MATH MESSAGE
Grade 5, Unit 1, Lessons 13 - 16
5TH GRADE
Objectives of Lessons 5 - 8
MATH
Unit 1: Place Value and Decimal Fractions
Math Parent Letter
The purpose of this newsletter is to guide parents,
guardians, and students as students master the math
concepts found in the St. Tammany Public School’s
Guaranteed Curriculum aligned with the state
mandated Common Core Standards. Fifth grade Unit
1 covers place value and decimal fractions. This
newsletter will address concepts found in Unit 1,
Lessons 13 - 16, Dividing Decimals
Words to know:

Dividend

Divisor

Hundredths
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
Quotient
Tenths
Thousandths
Dividend (whole)– a quantity to be divided.
Dividend 
Divisor – the quantity by which another quantity is
to be divided.
 Divisor
Hundredths – one part of 100 equal parts;
hundredth’s place – the second digit to the right of
the decimal point.
Quotient - the answer to a division problem.
Tenths – one part of 10 equal parts; tenth’s place –
the first digit to the right of the decimal point.
Thousandths – one part of 1,000 equal parts;
thousandth’s place - the third digit to the right of the
decimal point.
Objectives of Lessons 5 - 8
The students will learn to….

Read, write, and compare decimals to
thousandths.


Read and write decimals to thousandths
using base-ten numerals, number names,
and expanded form, for example, 347.392 =
3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9
× (1/100) + 2 × (1/1000).
Compare two decimals to thousandths based
on meanings of the digits in each place, using
>, =, and < symbols to record the results of
comparisons.
The students will learn to….

Add, subtract, multiply and divide decimals to
hundredths, using concrete models or
drawings and strategies based on place value,
properties of operations, and/or the
relationship between addition and
subtraction; relate the strategy to a written
method and explain the reasoning used.
LESSONS 13 - 16
Dividing Decimals
Unit 1 concludes with division of decimal numbers by
one-digit whole number divisors. Lessons 13 – 16
begin with multiples students easily recognize such
as 4.2 ÷ 6. Then lessons move to quotients which
have a remainder. Students begin to master the
algorithm before they move to division of two-digit
divisors in Unit 2.
Students will use their whole number experiences
with division as they begin to realize that division of
decimals is the same concept and process.
Example Problems and Solutions
 4.2 ÷ 7 = ____ tenths ÷ 7 = ____ tenths = ____
4.2 is 42 tenths. 42 tenths ÷ 7 is 6 tenths. 6 tenths
in standard form is 0.6.
 8 groups of ___ hundredths is 0.32.
0.32 ÷ 8
This problem reminds students of the relationship
between multiplication and division learned in
previous grades. (4 x 3 = 12  12 ÷ 4 = 3)
8 groups of 4 hundredths is the same as 8 x 0.04 =
0.32. Which means that 0.32 ÷ 8 = 0.04.
 3.96 ÷ 3 = ____ ones ÷ 3 + ____ hundredths ÷ 3
3.96 ÷ 3 = 3 ones ÷ 3 + 96 hundredths ÷ 3
1 ones + 32 hundredths = 1.32
Using a Place Value Chart
Students will use disks and place value charts to
develop their understanding.
Example Problem and Solution
Problem: 6.72 ÷ 3
Step 1: Draw a place value chart and separate the
bottom part into 3 groups because we are dividing
the whole (6.72) into 3 equal parts.
Example Problem and Solution:
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Solve using the standard algorithm. 9.1 ÷ 5
Students had
to think about
the dividend as
9 and 10
hundredths to
keep sharing
(dividing).
Step 2: Show 6.72 using disks in the place value
chart.
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Tape Diagram
A rope 8.7 m long is cut into 5 pieces how long is
each piece?
Step 3: Begin with the larger units which in this
problem is the ones place. Share the 6 ones equally
within the 3 groups. There will be 2 ones in each
group. Next, move to the tenths. We can share 7
tenths with three groups by giving each group 2
tenths. There will be 1 tenth left over. The one
tenth is renamed as 10 hundredths. Now there are
12 hundredths, which can be shared with 3 groups by
giving each group 4 hundredths.
Use a tape diagram to show your work. (A tape
diagram is a model with segments that may
represent units. Students use tape diagrams to
visualize number relationships during problem
solving.)
8.7
m
?
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There is 2.24 in each of the 3 groups.
Application Problem
Students need to find the value of one of the 5
segments.
8.7 ÷ 5
= 87 tenths ÷ 5
=174 hundredth
= 1.74
A bag of potato chips contains 0.96 grams of sodium.
If the bag is split into 8 equal servings, how many
grams of sodium will each serving contain?
= 96 hundredths
The segment is divided into 5 equal parts (units)
since the rope will be cut into 5 equal pieces.
8
= 12 hundredths
=0.12 g of sodium per serving
What other ways can the bag be divided into equal
servings so that the amount of sodium in each
serving has two digits to the right of the decimal and
the digits are greater than zero in the tenths and
hundredths place?
96 can be divided by:
2  0.48g 
6  0.16 g 
3  0.32g 
7  too many decimal places X
4  0.24g 
9  too many decimal places X
5  0.192g X
10  less than 0.11 X
Each piece of rope is 1.74 m long.