Wichita falls ISD
3rd Grade Math
Topic 11: Understanding Fractions
Lessons: 1 – 13
Time Frame: 11 days
Revised TEKS Check- Before the Chapter
Reteach/review GAP Alerts from last school year.
Students may not have experienced:
• Compose/decompose numbers to 1,200 as a sum of so many thousands, so many
hundreds, so many tens, and so many ones using concrete and pictorial models
• Use standard, word, and expanded form to represent numbers up to 1,200
• Generate a number that is greater than or less than a given whole number up to
1,200.
• Use place value to compare and order whole numbers to 1,200 using comparative
language, numbers and symbols
• Explain that the more fractional parts used to make a whole, the smaller the part;
and the fewer the fractional parts, the larger the part.
• Use concrete models to count fractional parts beyond one whole using words,
and recognize how many parts it takes to equal one whole.
• Recall basic facts to add and subtract within 20 with automaticity.
• Solve one-step and multistep word problems involving addition and subtraction
within 1,000 using a variety of strategies based on place value, including
algorithms.
• Generate and solve problem situations for a given number sentence involving
addition and subtraction of whole numbers within 1,000.
• Use the understanding of place value to determine the number that is 10 or 100
more or less than a given number up to 1,200.
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Objectives
Skills: The student will be able to…
Solve problems involving partitioning an object or a set of objects among two or
more recipients using pictorial representations of fractions with denominators of 2,
3, 4, 5 and 8.
Use a problem-solving model that incorporates analyzing given information.
Compare two fractions having the same denominator in problems by reasoning
about their sizes and justifying the conclusion using symbols, words, objects, and
models.
Compare two fractions having the same numerator in problem by reasoning about
their sizes and justifying the conclusion using symbols, words, objects, and pictorial
models.
Represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety
of objects and pictorial models.
Explain that two fractions are equivalent if and only if they are both represented by
the same point on the number line.
Represent fractions of halves, fourths, and eighths as distances from zero on a
number line.
Use a problem-solving model that incorporates analyzing information, formulating a
plan or determining a solution, justifying the solution, and evaluating the
reasonableness of the solution.
Wichita Falls ISD (2014-2015)
3M Topic 11
Topic Planner
The Mathematical Process Standards must be incorporated into
instruction as appropriate throughout the school year.
TEKS
2.2A, 2.2B, 2.2C, 2.2D,
2.3B, 2.3C, 2.4A, 2.4C, 2.4D
2.7B
TEKS
Readiness: 3.3A, 3.3F,
3.3H, 3.4A, 3.4K
Supporting: 3.3C, 3.3B,
3.3D, 3.3E, 3.3G, 3.7A
Process Skills: 3.1A, 3.1B,
3.1C, 3.1D, 3.1E, 3.1F, 3.1G
ELPS: 1F, 2C, 2D, 2I, 3D,
3F, 3H, 4C, 4F
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Performance Indicators
By the end of the lesson the student will be able to…
Lesson 11-1: use a unit fraction to describe each of the equal parts of a whole, use a fraction to describe a part of a
region, and draw a picture of a region to model a fraction.
Lesson 11-2: use a fraction to describe a part of a set of objects. They will also draw a picture of a set of objects to
model a fraction.
Lesson 11-3: divide a number line from 0 to 1 into equal parts and then represent fractions on the number line.
Lesson 11-4: use number lines to locate and write fractions on number lines.
Lesson 11-5: use a fraction to describe a part of a length of an object and show that part of a length of an object can
be expressed as the sum of unit fractions.
Lesson 11-6: break apart any fraction whose numerator is greater than 1 into a sum of unit fractions (example: 4/6 =
1/6 + 1/6 + 1/6 + 1/6).
Lesson 11-7: partition objects among two or more people using division and pictorial representations of fractions.
Lesson 11-8: analyze given information in a problem to determine if there is enough or not enough information to
solve it.
Lesson 11-9: use models and quantitative reasoning to compare fractions with the same denominator.
Lesson 11-10: use models and quantitative reasoning to compare fractions with the same numerator.
Lesson 11-11: use models to find different fractions that are equivalent to a given fraction.
Lesson 11-12: use a number line to find equivalent fractions.
Lesson 11-13: use reasoning and draw representations to solve problems.
Lesson Information
Activities
• Lone STAAR Rigorous Problem Solving+ must be consistently used.
(Click here to see Revised TEKS Correlation Chart.)
• THINK Framework must be incorporated into your problem solving strategies:
T: Talk about the problem
H: How can it be solved?
I: Identify a strategy to solve the problem
N: Notice how your strategy helped you solve the problem
K: Keep thinking about the problem. Does it make sense? Is there another way to solve it?
• Suggested strategy for problem solving: CUBES:
C: Circle the numbers
U: Underline the question
B: Box in key words
E: Eliminate what you DON’T need
S: Does your answer make sense?
Suggested Activities:
• Introduce Topic using Children’s Literature Suggestions: Full House: An Invitation to Fractions
by Dayle Ann Dodds, Wholey Cow: Fractions Are Fun by David Adler and Nancy Tobin, Polar
Bear Math Learning About Fractions from Klondike and Snow by Ann Whitehead Nagda and
Cindy Bickel, The Lion’s Share: A Tale of Halving Cake and Eating It Too by Matthew
McElligott, Working With Fractions by David Adler and Edward Miller, The Hershey’s Milk
Chocolate Fractions Book by Jerry Pallotta and Rob Bolster
• Activities in enVisionMath 2.0
On-Level and Advanced Activity Center “Teamwork” pg 569A
On-Level and Advanced Activity “Tic-Tac-Toe” pg 575A
Math and Science STEM “A Landslide” pg 581A
On-Level and Advanced Activity “Toss and Talk” pg 593A
Math and Science STEM “Earthquake” pg 599A
Wichita Falls ISD (2014-2015)
3M Topic 11
The Mathematical Process Standards must be incorporated into
instruction as appropriate throughout the school year.
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Vocabulary
Unit fraction:
represents one
part of a whole
that has been
divided into
equal parts.
Fraction: A
symbol, such as
½, used to name
a part of a
whole, a part of
a set, or a
location on a
number line.
Denominator:
the number
below the
fraction bar in a
fraction. It
shows the total
number of equal
parts.
Numerator: the
number above
the fraction bar.
It shows how
many equal
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revised 1/5/15
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On-Level and Advanced Activity “Display the Digits” pg 605A
On-Level and Advanced Activity “Teamwork” pg 611A
On-Level and Advanced Activity “Tic-Tac-Toe” pg 617A
On-Level and Advanced Activity “Display the Digits” pg 629
On-Level and Advanced Activity “Toss and Talk” pg 635A
Lucky Charms Fractions Activity
Rice Crispy Treats Fractions Activity
Pizza Fractions
Fraction Games (Basketball)
Fractions with Student Names
Fractions Chart*
Fraction Benchmark Assessment Sticks*
Fraction “Roll Shake Dump”*
Fraction Multi-Step Story Problems*
Skittle Fractions Worksheet*
Fraction Family Flip Book*
Go Darth Equivalent Fraction Go Fish Card Game*
Blank Fraction Strips
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Number parts of a whole to demonstrate which is numerator and which is denominator.
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2
3
4
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6
=
3 numerator/# on top
6 denominator/# down
Tips for remembering numerator and denominator: Nod your numerator (head)/Dip your
denominator (hips); Numerator=North/Denominator=Down; Numerator=number on
top/Denominator= down below.
Fractions on a Number Line. Show “hops” between two whole numbers. The number of
hops to the point on the number line is the numerator. The total amount of hops is the
denominator.
1
l
0
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parts are
described.
Equivalent
fractions:
Fractions that
name the same
part of a whole
or the same
location on a
number line.
2
l
3
l
4
l
5
l
6
l
l
1
=
3/6 = 1/2
You can also draw a rectangle between two whole numbers to help students visualize the
fraction. The lines on the number line separate the rectangle into parts. Shade up to the
point
l 1 l 2 l 3
0
Wichita Falls ISD (2014-2015)
3M Topic 11
l 4
l 5
l 6 l
1
=
3
6
shaded parts = 1
total parts
2
The Mathematical Process Standards must be incorporated into
instruction as appropriate throughout the school year.
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revised 1/5/15
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Additional Information
Materials/Resources
enVisionMath 2.0 textbook Teacher’s Edition pg 561A-652B
Topic 11 Parent Letter
Study Jams Video Fractions
Khan Academy Introduction to Fractions and other videos
Dina Zike’s Big Book of Math: Understand numerators and
denominators by making a two tab book. Pg 68
Fraction Anchor Chart Idea*
Math Matters Clean-Sweet Campers book
Fraction Pizza book
Fraction Families and Equivalent Fractions Cards*
Equivalent Fractions Anchor Chart idea
Dinah Zike’s Big Book of Math
STAAR Ready Instruction**+
Measuring Up to the TEKS: STAAR Edition**
Motivation Math (2014 Edition)**
o Units 5, 6, 7, 8, 9, 10, 11, 12
Motivation Math**+
Countdown to the Math STAAR**+
STAAR Fast Focus**+
Supporting STAAR Achievement+
Plastic coins, paper money, spinners, dice, graph paper
STAAR Master**+
Textbook Correlations:
MATH Volume 2A
Lone STAAR Rigorous Problem Solving
Cluster 1 Set 1, Cluster 1 Set 7, Cluster 2
Set 11, Cluster 2 Set 17, Cluster 3 Set 21,
Cluster 3 Set 27, Cluster 4 Set 31, Cluster
4 Set 37, Cluster 5 Set 41, Cluster 5 Set
47, Cluster 6 Set 51, Cluster 6 Set 57,
Cluster 7 Set 61, Cluster 7 Set 67, Cluster
8 Set 71, Cluster 8 Set 77, Cluster 9 Set
81, Cluster 9 Set 87, Cluster 10 Set 91,
Cluster 10 Set 97
• Digital Resources: Today’s Challenge
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Notes from Council
Two days are allocated in this topic for
re-teaching and assessment.
• Combine foldables into Math Journals
• Send Home/School Connection Letter
home at the beginning of each topic.
This can be found in the Topic 1 folder
and the Teacher’s Resource Masters.
• Incorporate Lone STAAR Rigorous
Problem Solving sets throughout the
topic as fits in your schedule at least 3
times a week. (Click here to see Revised
TEKS Correlations)
•
*free download from Teachers Pay Teachers - A
free subscription is required for
www.teacherspayteachers.com in order to
download any material from TpT.
**availability depends on each campus
+ use items/activities aligned to the revised TEKS
Misconceptions/Underdeveloped Concepts
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Students confuse which number is the numerator and which number is the denominator. Have them describe a
situation by saying “____ out of ____ equal parts.” Then, have them write the numbers in the same order from top
to bottom in a fraction.
Students may think that the fraction with the larger digit has the larger value.
Students may confuse the parts being counted with the parts not being counted.
Students may forget to count the number of the fraction bars and name only the fraction bar when writing
equivalent fractions.
Some students may not understand that 6/8 is the quantity formed by 6 parts of the size of 1/8. Have them explain
that 6 kittens are orange and each kitten is 1/8 of the whole set. Therefore, six one-eighths or 6/8 are orange
Wichita Falls ISD (2014-2015)
3M Topic 11
The Mathematical Process Standards must be incorporated into
instruction as appropriate throughout the school year.
4
revised 1/5/15
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kittens. See pg 572 enVisionMath.
Pg 584 of enVisionMath – point out that these number lines show fourths. Tell students that fractions with other
denominators can be shown on a number line.
Students may think that there are fractions that name ½ with every different denominator. Use drawings of models
or fraction strips to show counter examples. See pg 626 of enVisionMath
Students may think that the fractions they see written on the number line are the only fractions there are. Ask them
to name another fraction with a denominator not equal to 2 or 4 and decide where it would be located on the
number line. Use ½ as a benchmark fraction. See pg 632 enVisionMath
As students work through problems in the lesson, encourage them to go back to make sure they have drawn a
representation that matches the information given and answered the question posed in the problem.
Parent Resources
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enVisionMath 2.0 Textbook
Download the free BouncePages app on your smartphone or tablet via your mobile app store. For Topic 11
scan the following pages with the visual learning icon: pg 572, 578, 584, 590, 596, 602, 608, 614, 620, 626,
632, and 638.
http://www.khanacademy.org/
Mr. R’s Songs for Teaching http://www.youtube.com/user/mathsongs1
http://www.khanacademy.org/
www.thinkthroughmath.com
www.xtramath.org
www.mathplayground.com
www.softschools.com
www.dad’sworksheets.com
www.poptropica.com
www.kidsmathgamesonline.com
www.brainpop.com
www.coolmath4kids.com
Wichita Falls ISD (2014-2015)
3M Topic 11
The Mathematical Process Standards must be incorporated into
instruction as appropriate throughout the school year.
5
revised 1/5/15