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OBJECTIVES OF TOPIC A
Make equivalent fractions with the number line, the areamodel, and numbers.
Make equivalent fractions with sums of fractions with like denominators.
5th Grade Math Module 3: Addition and Subtraction of Fractions
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage New
York material which is taught in the classroom. Grade 5 Module 3
of Eureka Math (Engage New York) covers Addition and
Subtraction of Fractions. This newsletter will address making
equivalent fractions.
Topic A. Equivalent Fractions
Words to know
Equivalent Fractions Numerator
Vertically Denominator
Horizontally Expression
Things to Remember:
Equivalent Fraction – fractions that have the same value, even
though they many look differently. Example: and
Numerator – A number written above the line in a common
fraction to indicate the number of parts of the whole
Denominator – The number below the line in a fraction,
indicating the number of equal parts into which one whole is
divided.
Vertically –
Horizontally –
Focus Area– Topic A Module 3: Addition and Subtraction of Fractions
Mark 0 and 1 above the number line and
below
the number line.
0 1
To find fractions equivalent to , draw three vertical lines in each
rectangle creating four parts. Shade in two section to create the
fraction . Now partition with horizontal lines to show the
equivalent fractions
.
Show the expression on a number line then solve.
0 1
=
Each
secti
on
is c
ut
into
2
eq
ual
part
s.
Each
secti
on
is c
ut
into
3
eq
ual
part
s.
Each
secti
on
is c
ut
into
4
eq
ual
part
s.
Grade 5, Module 3, Topic A
Math News!
Express the fraction as the sum of two or three equal fractional parts. Rewrite each as a multiplication equation.
OR
Express each of the following as the sum of a whole number and a fraction.
Rachel cut six equal lengths of yarn. Each piece was 4 sevenths of a foot long. How many feet of yarn did she cut? Express your
answer as the sum of a whole number and the remaining fractional part.
=
+
+
+
1 +
=
Rachel cut
feet of yarn.
= 1 + 1 + 1 + 1 +
= 4
= 4
= 3 x
+
= 3 x 1 +
=
This information was generously shared by LPSS, Lafayette, LA
OBJECTIVES OF TOPIC B
Add and subtract fractions with unlike units using the strategy of creating equivalent fractions.
Add and subtract fractions with sums between 1 and 2.
Solve two-step word problems.
5th Grade Math Module 3: Addition and Subtraction of Fractions
Math Parent Letter
This document is created to give parents and students a better
understanding of the math concepts found in Eureka Math (©
2013 Common Core, Inc.) that is also posted as the Engage New
York material which is taught in the classroom. Grade 5 Module 3
of Eureka Math (Engage New York) covers Addition and
Subtraction of Fractions. This newsletter will address making like
units pictorially.
Topic B. Making Like Units Pictorially
Words to know
Unit Fraction Improper Fraction Product Factor
Simplest Form
Equivalent Fraction
Mixed Number
Associative Property
Estimate
Decimal Fraction
Standard Algorithm
Things to Remember:
Unit Fraction – A fraction whereby the numerator (the “top number”) is 1.
Examples:
Improper Fraction- An improper fraction is a fraction where the numerator
(the top number) is greater than or equal to the denominator (the bottom
number.
Examples:
Simplest form (fraction)- A fraction is in simplest form when the
numerator and denominator only have 1 as their common factor.
Example:
½ is in simplest form because the only common factor for 1 and 2 is 1.
Mixed Number-A mixed number is a whole number and a fraction
combined into one “mixed” number.
Example:
Equivalent Fraction-Fractions which have the same value, even though
they may look different.
Example:
Associative Property - Associative Property states that you can add or
multiply regardless of how the numbers are grouped. By ‘grouped’ we mean
where the parentheses are placed.
Example: 5 x 7 x 2 = (5 x 2) x 7 or 5 x (2 x 7)
Focus Area– Topic B Module 3: Addition and Subtraction of Fractions
Problem 1:
Step 1: Ask yourself can the fraction one third be added to the fraction one fourth? No, because the units are not the same. We need to find like units.
Step 2: Begin the process of finding like units (denominators) by drawing two rectangular models. Each rectangular model will represent a different unit fraction shown above.
Step 3: Have both rectangular models show the same size units.
Step 4: Rename each fraction showing like units(denominators).
Now, we can add the units.
)
Divide the rectangular model vertically into three equal units. Shade in one unit to represent one out of three.
Divide the rectangular model horizontally into four equal units. Shade in one unit to represent one out of four.
Divide the rectangular model showing
into fourths using three horizontal lines.
Divide the rectangular model showing
into thirds using two vertical lines.
Each rectangular model now has 12 units.
Application Problem:
Gabe ran
miles on Monday and
miles on Tuesday. How far
did Gabe run on both days. Answer:
(The steps above would be used to determine how far Gabe ran on both days.)
Grade 5, Module 3, Topic B
Math News!
For the following problem, draw a picture using rectangular models.
Solve the following problem using the Associative Property.
The fraction
to
. The only common
factor for 2 and 3 is 1; therefore it is in simplest form.
To find the simplest form we divide both the numerator and denominator by a common factor.
Marco bought two pizzas for dinner. He ate
of the pizza for dinner and
for breakfast the next morning. Marco took the remaining pizza to school for lunch. How much total pizza did he eat for breakfast and lunch? How much pizza did Marco take to school for lunch?
Marco ate a total of one whole pizza and one-sixth of the second pizza for dinner and breakfast.
Mixed Number
therefore, you can rewrite the problem using the Associative Property.
Question 2: How much pizza did Marco take for lunch?
Strategy 1: 1 whole pizza
Strategy 2: 1 whole pizza –
pizza eaten =
Marco took five-sixths of a pizza to school for lunch.
Example 1:
Example 2:
Example 3:
= 1 whole pizza
This information was generously shared by LPSS, Lafayette, LA
OBJECTIVE S OF TOPIC C
(
5th Grade Math Module 3: Addition and Subtraction of Fractions
Math Parent Letter
This document is created to give parents and students an
understanding of the math concepts found in Eureka Math
(© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the classroom.
Grade 5 Module 3 of Eureka Math (Engage New York)
covers Addition and Subtraction of Fractions. This newsletter
will discuss Module 3, Topic C.
Topic C: Making Like Units Numerically
Words to know:
equivalence difference
numerically mixed number
sum improper fraction
Things to Remember!!!
Equivalence - being equal, having the same value
Numerically - using numbers
Sum - the answer to an addition problem
Difference - the answer to a subtraction problem
Number Line - a line used to show placement of wholenumbers, fractions, and mixed numbers
Mixed Number – a whole number plus a fraction
smaller than 1, written without the + sign, e.g. 5 means
5 +
Improper Fraction – a fraction with the numeratorequal to or greater than the denominator
Add fractions to and subtract fractions from wholenumbers using equivalence and the number line asstrategies.
Add fractions making like units numerically.
Add fractions with sums greater than 2.
Subtract fractions making like units numerically.
Subtract fractions greater than or equal to 1.
Focus Area– Topic C: Making Like Units
Problem 1: 2 + 2
= 4
0 1 2 3 4 4
5
Problem 2:
0 1 2 3 4 5
Problem 3: ( ) (
)
Problem 4:
=
= = (
) (
)
+
=
= 15 + 1 +
= 16
Step 1: Subtract the whole numbers.
Step 2: Subtract the fraction.
Step 1: Add the whole numbers.
Step 2: Add the fraction.
1
Step 1: Make like units numerically. Step 2: Add fractions.
Step 1: Add the whole numbers.
Step 2: Make like units numerically.
Step 3: Add fractions.
Step 4: If sum is an improper fraction, rename fraction as a mixed number.
Step 5: Add whole number to fraction.
Step 6: Simplify sum if possible.
4 - 2
= 1
2 +2 +
-2
-
- =
4
Grade 5, Module 3, Topic C
Math News!
Problem 5: 5
- 2
=
(Step 1: Subtract the whole numbers.)
= 3 +
=
(Step 2: Subtract the second fraction from the whole number.)
= 2
(Step 3: Make like units numerically.)
= (
) (
)
= 2 +
+
(Step 4: Add the fractions.)
= 2 +
(Step 5: If sum of the fractions is an improper fraction, rename as a whole or mixed number.)
= 2 + 1 +
(Step 6: Add fraction to whole numbers.)
= 3
(Step 7: Simplify fraction if possible.)
Problem 6: Mrs. Sanchez made 7 gallons of punch for a party. If there were 10
gallons in the mixture, how many gallons did
she have left in the mixture?
10
= (
= 3 +
-
= ( )
= 2
+
= (
) (
)
= 2 +
+
= 2
There are 2
gallons of Mrs. Sanchez’s punch mixture left.
Problem 7: Bryant has a goal to drink at least 6
quarts of water during his day of training for the big marathon race. On his first
break he drank 1 quarts, and during his second break he had another 2
quarts. How many quarts of water should
Bryant drink on his last break of the day to reach his goal?
(
)
(
)
(
)
(
)
(
) (
)
Or
(
) (
)
Bryant should drink 2
quarts of water to reach his goal.
****The strategy above is a possible approach. The student could have first added 1
+ 2
. Then take the sum and subtract
from 6
.
Students do not have to use the least common denominator. They are just expected to create common denominators. In the end the answers will be the same.
This information was generously shared by LPSS, Lafayette, LA
OBJECTIVE S OF TOPIC D
(
5th Grade Math Module 3: Addition and Subtraction of Fractions
Math Parent Letter
This document is created to give parents and students an
understanding of the math concepts found in Eureka Math
(© 2013 Common Core, Inc.) that is also posted as the
Engage New York material which is taught in the classroom.
Grade 5 Module 3 of Eureka Math (Engage New York)
covers Addition and Subtraction of Fractions. This newsletter
will discuss Module 3, Topic D. In this topic students will
use reasoning to estimate the value of expressions, strategize
to solve problems involving more than two fractions, and
assess the reasonableness of their solutions to word problems.
Topic D: Further Applications
Words to know:
expression estimate/about
benchmark fraction
sum
solution
reasonableness
difference
Things to Remember!
Expression – a group of numbers and symbols thatshows a mathematical relationship
Example: + +
Symbol for meaning ‘about’ - ≈
Benchmark fraction - is a benchmark fraction when
comparing fractions
Example: and is less than or < is greater than or >
Therefore is less than or < .
Use fraction benchmark numbers to assessreasonableness of addition and subtraction equations.
Strategize to solve multi-term problems.
Solve multi-step word problems; assess reasonablenessof solutions using benchmark numbers.
Explore part to whole relationships.
We know that + = 1.
Since is more than half
and we are adding more, the sum will be greater than 1.
Since
and are less than half, the sum will be less than 1.
+
< 1
Also
needs
to be a half. of a whole is greater than
of the same whole, so adding
more to
will give us a
sum greater than .
+
>
Focus Area– Topic D Module 3: Addition and Subtraction of Fractions
Use benchmark fraction to estimate the value of expressions:
Example 1:
+
> 1
Example 2:
+
< 1 and
+
<
Example 3: 1
-
< 1
We know
is less than
and
is greater than
. We can’t
subtract
from
since
is larger so we’ll need to subtract
from the one whole. 1-
=
-
=
Since and
are both less than half, we know when we
combine the two fractions the answer will be less than 1.
Problem: Use >, < or = to make the following statement true.
4
- 1
_____ 2
+
4
- 1
≈ 4 2
+
≈ 2
4
- 1
> 2
+
≈5 ≈1 =2𝟏
𝟐
𝟐
𝟕<
Grade 5, Module 3, Topic D
Math News!
Strategize to solve an addition or subtraction problem involving more than 2 fractions and/or mixed numbers.
Example 1:
+
+
+ 1
Example 2: 4
-
-
- 1
Application Problem:
During lunch, Chris drinks 2
cups of milk. Allie drinks
cup of milk. Carmen drinks
cup of milk. How much milk do the 3
students drink?
2
+
+
3 +
= 3
Chris, Allie, and Carmen drank 3
cups of milk.
Assess Reasonableness of Solution:
John used 1
kg of salt to melt the ice on his sidewalk. He then used another 3
kg on the driveway. If he originally bought 10 kg of
salt, how much does he have left? (This is an example of a multi-step problem.)
Possible Approach:
1
kg + 3
kg 10 kg - 5
kg
= 1
+ 3
= 5 -
= 4
= 4
= 4 +
+
= 5
kg of salt used John had 4
kg of salt left.
This problem is adding thirds and fifths. The most efficient approach would be to first add the like
units together. Then combine the sums.
= 1 1
= 2
3
In this problem we are subtracting ,
and 1
from 4
. We
begin by subtracting
from 4
. Now you don’t subtract
from
1
. Remember we are subtracting both
𝟏
𝟐 and 1
𝟏
𝟐 from what is
left. So we add and 1
. The sum of 2 is subtracted from the 4.
4 2
4 – 2 = 2
Assess reasonableness of answer:
1
+ 3
10 – 6 = 4
2 + 4
= 6
4
falls between 4 and 5. Since 4
is less than half, 4
is closer to 4
than 5 which we can say the solution is reasonable.
2
= 3
Ste
p 1
Ste
p 2
This information was generously shared by LPSS, Lafayette, LA
