MATH MESSAGE
Grade 5, Unit 1, Lessons 1 - 4
5TH GRADE MATH
Objectives of Lessons 1 – 4
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 1 – 4, Multiplicative Patterns on the Place
Value Chart.
Words to know:

Decimal Fraction

Digit

Equation

Exponent

Factor





Hundredths
Place Value
Product
Tenths
Thousandths
Decimal Fraction – a fractional number with a
denominator of 10 or a power of 10 (10, 100, 1000).
It can be written with a decimal point.
Digit – any one of the ten symbols, 0, 1, 2, 3, 4, 5,
6, 7, 8, and 9 used to write numbers.
Equation – statement that two mathematical
expressions have the same value, indicated by use of
the symbol =. Example: 12=4 x 2 + 4.
Exponent – tells the number of times the base is
used as a factor or how many times a number is to
be used in a multiplication sentence. Example: 103
= 10 x 10 x 10.
Factor – A number that is multiplied by another
number to find a product.
Hundredths – one part of 100 equal parts.
hundredth’s place – the second digit to the right of
the decimal point.
Place Value - the numerical value that a digit has
by virtue of its position in a number.
Product - the answer to a multiplication 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;
thousand’s place - the third digit to the right of the
decimal point.
The students will learn to….

Reason concretely and pictorially using
place value understanding to relate
adjacent base ten units from millions to
thousandths.

Reason abstractly using place value
understanding to relate adjacent base
ten units from millions to thousandths.

Use exponents to name place value units
and explain patterns in the placement of
the decimal point.

Use exponents to denote powers of 10
with application to metric conversions.
LESSONS 1 - 4
Multiplication and Division Patterns on the Place
Value Chart
Students will use place value charts to explore
changes in place value position as they multiply and
divide multi-digit whole numbers and decimals by
powers of 10. When we multiply a decimal fraction
by a power of 10, the product will be larger than the
original number. We are shifting to the left on the
place value chart. The number of times we shift to
the left depends on the power of 10. When
multiplying by 10, we shift one place to the left. If
multiplying by 100, we shift two places to the left. If
multiplying by 1,000, we shift three places to the left.
Example: Record the digits of the first factor on the
top row of the place value chart. Draw arrows to
show how the value of each digit changes when you
multiply. Record the product on the second row of
the place value chart.
a)
3.452 x 10 = 34.52
(34.52 is 10 times greater than 3.452.)
When we divide a decimal fraction by a power of
10, the quotient will be smaller than the original
number. We are shifting to the right on the place
value chart. The number of times we shift to the
right depends on the power of 10. When dividing by
10, we shift one place to the right. If dividing by
100, we shift two places to the right. If dividing by
1,000, we shift three places to the right.
a)

After a lesson on exponents, Tia went home
and said to her mom, “I learned that 104 is
the same as 40,000.” She has made a
mistake in her thinking. Use words,
numbers or a place value chart to help Tia
correct her mistake.
Tia thinks that 104 means to multiply 1 by 4 and
then add 4 zeros behind the 4. She is correct in
her thinking of adding 4 zeros, but she was not
supposed to multiply 1 by 4. 104 means 10 x 10
x 10 x 10. 10 is being multiplied by itself 4 times
or 10,000.
345 ÷ 10 = 34.5
Note: This solution uses both words and
numbers. Students could have also solved this
problem by drawing a place value chart and
shifting 10 four places to the left.
Exponents:
Students will learn a more efficient way to represent
place value units, using exponents. Students will
see that the number of zeros in the product
(answer) is the same as the number of factors of 10
being multiplied.

A honey bee’s length measures 1 cm.
Express this measurement in meters.
a.
Explain your thinking using a place value
chart.
1
Example:
104 = 10 x 10 x 10 x 10=10,000 (4 factors of 10 – 4
zeros in the product)
103 = 10 x 10 x 10 = 1,000 (3 factors of 10 – 3 zeros
in the product)
Students will apply their knowledge of exponents to
converting metric units.
Example:
3 x 102= 3 x 10 x 10 or 300
Convert 3 meters to centimeters. (1 meter = 100
centimeters) 100 is the same as 102.
3 meters = 300 cm
0
●
0
1
There are 100 centimeters in 1 meter. To
convert to meters from centimeters, I have to
divide 1 by 100. To show this on a place value
chart, I shifted 1 two places to the right.
1 cm = 0.01 meters
b.
Explain your thinking using an equation that
includes an exponent.
SAMPLE PROBLEMS AND ANSWERS

Alaska has a land area of about 1,700,000
km2. Florida has a land area 1/10 the size of
Alaska. What is the land area of Florida?
Explain how you found your answer.
1 meter = 100 centimeters.
1/10 is the same as dividing by 10. To find the
area of Florida, I divided 1,700,000 by 10 which
equals 170,000. I pictured the place value chart
in my head. I shifted the 1,700,000 one place to
the right. That shifted one of the zeros to the
tenths place. So instead of having 5 zeros, the
number now has 4 zeros.
1 ÷ 102
1,700,000 ÷ 10 = 170,000.
The land area of Florida is 170,000 km2.
100 is the same as 102.
= 1 ÷ (10 x 10)
= 1 ÷ 100
= 0.01 m
Students are showing
that they understand
that 102 is 10 x 10 or
100. It is acceptable if
students don’t show the
step, 1 ÷ (10 x 10).