reasons to estimate. Many different estimates
are acceptable, depending on the situation.
For example, $2.00 might be as good an
estimate as $2.30 if you have $5.00.
Ask a volunteer to choose two or more items from the poster.
Record the items and the children’s estimates of their total cost on
the board. Record and label the exact costs. Then have children
compare their estimates to the exact costs. Repeat this activity
with several sets of items. Do not erase the board.
Student Page
Date
Time
LESSON
10 5
Practicing Estimating and
Estimating and Buying Food
Choose items to buy from the Good Buys Poster on journal page 230.
For each purchase:
Finding Exact Costs
Record the items on the sales slip.
Write the price of each item on the sales slip.
PARTNER
ACTIVITY
PROBLEM
PRO
PR
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VIN
ING
(Math Journal 2, pp. 230 and 243)
Estimate the total cost and record it.
Your partner then uses a calculator to find the exact total cost and
Work with children to complete the first sales slip on journal
page 243 by completing the steps listed on the journal page.
writes it on the sales slip.
Purchase 1
Items: Sample
answers:
banana
wheat bread
Price
$
$
Estimated cost: about
$
Exact total cost:
$
Purchase 2
Items:
Estimated cost: about
Exact total cost:
. 59
1. Choose two items from the Good Buys Poster and record them.
. 99
. 60
2. Write the cost of each item on the sales slip. Point out that all
decimal points line up one under the other.
. 58
Price
$
$
.
.
$
$
.
.
Purchase 3
Items:
Estimated cost: about
Exact total cost:
0
0
1
1
3. Estimate the total cost of the items and record it. Children
may use the blank space to make notes to help them keep
track of the amounts.
Price
$
.
$
$
$
.
.
.
4. A partner then finds the total cost of the items with
a calculator.
Children complete the other two sales slips with a partner.
Math Journal 2, p. 243
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Student Page
Date
Time
LESSON
10 5
Ongoing Assessment: Informing Instruction
Math Boxes
1. Show $1.73 in two different
Watch for children who hesitate to make estimates. Most children will become
adept at making estimates given time and experience. Remind children that
some estimates are closer to the exact amount than others. Different estimates
are acceptable depending on the situation.
2. A notebook costs $2.00. A
ways. Use Î, Â, Í, and ‰.
pen costs 50¢ less than the
notebook. How much do they
cost together?
Sample answers:
‰‰‰‰‰‰
ÍÍÎÎÎand
‰‰‰‰‰
‰ÍÂÂÎÎÎ
Answer:
3. Fill in the rule and the missing
in
out
numbers.
2 Ongoing Learning & Practice
Displaying Shoe Length Data
WHOLE-CLASS
ACTIVITY
on a Line Plot
(My Reference Book, pp. 41, 45, and 46)
1,342
Rule
+1,000
4. Solve.
4,019
4,650
5,650
5,700 6,700
Answers vary.
5. Write <, >, or =.
6. There are 3 drink boxes per
> 1 pt
3 c < 1 gal
1 qt = 4 c
1 gal > 5 pt
pack. How many packs are
needed to serve 25 second
graders and 2 teachers one
drink box each? Draw an array.
Circle the best answer.
packs are needed.
1 qt
A. 30
Use pages 41, 45, and 46 in the My Reference Book to review line
plots and data landmarks. Have partners measure their shoe
lengths to the nearest whole inch, and then have children
individually record their measure on a stick-on note. As children
share their measures, record them on the board. Ask children to
identify the shortest (minimum) and longest (maximum) lengths.
Draw a line plot on the board or Class Data Pad labeled Number
of Children and Class Shoe Lengths in Inches. Add the scale to
the line plot in 1-inch increments beginning with the minimum
length and ending with the maximum length for the class. (See
the line plot routine in Lesson 9-8.) Ask children why the line
plot can begin with a number other than zero. Sample answers:
No length is zero; there is no shoe length in the class shorter than
the minimum. Invite children to place their stick-on notes above
the corresponding lengths on the line plot. Have the class
calculate the difference between minimum and maximum (range)
and identify the length that occurs the most (mode). Next, to find
the middle (median) class shoe length, have children remove the
last stick-on note from each end of the line plot over and over
until one (or two) remains.
Unit
11
km
60 + 50 = 110
1,100
600 + 500 =
6,000 + 5,000 = 11,000
6+5=
2,342
3,019
$3.50
B. 8
C. 9
D. 10
9
112 113
Math Journal 2, p. 244
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NOTE Prior to having children complete
Math Boxes, Problem 5, you may want to
refer children to My Reference Book,
pages 70 and 72. Together, read about the
tools used to measure capacity and the
Tables of Measures of Capacity.
Home Link Master
Name
Date
Time
HOME LINK
10 5 Estimation to the Nearest 10¢
Family
Note
In today’s lesson, your child estimated sums by first finding the nearest ten cents for each
amount of money being added and then adding the amounts for the nearest ten cents
together. For Problems 1–7, ask your child how she or he arrived at each answer. If needed,
use coins to show which amount is actually closer. For Problems 8–11, help your child find
the totals by thinking of a problem like $1.20 + $0.60 as 12 + 6 or as 120 cents + 60 cents.
Please return this Home Link to school tomorrow.
Math Boxes 10 5
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 244)
Write the correct answer to each question.
Talk with someone at home about your answers.
$0.70
$2.60
$1.00
$1.30
$4.00
$1.20
$2.30
1. Is $0.69 closer to $0.60 or $0.70?
2. Is $2.59 closer to $2.50 or $2.60?
3. Is $0.99 closer to $0.90 or $1.00?
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 10-1 and10-3. The skill in
Problem 6 previews Unit 11 content.
4. Is $1.31 closer to $1.30 or $1.40?
5. Is $3.99 closer to $3.90 or $4.00?
6. Is $1.17 closer to $1.10 or $1.20?
7. Is $2.34 closer to $2.30 or $2.40?
Fill in the blanks and estimate the total cost in each problem.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 3
Use Math Boxes, Problem 3 to assess children’s progress toward identifying a
rule for a function. Children are making adequate progress if they correctly identify
the rule and apply it to find an out number. Some children will be able to apply the
rule to find the missing in number.
[Patterns, Functions, and Algebra Goal 1]
Example:
$1.19 + $0.59 is about $1.20 + $0.60 = $1.80 .
8. $1.29 + $0.48 is about
9. $0.79 + $0.39 is about
10. $0.69 + $0.89 is about
11. $1.41 + $0.77 is about
$1.30
$0.80
$0.70
$1.40
+
+
+
+
$0.50
$0.40
$0.90
$0.80
=
=
=
=
$1.80 .
$1.20 .
$1.60 .
$2.20 .
Math Masters, p. 307
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Lesson 10 5
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Teaching Master
Name
Date
Home Link 10 5
Time
LESSON
10 5 Rounding Numbers
INDEPENDENT
ACTIVITY
(Math Masters, p. 307)
When we round a number, we find a number that is close to it.
1. Here is one strategy for rounding a number:
Home Connection Children select the closest multiple of
ten cents for different money amounts. Then children
estimate totals by adding multiples of ten cents.
To round 27, put your finger on 27 on the number grid.
Move it up or down to the nearest multiple of 10.
a. Is it fewer steps from 27 to 30 or from 27 to 20?
27 to 30
Use your number grid to round these numbers:
b. 22
20
c. 38
40
50
d. 51
80
e. 75
(Hint: If a number is halfway between, we always round to
the higher number.)
2. Here is another way to think of rounding numbers:
15
a. To round 17, think: What would be multiples of 10
that are close to 17?
10 and 20
17
10
3 Differentiation Options
20
15
c. Would 17 be heading toward 10 or toward 20? 20
b. What number would be at the top of the hill?
3. Draw a picture to show how
4.
Draw a picture to show how
you would round 234.
you would round 63.
63
60
65
234
70
250
200
300
READINESS
Rounding Numbers
SMALL-GROUP
ACTIVITY
5–15 Min
(Math Masters, pp. 308 and 418)
Math Masters, p. 308
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To explore making estimates by using rounding strategies, have
children solve the problems on Math Masters, page 308. If
children have not already shaded the multiples of 10 on their
number grid on the inside back covers of their journals, consider
having them do so before beginning this activity. Have children
use that number grid for this activity or make a copy of Math
Masters, page 418 for each child. Explain to students that
sometimes we do not need an exact answer to a problem, but we
want to find an answer that is close to the exact answer. To do
this, we can round the numbers in the original problem.
ENRICHMENT
Solving Tic-Tac-Toe
Date
15–30 Min
Addition Problems
Teaching Master
Name
INDEPENDENT
ACTIVITY
(Math Masters, p. 309)
Time
LESSON
10 5 Tic-Tac-Toe Addition
To apply children’s knowledge of estimating and finding the exact
amount, have children solve Tic-Tac-Toe Addition problems.
Children find any 3 numbers in a row, in a column, or on a
diagonal whose sum is the target number in the box. They draw a
line through these 3 numbers.
Draw a line through any three numbers whose sum is the
target number in the square. The numbers may be in a row, in
a column, or on a diagonal. Draw a line for each correct sum.
Example:
1.
$8.27
$5.09
$2.08
$1.10
$1.52
$3.18
$7.17
$6.31
$3.01
$0.00
2.
$14.62
ELL SUPPORT
$18.05
$3.40
$4.15
$7.07
$6.25
$3.75
$3.05
$1.75
$8.22
$6.00
$6.10
$8.50
$4.90
$5.00
$2.25
$3.00
$6.50
$5.80
$9.10
4.
Math Masters, p. 309
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752
5–15 Min
(Differentiation Handbook, p. 142)
To provide language support for estimation, have children use the
Word Bank template found on Differentiation Handbook, page 142.
Ask children to write the terms exact and estimate, draw pictures
representing each term, and write other related words. See the
Differentiation Handbook for more information.
Try This
Write a target number in the box. Fill in the rest of the spaces
to reach the target.
3.
Building a Math Word Bank
SMALL-GROUP
ACTIVITY
309
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