Mathematics Alignment Lesson
Grade 5 Quarter 1 Day 15
Common Core State Standard(s)
5.NBT.3 Read, write, and compare decimals
to thousandths.
a. Read and write decimals to thousandths
using base-ten numerals, number names,
and expanded form, e.g., 347.392 = 3 x
100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x
(1/100) + 2 x (1/1000)
b. Compare two decimals to thousandths
based on meanings of the digits in each
place, using >, =, and < symbols to
record the results of comparisons.
Standards for Mathematical Practice
Standard 7 – Look for and make use of
structure.
Materials Needed:



Base Ten Blocks for each student (flats,
rods, units)
Blackline Masters, “Blank Base Ten
Grids A,” “Blank Base Ten
Grids B,”
Transparency/Blackline Master“Base Ten Grids”
Assessment
Informal:
 Circulate to check for understanding
during partner and independent practice
times.
 “Blank Base Ten Grids A and B” and
“Decimal Place Value Practice
Homework
Blackline Master- “Decimal Place Value
Practice”
Vocabulary
Thousandth: one part out of 1,000 equal
parts of a whole; the position of the third
digit to the right of the decimal point
Wake County Public School System, 2012
Alignment Lesson
Decimal Place Value with Base Ten Blocks and Grids
1. Distribute base ten blocks to each student and instruct them to
use rods to cover a flat. Discuss “Question Set A” on Teacher
Guide, “Decimal Place Value Discussion Questions.”
2. Engage the class in a discussion about the corresponding
decimal notations from questions 2–4 (0.1, 0.7, and 0.4) and
the relationship between fractions and decimals. Then,
discuss “Question Set B” on Teacher Guide, “Decimal Place
Value Discussion Questions.”
3. Ask students to write the number that represents 3 flats, 5
rods, and 7 units using decimal notation. (3.57)
4. Ask students to arrange their base ten blocks to show 2.34. (2
flats, 3 rods, 4 units)
5. Engage students in several more whole class examples, similar
to the ones in steps 3 and 4, to check for understanding. Then,
invite student pairs to ask each other similar types of questions
to practice.
6. Display Transparency/Blackline Master, “Base Ten Grids”
and present Grid A. Discuss “Question Set C” on Teacher
Guide, “Decimal Place Value Discussion Questions.”
7. Distribute Blackline Master, “Blank Base Ten Grids A,” and
write several numbers on the board for students to shade,
including numbers less than 1, numbers between 1 and 2, and
numbers greater than 2. Circulate to check for understanding
and assist individual students, referencing the base ten blocks
for students needing more concrete practice.
8. Display Transparency/Blackline Master, “Base Ten Grids”
and present Grid B. Discuss “Question Set D” on Teacher
Guide, “Decimal Place Value Discussion Questions.”
9. Distribute Blackline Master, “Blank Base Ten Grids B,” and
write several numbers on the board for students to shade,
including numbers less than 1, numbers between 1 and 2, and
numbers greater than 2. Circulate to check for understanding
and assist individual students.
10. Students should complete “Decimal Place Value Practice” for
homework.
Note: There are a large number of discussion questions in today’s
lesson. To actively engage all students in continual thinking
during the lesson, you may wish to have students turn and talk
with established partners and then choose one person to share with
the class for some of the “Decimal Place Value Discussion
Questions.”
Source: Teacher Created
Teacher Guide Grade 5
Day 15
Standard 5.NBT.3
Decimal Place Value Discussion Questions
Question Set A:
1.
2.
3.
4.
How many rods did you use to cover the flat? 10
If a flat represents 1 whole, then what fraction does one rod represent? 1/10
What fraction of the flat is 7 rods? 7/10
What fraction of the flat is 4 rods? 4/10
Question Set B:
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
What decimal number is represented by 10 rods? 1.0
What decimal number is represented by 1 flat and 5 rods? 1.5
How many tenths are in two wholes? 20
How would you write 20 tenths using decimal notation? 2.0
How many small squares are in a flat? 100
Which base ten piece would you use to show one hundredth? unit
Why? 100 units are in a flat, so one unit represents 1/100 of a flat
How many hundredths does a rod represent? 10
How would you write 10 hundredths using decimal notation? 0.10
Do 0.10 and 0.1 represent the same number? yes
Explain why 0.10 and 0.1 represent the same number using the base ten blocks. 0.10
represents 10 units and 0.1 represents 1 rod. Since 1 rod is equal to 10 units, 0.10
and 0.1 represent the same number.
Question Set C:
16.
17.
18.
19.
20.
How many small squares are on this grid? 100
What fraction of the grid does each small square represent? 1/100
What is the decimal representation for each small square? 0.01
What is the decimal representation for each row or each column? 0.10 or 0.1
If I shade 2 columns and 4 small squares, what decimal have I represented? 0.24
(Shade as you ask the question to aid student understanding.)
Question Set D:
21. How many tiny rectangles are on this grid? 1,000 (You may wish to break each piece
22.
23.
24.
25.
down to aid understanding… in each small square there are 10 tiny rectangles, and in
each row of small squares, there are 100 tiny rectangles, so in 10 rows, there are
1,000 tiny rectangles)
What fraction of the grid does each tiny rectangle represent? 1/1000
How do you think we might represent this number using decimal notation? 0.001
What do you think this place value is called? a thousandth Why? It represents a
tenth of one hundredth or 1/1000 of a whole.
If I shade 2 rows, 8 small squares, and 9 tiny rectangles, what decimal have I
represented? 0.289 (Shade as you ask the question to aid student understanding.)
Wake County Public School System, 2012
Transparency/Blackline Master
Grade 5
Day 15
Base Ten Grids
Grid A
Grid B
Wake County Public School System, 2012
Standard 5.NBT.3
Blackline Master
Grade 5
Day 15
Standard 5.NBT.3
Name: ________________________
Date: ________________________
Blank Base Ten Grids A
Wake County Public School System, 2012
Blackline Master
Grade 5
Day 15
Standard 5.NBT.3
Name: ________________________
Date: ________________________
Blank Base Ten Grids B
Wake County Public School System, 2012
Blackline Master
Grade 5
Day 15
Standard 5.NBT.3
Name: ________________________
Date: ________________________
Decimal Place Value Practice
1. What number is represented by 3 flats, 7 rods, and 9 units? Write your answer in
decimal notation.
2. What number is represented by 8 units, 1 flat, and 6 rods? Write your answer in
decimal notation.
3. Shade 2.793 on the grids below.
4. Explain why 0.3, 0.30, and 0.300 are equivalent. Include base ten blocks or grids in
your description.
5. Explain the relationship between thousandths and hundredths.
Wake County Public School System, 2012
Answer Key Grade 5
Day 15
Standard 5.NBT.3
Decimal Place Value Practice
Answer Key
1. What number is represented by 3 flats, 7 rods, and 9 units? Write your answer in
decimal notation.
3.79
2. What number is represented by 8 units, 1 flat, and 6 rods? Write your answer in
decimal notation.
1.68
3. Shade 2.793 on the grids below.
Students should have shaded 2 whole squares, 7 columns, 9 small squares, and 3
tiny rectangles.
4. Explain why 0.3, 0.30, and 0.300 are equivalent. Include base ten blocks or grids in
your description.
0.3 is equal to 3 tenths of the flat or 3 rods. Each of the rods can be broken into 10
units making 30 hundredths of the flat. The units are represented by the small
squares on the base ten grid, and each of the small squares can be divided into 10
tiny rectangles, making 300 thousandths of the whole.
5. Explain the relationship between thousandths and hundredths.
There are 10 thousandths in one hundredth, so a thousandth is one tenth of a
hundredth, making it one thousandth of the whole.
Wake County Public School System, 2012