Math Trailblazers Homework Help-Fifth Grade
Unit 4
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 4 Background Info
Unit 4 DAB p. 43
Area
Unit 4 DAB p. 44
Multiplication and division practice
Unit 4 DAB p. 45
Comparing prices
Unit 4 DAB p. 46
Word problems
Unit 4 page 105
Finding area
Unit 4 pages 111-112
Relating multiplication and division
Unit 4 pages 116-117
More multiplication and division work
Unit 4 page 122
Finding 10% of amounts
Unit 4 pages 129-130
Finding the mean or average
Unit 4 page 138
Finding a ratio on a data table
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 4 – Homework Help
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Unit 4 Background Information
The main emphasis of this unit is whole number division. Children have done division using
models since kindergarten. They were introduced to the Forgiving Division algorithm in grade
four but some of them may not remember the procedure.
Forgiving Division
This pattern allows children to choose numbers that are easy for them
266
.
to multiply. In the example at the right, the child knew that 4 x 100
4 ) 1064
.
was 400 and used that fact twice.
400 100.
Next the child reasoned that if four 100s made 400, four 50s would be
664
.
half as much or 200. The partial quotients are placed to the right of
400 100.
the vertical line and then added together and written above the bridge
264
.
(division symbol).
200 50.
This method of division is explained using different numbers on student
64
.
guide pages 113-115
40 10.
24
.
24
6.
0
.
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Fifth Grade – Unit 4 – Homework Help
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Area:
Most of these area problems are pretty straight
forward but 4B is a little tricky. Since 12 x 8 = 96 the
first thought is that 96 is less than 100 and the run
should fit. What if the yard is 10 x 10 to make the 100
square feet? Will a 12 foot run fit?
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Multiplication and Division Practice:
In fourth grade, students learned the forgiving division
algorithm. Click here for a review of the forgiving
division pattern.
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Fifth Grade – Unit 4 – Homework Help
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Comparing Prices:
Students have been making point graphs with best-fit
lines since the end of third grade so the graphing part
of this task should be something they can reasonably
accomplish independently.
Ratios were introduced in the previous unit and will be a
newer concept. The ratio of cost to number for Sharpy
Pencils is 20 cents to 2 pencils.
One way to show the cost is on the graph. Start at 4
pencils, go up to the best fit line and then go across to
40 cents.
Another way is with equivalent ratios 2
= 4
20
40
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Word Problems:
One of the most important aspects of this page is that
different problems use different combinations of
operations. This is the way adults encounter problems
in real life. If you child is struggling, help the child try
to understand the action in the situation. Relate the
action to the operations table listed below.
Put together
Take apart
Individual items
Addition
Subtraction
Equal size groups
Multiplication
Division
Additionally, comparisons are made using subtraction.
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Fifth Grade – Unit 4 – Homework Help
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Unit 4 Page 105
Q 1. Shapes A and C can be completed easily by
counting squares. A possible equation
(number sentence for shape A could be
(1x4)+(1x4)=8 cm2. Another view could be
(1x2)+(2x2)+(1x2)=8 cm2.
Shape B be can be done by inference.
Image a rectangle that goes behind the
left end of shape C. Find the area of the
rectangle and divide that area by two to
determine the area of the triangle.
Place the grid paper over shape D or
measure the sides using a ruler to
determine the area.
Q 2 This can be any shape. It can be checked
by counting the squares inside..
Q 3. If the child makes a 2X7 rectangle and
then draws a shape with part of the line
outside the rectangle and approximately
the same area inside the square, this task
will be accomplished.
Q 4 This could be a 3x7 rectangle but other
shapes will also work such as a rectangle
that is 3½ x 6.
Q 5 The easiest way might be to draw a
rectangle with an area of 12 sq. cm and
then cutting it in half from corner to
corner.
Q 6 An “L” shaped hexagon might work well for
this but there are many other possible
shapes that will work.
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Unit 4 Page 111-112
Q 1 through 4 Base ten shorthand for 144÷3
looks like this. From this, you can probably
decide on the other answers.
Q 5 and 6 Encourage your child to identify how
the significant digits remain the same as
the number of zeros changes.
Q 7 This shows how multiplication and division
are related to each other.
Q 8 and 9 The remainders for question 8 could
be arranged in a variety of ways. Question
9 will not have a remainder.
Q 10 Since the number is being divided by
four and the remainder is .25 or ¼ then ¼
of four has to be one.
Q 11 If your child is struggling with these
calculations, figure the result with the
zeros covered and then see how the
answer changes when the zeros are
included.
Q 12 through 15 These are more division
calculations embedded in story settings.
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Fifth Grade – Unit 4 – Homework Help
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Unit 4 Page 116-117
Q 1 through 3 These questions show the
relationship between multiplication and
division. Combining amounts to get a larger
total means multiplication. Sorting into
smaller, equal size groups involved division.
Q 4 through 9 Click here for a review of the
forgiving method of division.
Q 10 A story for Q 4 might be… “The choco
company had 586 candy bars come off the
assembly line in one hour. If four
different machines are making candy bars
at about the same speed, how many bars
came from each machine?”
Q 11 through 17 These are problems involving
all four operations. Children may solve
them in any manner they feel is best for
them. If they decide to use a calculator
have the children tell you, using estimates,
why the number on the calculator is
reasonable.
Q 18 through 20. Calculate in any method
except the use of a calculator. Since
the object of these tasks is to calculate,
then a calculator is not appropriate.
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Unit 4 Pages 129-130
Q 1 through 6 This book uses the word
average to describe methods for finding
numbers in the middle of a set. It
identifies mean, median and mode as
different averages. That is why question
2 says “Use the mean” to describe the
average.
Q 7 through 22 Be sure to remember to use
order of operations with these equations.
Multiplication and division are done before
addition and subtraction. The correct
answer for number seven is 12 because
3x3=6 plus 6 more makes 12. Eighteen is
not correct because that requires adding
to be done before the multiplying. Also
remember that all numbers within
parentheses are completed before the
other four operations. Number eighteen is
the same as 9x3 because the addition and
subtraction inside the parentheses is done
before the multiplication which is outside
of them.
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Unit 4 Page 138
Q 1 through 3 Students have explored this
area of water on paper towels in fourth
and fifth grade. The new idea this year is
to express the area to drops comparison
as a ratio. In this case, the area to drops
ratio is 2 to 1. Children have been doing
best fit lines and point graphs since third
grade and should be familiar with their
construction.
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Unit 4 Page 122
Q 1 through 8 These tasks all work with 10%
or multiples of 10%. The easiest way to
find 10% is to just cover the last digit of
the number. For example, 10% of 5,282 is
about 528. One error students often
make is finding 10% of the estimate
instead of 10% of the original.
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Fifth Grade – Unit 4 – Homework Help