Download math message - St. Tammany Parish School Board

MATH MESSAGE
Grade 5, Unit 1, Lessons 9 - 12
Objectives of Lessons 5 - 8
5TH GRADE MATH
Unit 1: Place Value and Decimal Fractions
The students will learn to….
Math Parent Letter

Explain patterns in the number of zeros of the
product when multiplying a number by powers
of 10, and explain patterns in the placement of
the decimal point when a decimal is multiplied
or divided by a power of 10. Use whole-number
exponents to denote powers of 10.

Read, write, and compare decimals to
thousandths.
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 9 - 12, Adding, Subtracting, and Multiplying
Decimals.
Words to know:

Addend

Decimal Fraction

Difference

Estimate

Factor

Hundredths






Product
Sum
Tenths
Thousandths
Unit Form
Addend - any number being added. For example in
the equation, 33 + 4.7 = 37.7; 33 and 4.7 are the
addends.
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.
Difference – answer to a subtraction problem.

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.
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 9 - 12
Adding, Subtracting, and Multiplying Decimals
Estimate – a number close to an exact amount. An
estimate tells about how much.
Factor – an integer that divides evenly into another
integer.
Hundredths – one part of 100 equal parts;
hundredth’s place – the second digit to the right of
the decimal point.
Product - the answer when two or more factors are
multiplied together. 7 x 3 = 21 product
Sum – the answer to an addition problem.
Tenths – one part of 10 equal parts; tenth’s place –
the first digit to the right of the decimal point.
Students use place value charts to add decimals.
Students begin by representing each digit by drawing
or placing disks in the correct place value column of
the chart. Students regroup or “bundle” when there
are ten or more disks in one place value column.
Students will see that when adding decimals, they
record their thinking the same way as they did with
whole numbers. They align like units.
Example Problem and Solution
Find the sum of 0.74 + 0.59. Use disks on your
place value chart and record. (Students may also
see problems with addends in unit form. For
example 74 hundredths + 59 hundredths.)
Ones
●
Thousandths – one part of 1,000 equal parts;
thousandths place - the third digit to the right of the
decimal point.
Unit Form – a number written using digits and the
unit form they represent. For example 3.21 = 3 ones
2 tenths 1 hundredth or 321 hundredths.
Hundredths
●●●●
●●●●●
●●●●●
●●●●
●
3
0.74
+ 0.59
1
●
●
1
Tenths
●●●●●
●●
3
1
1.33
When solving the problem, 0.74 + 0.59, students
needed to regroup in two places. First, they had to
rename 13 hundredths as 1 tenth 3 hundredths.
Students also had to rename or “bundle” 13 tenths
as 1 one and 3 tenths.
Ones
3
groups
of
0.423
Students will use unit form when subtracting
decimals. This will help them make the connection
between whole number subtraction and decimal
subtraction. Students will continue to represent digits
with disks on a place value chart until they begin to
move toward an understanding of the written
algorithm.
I have 8.3,
but I need
i
to remove
6.4.
●
Tenths
●
●●●
●●●●●
●●●●●
9
●● ●
1
I started with 8 ones disks and 3 tenths disks. There
are only 3 tenths, but I need to subtract 4 tenths. I
will need to regroup before I can subtract. I circled
one of the one disks to show how I regrouped 1 one
as 10 tenths. Now I have 7 ones and 13 tenths. First
I crossed out 4 tenths. Then I crossed out 6 ones. I
had 1 one and 9 tenths left. 7 ones 13 tenths – 6
ones 4 tenths = 1 one 9 tenths (1.9).
Application Problem and Solution
Mr. Pham wrote 8 tenths – 5 hundredths on the
board. Michael quickly said the answer is 3 tenths
because 8 minus 5 is 3. Is he correct? Explain.
Hundredths
thousandths
●●●●
●●
●●●
●●●●
●●
●●●
●●●●
●●
●●●
Method 2: Using Area Model
Students write the decimal fraction in unit form.
Then they write the unit form of each digit above the
area model. The other factor is written to the side.
Students multiply the unit form of each digit at the
top by the factor on the side. Students add each of
the partial products to find the product.
83 tenths – 64 tenths. Solve using a place value
chart. Then solve using the standard algorithm.
Explain your thinking.
●●●●●
●
Tenths
3 x 0.423 = 1.269
Example Problem and Solution
Ones
●
3
4 tenths
+ 2 hundredths + 3 thousandths
3 x 4 tenths
= 12 tenths
3 x 2 hundredths
= 6 hundredths
1.2
+
Partial Products:
+
0.06
3 x 3 thousandths
= 9 thousandths
+
0.009 = 1.269
Algorithm:
1.2
0.423
0.06
x
0.009
1.269
3
1.269
Using Estimation
Students can use estimation to confirm that the
decimal has the correct placement in the product.
Students also use estimation to determine the
reasonableness of the product.
Example Problems and Solutions
Michael is mistaken. He subtracted unlike units. He
subtracted 8 tenths – five tenths. The problem is 0.8
– 0.05. The 8 tenths can be renamed as 80
hundredths. 0.80 - 0.05 = 0.75.
1. Circle the reasonable product for the expression.
Explain your reasoning using words, pictures or
numbers.
Students will multiply a decimal fraction by a onedigit whole number in lesson 11. Students will use
place value understanding of whole number
multiplication along with an area model of the
distributive property. This combination will build
connections between whole number products and
decimal products. Students will use an estimation
based strategy to confirm reasonableness of their
decimal placement.
3.14 is close to 3. 3 x 7 = 21. The only product
close to 21 is 21.98. 21.98 is the only reasonable
product.
Example Problem and Solution
3 x 0.423= _________
Method 1: Place Value Chart:
Students know that 423 times 3 also means 3 groups
of 423; therefore 0.423 times 3 means 3 groups of
0.423.
In the place value chart, students will represent
0.423 three times. Students will regroup when there
are ten or more in one place.
3.14 x 7
2198
219.8
21.98
2.198
2. The poetry club had its first bake sale, and they
made $79.35. The club members are planning to
have 4 more bake sales. Leslie said, “If we make the
same amount at each bake sale, we’ll earn
$3,967.50.” Peggy said, “No way, Leslie! We’ll earn
$396.75 after five bake sales.” Use estimation to
help Peggy explain why Leslie’s reasoning is
inaccurate.
$80
Leslie’s reasoning is inaccurate
because $79.35 is close to $80
and $80 x 5 = $400. I also know
that 40 tens ≈ 39 tens. That
means that Peggy’s answer of
$396.75 is reasonable.
$79.35
$75
$70