Download GRADE 5 • UNIT 4

GRADE 5 • UNIT 4
Table of Contents
Multiplication and Division of Fractions and Decimal
Fractions
Lessons
Topic 1: Line Plots of Fraction Measurements
1
Lesson 1: Measure and compare pencil lengths to the nearest ½, ¼, and 1/8
of an inch, and analyze the data through line plots.
Topic 2: Fractions as Division
2-5
Lesson 2 & 3: Interpret a fraction as division.
Lesson 4: Use tape diagrams to model fractions as division.
Lesson 5: Solve word problems involving the division of whole numbers with answers in the form
of fractions or whole numbers.
Topic 3: Multiplication of a Whole Number by a Fraction
6-9
Lesson 6: Relate fractions as division to fraction of a set.
Lesson 7: Multiply any whole number by a fraction using tape diagrams.
Lesson 8: Relate a fraction of a set to the repeated addition interpretation of fraction
multiplication.
Lesson 9: Find a fraction of a measurement, and solve word problems.
Topic 4: Fraction Expressions and Word Problems
Lesson 10: Compare and evaluate expressions with parentheses.
Lessons 11 & 12: Solve and create fraction word problems involving addition,
subtraction, and multiplication.
10-12
Topic 5: Multiplication of a Fraction by a Fraction
13-20
Lesson 13: Multiply unit fractions by unit fractions.
Lesson 14: Multiply unit fractions by non-unit fractions.
Lesson 15: Multiply non-unit fractions by non-unit fractions.
Lesson 16: Solve word problems using tape diagrams and fraction-by- fraction multiplication.
Lessons 17 & 18: Relate decimal and fraction multiplication.
Lesson 19: Convert measures involving whole numbers, and solve multi- step word problems.
Lesson 20: Convert mixed unit measurements, and solve multi-step word problems.
Topic 6: Multiplication with Fractions and Decimals as Scaling and Word
Problems
21-24
Lessons 21: Explain the size of the product, and relate fraction and decimal equivalence
to multiplying a fraction by 1.
Lessons 22 & 23: Compare the size of the product to the size of the factors.
Lesson 24: Solve word problems using fraction and decimal multiplication.
Topic 7: Division of Fractions and Decimal Fractions
25-31
Lesson 25: Divide a whole number by a unit fraction.
Lesson 26: Divide a unit fraction by a whole number.
Lesson 27: Solve problems involving fraction division.
Lesson 28: Write equations and word problems corresponding to tape and number line
diagrams.
Lesson 29: Connect division by a unit fraction to division by 1 tenth and 1 hundredth.
Lessons 30 & 31: Divide decimal dividends by non-unit decimal divisors.
Topic 8: Interpretation of Numerical Expressions
32-33
Lesson 32: Interpret and evaluate numerical expressions including the language of scaling and
fraction division.
Lesson 33: Create story contexts for numerical expressions and tape diagrams, and solve word
problems.
Grade 5, Math Unit 4 for Parents and Students
Vocabulary
Familiar Terms and Symbols
Array – an arrangement or display of a number in equal rows and columns
Conversion factor - a multiplier for converting a quantity expressed in one unit into an equivalent
expressed in another unit.
Commutative property – the order of the numbers added or multiplied can be changed and the
answer will remain the same. (i.e. 4 × ½ = ½ × 4)
Decimal fraction - A decimal fraction is a fraction where the denominator (the bottom number) is a
power of ten (such as tenths, hundredths, thousandths, etc). i.e. 43/100 is a decimal fraction and can be
written as 0.43
Denominator – the number on the bottom (names the fractional unit: fifths in 3 fifths, which is
abbreviated to the 5 in 3/5)
Distribute - with reference to the distributive property, (i.e. in 1 2/5 × 15 = (1 × 15) + (2/5 × 15))
Divide/division - partitioning a total into equal groups to show how many units in a whole,
(i.e. 5 ÷ 1/5 = 25)
Equation – a statement that two expressions are equal, will always have an equal sign
(i.e. 3×4 = 6×2)
Equivalent fraction – fractions that name the same amount or part using different units
(i.e. 3/5 = 6/10)
Equivalent fractions - represent the same amount of area of a rectangle, the same point on the number
line.
Evaluate – to find the value of an expression
Expression - a group of numbers and symbols that shows a mathematical relationship (i.e. ½ + ¼ + ¾)
Factors - numbers that are multiplied to obtain a product)
Fraction – a number that names a part of a whole or part of a group (i.e. 3 fifths or 3/5)
Fraction greater than or equal to 1 – can be written as an “improper fraction” where the
numerator is greater than a the denominator or as a “mixed number” with a whole and
a fraction part (i.e. 7/2 = 3 ½ , an abbreviation for 3 + ½ )
Fractional unit (e.g., the fifth unit in 3 fifths denoted by the denominator 5 in 3/5)
Hundredth - (1/100 or 0.01)
Line plot - data shown on a number line using x’s to show the number of times a particular fraction is
used in the data (the frequency). (Examples located in Lesson 1)
Mixed number – names a whole plus a fractional part (i.e. 3 ½ , an abbreviation for 3 + ½ )
Numerator - the number on the top (names the count of fractional units: 3 in 3 fifths or 3 in 3/5)
Parentheses - symbols ( ) used around a fact or numbers within an equation or expression)
Product – the answer to a multiplication problem
Quotient - the answer when one number is divided by another
Tape diagram – visual method for modeling problems, the whole is labeled on the top and the tape is
broken into the known and unknown parts.
273 vehicles
Example of Tape Diagram:
Two hundred seventy-three vehicles were parked in a
parking lot. One-third of the vehicles were trucks. How
many trucks were in the parking lot?
3 units (sections) = 273
1 unit (section)
= 273 ÷ 3 = 91 trucks
Tenth - (1/10 or 0.1)
Unit fraction – a fraction with a numerator of 1
Units of measurement - feet, mile, yard, inch, gallon, quart, pint, cup, pound, ounce, hour, minute,
second
Whole unit (e.g., any unit that is partitioned into smaller, equally sized fractional pieces – called “units”)
New Terms for 5th Grade Unit 4
Decimal divisor - the number that divides the whole (dividend) and has units of tenths, hundredths,
thousandths
Frequency – the number of times something occurs
Simplify (using the largest fractional unit possible to express an equivalent fraction)
Scaling – may increase or decrease the size or quantity of something
Lesson by Lesson Suggestions
Lesson 1: Line Plots and Fraction Measurements
Students will read and create line plots using fractional measurements.
In this lesson it is important that students be able to read a customary
ruler with increments of halves, fourths, and eighths.
Students use their knowledge of fraction operations to answer questions about the data such as, “What is the total
length of the five longest pencils in our class?” It helps for students to interpret fractions as division in this lesson.
To measure to the quarter inch, one inch must be divided into 4 equal parts, or 1÷4.
Example of a Line Plot
The line plot below shows the growth of 10 sunflowers plants. The cross marks (x’s) above each fraction
represents the height of each plant after one month of planting.
To summarize the data:
2 plants grew to 1 ¾ ft,
2 plants grew to 2 feet,
2 plants grew to 2 1/8 ft,
2 plants grew to 2 ½ ft,
1 plant grew to 2 5/8 ft and
1 plant grew to 2 7/8 ft.
There are 10 x’s because there were 10 plants measured.
Example of a Line Plot 2
Joseph recorded the lengths of his classmates’ pencil erasers in the chart to the right.
Students Length
Examples of questions that may be asked:
Student 1
Student 2
Student 3
Student 4
Student 5
Student 6
Student 7
Student 8
Student 9
Student 10
Student 11
Student 12
Student 13
Student 14
Student 15
Student 16
1. How many erasers have a length of at least 1 ½ inch? 9 erasers
2. How many erasers measure less than a half inch? 2 erasers
*3. What is the total length of all the erasers? 20 1⁄2 inches
4. What is the difference between the shortest and longest erase lengths? 1 ¾ inches
1⁄2 inch
1 inch
2 inches
1⁄4 inch
1 1⁄2 inches
1 1⁄2 inches
2 inches
2inches
1⁄4 inches
3⁄4 inches
3⁄4 inches
2 inches
13⁄4 inches
1 3⁄4 inches
1 1⁄2 inches
1 inch
5. Which measurement appears most frequently? 2 inches
*6. How many ¼-inch erasers would it take to equal the length of a 2-inch eraser? 8 one-fourth inch erasers
*explanations on the next page*
Explanations and work to be shown for questions 3 & 6.
*3. What is the total length of all the erasers?
20 1⁄2 inches
6. How many ¼-inch erasers would it take to equal the length of a 2-inch eraser?
To solve this problem you can use different strategies. One strategy is to take two whole rectangles and
divide the rectangles into fourths.
It would take 8 one-fourth inch erasers to equal the length of a 2-inch eraser.
Lessons 2-5: Fractions as Division
Students will practice interpreting fractions as division. Students will solve problems using equal sharing
with area models & tape diagrams to understand the division of whole numbers with answers in the form
of fractions or mixed numbers (e.g., seven brownies shared by three girls, three pizzas shared by four
people). Students will also interpret remainders as fractions. Students will solve real world problems
using models and equations while reasoning about their results (e.g., between what two whole numbers
does the answer lie?).
Example 1:
Regg has 7 crackers that he wants to share between his friend Gabe and himself equally.
Method 1: If there are 7 crackers, you could give
each boy 3 crackers. Then take the last cracker and
split it in half and give each boy one of the halves.
Method 2: Split all the crackers in half first, and
then share.
How many halves do we have to share in all? 14 halves
Share them equally with each boy. How many crackers did each
boy get? Each boy would get 7 halves.
Although the crackers were shared in units of one-half, what is
the total amount of crackers each boy receives?
3 whole crackers and 1⁄2 of another cracker.
Each boy would get 3 1⁄2 crackers.
Example 2:
Using a picture, show how friends Sally, Adam, and Mandy could share two candy bars. Write an equation,
solve, and check.
Strategy: Draw two tape
diagrams since there are 2 candy
bars. Divide each candy bar into
3 equal parts and then share
among the three friends.
Unit Form: 6 thirds ÷ 3 = 2 thirds
Example 3:
Mark ran a total of 5 miles in 3 days. If Mark runs the same distance every day, how many miles does he run
each day?
To solve this problem use a tape
diagram.
We know that 3 units are equal to
5 miles.
We want to know what 1 unit is
equal to.
Example 4:
American Cookie Company uses 6 cups of chocolate chips to make 8 batches of mini chocolate chip cookies. If
each batch uses the same amount of chocolate chips, how many cups of chocolate chips are used? (Solve using
drawing, a standard algorithm, and check your answer.)
6 cups shared equally in 8 batches of cookies
Lessons 6-9: Multiplication of a Whole Number by a Fraction
Students will use arrays and tape diagrams to find the fraction of a set. Students will then use the fraction
of a set thinking to multiply a fraction times a whole number understanding that the word “of” is a signal
to multiply. Students will also link division of a whole number to multiplication of a fraction, i.e. dividing
by 2 is the same as multiplying by ½.
Students also use the commutative property to relate fraction of a set to the Grade 4 repeated addition
interpretation of multiplication by a fraction. This offers opportunities for students to reason about
various strategies for multiplying fractions and whole numbers. Students apply their knowledge of
fraction of a set and previous conversion experiences to find a fraction of a measurement, including
converting a larger unit to an equivalent smaller unit (i.e. 1/3 min = 20 seconds and 2 1/3 feet = 27
inches).
Lesson 6: Relate fractions as division to fraction of a set.
Example 1:
Tommy bought a dozen cookies, ¼ of the cookies were oatmeal. How many cookies were oatmeal?



To find ¼ of 12, make an array with 12 circles.
Use lines to divide the array into 4 equal groups.
Write a division sentence to represent what was done.
12 ÷ 4 = 3
or
12/4 = 3
 Each group is ¼ of all the circles.
 So ¼ of 12 = 3
Example 2:
In a class of 15 students, 4/5 are boys. How many students are boys?
or
Lesson 7: Multiply any whole number by a fraction using tape diagrams.
There are 42 students going on a field trip. Three-sevenths are girls. How many are boys?
How many are girls? Solve using a tape diagram.
The tape diagram shows that three sevenths of the 42 students are girls so the remaining pieces are boys
which are 4 pieces or four sevenths.
Each unit is equal to 6 students. The girls are 3 of the 7 units. To find how many girls are on the field trip
we multiply 3 units by 6.
3 units = 6 x 3 = 18 students
There is a total of 18 girls on the field trip.
Boys are 4 of the 7 units. To find how many boys are on the field trip we multiply 4 units by 6.
4 units = 6 x 4 = 24 students
There is a total of 24 boys on the field trip.
Check: 18 girls + 24 boys = 42 total students
Lesson 8: Using multiple ways to solve a multiplication of a fraction and a whole number.
Ways to interpret the expression:
Lesson 9: Find a fraction of a measurement, and solve word problems.
Example 1:
Mrs. Collins baked 3 dozen cookies. Two-thirds of them were chocolate chip. How many chocolate chip
cookies did she bake?
1 dozen is 12 cookies, so 3 dozen is 36 cookies (12 x 3)
2/3 of 36 cookies = _____ chocolate chip cookies
Using a Tape Diagram
Example 2:
Tape Diagram
Using a Numerical Procedure
lb – pound
oz – ounce (16 oz is equal to 1 lb)
Equation
Example 3:
Amanda measured the length of one of her books. It was ¾ of a foot. How long is her book in inches?
¾ of 1 foot = _____ inches
Tape Diagram
ft – foot in – inches
Equation
Lesson 10 - 12: Fraction Expressions and Word Problems
In this topic students will write and evaluate expressions with parentheses, interpret numerical
expressions, and solve and create fraction word problems.
Lesson 10: Compare and evaluate expressions with parentheses.
Write an expression to match a tape diagram. Then evaluate.
Example 1:
Example 2:
Write and evaluate an expression from word form.
Lesson 11 & 12: Solve and create fraction word problems involving addition, subtraction, and
multiplication.
Example 1:
Crissy and Crystal share a 16 ounce box of cereal. By the end of the week, Crissy has eaten 3/8
of the box and Crystal has eaten ¼ of the box of cereal. What fraction of the box is left?
3/8 of the box of cereal is left.
Example 2:
Create a story problem about a fish tank for the tape diagram below. Your story must
include a fraction.
There are 12 mollies in the fish tank.
Lesson 13 - 20: Multiplication of a Fraction by a Fraction
Topic 5 introduces students to multiplication of fractions by fractions—both in fraction and decimal
form. The topic starts with multiplying a unit fraction by a unit fraction, and progresses to
multiplying two non-unit fractions. Students use area models, rectangular arrays, and tape diagrams
to model the multiplication. Students will also find fractional parts of customary measurements and
calculate measurement conversion. Students will convert smaller units to fractions of a larger unit
(i.e. 6 inches = ½ feet).
Example 1: Solve. Draw a model to explain your thinking.
Joseph has ¼ of a pound of strawberries. He gave his teacher 1/5 of the strawberries.
What fraction of strawberries did Joseph give to his teacher?
Think: We need to find
1/5 of ¼ strawberries.
Step 1: Draw a rectangle and cut it
vertically into 4 equal parts.
Shade 1 part and label it ¼.
Step 2: We need to find 1/5 of ¼. Split the whole
rectangle into 5 equal parts by drawing
horizontal lines. Now, shade 1 of the 5 parts
(that are already shaded) and label it 1/5.
Example 2:
Of the students on Nia's track team, 3/5 participate in running events. Of the students who participate in
running events, 2/3 are in the relay race. What fraction of the students on the track team ran in the relay race?
Think: We need to
find 2/3 of 3/5.
Step 1: Draw a rectangle and cut it vertically into
5 equal parts. Shade 3 parts and label it 3/5.
Step 2: Split the rectangle into 3 equal parts by
drawing horizontal lines. Now shade 2 of the 3 parts
(that are already shaded) and label it 2/3.
How many units make our whole? 15
What’s the name of these units? Fifteenths
In lesson 15 students will begin to recognize numerical strategies to multiplying fractions.
Method 1: Students will eventually see a pattern and multiply numerator times numerator and
denominator times denominator.
Method 2: Students divide by common factors prior to multiplying. (*See video resources*)
A common factor of 2 and 12 is 2.
A common factor of 10 and 5 is 5.
Students will also solve word problems using a tape diagram.
Example: Dell has 14 blue marbles. His blue marbles make up 2/3 of his total number of
marbles. How many marbles does Dell have?
Dell has 35 marbles.
Relate decimal and fraction multiplication
Convert mixed unit measurements
2 ¼ ft = _____ in
9 inches = ____ ft
Rename1 foot
as 12 inches.
Problem: A container can hold 4 ½ pints of water. How many cups can 2
containers hold? ( 1 pint = 2 cups)
Lesson 21 - 24: Multiplication with Fractions and Decimals as Scaling and Word Problems
Students will extend their understanding of multiplication to include scaling. Students compare the
product to the size of one factor, given the size of the other factor without calculation (i.e. 486 × 1,327.45
is twice as large as 243 × 1,327.45 because 486 = 2 × 243). Students will begin to reason about the size of
products when quantities are multiplied by 1, by numbers larger than 1, and numbers smaller than 1.
Multiplying a number times a number equal to 1, results in the original number.
***These examples prove the statement that
multiplying a number times a number equal to 1,
does result in the original number. Therefore, if
the scaling factor is equal to 1, the original
number does not change.
Multiplying a number times a number less than 1 results in a product less than the original
number.
***These examples prove the statement that
multiplying a number times a number less
than 1, does result in a product less than the
original number. Therefore, if the scaling
factor is less than 1, the product will be less
than the original number.
Multiplying a number times a number greater than 1, results in a product greater than the
original number.
***These examples prove the
statement that multiplying a number
times a number greater than 1, does
result in a product greater than the
original number. Therefore, if the
scaling factor is greater than 1, the
product will be greater than the
original number.
A common misconception students have is the belief that multiplication always makes a quantity bigger.
That is not always true. Suppose there are 6 students standing in line and ½ are wearing red shirts. How
many students are wearing red shirts? ½ x 6 = 3 students. The product is smaller than the original number.
Practice Problem:
Without doing any calculating, choose a
fraction to make the number sentence true.
Explain how you know.
Application Problem:
At the book fair, Van spent all of his money on new books. Paul spent 2/3 as much as Van.
Elliot spent 4/3 as much as Van. Who spent the most money? Who spent the least?
Paul and Elliot are being compared to Van. Van
spent all his money which is considered 1 whole in
this problem.
Using what we learned about scaling factor, 2/3 is
less than 1
so Paul spent less than Van. 4/3 is greater than 1,
so Elliot spent more than Van.
Scaling with Decimals
Whether you are working with fractions or decimals, the scaling factor statements still apply.
Problem:
Without calculating, fill in the blank
using one of the scaling factors to
make each number sentence true.
Explain how you know.
a. 4.72 x _______ < 4.72
(4.72 x 0.761 < 4.72)
Since 0.761 is less than 1, then the product will be less
than 4.72.
b. ____ x 4.72 > 4.72
( 1.024 x 4.72 > 4.72 )
Since 1.024 is greater than 1, then the product will be
greater than 4.72.
c. 4.72 x _____ = 4.72
(4.72 x 1.00 = 4.72)
Since 1.00 is equal to 1, then 4.72 does not change.
Lesson 25 - 31: Division of Fractions and Decimal Fractions
Topic 7 begins the work of division with both fractions and decimal fractions. Students use tape
diagrams and number lines to reason about the division of a whole number by a unit fraction
and a unit fraction by a whole number. Using the same thinking developed in Unit 2 to divide
whole numbers, students reason about how many fourths are in 5 when considering such cases
as 5 ÷ ¼. They also reason about the size of the unit when ¼ is partitioned into 5 equal parts: ¼ ÷
5. Using this thinking as a backdrop, students are introduced to decimal fraction divisors and use
equivalent fraction and place value thinking to reason about the size of quotients, calculate
quotients, and sensibly place the decimal in quotients.
Divide a whole number by a unit fraction.
Example:
Garret is running a 5-K race. There are water stops every ½ kilometer, including at the finish line. How
many water stops will there be?
Number Sentence: 5 ÷ ½
Step 1: Draw a tape diagram to model the problem.
The tape diagram is partitioned into 5 equal units.
Each unit represents 1 kilometer of the race.
Step 3: Draw a number line under the tape
diagram to show that there are 10 halves in
5 wholes.
Step 2: Since water stops are every ½ kilometer,
each unit of the tape diagram is divided into 2
equal parts.
When you count the number of halves in the
tape diagram, you will determine that there
are a total of 10.
Therefore, there will be 10 water stops
during the 5-K race.
Misconception: Students may believe
that the quotient in division is always
smaller than the dividend (whole) and
the divisor. It is about asking how
many groups there are of a certain
size. For example, what happens to
the number of pieces if we cut a
carrot into 6 equal pieces? (There are
more pieces of carrot.) This is the
meaning of dividing a whole by a unit
fraction.
Practice Problem:
Francois picked 2 pounds of blackberries. If he wants to
separate the blackberries into pound bags, how many bags
can he make?
Number Sentence: 2 ÷ ¼ = 8
One whole has 4 fourths and 2 wholes has 8 fourths.
Francois can make 8 bags with ¼ pound of blackberries in each.
Divide a unit fraction by a whole number
Randy and 2 of his friends will share a
pizza equally. What fraction/portion of
the pizza will each get?
Number Sentence: 1 ÷ 3
Now suppose there is only ½ of a pizza that is shared equally among Randy and his 2 friends. What
fraction/portion of the pizza does each person get? Number Sentence: ½ ÷ 3
½ ÷ 3 = 1/6
3 sixths ÷ 3 = 1 sixth
(The unshaded part is
showing 3 sixths.)
Each person will receive 1/6 of the
pizza.
Practice Problem:
If Bridget poured ½ liter of lemonade equally into 4
bottles, how many liters of lemonade are in each
bottle?
Number Sentence: ½ ÷ 4 = 1/8
There is 1/8 liter in each bottle.
1
Divide by decimal divisors
Example 1:
0.24 ÷ 0.4
Step 1: Rewrite the division expression as a fraction.
Step 2: Rename the divisor/denominator as a whole
number by multiplying a fraction equal to 1.
Step 3: Divide.
Example 2:
2.7 ÷ 0.03
Step 2:
Step 1:
Step 3:
18 ÷ 2 = 9
Application Problem:
Explain why it is true that 1.8 ÷ 0.2 and 0.18 ÷ 0.02 have the same quotient.
They all have the same quotient because I can rename each fraction without changing their value by
multiplying each by a fraction that equals 1. In the first fraction since both the numerator and
denominator are in tenths, multiplying by 10/10 resulted in both the numerator and denominator being
whole numbers. In the second fraction both numerator and denominator are in hundredths. When I
multiply each by 100/100, it resulted in both numerator and denominator being whole numbers. Each
fraction resulted in 18 ÷ 2.
Application Problem:
Mrs. Morgan has 21.6 pounds of peaches to pack for shipment. She plans to pack 2.4 lb of
peaches in each box. How many boxes are required to ship all the peaches?
Mrs. Morgan needs 9 boxes to ship all the peaches.
Lesson 32 - 33: Interpretation of Numerical Expressions
In the last topic of this unit numerical expressions involving fraction-by-fraction multiplication
are interpreted and evaluated. Students create and solve word problems involving both
multiplication and division of fractions and decimal fractions.
Write word form expressions numerically
Example 1:
Half the sum of 3/5 and 1 ½
Possible Responses:
Example 2:
3 times as much as the quotient of 1.2 and 0.4
Possible Responses:
3 x (1.2 ÷ 0.4)
or
(1.2 ÷ 0.4) x 3
Practice Problem:
Which expression is equivalent to “the sum of 5 and 3 divided by ½?”
Correct answer: C
Some will pick A but this expression
represents “the sum of 5 and 3 divided by 4.”
Application Problem:
Susie picked 12 cucumbers from her garden. She cut up 2 of them for a salad and then gave
2/5 to her neighbor. Write an expression that tells how many cucumbers she gave to her
neighbor.
Expression:
2/5 x (12 – 2)
Write a numerical expression in word form
Example 1: (1/4 + 1.25) ÷ 1/2
The sum of 1/4 and 1.25 divided by ½
Example2: 5/6 – (1/5 x 0.2)
The difference between 5/6 and the product of 1/5 and 0.2
Evaluate the following expressions:
Students should recognize that when evaluating expressions that contain grouping symbols, any
operation inside grouping symbols should be performed before operations outside of grouping symbols.
Extra Example Problems
Problem:
Without evaluating, compare the first expression to the second expression. Explain your reasoning.
(1.25 + 3/4) x 3/2
2/3 x (1.25 + 3/4)
In both expressions you are finding the sum of the same two numbers. In the first expression the sum is being
multiplied by a fraction greater than 1, which would result in an answer greater than the sum of the two numbers.
In the second expression the same sum is being multiplied by a fraction less than 1 which would result in an answer
less than the sum of the two numbers. Therefore first expression will be greater than the second expression.
(1.25 + 3/4) x 3/2
>
2/3 x (1.25 + 3/4)
Problem Solving:
Luke has 3.5 hours left in his workday as a car mechanic. He needs ½ of an hour to complete
one oil change.
a. How many oil changes can Luke complete during the rest of his workday?
Luke can complete 7 oil changes during the 3.5 hours.
b. Luke can complete two car inspections in the same amount of time it takes him to complete one oil
change. How long does it take him to complete one car inspection?
Luke can complete one car inspection in ¼ hour.
c. If he only completes car inspections in the rest of his workday, how many can he complete?
7 x 2 = 14
Since Luke can complete 2 car inspections in the same amount
of time it takes him to complete one oil change, he can
complete 14 inspections (twice as many as 7) in 3.5 hours.
Recommended Resources
IXL skills covered in this unit:
S.10 Interpret line plots
S.11 Create line plots
S.12 Create and interpret line plots with fractions
N.1 Multiply unit fractions by whole numbers using number lines
N.2 Multiply unit fractions by whole numbers using models
N.3 Multiples of fractions
N.4 Multiply unit fractions and whole numbers: sorting
N.5 Multiply fractions by whole numbers I
N.6 Multiply fractions by whole numbers using number lines
N.7 Multiply fractions by whole numbers using models
N.8 Multiply fractions by whole numbers II
N.9 Multiply fractions and whole numbers: sorting
N.10 Multiply fractions by whole numbers: word problems
N.11 Multiply fractions by whole numbers: input/output tables
N.12 Multiply two unit fractions using models
N.13 Multiply two fractions using models: fill in the missing factor
N.14 Multiply two fractions using models
N.15 Multiply two fractions
N.16 Multiply two fractions: word problems
N.17 Scaling whole numbers by fractions
N.18 Scaling fractions by fractions
N.21 Complete the fraction multiplication sentence
**This site has a video providing guidance for every homework page.**

http://www.oakdale.k12.ca.us/ENY_Hmwk_Intro_Math
(Click on 5th Grade – Select the Module 4– Select the lesson)
Videos
Using a ruler & line plots:
https://www.youtube.com/watch?v=o7slAZtt3jo “Reading a ruler”
https://learnzillion.com/lessons/2683-collect-and-show-data-on-a-line-plot
Or use quick code: LZ2683
Multiply fractions by whole numbers using repeat addition:
https://learnzillion.com/lessons/210-multiply-whole-numbers-by-fractions-usingrepeated-addition
Or use quick code: LZ210
Multiply fractions by whole numbers using tape diagrams/bar models:
https://learnzillion.com/lessons/212-use-bar-models-for-multiplication-of-fractions-bywhole-numbers
Or use quick code: LZ212
Multiply fractions by fractions using area models:
https://learnzillion.com/lessons/213-multiply-fractions-by-fractions-using-area-models
Or use quick code: LZ213
Scaling with multiplication:
http://learnzillion.com/student/lessons/3401-predict-the-product-of-multiplying-afraction-less-than-one-by-a-whole-number
Simplify fraction multiplication problems: cancelling common factors (lesson 15 method 2 )
https://learnzillion.com/lessons/373-simplify-fraction-multiplication-problems-cancellingcommon-factors
Or use quick code: LZ373