Week 1: Day 1-5
Lesson Goal: Students will use number lines and pattern blocks to recognize equivalent fractions. They will begin to notice patterns in creating
common equivalent fractions. It’s important not to tell students to multiply the top and bottom by the same number. They need to look at the
number lines, see the equivalent fractions, and draw their own conclusions about how multiplication/division can help them find equivalent
fractions. Once a student sees this pattern, have them share their conjecture with the class. Take a break from the lesson and allow students to use
the number lines from the lesson, fraction bars, or another model to prove the students’ conjecture.
Activity
Math Trailblazers Lesson 1: Wholes and Parts
Math Trailblazers 2: Fraction Sentences
Math Trailblazers Unit 3 Lesson 3: Equivalent
Fractions
http://webcom4.grtxle.com/index.cfm?cu=mtb3
Assessment
Look for students to create the same part of the
pattern block by using different colored pattern
blocks.
Differentiation
Students who understand right away should be
given blank number lines and told to find
fractions that are equivalent to 2/3.
Ask students questions such as:
What fractional name describes each model you
made?
Your numerator is _____; can you show it to me
in the model?
Your denominator is ____; can you show it to
me in the model?
How are your fractions related? What patterns
can you see?
Week 2: Day 6
Lesson Goal: Students will use models (pattern blocks) to add mixed numbers. They will practice changing denominators in order to add more easily.
They will do this by physically replacing the given pattern block pieces with all the same piece in order to show like denominators.
Activity
Assessment
Differentiation
Math Trailblazers Unit 12 Lesson 2: Adding
Ask students the same questions as above.
Some students may not need to use the blocks.
Mixed Numbers
Look for students to switch unlike pattern block They may understand by now how to use
pieces with the same color pattern block piece
multiplication and division to get like
in order to show like denominators.
denominators. If so, encourage them to show
Ask students to write each problem in numbers how their work relates to the model.
as well as demonstrating it with the blocks.
Day 7 and Day 8
Lesson Goal: Students will learn how to use multiplication and division to find common denominators in order to compare fractions.
Activity
Assessment
Differentiation
Math Trailblazers Unit 5 Lesson 4: Common
Look for students to draw rectangles and create Some students may not need to use the blocks.
Denominators
the two fractions with unlike denominators.
They may understand by now how to use
Then they should decide how to divide the
multiplication and division to get like
rectangles up in order to have the same number denominators. If so, encourage them to show
of pieces.
how their work relates to the model.
Day 9 and Day 10
Lesson Goal: Students should be able to prove that fractions with different numerators and denominators are equivalent by using models or
multiplication and division. They may choose to use number lines, drawings, fraction tiles, or multiplication and division strategies. Students need
time to work in partners and individually. They need to be able to share their strategies and justify their answers.
Activity
Assessment
Differentiation
Smartboard Lesson: Grade 5 Fraction
Your first job is to question students while they Choose students strategically to share as
Equivalence
are working and look for students who have
students are working. If students are using
unique strategies or strategies that most
interesting strategies or ones that the other
students should be using. In order to find out
students would benefit from seeing, have them
what students understand, ask these types of
share. Allow students to share in order from
questions:
least elaborate strategy to most elaborate
1. How does your model demonstrate this
strategy.
problem?
2. Where is the numerator in your model? Where
is the denominator? What do these numbers
tell you?
3.
4.
5.
6.
How can you find an equivalent fraction?
What important information from the problem
can you see in ______’s model?
How can your strategy help you solve similar
problems?
Will your strategy always work?
Day 11 and Day 12
Lesson Goal: Students should be able to use what they learned about finding equivalent fractions to change fractions in order to add and subtract.
Activity
Assessment
Differentiation
MTB Unit 5 Lesson 6
Ask students questions similar to the ones
The problems are differentiated. Each problem
above to determine if they are able to find
has several number choices so that students can
Smartboard Lesson: Grade 5 Add and Subtract
equivalent fractions, use them to add or
decide which set they are most comfortable
Fraction Equivalence
subtract, and then determine if their answer is
with. The sets of numbers near the top are
reasonable.
easier and the ones near the bottom are more
difficult.
Day 13
Lesson Goal: Students will find the best strategies for winning the game by using what they know about equivalent fractions. This task was
developed to help students develop and use relationships between certain fractions for fraction computation.
In this task students will play a game to see who can flip over their cards first. This game will allow students to use their fractional understandings
and build their fractional computation strategies. Logical thinking and problem solving skills will begin to develop their game playing strategies, the
more students play the game.
Activity
Assessment
Differentiation
https://www.georgiastandards.org/CommonAsk questions such as:
Multiple fraction models, in addition to those
Core/Common%20Core%20Frameworks/CCGPS
included in the task, should be made available to
 How can fractions with different
_Math_5_Unit4FrameworkSE.pdf
the students as support for those who need it. In
denominators be added together?
Play two of the following games as a class: “Flip
• What strategies can we use for adding and addition, fractional number lines (or open
it Over,” “Up and Down the Number Line,” or
number lines) could benefit many students with
subtracting fractions with different
“Create Three”
this task.
denominators?
• What models can we use to help us add and
subtract fractions with different
denominators?
• What do equivalent fractions have to do
with adding and subtracting fractions?
 What fractions do you find easy to work
with? Why?
• Which fraction do you like to spin? Why?
• What strategies do you use when playing
this game?
Day 14
Lesson Goal: Students will practice what they have learned about adding and subtracting fractions with unlike denominators.
Activity
Assessment
Differentiation
Common Assessment:
http://nrich.maths.org/6870 Mixing Lemonade
5.NF.1a
As students turn these in, sort them according to
how well students understand. Students can
play one of the games from yesterday while the
teacher pulls small groups of students who have
had trouble with changing denominators in
order to add and subtract. Use the problems on
pages 171-172 in the Student Guide.
Day 15
Lesson Goal: Students will use pictures to understand that fractions can be expressed as the numerator divided by the denominator. They will use
their calculators and centiwheels to find decimal equivalents for fractions.
Activity
Assessment
Differentiation
Math Trailblazers Unit 9 Lesson 1
Which operation did the boys use to share
Students who already understand can play the
the brownies? Why?
Fraction Track game as a review.
How does the picture show 2 divided by 3? If
http://illuminations.nctm.org/activitydetail.asp
you divide 2 by 3, what is the result? How
does this relate to the problem? Does this
always work? (Answer: 2 divided by 3 is 2/3.
This always works.)
x?id=18 (individual)
http://www.nctm.org/standards/content.aspx?
id=26975 (teams)
Day 16
Lesson Goal: Students will use a set model to demonstrate fractions of a set, or fractions of a whole number.
Activity
Assessment
Differentiation
Math Trailblazers Unit 12 Lesson 3
Look for students to find one part of the total Students may need to use concrete materials to
set first (1/3 of 12, for example). Then the
demonstrate the problems, such as two color
student might repeatedly add that group to
counters or centimeter tiles.
show multiple groups of that amount. (1/3 of
Caution:
12 is 4, so 4 + 4 represents 2/3 of 12).
Students who are immediately successful can do
the Fraction Think Dots. They roll a number
cube and complete the corresponding problem.
Several sheets of problems are included, and can
be used with several students or on several
different days.
Day 17 and Day 18
Lesson Goal: Students will learn strategies for multiplying a whole number times a fraction through the context of a 6 km hiking trail that will have
certain landmarks at fractional distances along the way. This lesson uses a linear representation.
Activity
Assessment
Differentiation
Georgia Unit 4 Hiking Trails (pages 39-42)
Look for students who are using these
Students who may have trouble with the
https://www.georgiastandards.org/Commonstrategies:
decimals associated with a 6 km hiking trail can
Core/Common%20Core%20Frameworks/CCGPS
be given an alternate scenario of a 60 km hiking
 Halving. They may take half of the halves
_Math_5_Unit4FrameworkSE.pdf
to find fourths, and take half of the fourths trail. They can use 60 square tiles to represent
The teacher needs to make a point to bring up
this distance and physically manipulate the tiles
to find eighths.
the idea that, if the first camping area is ¼ of the  Dividing by the denominator. Students
to figure out the answer to each problem.
way along the trail, then the second camping
may think of 1/5 of 6.0 = 6.0/5
area is 2/4 of the way along the trail, the third is  Adding parts. Students may think about
¾ of the way along the trail, and the fourth one
3/8 as 1/8 more than 2/8.
is 4/4 of the way, or at the very end of the trail.
Ask:
In order to get students thinking about this, ask
 How can you tell that your answer is
questions such as:
correct?
How far down the trail is the first resting point?
• How do you know that marker goes there?
How far down the trail is the second resting
Show me your thinking.
point?
• How can you tell that your markers are in
If I asked you to place a resting area 3/5 of the
the correct place? Is there another way to
way down the trail, what strategies might you
think about this?
use?
• Did you develop a shortcut to find your
answers?
• Did you identify any patterns or rules?
Explain what you have found!
Day 19
Lesson Goal: Students will understand that multiplying a fraction by a whole number is the same as adding the fraction repeatedly. They will model
this with number lines, drawings, fraction tiles, etc.
Activity
Assessment
Differentiation
Multiple Groups problems from How to Teach
How does your model represent what’s
The problems are differentiated. The problems
Fractions- Copy each problem onto a notecard
happening in the problem?
in the second column are sometimes the same
and place the notecards around the room. Also
What other way could you model this
as, but mostly a bit easier than, the problems in
put out various manipulatives for students to
problem? (or How would it look on a number the third column. Designate a section of the
use. Have students move around the room in
line? Etc.)
room that has harder cards and a section with
partners and solve the problems. Come back
What is the same for each of these problems? easier cards. Choose whether to have students
together after the first problem to share
Will these strategies always work?
decide where they go or to assign students a
strategies. Make an anchor chart of strategies.
section of the room without them knowing the
Make sure to find students who have used
problems are leveled.
number lines, drawings, fraction tiles, etc. Send
students out again to work more problems.
Come back together to share learning and
discuss student misconceptions after giving work
time.
Homework?:
http://webcom4.grtxle.com/MTB3/uploads/G
r5_CCSS_Activity_30_Lesson_4_Unit_16_with
_Student_Master.pdf
Day 20
Lesson Goal: Students use pattern blocks to explore multiplication of fractions. First they model multiplying a fraction times a whole number. Then
they model multiplying two fractions.
Activity
Assessment
Differentiation
Math Trailblazers Unit 12 Lesson 4
If students understand right away, they can
work on the Fractions task “Fraction Clothesline
Activity”
Day 21 and 22
Lesson Goal: Students will explore products of fractions and whole numbers.
Activity
Assessment
Give students the following problems to help
Students complete the following problem:
them understand that multiplying a number
Mrs. Jones plants two gardens. Garden A is 5
times a fraction less than one will produce a
meters long and 5/6 meters wide. Garden B
product that is less than the original number,
is 5 meters long and 6/5 meters wide. How
while multiplying a number by a fraction greater do the areas of the two gardens compare?
than one will produce a product that is greater
than the original number. Have them draw
Prove your thinking with pictures, words, and
pictures to prove their answers to the first and
numbers.
second problem. Then have them write
conjectures about what they notice. (Ex. Every
time you multiply a whole number by a fraction
less than one, you get a product that is less than
the whole number.) Then have them try to
prove their conjectures by testing them out
repeatedly, drawing pictures, using what they
already know about math, etc.
Solve the following problems. Sort your answers
into the chart below.
12 x ¼
12 x 2/4
12 x ¾
12 x 4/4
12 x 5/4
12 x 6/4
12 x 7/4
Less than 12
Equal to 12
Greater than 12
Make up some problems that involve multiplying
by 24. For each problem, predict whether the
answer will be less than, equal to, or greater
than 24. Then solve each problem and check
your predictions.
Less than 24
Equal to 24
Greater than 24
What conjecture (hypothesis) can you make
based on your work today? Come up with a plan
to prove your conjecture.
Sentence starter: Every time you _________,
you always get _________________.
Georgia Unit 4: Reasoning with Fractions
Differentiation
If students understand right away, they can
work on the Fractions task “Stack Em Up
Estimation”
At this point, begin the DPI Fraction Multiplication and Division unit. If extra support is needed, use one of these resources:
MTB Unit 12 Lesson 5
Georgia Unit 4: Comparing MP3s
Georgia Unit 4: Measuring for a Pillow
Differentiation for above level learners:
Keep it Simple http://nrich.maths.org/6540, Egyptian Fractions http://nrich.maths.org/1173 (follow up from Keep it Simple task), Fractional
Figures, Fractions Magic Squares, Triangle Fractions Enrichment, Triangle Challenge Puzzle Group D
Assessment ideas: http://webcom4.grtxle.com/MTB3/uploads/Gr5_CCSS_Activity_26_Lesson_1_Unit_15_with_Student_Master.pdf