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Campus: Godwin Elementary, Harper Elementary
Author(s): Laurie Collins, Joell Morris, Rachel
Nicks
Date Created / Revised: 9-24-13
Six Weeks Period: 2nd
Grade Level & Course: 3rd Grade Math
Timeline: 14 days
Unit Title: Unit 4: Multiplication and Division
Foundations
Stated Objectives:
TEK # and SE
Lesson # 2
of 3 (4 days)
3.4C Use models to solve division problems and use number sentences to record the solutions.
Readiness Standard
3.6C Identify patterns in related multiplication and division sentences (fact families) such as 2 x 3
= 6, 3 x 2 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2. Supporting Standard
3.10 Locate and name points on a number line using whole numbers and fractions, including
halves and fourths. Readiness Standard
3.14A Identify the mathematics in everyday situations.
3.14B Solve problems that incorporate understanding the problem, making a plan, carrying out the
plan, and evaluating the solution for reasonableness.
3.14C Select or develop an appropriate problem-solving plan or strategy, including drawing a
picture, looking for a pattern, systematic guessing and checking, acting it out, making a table,
working a simpler problem, or working backwards to solve a problem.
3.14D Use tools such as real objects, manipulatives, and technology to solve problems.
3.15A Explain and record observations using objects, words, pictures, numbers, and technology.
3.15B Relate informal language to mathematical language and symbols.
3.16B Justify why an answer is reasonable and explain the solution process.
See Instructional Focus Document (IFD) for TEK Specificity
Key
Understandings
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Misconceptions
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Division facts can be recalled using a variety of concrete models (e.g., base-ten blocks,
counters, etc.) which can be connected to various pictorial representations and/or
strategies such as arrays, area models, number lines, patterns in fact families, problems
in context, and other known facts.
The relationship between multiplication and division can be used to develop an efficient
procedure to find the quotient and justify the solution for a whole number division problem.
Fact families and area models can be used to demonstrate the special inverse
relationship between multiplication and division, where the product in a multiplication
problem is the dividend in a division problem and the two factors in a multiplication
problem are the divisor and quotient in a division problem.
Real-life division problems involving whole numbers can be solved using a variety of
models and strategies including problems in context, patterns in fact families, area
models, partitioning, and other known facts.
Problem solving with division of whole numbers involves analyzing the given information,
the missing information, and the question(s); developing a plan with strategies; observing
and communicating the mathematical ideas through verbal/written descriptions or
statements, and/or equations; and evaluating the solution for reasonableness.
Some students may have difficulty continuing repeated subtraction on a number line all
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the way to zero.
Some students may think that a division problem represented using traditional division is
read from left-to-right. They may incorrectly write a division number sentence by not
placing the dividend first.
Some students may think that when given “24 balloons shared by 3 people results in 8
balloons per person” or 24 ÷ 3 = 8, they should record:
__8__
24 I 3
Key Vocabulary
Dividend, Division, Divisor, Quotient
Suggested Day
5E Model
Instructional Procedures
Day 1- Engage/
Explore/Explain
(Engage, Explore, Explain, Extend/Elaborate, Evaluate)
1. Problem solving
2. Place students into groups of 4 and distribute a Bag of
Counters to each group. Instruct student groups to count out
24 of the counters from their bag.
3. Instruct student groups to distribute the “counted-out”
counters so that each student in the group has the same
amount of counters. Ask: How did you share or distribute
your counters evenly among the members of your group?
Did everyone get the same amount? What is the process of
separating into equal groups called? When have you used
division in real life? What division sentence could be written
for this situation?
4. Display the following word and definition for division for the
class to see:
Division –one of the four basic operations of arithmetic where
in the division statement a ÷ b = c, a is the dividend, b is the
divisor, and c is the quotient.
5. Instruct students to record this definition and a model of the
division of counters situation in their math journal.
6. Remind students that when they combined equal groups,
they multiplied. Explain to students that they will learn that
when they share equally, they divide.
Ask: How is multiplication similar to division? How is
multiplication different from division? How did the counters
help you divide?
7. Place students into groups of 4. Distribute 5 paper plates and
a Bag of Counters to each group. Instruct students to count
out 20 of the counters from their bag.
8. Display teacher resource: Apple Time. Explain to students
that the counters will represent the apples that are being
shared in the problem. Instruct student groups to use their
plates to make equal groups of the apples. Ask: How many
groups did you make using the paper plates? How many
counters (apples) were in each group?
9. Explain to students that they can draw a picture to show a
division problem. Model for students. Ask: Why did you draw
5 sections? How many apples will go into each section? What
division sentence is represented by this model?
10. Explain to students that there are 2 ways to write a division
problem. Record the following division representations for the
class to see. Instruct students to record each representation
in their math journal.
Materials, Resources,
Notes
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Counters
Math journals
Paper plates
Apple Time (see Pshare)
Modeling Division
with Counters (see
P-share)
11. Divide students into pairs and distribute handout: Modeling
Division with Counters to each student. Instruct student pairs
to use their Bag of Counters to model each situation and
record their solutions on their handout. Facilitate a class
discussion to debrief and discuss solutions.
Day 2 – Explore/
Explain
Day 3 – Explore/
Explain
1. Problem solving.
2. Review learning from yesterday. Focus on the definition
of division and related vocabulary (dividend, divisor,
quotient).
3. As a class have a discussion about how division and
multiplication are related. Tie into fact families.
4. Complete “Fact Family House (Multi & Div)” Mimio.
5. Students will pick a fact and make their own fact family
houses.
6. Ask: How can understanding fact families help you solve
problems? Have students answer in math journals.
Discuss answers together.
7. For independent practice, students will complete PW78.
1. Problem solving.
2. Display teacher resource: Donna’s Donuts. Demonstrate the
solution process using a Bag of Counters for the class to see.
Ask: How many donuts did Donna make in all? How many
donuts did Donna give to her first friend?
3. Demonstrate taking away 2 counters. Ask: What subtraction
sentence could I use to show what I just did?
4. Continue removing counters in groups of 2 until there are no
counters left. Record each subtraction sentence as each
group is removed for the class to see.
5. Ask: How many times did you subtract 2? How many groups
of 2 did you separate your counters into? How does the
number of times you subtracted 2 from each group compare
to the number of groups of 2 you made? How could you write
this as a division sentence? What does the 12 stand for in
this problem? What does the 2 stand for in this problem?
What does the 6 stand for in this problem?
6. Display Repeated Subtraction Number Lines. Ask: How did
you use number lines to multiply? Could you use number
lines to divide? How could you use this number line to show
20 ÷ 4?
7. Display a drawn number line for the class to see. Use the
number line to model how to skip-count backwards by 4s
from 20 to 0. Explain to students that when they skip count on
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“Fact Family House
(Multi & Div)” Mimio
(see P-share)
Fact family house
templates
(http://3.bp.blogspot
.com/OhSItnQ26A0/UIxw
SYXxfcI/AAAAAAA
AC-M/u8dhwh3RR4/s1600/Sli
de17.jpg)
Math journals
PW78 in math
workbooks
Donna’s Donuts
(see P-share)
Counters
Repeated
Subtraction Number
Lines (see P-share)
PW75 in math
workbooks (save
backside for Day 4)
a number line to show multiplication or repeated addition,
they always start at zero. Emphasize that when they skip
count backwards on a number line to show division or
repeated subtraction, they must end at 0.
8. Ask: How is skip counting backwards on a number line like
skip counting forwards? How is skip counting backwards on a
number line different from skip counting forwards? Record
the following division problems for the class to see.
9. Place students in pairs. Instruct student pairs to solve each
problem using a number line on their handout: Repeated
Subtraction Number Lines. Facilitate a class discussion to
debrief and discuss each number line solution. Ask: How are
subtraction and division related?
10. For independent practice, students will complete PW75. (You
will need the other side of this page for Day 4.)
Day 4 – Elaborate/
Evaluate
1. Problem solving.
2. Remind students that they have already learned how to
model division with counters by making equal groups, by
using repeated subtraction, and by showing repeated
subtraction on a number line. Distribute a whiteboard and dry
erase marker to each student and a Bag of Counters to each
pair. Instruct students to count out 16 of the counters from
their bag. Ask: How many counters are in 4 equal groups of
4? How many groups of 4 are in 16?
3. Instruct students to use their Bag of Counters to create an
array of counters that models 4 equal groups of 4 and record
the model and related multiplication sentence on their
whiteboards: (4 x 4 = 16). Ask: What division problem could
be written using this same array? Explain.
4. Instruct students to circle rows of 4 on their whiteboard.
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White boards
Dry erase markers
Counters
PW76 in math
workbooks (saved
from Day 3)
Ask: How many groups of 4 are in 16? How does making an
array help you to divide? What does this model tell us about
the relationship between multiplication and division? Why can
we use arrays for both multiplication and division?
5. For independent practice, complete PW76 (saved from Day
3). Students can use counters to complete. Some questions
require more counters than students have in their bags. You
can either eliminate these questions or have students work in
pairs.
Accommodations
for Special
Populations
Accommodations for instruction will be provided as stated on each student’s (IEP)
Individual Education Plan for special education, 504, at risk, and ESL/Bilingual.