Math Trailblazers Homework Help-Fifth Grade
Unit 3
Dear fifth grade parents,
Thank you so much for coming to this page to find out more about the math your child is
bringing home. Every page that your child could bring home is listed in this chart. Do not expect your
child to bring every page home. Often a teacher will note that the student already has a healthy
command of a skill, making assignment of homework unnecessary. At other times the teacher may
have a different assignment that (s)he feels is more appropriate.
To use these pages, find the Unit and Lesson numbers on the bottom of your child’s assignment
page or textbook and then click on the corresponding blue link in the table. You will find information
about the skills being practiced and occasionally extra notes will provide background information or
tips on how to extend the activity to make it more or less challenging.
Click links
in this column
Activity
Unit 3 Background Info
Unit 3 DAB p. 27
Rounding numbers
Unit 3 DAB p. 28
Fractions and number operations
Unit 3 DAB p. 29
Exercising at the gym
Unit 3 DAB p. 30
A fraction more
Unit 3 DAB p. 37
Wholes and parts
Unit 3 DAB p. 38
Wholes and parts (2)
Unit 3 page 76
Understanding mixed and improper fractions
Unit 3 page 81
Understanding equivalent
Unit 3 page 84
Ordering fractions
Unit 3 pages 92-93
Using fractions in real situations
Unit 3 page 98
Fractions on a graph
To read the small pages more easily, set the image size to 200%.
Please remember that skills in our Trailblazers program are repeated many times during the year. If
your child is struggling with a skill in Unit One it should not be as much of a concern as if your child
continues to struggle with the same skill when you see it reviewed near the end of the book.
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Fifth Grade – Unit 3 – Homework Help
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Unit 3 Background Information.
Students have been working with models of fractions and symbols for fractions (like 1/2)
since first grade. This is where they practice using the terms numerator and denominator.
While most adults worked with fractions by memorizing rules (often with no meaning to
them), Trailbalzers emphasizes student understanding. This can be seen with the way
children are asked to represent fractions as mixed numbers or improper fractions. It can
also be seen with the way equivalent fractions are understood. There is strong research
indicating that teaching children the short, cross-multiplication method that adults learned
actually reduces their understanding of the fraction relationships that are occurring. While
not stated as a rule, students recognize the concept that fractions are directly related to
the size of the whole. (Half a glass of water is less than half a pail of water.) This
recognition is constantly reinforced throughout the text with the use of different size
wholes.
Ratio’s are not dependent on size at all. They are simply a comparison of the count of
objects. If a coat has four buttons, the ratio of coats to buttons is 1 to 4 and size doesn’t
matter. The ratio can still be written in a form that looks like a fraction ( ¼ ) and
manipulated in the same ways that fractions are.
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Rounding numbers:
Watch out for 1F. Rounding the 900 to ten hundred
produces another thousand.
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Fractions and Number Operations:
While most people think of other sixths as fractions
between 1/6 and one whole, it is perfectly find to say
that ½ or ¾ also come between those two fractions.
One way (and the way a person working a cash register
would be most likely to use) to determine the change is
to start at the purchase price and then count up to the
value of the $10 bill.
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Fifth Grade – Unit 3 – Homework Help
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Exercising at the gym:
Students have been making point graphs and best-fit
lines since the end of third grade so this task should be
something they can reasonably accomplish independently.
This will be a 9 calories to 1 minute ratio. Any other
pairs of numbers should have that 9 to 1 relationship.
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A Fraction More:
Most of these fraction calculations can be completed
using methods parents learned in school. The thinking
process for #2B sounds like this. “Each whole makes
3/3 so this is 3/3 + 3/3 +3/3 + 3/3 + 3/3 + 2/3 or 17//3.
Children might draw pictures or use pattern pieces to
model this thinking. For question 3A the thinking is
opposite. “Each whole is 4/4 or I’ll subtract 4/4 to get
5/4 and another 4/4 to get ¼. I’ve subtracted 2 wholes
and have ¼ left.
Question 4B is very difficult to complete by using a
common denominator. The smallest denominator
available would be 336ths. That is unreasonable.
When putting fractions in order, here are some
strategies to use. 1) Same numerators- look at the
denominators and put the largest numbers first. The
large numbers in the denominator mean very small
pieces. 2) Same denominators- put the numerators in
order from smallest to largest, the numerator tells the
number of pieces that are being used. 3) Use estimation
8/7 is a little larger than one whole
5/6 is a little smaller than one whole
7/12 is a little larger than one half
1/8 is a little larger than zero
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Fifth Grade – Unit 3 – Homework Help
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Wholes and parts:
These activities emphasize that a fraction is dependent
on the size of the whole. Remind your child that ½ of a 2
liter bottle of soda is much more than ½ a glass of soda.
In each case, the children should determine what one
part is worth and then add more of those parts to make
the required amount.
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Wholes and parts (2):
For this entire page the hexagon is worth one whole.
That means the amount shown in parts D and F each
represent two wholes. In part D the child is asked to
shade in 1 whole plus five sixths more. (Be careful, the
hexagon is sliced into twelfths so the child must
understand that five sixths is the same as ten twelfths.)
For many years children have used green triangles that
are 1/6 of a yellow hexagon. They may use this
knowledge to shade 5/6 rather than the 10/12
relationship.
Students must be careful to use the denominator to
decide the size of the fractions and the numerator to
count the number of parts.
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Fifth Grade – Unit 3 – Homework Help
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Unit 3 Page 76
Q 1. The following number sentences go with
pictures A-D but they are in scrambled
order. Can you link the answers with the
pictures?
1/3 + 1/4 + 1/12 = 2/3
1/3 +1/4 +1/6 = 3/4
1/3 + 1/4 + 1/12 + 2/6 = 1
1 + 3/6 = 1 3/6 or 1½
Q 2 Students may complete these in
unexpected ways. Part A might cause a
child to say, “I know 10/2 is five so 11/2
has to be 5½”
Q 3. This is another place where children may
not follow the shortcut rule that adults
learned. Presenting that rule as something
to be memorized is a much less effective
way of teaching it than having the children
complete Parts A through H and then
asking, and possibly helping them discover
the rule.
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Unit 3 Page 84
Q 1 While it is possible to use the common
denominator method to order these
fractions, the numbers create large
denominators. This example would require
a denominator of 60. Using logic is often
just as good a method to order fractions.
Arranging the denominators from smallest
to largest they are 12ths, 10ths, 5ths and
3rds. Since the numerators are all 2 the
order of the denominators is the correct
order.
Q 2 Seven eights is close to one whole. 1/12 is
close to zero, 3/6 is exactly one half.
13/5 is greater than one. Order these in
relation to their “benchmark” amounts.
Q 3 The denominators are the same so order
the numerators.
Q 4 Us a method similar to Q. 2.
Q 5 The numerators are all the same so
compare the denominators.
Q 6 This is the exact same kind of task put in
a story format.
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Unit 3 Page 81
Q A through I While the “cross multiplication”
method is an efficient method to calculate
equivalent fractions, it does not promote
understanding. This page works on
understanding.
8 ÷2=4
10 ÷ 2 = 5
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Unit 3 Page 92-93
Q 1 The students may choose any number of
nickels or quarters they wish to put in the
data tables. They manipulate these
numbers so the manipulated variable goes
on the “x” or horizontal axis of the graph.
The points should form a straight line if
the data was entered correctly. The
ratios will all be equivalent ratios to the
two initial ones presented in the text.
Q 2 and 3 These calculations are about the
same as those in task 1, without the
graphing.
Q 4 The wording of this task is a little
confusing. The first ration is 50¢ to 1
brownie. The second ratio is $1.00 to 3
brownies. They are unequal.
Be careful not to say “eight tenths divided by
two” in this calculation. The eight tenths is
being divided by two halves (another name
for one whole) and any number multiplied or
divided by one equals the same number.
8/10 ÷ 2 = 4/10 (not 4/5)
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Fifth Grade – Unit 3 – Homework Help
Q 5 The graphing is straight-forward. The
ratios will all be equivalent to 5 to 1.
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Unit 3 Page 98
Q 1 and 2 The questions are straight-forward
graph reading tasks.
Q 3 All ratios should be equivalent to
1 mile to 5 minutes.
Q 4 I would take the distance she rode in one
hour (60 minutes) and add it to the
distance she rode in half an hour (30
minutes)
Q 5 Using equivalent ratios, a student can
extrapolate (make a prediction outside the
collected data) times beyond the range of
the graph.
Q 6 All speeds are ratios of distance compared
to time. Think of all the speeds measured
that way.
Mph = miles per hour
Kph = kilometers per hour
Bpm = heartbeats per minutes
Rpm = revolutions per minute
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Fifth Grade – Unit 3 – Homework Help