5th grade – Unit 5 – Decimal Multiplication and Division
5E Lesson Plan Math
Grade Level: 5
Subject Area: Math
Lesson Title: Decimal Multiplication and
Unit Number: 5
Lesson Length: 14
Division
days
Lesson Overview
During this unit, students represent multiplicative structures (multiplication and division) of
problem situations with products and decimals to the hundredths with the use of concrete
objects, pictorial models, and area models. These models serve as a bridge between wholenumber multiplication and division should help students to assimilate new understandings
involving decimal multiplication and division. There is an emphasis on representing
multiplication and division before solving for products and quotients of decimals to allow for the
development of the conceptual understanding before procedural understanding. Students are
expected to estimate to determine products and quotients, solve for products and quotients,
and simplify numerical expressions that include multiplication and division of whole numbers
and decimals. The number set within this unit is limited to products and quotients to the
hundredths. Factors may include decimals through the thousandths place as long as the
product is only through the hundredths place. Division is limited to, four-digit dividends and
two-digit whole number divisors.
Unit Objectives:
Students will…
 Represent multiplicative structures (multiplication and division) of problem situations
with products and decimals to the hundredths with the use of concrete objects, pictorial
models, and area models.
 Estimate to determine products and quotients. (through hundredths)
 Solve for products and quotients. (through hundredths)
 Simplify numerical expressions that include multiplication of whole numbers and
decimals. (through hundredths)
**Note: 1.) Factors may include decimals through hundredths as long as product is
only through hundredths.
2.) Division is limited to 2 digit WHOLE NUMBER divisors and 4 digit
dividends.
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.
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.
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5th grade – Unit 5 – Decimal Multiplication and Division
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.
5.3A - Estimate to determine solutions to mathematical and real-world problems involving
addition, subtraction, multiplication, or division.
5.3D - Represent multiplication of decimals with products to the hundredths using objects and
pictorial models, including area models.
5.3E - Solve for products of decimals to the hundredths, including situations involving money,
using strategies based on place-value understandings, properties of operations, and the
relationship to the multiplication of whole numbers.
5.3F -Represent quotients of decimals to the hundredths, up to four-digit dividends and twodigit whole number divisors, using objects and pictorial models, including area models.
5.3G -Solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit
whole number divisors, using strategies and algorithms, including the standard algorithm.
5.4F - Represent quotients of decimals to the hundredths, up to four-digit dividends and twodigit whole number divisors, using objects and pictorial models, including area models.
ELPS:
ELPS.c.1A - use prior knowledge and experiences to understand meanings in English
ELPS.c.1E - internalize new basic and academic language by using and reusing it in
meaningful ways in speaking and writing activities that build concept and language attainment
ELPS.c.1F - use accessible language and learn new and essential language in the process
ELPS.c.2D - monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.3D - monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.5B - write using newly acquired basic vocabulary and content-based grade-level
vocabulary
Misconceptions:
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Some students may oversimplify dividing by 10 to mean “move the decimal point to the
left”, rather than understand the multiplicative nature of 10s in the place value system or
the magnitude of making a number 10 times smaller.
When using standard algorithm for multiplying, some students may forget to place a
zero in the second partial product to hold the number of tens by simply using the digits
and not paying attention to place value. (e.g., when multiplying 35 and 26, students
correctly multiply 6 and 35 to make a partial product of 210, then use the 2 instead of 20
to multiply by 35 to make a partial product of 70 and not 700.)
When students work through the standard algorithm procedures, students may use
whole number concepts to multiply, but then not know where to place the decimal (e.g.,
2.7 x 15 becomes 27 x 15 = 405 and now student is not sure where the decimal should
be placed to compensate for thinking 2.7 as a whole number).
Some students may think that area models are not related to standard algorithms,
rather than realizing that area models are a visual representation of multiplication and
division and can be used to show the partial products or quotients produced through
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5th grade – Unit 5 – Decimal Multiplication and Division
standard algorithms.
 Some students may think that the most efficient way to break up an area model into
chunks (distributive property) is to break it up by place value, rather than thinking about
the numbers and then determining the most efficient way to solve from a variety of
strategies. (e.g., when multiplying 1.25 by 13 by place value using an area model, the
dimensions would become (1 + 0.2 + 0.05) and (10 + 3) which would create six partial
products (1 x 10) + (0.20 x 10) + (0.05 x 10) + (1 x 3) + (0.20 x 3 ) + (0.05 x 3) = 10 + 2
+ 0.5 + 3 + 0.60 + 0.15 = 16.25; rather than possibly breaking it up in fewer partial
products such as (1.25 x 10) + (1.25 x 3) = 12.50 + 3.75 = 16.25 or (10 x 0.25) + (3 x
0.25) + (13 x 1) = 2.50 + 0.75 + 13 = 16.25.
 Some students may think that the standard algorithm is always the most efficient way to
solve a multiplication or division problem, rather than thinking about the numbers and
then determining the most efficient way to solve from a variety of strategies. (e.g. when
multiplying 3.5 by 12 a student could think about multiplying (3.5 x 10) + (3.5 x 2) = 35 +
7 = 42, or using the associative property to double and half, such as doubling 3.5 to
make 7 and halving 12 to make 6, then using a basic fact to solve 7 x 6 = 42.)
 Some students may think the dividend always goes on the left side of a division
sentence, rather than understanding where to place the dividend and divisor based on
the symbol being used.
 Some students may think that rounding is the only way to make an estimate, rather than
understanding that there are multiple ways to determine an estimate.
 Some students may think that rounding and estimating are the same skill, rather than
rounding as one way to make the numbers friendly in order to compute and determine a
reasonable estimate.
 Some students may be able to perform a symbolic procedure for decimal multiplication
or division with limited understanding of the multiplication or division concepts involved.
Vocabulary:
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Associative property of multiplication – if three or more factors are multiplied, they
can be grouped in any order, and the product will remain the same
Commutative property of multiplication – if the order of the factors are changed, the
product will remain the same
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
Distributive property of multiplication – if multiplying a number by a sum of numbers,
the product will be the same as multiplying the number by each addend and then
adding the products together
Dividend– the number that is being divided
Divisor – the number the dividend is being divided by
Estimation – reasoning to determine an approximate value
Expression – a mathematical phrase, with no equal sign, that may contain a
number(s), a unknown(s), and/or an operator(s)
Factor – a number multiplied by another number to find a product
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5th grade – Unit 5 – Decimal Multiplication and Division
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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 considered or ignored (compensation)
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
Product – the total when two or more factors are multiplied
Quotient – the size or measure of each group or the number of groups when the
dividend is divided by the divisor
Rounding – a type of estimation with specific rules for determining the closest value
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Related Vocabulary:
 About
 Approximately
 Area model
 Base 10 place value system
 Decimal grid
 Hundredths
 Multiple
 Number line
 Position
 Ratio table
 Remainder
 Tenths
 Thousandths
List of Materials:
Newspaper circulars
Math Journal
White boards for seat work
Construction paper
Popsicle sticks
Order of operations flowchart/poster
Sticky notes
Index cards
INSTRUCTIONAL SEQUENCE
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5th grade – Unit 5 – Decimal Multiplication and Division
Phase: Day 1
Activity:
Day 1 – Estimating Decimals in Multiplication and Division and Dividing by 10, 100, 1000
Materials: Newspaper circulars, journals
Engage –
Provide groups of 3 or 4 students with copies of circulars from newspapers and have
students write down the prices of 3 items in their journals. Make sure you provide
circulars that have various price ranges. Have students estimate how much it would
cost to buy 2 of those items, 3 of those items, etc. with their groups.
Facilitate a discussion of how much original items were and then how much the estimates
were for different amounts of objects. Include the following discussion:
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What kinds of estimation strategies did you use to help solve these computation
problems? Front end estimation, estimation with adjustment, etc.
 How do different estimation strategies compare with the actual answer? Some
methods will make it closer than others, all answers should be close, but not exact
 When are some times you could think of when it would be necessary or
beneficial to estimate with decimals? Answers will vary..When working with money,
when an exact answer isn’t needed, etc.
Engage 2 –
Display the following patterns on the board. Have students look at the examples and
see if they can come up with strategies that would be helpful to solve these problems.
1 x 0.75 = 0.75
10 x 0.75 = 7.5
100 x 0.75 = 75.
1000 x 0.75 = 750.
Facilitate a class discussion about how these answers were determined. Be sure and
include the following questions.
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As you multiply by 10, 100, and 1000, how does the position of the decimal point
change in the product? Moves to the right
Look at the last equation in the pattern. How is it different from the previous
three equations? We had to add a 0.
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5th grade – Unit 5 – Decimal Multiplication and Division
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What does the additional 0 in the last equation represent? hundreds
Explore –
Make teacher copy of Baker Ingredients for students to see on overhead. Have
students work in their journals to determine how many cups of each ingredient the
baker has.
*Guide students to use patterns to determine.
*Make sure students understand how the patterns work.
*It is important that students remember that when a decimal number is multiplied by a
multiple of 10 that the decimal moves to the right.
Debrief and discuss patterns, relationships, and how multiplication works with the
problem.
Explain–
Use Multiplying Decimals by 10, 100, or 1,000 Notes as a guided practice to help
students determine how to solve these kinds of problems. Teacher should lead
students through this and facilitate as students as questions.
Explain/Elaborate –
Independent practice Independent Practice Multiplying Decimals by 10, 100, 1000
provided to help students determine answers to multiplying by multiples of 10. Students
can begin practice in class if time allows.
Evaluate –
Run off and cut in half (2 per sheet) and have students use Exit Ticket x Dec by
10,100,1000 to provide teacher with clear indication of how students are understanding
today’s lesson
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
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5th grade – Unit 5 – Decimal Multiplication and Division
Phase Day 2
Activity:
Day 2 – Multiply Decimals by Whole Numbers
Engage –
Give students handout Giant Tortoises with examples charts and have students follow
directions to shade in problems representing multiplying decimals by whole numbers.
After students have had time to work on these problems. Discuss and debrief what
these might look like and how they represent multiplying by decimals.
Explore/Explain –
Have students work and then “share and show” with their neighbors how the examples
in Decimal x Whole Numbers Share and Show would be shaded, and how they
represent multiplication. Debrief.
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What does one column of the model represent? How do you know that? One
tenth or ten hundredths because there are 10 rows of 10 columns
How does knowing what one column represents make finding the product
easier? Answers will vary – it makes it easier to count and multiply
Explain/Elaborate/Evaluate –
Allow students work in a group (there will need to be 5 groups) to determine answers to the
following questions on Multiplying Decimals by Whole Numbers powerpoint. This activity will
require students to use multi-tasking skills, patience, and team work to determine the answers
because the questions are rotating. (Or you can print the powerpoint and hand out a question
to each group.) After students are finished, have the groups (order determined by random
draw) decide which question their group would like to do. Allow groups 5 minutes to prepare,
with the instructions that each member must make a contribution in the presentation. Stop
powerpoint on the question being done at the time. Have that group present their problem at
the board. Allow them to answer questions from other students.
What’s the teacher doing?
What are the student’s doing?
Facilitating
Monitoring
Motivating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Observing and evaluating
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5th grade – Unit 5 – Decimal Multiplication and Division
Phase: Day 3
Activity:
Day 3 - Multiply Decimals
Engage –
Display on the board Area Model Decimal Multiplying (hundredths grid). Facilitate
the following discussion.
Let’s start by thinking of a decimal in terms of a picture. We can use a hundreds grid to
represent the hundredths of a decimal.
0.3 = 0.30 = 30 hundredths
Shade 30 squares green because we are looking at 30 out of 100 or 30 hundredths.
Let’s say that this is our first decimal. We are going to multiply it with another decimal.
Let’s say that we are going to multiply .30 .40.
Here is a visual picture of what .40 or 40 hundredths looks like.
0.4 = 0.40 = 40 hundredths
Shade 40 squares yellow.
Now we have two visuals of the decimals that we are multiplying. If we put them both
together, then we can see what it would look like to multiply these two decimals
together.
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5th grade – Unit 5 – Decimal Multiplication and Division
Notice that the overlapping part is the product of this problem. Our answer is .12 or 12
hundredths.
Explore/Explain How can we multiply two decimals without using a hundreds grid? One of the ways
that we can do it is to work on it just like we did when we multiplied decimals and whole
numbers together.
o
First, we ignored the decimal point and multiplied just like it was two whole numbers
that we were multiplying.
o
Second, we counted our decimal places and inserted the decimal into the product when
we had finished multiplying.
We can approach two decimal multiplication in the same way.
Demonstrate the following on the board as you explain.
Example
1.3
2.4 = ______
To work on this problem, let’s start by writing it vertically instead of horizontally. Then we
multiply.
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5th grade – Unit 5 – Decimal Multiplication and Division
Example
1. 3
X
2. 4
5 2
+2 6 0
3 1 2
Now that we have finished the other steps, our final step is to put the decimal point in the
correct spot. To do this, we need to count the decimal places in each number from right
to left. The first number has one decimal place.
1.3
The second number has one decimal place.
2.4
This is a total of three decimal places that need to be placed into the product. Our final
answer is 3.12.
Explain/Elaborate –
Guided practice. Provide students with example problems Multiplying Decimal
Numbers Notes and guide students through as teacher facilitates discussion and leads
students through problems. Decompose each question as you go with students. Make
sure to monitor and correct misconceptions throughout. As students begin to
understand, allow students to go to the board to work out problems on the guided
practice they have completed. Discuss and debrief.
Evaluate –
Provide students with copy of Exit Ticket for Multiplying Decimals. Students hand in exit
ticket as they exit room. Evaluate those tickets prior to Day 4 to determine misconceptions
and extra practice needed.
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5th grade – Unit 5 – Decimal Multiplication and Division
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Phase: Day 4
Activity:
Day 4 – Multiplying Decimals continued
Materials: seat white boards
Engage/Explore –
Another way to demonstrate multiplying decimals is by using a number line. Provide a
copy of the Number Line Multiplication for the students. Have your students study
this problem and then get with a partner. Use the “think, pair, and share” method to
have students discuss how this problem is being represented through the number line
with each other. Have groups share (as you facilitate) with the class what they
determine through this problem and representation.
Explain /Elaborate –
Guided practice. Provide students with example problems Multiplying Decimal
Numbers – Day 2 and guide students through as teacher facilitates discussion and
leads students through first 4 problems. Decompose each question as you go with
students. Make sure to monitor and correct misconceptions throughout. Have students
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5th grade – Unit 5 – Decimal Multiplication and Division
complete last 4 problems and check with elbow partner as they finish. Monitor students
and correct misconceptions as needed.
*Remind students about examples of whole numbers being multiplied by decimal
numbers. Make sure they remember where the decimals are in those whole numbers.
Decimal points are always behind the ones place. In those whole numbers, there is a
(understood but not seen) decimal point, but there are no written numbers behind it.
Evaluate –
Have students use seat white boards to work the following problems and display to
teacher for evaluation prior to leaving class.
1.)
9.6 x 0.4
2.) 14.2 x 3.5
3. 6.5 x 8
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
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5th grade – Unit 5 – Decimal Multiplication and Division
Phase: Day 5
Activity:
Day 5 – Multiplying Decimals continued
Materials: light colored construction paper
Engage –
Display the provided sheet Area Model. Give students 2-3 minutes to “think, pair, and
share” what they know and can determine from this problem with a neighbor. After,
facilitate a discussion about the table and how it was used as an example of multiplying
decimals.
Explore/Explain –
Review algorithm for solving multiplication problems with the problem. 6.2 x 9.4. Hand
out light colored construction paper, and have pairs of students create a poster
explaining the steps to solving multiplication problems involving decimal numbers.
Have students not only write the steps out, but show a problem with instructions, and
demonstrate the steps. Teacher should monitor and assist as needed.
Elaborate/Evaluate –
Provide students with a copy of the Decimal Multiplication Homework to complete for a
grade.
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5th grade – Unit 5 – Decimal Multiplication and Division
What’s the teacher doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
What are the students doing?
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Day 6
Activity:
Day 6 – Dividing Decimals by 10, 100, 1000
Engage –
Display the teacher copy of Division Patterns . Have students write in their journals
what strategies they could use to solve the division problems on the page. Lead class
discussion and include the following questions.
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Look at the division pattern and determine what happens to the divisor each time.
It increases by a multiple of ten
What happens to the quotient each time? It decreases
Describe the patterns you see. Answers vary – the quotients get smaller, the divisors
get larger, the decimal in the quotient moves 1 place to the left each time, etc.
How does the position of the decimal point change in the quotient? It moves to
the left
How does this differ from what happened when we multiplied? When we
multiplied it moved to the right and the product increased.
Explore –
Have the students write a few sentences to explain how you can determine where to
place the decimal point in the quotient in 47.2 ÷ 100. Watch as students are working.
Make suggestions, point out possibilities to encourage struggling students. When
students have completed this, call on a few to read aloud what they have written. Allow
for discussion and correction.
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5th grade – Unit 5 – Decimal Multiplication and Division
Explain/Elaborate –
Provide each student with a copy of Dividing Decimal Numbers by 10, 100, 1000.
Guide students through as teacher facilitates discussion through problems. Decompose
each question as you go with students. Make sure to monitor and correct
misconceptions throughout. As students begin to understand, allow students to go to the
board to work out problems on the guided practice they have completed. Discuss and
debrief.
Elaborate/Evaluate –
During last 5 minutes of class, have students make up 4 multiplication problems using a
decimal number and multiplying it by 1, 10, 100, and 1000 and solve. Make sure they
use the same decimal number on all 4 problems and show how the pattern works.
Have students display their problems on white boards and display for teacher to see.
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Phase: Day 7
Activity:
Day 7 – Dividing Decimal Numbers by Whole Numbers
Materials: journal
Engage –
Display teacher page Money, Money, Money. Have students work in their journals to
determine strategies for splitting up the money as listed. Facilitate discussion.
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5th grade – Unit 5 – Decimal Multiplication and Division
*Not every decimal problem is money, but they work the same way.
Turn page over and rewrite the questions on the back exactly the same, but without the
dollar signs, and solve. Lead discussion.
*Discuss similarities.
*Discuss differences.
Explore –
Have students work and then “share and show” with their neighbors how the examples
in Dividing Decimals by Whole Numbers Share and Show would be shaded, and
how they represent division. Debrief.
Show video: http://www.pinterest.com/pin/535013630706888311/
Video is nice visual representation of what they have done on paper.
Explain/Elaborate –
Guided practice. Provide students with example problems Practice Dividing Decimal
Numbers and guide students through as teacher facilitates discussion and leads
students through first 4 problems. Decompose each question as you go with students.
Make sure to monitor and correct misconceptions throughout. Have students complete
last 4 problems and check with elbow partner as they finish. Monitor students and
correct misconceptions as needed.
*Students will need to be briefed on how to handle problems with remainders. We will
not be having remainders, we will be adding “0’s” to the back of numbers as needed
and we will continue dividing until we end up with a remainder of 0.
*Students were led into this on Money, Money, Money as they had to separate a whole
dollar amount into change. They will need reminding, and instruction as they transfer
this knowledge to numbers with decimals that are not money amounts.
Evaluate –
Students will be given Dividing Decimal Numbers Homework for independent practice. May
finish for homework as necessary.
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5th grade – Unit 5 – Decimal Multiplication and Division
What’s the teacher doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
What are the students doing?
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Phase: Day 8
Activity:
Day 8 – Dividing Decimals by Whole Numbers – 2 digit divisors
Materials: journal
Engage –
Provide students with examples on the board of the following 2 digit divisor problems.
Have students work these problems in their journals. Ask for volunteers to work the
problems out on the board.
468 ÷ 18
1372 ÷ 14
Explore As students finish up, have new volunteers go up to the board and place a decimal
anywhere they would like in the dividend of the original problem. Discuss and decide
where the decimal should go in the quotient, based upon where it is in the dividend.
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How is dividing a decimal by a whole number similar to dividing a whole number
by a whole number? The actual steps to divide (the algorithm) is the same
If the dividend increases but the divisor stays the same, will the quotient
increase, decrease, or stay the same? Why? The quotient will increase because a
larger number is being divided.
If the divisor increases but the dividend stays the same, will the quotient
increase, decrease, or stay the same? Why? The quotient will decrease because
you are dividing into more pieces.
Explain/Elaborate/Evaluate –
Practice problems provided for dividing decimal numbers by 2 digit numbers. Hand out
Dividing Decimal Numbers by 2 Digits and allow students time to work as you walk around
and correct misconceptions. Can finish for homework if necessary.
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5th grade – Unit 5 – Decimal Multiplication and Division
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Day 9
Activity:
Day 9 –
Engage/Explore – Dividing Decimal Numbers by 2 Digit Divisors
Display the following problem on the overhead. Have students work the problem and
determine what Dianne did. Have them write a sentence or two describing what is
wrong with Dianne’s problem.
Dianne divided 812.5 by 50.
She says the quotient is 1.625.
Describe Dianne’s error.
Explain/Elaborate –
Make a copy of Place the Decimal and Justify from
http://www.mathcoachscorner.com/2012/07/06/multiplying-and-dividing-decimals-usingnumber-sense/ Go down and click on the “here” link to access cards. Cut apart and
place on overhead one at a time. Ask the kids to determine where you would place the
decimal in the quotient based on what they have learned and why?
Evaluate –
Have students work the following 3 problems on notebook paper and hand in as they
are leaving to determine understanding.
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5th grade – Unit 5 – Decimal Multiplication and Division
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Phase: Day 10
Activity:
Day 10 – Dividing Whole Numbers into Smaller Whole Numbers
Materials: journal
Engage –
Place the following problem on the board and ask students to work this problem in their
journals.
3÷4
Use this opportunity to point out that we will have to be very careful on our division
problems now. We will have problems where the dividend is smaller than the divisor,
so we will have to pay close attention when writing our problems so that we put the
numbers in the correct place. Work through the problem, explaining how this situation
could occur.
Let’s suppose we have 3 apples we want to share among 4 people, so we would be
dividing 3 apples into 4 parts or “3 is being divided by 4”. Follow through with the
algorithm being careful to add the decimal after the 3 and following with 0’s until the
problem is complete.
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5th grade – Unit 5 – Decimal Multiplication and Division
Explore/Explain –
Hand each student a copy of Dividing Whole Numbers By Larger Whole Numbers.
Demonstrate on the board as you go through the problems with the students. Monitor
students’ progress and correct misconceptions. As students become more confident,
ask for volunteers to demonstrate and talk through the steps while working at overhead.
Elaborate/Evaluate –
Run a copy of Dividing With Decimals for students to work on in class or finish for
homework as necessary.
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
Phase: Day 11
Activity:
Day 11 – Solving Equations Parentheses and Brackets
Materials: journal
Engage –
Students write in their journals the method they use for remembering the order in which
operations are performed in an equation from Unit 2. Discuss and debrief. Correct any
misconceptions.

Why do we need to follow the order of operations whenever we simplify an
expression that has more than one operation? If you don’t follow the correct order,
the answer will be incorrect.
OPTION: I found a video online that is an example to help students remember the
Order of Operations. I am going to create the hopscotch outside and have my students
go through it several times to get them up and moving and get their bodies working with
their minds to help them remember the order of operations.
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5th grade – Unit 5 – Decimal Multiplication and Division
Here is the link: http://www.pinterest.com/pin/535013630706888795/
Explore/Explain –
A numerical expression is a mathematical phrase that has numbers and operation signs
but does not have an equal sign. Some numerical expressions have parentheses.
Stress to students that when they see parentheses in an expression, they must perform
the operation in the parentheses first.
Display Mark’s Fishing Trip on the overhead for students to see. Have students write
an expression in their journals to match the problem.
Discuss and explain as you debrief students.
*Think: Each day he took $15 and had $5 left. He did this for 3 days.



*Why do you have to subtract $5 from $15 before you multiply by 3? He took $5
from $15 each day.
How does this expression compare to what it would look like if Mark had only
gone fishing for 1 day? If he had only gone 1 day, the answer would be 1/3 of what it
is now.
*If there were no parentheses in this problem, would the solution be the same?
Why or why not? The solution would not be the same because it would be done out of
order.
****Make sure students understand the new division and multiplication symbols.



/ for divide
·
for multiply
A number directly beside a parenthesis indicates multiplication. Ex. 8(4) means
8 x 4.
Work through some of the problems orally while circulating and assisting with work as
needed in room.
Explain/Elaborate –
Tell students you will display some expressions and students are to create a problem
with their elbow partner to match the expression. Also display some problems and
have student partners create expressions to match the problems.
1.) 34 – 17
2.) $8 + (4 x $5)
3.) 25 – (10 + 8)
4.) Michelle walks dogs for 4 days. She walks 3 in the afternoon and 2 in the morning.
5.) Kari has 31 fewer pencils than Rob does. Rob has 57 pencils.
6.) Sherry divided all her Dum-Dums between 5 friends. She had 21 in one bag and 14
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5th grade – Unit 5 – Decimal Multiplication and Division
in another bag.
Discuss and debrief as needed.
Elaborate –
Provide students a copy of Simplifying Numerical Expressions . Work through
problems while monitoring students. Be sure to have a copy of the order of operations
available for students to see and stress with each step how you are following through
the order. Pay special attention to parentheses/brackets and parentheses inside
parentheses (the innermost expressions) where you begin.
Possible questions:



How could you solve these problem by breaking it into a series of simpler
problems? You break it into several steps, making sure to do those things that would
go in parentheses/brackets first.
How do your steps relate to the expressions in the parentheses and brackets?
You have to do the steps in the parentheses and brackets as the first steps if you break
it into simpler problems.
What does this tell you about the order in which to perform operations using
parentheses and brackets? If you do them in the wrong order, the answer will be
wrong.
Evaluate –
Simplifying Numerical Expressions Exit Ticket provided. Be sure and evaluate prior to
tomorrow’s lesson to correct misconceptions.
What’s the teacher doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
What are the students doing?
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
22
5th grade – Unit 5 – Decimal Multiplication and Division
Day 12
Activity:
Day 12 – Simplifying Expressions Further
Materials: popsicle sticks to make game
Engage/Explore/Explain –
Using popsicle sticks, make a game of “I Have, Who Has” by writing expressions for
students to solve on each popsicle stick along with an answer. Students must work the
expression given to determine who has the next stick. Hand out sticks to individuals or
partners so that everyone participates and has an equation to work.
Elaborate/Evaluate Allow students time to work on Simplifying Expressions Further as class time allows. May
finish for homework as needed.
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
23
5th grade – Unit 5 – Decimal Multiplication and Division
Phase: Day 13
Activity:
Day 13 – Properties
Materials: journal, sticky notes, index cards
Engage/Explore/Explain –
Have students write in their journals what they remember about the properties of
multiplication and then share ideas with partner.
*Be sure to discuss the following properties, giving examples on the board and showing
how these properties relate to one another.
*Show examples on board or overhead and facilitate a discussion that explains all 3
properties.

Properties of operations
o Commutative property of multiplication – if the order of the factors are
changed, the product will remain the same
 a x b = c; therefore, b x a = c
o Ex: 2.5 x 1.1 = 2.75 and 1.1 x 2.5 = 2.75
Therefore, 2.5 x 1.1 = 1.1 x 2.5
o Associative property of multiplication – if three or more factors are multiplied,
they can be grouped in any order, and the product will remain the same
o a x b x c = (a × b) × c = a × (b × c)
o Ex: 2.5 x 1.1 x 3
(2.5 x 1.1) x 3 = 2.75 x 3 = 8.25 or 2.5 x (1.1 x 3) = 2.5 x 3.3 =
8.25
Therefore, 2.5 x 1.1 x 3 = (2.5 x 1.1) x 3 = 2.5 x (1.1 x 3)
 Distributive property of multiplication – if multiplying a number by a sum of
numbers, the product will be the same as multiplying the number by each
addend and then adding the products together
 a x (b + c) = (a x b) + (a x c)
 Ex: 2.5 x 1.1 = 2.5 x (1.0 + 0.1) = (2.5 x 1.0) + (2.5 x 0.1) = 2.5 + 0.25 =
2.75
 Ex: 2.7 x 2.5 = (2.5 + 0.2) x 2.5 = (2.5 x 2.5) + (0.2 x 2.5) = 6.25 + 0.50 =
6.75
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5th grade – Unit 5 – Decimal Multiplication and Division
Explain/Elaborate –
ASSOCIATIVE PROPERTY - Have students create foldable like the one below to
demonstrate the Associative Property.
http://www.pinterest.com/pin/133982157636171046/
COMMUTATIVE PROPERTY - To help your students remember the Commutative
Property of Multiplication, give them sticky notes and have them put their own individual
numbers and signs on them and then guide them to manipulate the numbers and signs
to demonstrate the commutative property.
DISTRIBUTATIVE PROPERTY – Make poster similar to the one below to help show
students how the numbers are distributed much the same way it is in the food example
below. Students can make a similar picture in their journals. Provide numerical
examples for students to work in their journal to reinforce this numerically as well.
25
5th grade – Unit 5 – Decimal Multiplication and Division
http://www.pinterest.com/pin/178173728981130028/
Evaluate –
Have students divide a 4 x 6 index card in 3 pieces. Label each section as Associative,
Commutative, and Distributive and give an example of each kind of property in the box
beneath the word. Take these cards as students leave the class to determine levels of
understanding.
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
26
5th grade – Unit 5 – Decimal Multiplication and Division
Phase: Day 14
Activity:
Day 14 – Properties continued
Engage –
Have students write which property is shown in the example below. Have them explain
how they know this.
Facilitate discussion and correct misunderstandings as needed.
Explore/Explain Provide students with Properties – Try It where sample problems of each property
have been given. Students are expected to decide which property is represented on
some of the problems. On other problems, students are to demonstrate how the given
property would work on that particular problem.
Elaborate/Evaluate –
Homework page provided How Well Do You Know Your Properties? . Distribute to
students and have them complete in class or at home as time allows.
Evaluate –
PERFORMANCE ASSESSMENT
PA1
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.
27
5th grade – Unit 5 – Decimal Multiplication and Division
1) A gallon of lemonade sells for $3.40. Lucas’ mom wants to purchase 9.5 gallons of lemonade for his birthday
party.
a) Use an area model and another concrete or pictorial model to determine how much Lucas’ mom spent on
lemonade for his birthday party.
2) Lucas is selling lemonade for a school fundraiser. The large cup of lemonade sells for $1.55 and the small cup
of lemonade sells for $0.75. Lucas sold 38 large cups of lemonade and 32 small cups of lemonade.
a) Estimate how much Lucas made for his school fundraiser.
b) Demonstrate and explain a strategy to determine how much Lucas made for his school fundraiser.
c) Write and simplify an expression that can be used to determine the total amount of money Lucas raised for his
school fundraiser.
PA2
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.
1) The amount raised from a fundraiser event was $590.80. This money is going to be divided evenly to purchase
turkey dinners for 14 families for Thanksgiving.
a) Estimate how much money will be spent for each turkey dinner.
b) Use an area model and another concrete or pictorial model to determine how much will be spent on each
turkey dinner.
2) While shopping for items for turkey dinners to donate, Monica found a 9-pound turkey for $12.15.
a) Use the standard algorithm and another strategy to determine the price of the turkey per pound. Explain how
your selected strategy relates to the standard algorithm.
b) Monica had a coupon for $0.27 off the price per pound of a turkey. Write and simplify an expression that can
be used to determine the discounted price of the 9-pound turkey.
28
5th grade – Unit 5 – Decimal Multiplication and Division
What’s the teacher doing?
What are the students doing?
Facilitating
Monitoring
Motivating
Observing and evaluating
Listening to lesson and other students
Participating in discussion
Recording observations/problems
Providing reasonable answers
Asking questions
29