Unit 4 Extending Decimals
Grade 5
5E Lesson Plan Math
Grade Level: 5th
Lesson Title: Extending Decimals
Subject Area: Math
Unit Number: 4
Lesson Length: 6 days
Lesson Overview
This unit bundles student expectations that address foundational understandings of decimals
as well as adding and subtracting of decimals through the thousandths place. According to the
Texas Education Agency, mathematical process standards including application, a problemsolving model, tools and techniques, communication, representations, relationships, and
justifications should be integrated (when applicable) with content knowledge and skills so that
students are prepared to use mathematics in everyday life, society, and the workplace.
During this unit, students are formally introduced to the thousandths place. Students build
upon the idea that our base-ten place value system extends infinitely to very small values as
well as very large values, and that each place-value position is one-tenth the value of the
place to its left and 10 times the position to the right. Students relate previous representations
of decimals to the hundredths with concrete and pictorial models to develop their conceptual
knowledge of decimals through the thousandths. Students are expected to use expanded
notation and numerals to represent the value of a decimal through the thousandths. Students
use comparison symbols to compare and order decimals to the thousandths and round
decimals to the tenths or hundredths place. Students continue to estimate solutions and
extend addition and subtraction with decimals to include the thousandths place. Numerical
expressions are revisited as a means for students to communicate their solution process and
to solve problem situations involving decimals.
Unit Objectives:
Students will…
 Relate previous representations of decimals to the hundredths with concrete and
pictorial models to develop their conceptual knowledge of decimals through the
thousandths.
 Use expanded notation and numerals to represent the value of a decimal through the
thousandths.
 Use comparison symbols to compare and order decimals to the thousandths and round
decimals to the tenths or hundredths place.
 Estimate solutions and extend addition and subtraction with decimals to include the
thousandths place.
 Communicate solution processes and solve problem situations involving decimals using
numerical expressions.
Standards addressed:
TEKS:
5.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
5.1B Use a problem-solving model that incorporates analyzing given information, formulating a
plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
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Unit 4 Extending Decimals
Grade 5
5.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
5.1D Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
5.1E Create and use representations to organize, record, and communicate mathematical
ideas.
5.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
5.1G Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
5.2A Represent the value of the digit in decimals through the thousandths using expanded
notation and numerals. Supporting Standard
5.2B Compare and order two decimals to thousandths and represent comparisons
using the symbols >, <, or =. Readiness Standard
5.2C Round decimals to tenths or hundredths. Supporting Standard
5.3A Estimate to determine solutions to mathematical and real-world problems
involving addition, subtraction. Supporting Standard
5.3K Add and subtract positive rational numbers fluently. Readiness Standard
5.4F Simplify numerical expressions that do not involve exponents, including up to two levels
of grouping. Readiness Standard
ELPS:
1A use prior knowledge and experiences to understand meanings in English
2D monitor understanding of spoken language during classroom instruction and interactions
and seek clarification as needed
3C speak using a variety of grammatical structures, sentence lengths, sentence types, and
connecting words with increasing accuracy and ease as more English is acquired
3D speak using grade-level content area vocabulary in context to internalize new English
words and build academic language proficiency
4H read silently with increasing ease and comprehension for longer periods
5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
5E employ increasingly complex grammatical structures in content area writing commensurate
with grade-level expectations
5G narrate, describe, and explain with increasing specificity and detail to fulfill content area
writing needs as more English is acquired.
Misconceptions:
 Some students may think placing zeros at the end of a decimal number always affects
the value of the number rather than being used as a place-holder (e.g., In 0.400 the
zeros do not affect the value, but in 0.04 the zero in the tenths place does affect the
value.)
 Some students may think you can only round certain numbers to a specific place value,
rather than being able to round to any given place value (e.g., The decimal number
34.25 can be rounded to the nearest tenths place, ones place, tens place, hundreds
place, etc.)
 Some students may use the digit in the tenths place to determine how many boxes to
shade in on a hundredths grid (e.g., shading in 8 of the 100 boxes for 0.8) rather than
determining the value of the number written as hundredths (e.g., shading in 80 of the
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Unit 4 Extending Decimals
Grade 5
100 boxes of 0.80).
 Some students may order decimals incorrectly by trying to relate whole number
understandings to decimal understandings (e.g., 0.29 is greater than 0.6 because 29 is
greater than 6) rather than using decimal place value understandings (e.g. 0.29 is less
than 0.60).
 Some students may order decimals based on the number of digits in the number, rather
than determining its value. (e.g. 0.123 is greater than 0.45 because 0.123 has three
digits and 0.45 only has two digits.)
Vocabulary:
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Compare numbers – to consider the value of two numbers to determine which number
is greater or less or if the numbers are equal in value
Compatible numbers – numbers that are slightly adjusted to create groups of numbers
that are easy to compute mentally
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Decimal number – a number in the base-10 place value system used to represent a
quantity that may include part of a whole and is recorded with a decimal point
separating the whole from the part
Digit – any numeral from 0 – 9
Estimation – reasoning to determine an approximate value
Expanded notation – the representation of a number using place value (e.g.,
985,156,789.782 as 900,000,000 + 80,000,000 + 5,000,000 + 100,000 + 50,000 +
6,000 + 700 + 80 + 9 + 0.7 + 0.08 + 0.002 or 9(100,000,000) + 8(10,000,000) +
5(1,000,000) + 1(100,000) + 5(10,000) +6(1,000) + 7(100) + 8(10) + 9 + 7(0.1) +
8(0.01) + 2 (0.001) or 9(100,000,000) + 8(10,000,000) + 5(1,000,000) + 1(100,000) +
5(10,000) +6(1,000) + 7(100) + 8(10) + 9 + 7 ( ) + 8(
)+2(
))
Expression – a mathematical phrase, with no equal sign, that may contain a
number(s), a unknown(s), and/or an operator(s)
Fluency – efficient application of procedures with accuracy
Front-end method – a type of estimation focusing first on the largest place value in
each of the numbers to be computed and then determining if the next smallest place
value(s) when grouped should be
Numeral – a symbol used to name a number
Order numbers – to arrange a set of numbers based on their numerical value
Order of operations – the rules of which calculations are performed first when
simplifying an expression
Parentheses and brackets – symbols to show a group of terms and/or expressions
within a mathematical expression
Place value – the value of a digit as determined by its location in a number, such as
ones, tens, hundreds, one thousands, ten thousands, etc.
Positive rational numbers – the set of numbers that can be expressed as a fraction
where a and b are whole numbers, and b ≠ 0 which includes the subsets of whole
numbers and counting (natural) numbers (e.g., 0, 2,
etc.)
Rounding – a type of estimation with specific rules for determining the closest value
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Unit 4 Extending Decimals
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Grade 5
Standard notation – the representation of a number using digits (e.g.,
985,156,789.782)
Trailing zeros – a sequence of zeros in the decimal part of a number that follow the
last non-zero digit, and whether recorded or deleted, does not change the value of the
number
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Written notation – the representation of a number using written words (e.g.,
985,156,789.782 as nine hundred eighty-five million, one hundred fifty-six thousand,
seven hundred eighty-nine and seven hundred eighty-two thousandths)
Related Vocabulary:
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About
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Greater than (>)
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Approximately
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Less than (<)
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Ascending
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Magnitude
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Base-10 place value system
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Number line
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Descending
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Position
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Equal to (=)
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Tenths
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Equivalent
Estimate
Hundredths
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Thousandths
List of Materials:
Materials are listed each day
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Unit 4 Extending Decimals
Grade 5
Phase: 1 Engage
Day 1 Activity
Materials: Base Ten Blocks
●
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Provide students with sets of Base Ten Blocks.
Start by modeling whole numbers. Suppose a unit block equals 1.
● What is the value of a rod? (10)
● What is the value of a flat? (100)
● What is the value of a cube? (1000)
As each question is asked, allow students time to work with a partner to
model the question with their cubes and to discuss their answers before
sharing with the class.
After each question, ask students to explain their reasoning. (i.e., “There
are 10 units in a rod, so a rod equals 10.” or “There are 10 flats in a cube
and one flat equals 100, so 10 of these equals 1000.”)
Change the whole. Say: Suppose that a flat represents 1 whole.
●
What is the value of a rod?
●
What is the value of a unit?
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What is the value of a cube? (10)
Again, allow students time to work with a partner to model the question
with their cubes and to discuss their answers before sharing with the
class. Students should be asked to explain how they know. (i.e., “There
●
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1
10
1
100
1
are 10 rods in a flat, so one rod would be 10 of the flat.” Or “There are 10
flats in a cube. If one flat equals 1, then 10 flats would equal 10.”)
What’s the teacher doing?
Teacher provides concrete models for
students to explore decimals to the
thousandths
What are the students doing?
Students use the base ten blocks to explore
decimals to the tenth, hundredth and thousandth
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Unit 4 Extending Decimals
Grade 5
Phase 2 Explore
Day 1 Activity:
Materials: Dry erase markers and white boards
Students will represent value of digits in decimal numbers to the thousandths place with
standard, expanded and word notation. They will understand that numerals get 10 times
larger each time place value moves to the left.
𝟏
And numerals get 𝟏𝟎 smaller each time place value moves to the right:
Students will write numerals in their place value chart by placing the digits in the correct place.
Teacher writes three thousand forty seven on the board. On personal white boards, students
write this number in standard form and expanded form. Explain that you have written the word
form.
Tell students: Explain to your partner the purpose of writing this number in these
different forms.
Student Response: Standard form shows us the digits that we are using to represent that
amount. Expanded form shows how much each digit is worth and that the number is a total of
those values added together.
Explain that there is another form called unit form and unit form helps us see how many of
each size units are in the number. Example: 3 thousands, 4 tens, 7 ones.
Give students a place value chart that has decimal place values to the thousandths. Use
Teacher resource: Place Value Chart Day 1. Make enough copies for each student. Place in
a plastic sleeve or laminate so students can use a dry erase marker to write the numerals. Put
students in pairs.
Problem 1
Represent 1 thousandth and 3 thousandths in standard, expanded, and unit form.
Tell students to write one thousandth using digits on their place value chart. Ask: “How many
ones, tenths, hundredths, and thousandths?”
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Unit 4 Extending Decimals
Grade 5
Student response: Zero, zero, zero, one.
Teacher’s response: This is the standard form of the decimals for 1 thousandth.
𝟏
We write 1 thousandth as a fraction like this: (write 𝟏𝟎𝟎𝟎 on the board)
1 thousandth is a single copy of a thousandth. I can write the expanded form using a
𝟏
fraction like this, 1 x 𝟏𝟎𝟎𝟎
(saying one copy of one thousandth) or using a decimal like this 1 x 0.001 (write on the board)
The unit form of this decimal number looks like 1 thousandth (write on the board). We use a
numeral (point to the 1) and the unit (point to the thousandth) written as a word.
1
One thousandth = 0.001 = 1000
1
1000
1
= 1 x ( 1000)
0.001= 1 x (0.001)
1 thousandth
Tell the students to imagine 3 copies of 1 thousandth. How many thousandths is that?
Student response: 3 thousandths
(write that in standard form, decimal form, and a fraction)
Tell students to write that in their place value chart.
3 thousandths is 3 copies of 1 thousandth, turn and talk to your partner about how this
would be written in expanded form using a fraction and a decimal.
Three thousandths = 0.003 =
3
1000
3
1000
1
= 3 x ( 1000)
0.003 = 3 x (0.001)
3 thousandths
Students can copy these examples in their math journals along with explanations of expanded
form, standard form and unit form.
Problem 2
Represent 13 thousandths in standard, expanded, and unit form.
T: Write thirteen thousandths
in standard form, and
expanded form using
fractions and then using
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Unit 4 Extending Decimals
Grade 5
decimals. Turn and share
with your partner.
S: Zero point zero one three is
standard form. Expanded forms
are
1
1
1 x 100 + 3 x 1000 and 1 x 0.01 + 3 x 0.001
T: Now write this decimal in unit form.
S: 1 hundredth, 3 thousandths 
13 thousandths.
T: (Circulate and write responses on
the board.) I notice that there
seems to be more than one way to
write this decimal in unit form.
Why?
S: This is 13 copies of 1 thousandth.

You can write the units
separately or write the 1
hundredth as 10 thousandths.
You add 10 thousandths and 3
thousandths to get 13
thousandths.
13
Thirteen thousandths = 0.013 = 1000
13
1000
= 0.013 = 1 x 0.01 + 3 x 0.001
1 hundredth 3 thousandths
13 thousandths
Repeat with 0.273 and 1.608 allowing students to combine units in their unit forms (for
example, 2 tenths 73 thousandths; 273 thousandths; 27 hundredths 3 thousandths). Use more
or fewer examples as needed reminding students who need it that and indicates the decimal in
word form.
Problem 3
Represent 25.413 in word, expanded, and unit form.
T: (Write on the board.) Write 25.413 in word form on your board. (Students write.)
S: Twenty-five and four hundred thirteen thousandths.
T: Now, write this decimal in unit form on your board.
S: 2 tens 5 ones 4 tenths 1 hundredth 3 thousandths.
T: What are other unit forms of this number?
Allow students to combine units, e.g., 25 ones 413 thousandths; 254 tenths 13 hundredths;
25,413 thousandths.
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Unit 4 Extending Decimals
Grade 5
T: Write it as a mixed number, then in expanded form. Compare your work with your
partner’s.
413
Twenty-five and four hundred thirteen thousandths = 251000 = 25.413
413
1
1
1
25 1000= 2 x 10 + 5 x 1 + 4 x 10 + 1 x 100 + 3 x 1000
25.413= 2 x 10 + 5 x 1 + 4 x 0.1 + 1 x 0.01 + 3 x 0.001
2 tens 5 ones 4 tenths 1 hundredths 3 thousandths
25 ones 413 thousandths
Repeat the sequence with 12.04 and 9.495. Use more or fewer examples as needed.
Problem 4 Exit Ticket:
Write the standard, expanded, and unit forms of four hundred four thousandths and four
hundred and four thousandths.
T: Work with your partner to write these decimals in standard form. (Circulate looking for
misconceptions about the use of the word and.)
T: Tell the digits you used to write four hundred four thousandths.
T: How did you know where to write the decimal in the standard form?
S: The word and tells us where the fraction part of the number starts.
T: Now work with your partner to write the expanded and unit forms for these numbers.
What’s the teacher doing?
Teacher will model how the standard,
expanded and unit forms are written.
What are the student’s doing?
Students will work with their partners to write the
expanded, standard and unit form of several
decimal numbers.
Phase __2 Explore___
Day 2 Activity Materials: Nerf Ball, Starting Line-up Cards, Starting Line-up Grid and
Data Table, Trash Can, Masking Tape, “Post-it” notes, index cards and scissors
Tell students that today they will be learning about decimals and how to use
them.
Mention that decimals are just another way of recording fractions.
 Ask, “Who likes to play basketball?” Explain that they will be using
basketball to learn about decimals.
 Ask for a student volunteer. Tell the student to stand on a tapeline
placed 8 feet away from a trashcan. Have the student take 10 shots at the
trashcan baskets with a Nerf ball or wadded up piece of paper. Display
teacher resource “Trashcan Hoops” on an overhead projector to record
the results. Explain how the shots made are recorded as a decimal.
Repeat procedure with three more students.
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Unit 4 Extending Decimals
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Grade 5
Ask, “Who made the most shots? What does that decimal look like?”
Who made the least shots? What does that decimal look like?’
Ask, “Who do you think is the best player in the NBA?” Elicit responses from students.
Who do you think is better between Allen Iverson, LeBron James and Shaquille O’Neal?
Elicit responses from students.
 Say, “We are going to look at real data on these three players to help us better
understand decimals.” Display a transparency of Teacher Resource Sheet
“Player’s Stats.”
“How do you think that the people that keep the NBA statistics come
up with these numbers?” (They divide the number of shots that the
player attempts by the number of shots they actually made; just like we did
yesterday in our trashcan hoops game.)
 Ask, “Can anyone tell me anything they notice about the statistics?”
Elicit responses from students. Be sure and have them explain how they
made that observation.
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What do you notice about these decimals?”(They have three places
beyond the decimal point)
“Why do you think they did that?”
“If we compare Allen Iverson field goal average to LeBron James’ and
only look at the decimal to the tenths place what would happen?
(They would both have 0.4)
“If we continue to look at those same statistics and continue out to
the hundredths place what happens? (We have 0.42 and 0.47)
“If we keep looking at that third number beyond the decimal point,
which is called the thousandths place, then what 2 decimals are
we comparing? (0.424 and 0.472)
“So, how do you think extending the decimal out to the
thousandths place helps us? (It gives us more detail and makes the
number more accurate).
If available, illustrate the scenario above using overhead decimal squares
so that students have a visual representation of the relative size of the
tenths, hundredths and thousandths.
Students can use decimal place value charts to compare the decimals.
Continue in this manner comparing other averages to the thousandths
place.
Ask probing questions such as, “Who has a better field goal average?
How do you know? Who has a better three point shot average? How
do you know? Who has a better free throw average? How do you
know?
Write 0.649 on the chalkboard or overhead projector. Say, “We know
that decimals are composed of digits and one decimal point. Each
digit in relation to the decimal point has a particular value. What is
the value of 6 in 0.649? What is the value of 4? What is the value of
9? As with all numbers, decimals can be placed on a number line. We
can do this to illustrate how close they are to either 0 or 1.
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Unit 4 Extending Decimals
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Student Game:
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Grade 5
Say, “Think about what we know so far about decimals. What would
be an example of a digit that a decimal might have in the tenths place
that would make it fall very close to 1 on a number line? (List students’
responses.) What would be an example of a digit that a decimal
might have in the tenths place that would make it fall in the middle
of a number line between 0 and 1? (List students’ responses.) What
would be an example of a digit that a decimal might have in the tenths
place that would make it fall very close to 0 on the number line?
(List students’ responses.)
Write 0.751 and 0.708 on the board. Ask, “What if I have two decimals
that have the same digit in the tenths place how do I know which
one goes where on the number line?
Write 0.328 and 0.323 on the board. Ask, “If I have two decimals that
have the same digit in the tenths and the hundredths place, how do
I know where the numbers are on the number line?
Draw a line on the chalkboard that is at least 6 feet long (If you do not have
a chalkboard long enough, you may use a tape line on the wall or the
floor). Place Teacher Resource Sheets, “Backboard Benchmark Near
0”, on the far left end of the line, and “Backboard Benchmark Near 1”, on
the far right end of the line.
Distribute one 3”X 3” Post-It note and a marker to each student.
Instruct students to write a decimal to the thousandths on their post-it
using clearly visible digits. Challenge students to try to think of a
decimal that no one else will think of and to not let anyone else see their
decimal.
Have students trade their post-it with another student.
Tell students that they are going to use the number line on the board to
estimate the value of the decimal on their post-its.
Have 2-3 students at a time come up and place their decimal on the
number line in relation to being near 0 or near 1. Have each student
explain why he or she placed their decimal where they did.
Copy Teacher Resource Starting Line-Up cards and cut apart. Copy
Teacher Resource, “Starting Line- Up Grid and Data Table”.
Draw a copy of the “Starting Line-Up Grid” from Teacher Resource
“Starting Line-Up Grid and Data Table” on the board. Using your precut
“Starting Line-Up Decimal Digit Cards” select 5 random decimals.
Explain to students that the game is played by looking at the cards 1 at a
time and estimating where it should go on the grid in relationship to 0 and
1. Tell students that once they place a digit card on the grid they may not
change its position, so they must think very carefully about each decimal
and its relationship to 0 and 1 before they place it. Play one sample round
with students having them help you decide on each decimals placement
on the grid. Be sure to have them explain why they think each decimal
should go where they suggest on the grid.
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Unit 4 Extending Decimals
Grade 5
Demonstrate how the decimals are recorded on the data table. If decimals
are all placed correctly in at least to greatest sequence, tell students they will
place a star beside that row on their data table. If any decimals are out of
order, discuss with students how and why the error occurred.
 Distribute Teacher Resource, “Starting Line- Up Decimal Digit Cards”
and “Grid and Data Table” to each student. Have students cut the
Decimal Digit Cards apart.
 Allow time for students to play the game and record their results.
When students have played the game, give them 2 index cards and scissors. Tell them to cut
the cards in half and write the symbols for greater than, less than, and equal on each half card.
Tell them they have ordered the decimals now we will compare two decimals. Tell them to
pick two decimal cards and place them side by side. Talk about the symbols for greater than,
less than, and equal. Have them right them down in their math journals with examples and
non-examples. Using the cards the students will place the correct symbol between the two
decimal numbers.
Using place value charts, students will write the two decimals in the correct place value and
use the chart to compare.
If time allows show the video from Learn Zillion: https://learnzillion.com/lessons/35-compareand-order-decimals-to-the-thousandths-place. Students may access this video by going to the
Learn Zillion website and typing in the access code: LZ35.
For Extra practice use Day 2 Re-teaching Page
What’s the teacher doing?
While students are playing the game
observe and record. Share with
students that you will assess their
performance as they play the game.
Discuss with students the observable
behaviors you will be looking for and
establish an evaluation method to
assess the criteria. For example,
0- Student’s understanding is
completely incorrect 1- Student shows
minimal or partial understanding 2Student shows complete understanding
What are the students doing?
Students will play the game to demonstrate
understanding of ordering and comparing decimals
•
Collect each student’s completed
copy of Student Resource Sheet 3,
“Starting Line Up Grid and Data
Table.” Analyze for understanding
and/or error patterns.
Check for understanding of comparing
the two decimal cards.
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Unit 4 Extending Decimals
Grade 5
Phase ___Explore/Explain______
Activity: Day 3
Materials: White boards and dry erase markers
Rounding decimal numbers to the tenths place, and/or the hundredths place. Students will
first review rounding whole numbers from 4th grade. If Smart Board technology is available
use Day 3: Rounding Decimals to review and to reinforce the concept of rounding. Learn
Zillion website can also be used to teach the concept of rounding:
https://learnzillion.com/lessons/3094-represent-decimal-numbers-on-a-number-line
Use of a number line is important for students to grasp the concept of which number is closest.
In this activity students use number lines drawn on white boards to learn the concept. They
will also use Turn and Talk strategy to provide understanding of the concept. Modeling kneeto-knee, eye-to-eye body posture and active listening expectations (Can I restate my partner’s
ideas in my own words?) make for successful implementation of this powerful strategy.
First Round to the nearest whole number:
T: (Project 8.735.) Say the number.
S: 8 and 735 thousandths.
T: Draw a vertical number line on your boards
with 2 endpoints and a midpoint.
T: Between what two ones is the number 8.735?
S: 8 ones and 9 ones.
T: What’s the midpoint for 8 and 9?
S: 8.5
T: Fill in your endpoints and midpoint.
T: 8.5 is the same as how many tenths?
S: 85 tenths.
T: How many tenths are in 8.735?
S: 87 tenths.
T: (Write 8.735 ≈ _______.) Show 8.735 on your number line and write the number
sentence.
S: (Students write 8.735 between 8.5 and 9 on the number line and write 8.735 ≈ 9.)
Repeat the process for the tenths place and hundredths place. Follow the same process and
procedure for 7.458.
Next, project the following problem on the board:
Organic, whole-wheat flour sells in bags weighing 2.915 kilograms. How much flour is this
rounded to the nearest tenth? How much flour is this rounded to the nearest one? What is the
difference of the two answers? Use a place value chart and number line to explain your
thinking.
Allow students to complete the activity with a partner. Give students place value charts and
number lines to complete the activity.
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Unit 4 Extending Decimals
Grade 5
Next tell students to round 49.67 to the nearest ten.
T: Turn and talk to your partner about the different ways
49.67 could be decomposed using place value disks.
Show the decomposition that you think will be most
helpful in rounding to the nearest ten.
T: Which one of these decompositions did you decide
was the most helpful?
S: The decomposition with more tens is most helpful,
because it helps me identify the two rounding choices: 4
tens or 5 tens.
T: Draw and label a number line and circle the
rounded value. Explain your reasoning.
5 tens or 50
45.67
4 tens or 40
Repeat this sequence with rounding 49.67 to the nearest ones, and then tenths.
Problem 2
Decompose 9.949 and round to the nearest tenth and
hundredth. Show your work on
a number line.
100 tenths = 10
99 tenths = 9.9
9 ones
9 tenths
4 hundredths
9 thousandths
99 tenths
4 hundredths
9 thousandths
994 hundredths
9 thousandths
90 tenths
T: What decomposition of 9.949 best helps to round this number to the nearest
tenth?
S: The one using the most tenths to name the decimal fraction. I knew I would round to
either 99 tenths or 100 tenths. I looked at the hundredths. Nine hundredths is past the
midpoint, so I rounded to the next tenth, 100 tenths. One hundred tenths is the same
as 10.
T: Which digit made no difference when you rounded to the nearest tenth? Explain
your thinking.
S: The thousandths, because the hundredths decided which direction to round. As long
as I had 5 hundredths, I was past the halfway point so I rounded to the next number.
Repeat the process rounding to the nearest hundredth.
Problem 3
A decimal number has 1 digit to the right of the decimal point. If we round this number to the
nearest whole number, the result is 27. What are the maximum and minimum possible values
of these two numbers? Use a number line to show your reasoning. Include the midpoint on
the number line.
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Unit 4 Extending Decimals
Grade 5
T: (Draw a vertical number line with 3 points.)
T: What do we know about the unknown number?
S: It has a number in the tenths place, but nothing else past the decimal point. We know
that is has been rounded to 27.
T: (Write 27 at the bottom point on the number line and circle it.) Why did I place 27 as
the lesser rounded value?
S: We are looking for the largest number that will round down to 27. That number will be
greater than 27, but less than the midpoint between 27 and 28.
T: What is the midpoint between 27 and 28?
S: 27.5
T: (Place 27.5 on the number line.)
T: If we look at numbers that have exactly 1 digit to the right of the decimal point,
what is the greatest one that will round down to 27?
S: 27.4. If we go to 27.5, that would round up to 28.
Repeat the same process to find the minimum value.
To find maximum
To find minimum
28
26
27.5
27.4
26.5
27
27
26
As an exit ticket have students round several numbers to the nearest ten, whole number, tenth
and hundredth.
What’s the teacher doing?
Monitor partners and give feedback
during the exploration of the word
problems.
What are the students doing?
Students are working in pairs to work the problem.
Phase: Explore/Explain
15
Unit 4 Extending Decimals
Grade 5
Activity: Day 4
Materials: Take out Menus, Grocery Ads
Estimate decimal numbers to add and subtract. If technology is available use the website:
https://learnzillion.com/lessons/545-estimate-the-addition-and-subtraction-of-decimals-usingsmart-rounding for concept development.
Students use estimation to solve addition and subtraction problems. Teacher will give
students real world problems involving decimal numbers to solve. Using ads from grocery
stores or department stores, students can “purchase” items to buy with a specified amount of
money to spend. They must find the total cost of items purchased and how much money they
have left. They must use estimation and actual cost of items to solve the problem.
Students could also use menus from various restaurants and “play” restaurant with students
being customers, waiters, cashiers, etc. Included in resources is an optional Day 4 Menu
Math Binder to print and use.
Students will create a list of at least five items to purchase and complete an estimation and
actual cost of the items. They will determine, given a certain amount of money, if they will
have enough to pay the total bill and how much they either need or will receive as change.
Students will use various methods of estimation as explained in the examples below.
EX: Front End Rounding
16
Unit 4 Extending Decimals
Grade 5
EX: Rounding to the nearest place value and then solving the problem.
EX: Using compatible numbers and then solving the problem.
17
Unit 4 Extending Decimals
Grade 5
What’s the teacher doing?
What are the students doing?
Monitor students’ progress and offer
support and feedback.
Check for understanding of concepts of
estimation.
Students will use ads to “purchase” items and
compute the cost using estimation and actual
computations to find the total cost and amount of
change received.
Students will complete an estimation and actual
cost of at least five items and determine if they have
enough money to pay for the items.
Phase: Elaborate
Activity Day 5
Materials: Chart paper, scissors, glue sticks, menus and/or ads and markers
Students will continue with the menu/ads theme from yesterday. Students use menus or store
ads and create word problems that involve addition and subtraction of decimal numbers.
Place students in groups of 3 or 4. Give menus and/or ads to each group of students. Explain
to students that they will be creating their own word problems that involve addition and
subtractions of decimal numbers. They must create word problems that involve both
operations.
Students will be given a piece of chart paper, scissors, glue sticks and markers. Tell students
to write their problems on the chart paper and cut out pictures from the menus and/or ads to
help tell the story. They will then write the expression used to solve the problem. Students
must detail how they solved the problems on the chart paper. The solution to the problems
must be written in sentences.
Student groups will then present their problems to the class.
What’s the teacher doing?
Teacher will be walking around
monitoring student groups. Giving
feedback and asking questions as the
groups create word problems.
What are the students doing?
Students are working in groups to create word
problems from menus and/or store ads.
They will present their problems to the class.
Phase: Evaluate
Activity: Day 6
Performance Assessment:
Analyze the problem situation(s) described below. Organize and record your work for each of
the following tasks. Using precise mathematical language, justify and explain each
solution process.
Humboldt Paper Company sells different thicknesses of paper for different types of projects.
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Unit 4 Extending Decimals
Grade 5
1) The paper company wants to create a brochure that describes the products they sell. They
would like to order the types of papers from thinnest to thickest paper so that it is easy for their
customers to find the paper they want.
a) Represent the value of each of the thicknesses using numerals and expanded notation.
b) Create a table that orders the paper names and their thicknesses from thickest to thinnest.
c) Write a comparison statement using the symbols >, <, or = to compare the thickness of two
of the paper types.
2) The company looks at the table and wonders if rounding all of the thicknesses to a common
place-value might be easier for their customers to read. Before they round them all, they want
to make sure it doesn’t change the order of the papers from thinnest to thickest.
a) Explain how to round each of the thicknesses. Then, predict if it would change the order of
the different types of paper.
b) Round each of the paper thicknesses to the tenths place-value.
c) Write a comparison statements using symbols >, <, or = to explain any changes that may
occur in the original order of thinnest to thickest.
d) Round each of the paper thicknesses to the hundredths place-value.
e) Write a comparison statements using symbols >, <, or = to explain any changes that may
occur in the original order of thinnest to thickest.
f) Compare and contrast the effects of rounding the paper thicknesses to the tenths place
versus rounding the paper thicknesses to the hundredths place. Explain why there would be
changes to the order.
3) Another company who makes party invitations decides to purchase some of the paper to
create wedding invitations. Each invitation will have one layer of Vellum paper with a different
layer of paper on top. The envelope for the invitation can hold thicknesses up to 0.505 mm.
19
Unit 4 Extending Decimals
Grade 5
a) Write an expression that can be used to determine the maximum paper thickness that can
be paired with the sheet of vellum to create the invitation.
b) Estimate the thickness of paper that can be paired with the sheet of vellum to create the
initiation.
c) Simplify the expression and identify which paper type(s) can be paired with the vellum to
create the invitation.
Standard(s): 5.1A, 5.1B, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G, 5.2A, 5.2B, 5.3A, 5.3C, 5.3K, 5.
4F
What is teacher doing?
Monitor and check for understanding.
What is student doing?
Student will complete the steps to the problem.
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