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Grade 5 Number and Operations - Fractions
5.NF.4
2012 COMMON CORE STATE STANDARDS ALIGNED MODULES
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS
THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS
2012 COMMON CORE STATE STANDARDS ALIGNED MODULES
Page 2 of 35
Essential Questions:
What happens to a fraction when you multiply it
by a whole number?
What do the values of the numerator and
denominator tell you about the value of a
fraction?
Prerequisites: Whole Numbers
Fractions
Fraction models
Addition
Subtraction
Factors
Multiplication
Division
Goal:
Students will interpret the product (a/b) × q as a parts of a partition of q into b equal
parts; equivalently, as the result of a sequence of operations a × q ÷ b. Also,
students will find the area of a rectangle with fractional side lengths by tiling it with
unit squares of the appropriate unit fraction side lengths, and show that the area is
the same as would be found by multiplying the side lengths. Multiply fractional side
lengths to find areas of rectangles, and represent fraction products as rectangular
areas.
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Number and Operation – Fractions 5.NF.4
Apply and extend previous understandings of multiplication to
multiply a fraction or whole number by a fraction.
Lesson 1 5.NF.4.a Multiplying whole numbers by fractions
Lesson 2 5.NF.4.a Multiplying fractions by
fractions
Lesson 3 5.NF.4.b Tiling to find fractional area
Lesson 4 5.NF.4.b Multiplying to find
fractional area
Lesson 5 5.NF.4.a-b Golden Problem
Lesson Structure: Introductory Task Prerequisite Skills Focus Questions Guided Practice
Homework Journal Question
Embedded Mathematical Practices MP.1 Make sense of problems and persevere in solving
them
MP.2 Reason abstractly and quantitatively
MP.3 Construct viable arguments and critique the
reasoning of others
MP.4 Model with mathematics
MP.5 Use appropriate tools strategically
MP.6 Attend to precision
MP.7 Look for and make use of structure
MP.8 Look for and express regularity in
repeated reasoning.
Page 3 of 35
Understand Multiplication
Distributive Property
The Distributive Property states that when you multiply the sum of two or more addends by a factor, the product is the
same as if you multiplied each addend by the factor and then added the partial products. The Distributive Property is
illustrated below graphically, arithmetically, and algebraically. At this time, students do not need to know the algebraic
explanation of the Distributive Property.
To find the total number of squares, you can multiply 3 × (2 + 6) or you can add (3 × 2) and (3 × 6).
arithmetically
3 × (2 + 6) = (3 × 2) + (3 × 6)
3 × 8 = 6 +18
24 = 24
algebraically
a × (b + c) = (a × b) + (a × c)
Multiplication by a One-Digit Number
One way to multiply a number by a one-digit number is to multiply the value of each digit by that one-digit number and
then find the sum of the partial products. The traditional multiplication algorithm for multiplying by a one-digit number has
the product written in place with necessary regrouping recorded above the number being multiplied.
Examples:
The above example shows how the Distributive Property applies to the multiplication algorithm. 546 × 7 = (500 × 7) + (40
× 7) + (6 × 7) Emphasize that the traditional algorithm starts by multiplying in the ones place and that makes recording
and regrouping of the product easier. Students sometimes find it difficult to multiply numbers with internal zeros, such as
302 or 10,809, and may need extra practice with such examples.
To multiply money amounts by a one-digit number, students multiply as if the numbers were whole numbers. They place
the decimal point so the answer is given in dollars and cents.
Multiplication Patterns
Patterns can be used when multiplying multiples of 10.
8 × 7 = 56
80 × 7 = 560
Page 4 of 35
800 × 7 = 5,600
8,000 × 7 = 56,000
80 × 70 = 5,600
800 × 700 = 560,000
Think: (8 × 7) × 10
Think: (8 × 7) × 100
Think: (8 × 7) × 1,000
Think: (8 × 7) × (10 × 10)
Think: (8 × 7) × (100 × 100)
In each example, the number of zeros in the product is the same as the sum of the number of zeros in each factor.
Multiplication by a Two-Digit Number
To solve problems such as 392 × 50, students can use patterns and what they know about multiplication by 1-digit
numbers to find (392 × 5) × 10.
The algorithm for multiplying by a two-digit number simply extends the algorithm for multiplying by a one-digit number.
The Distributive Property can be used to show the multiplication.
Estimation can be used to check that the answer to a multiplication problem is reasonable. Students round each factor to
a multiple of 10 that has only one nonzero digit. Then they use mental math to recall the basic fact product and patterns to
determine the correct number of zeros in the estimate.
Page 5 of 35
Understand Fractions
Fractions
Fractions are numbers that are needed to solve certain kinds of division problems. Much as the subtraction problem
3 − 5 = −2
creates a need for numbers that are not positive, certain division problems create a need for numbers that are not
integers. For example, fractions allow the solution to 17 ÷ 3 to be written as
17 ÷ 3 = .
When a and b are integers and b ≠ 0, then the solution to the division problem a ÷ b can be expressed as a fraction, .
At this grade level, students should learn to identify fractions with models that convey their properties. Proper fractions
can be modeled in terms of a part of a whole. The whole may be a group consisting of n objects where part of the group
consists of k objects and k < n. The fraction can be modeled as follows.
Equivalently, the whole may consist of a region that is divided into n congruent parts, k of which belong to a subregion.
For example, the fraction can be identified as the shaded part of the region below.
A unit fraction is a fraction with a numerator of 1 (for example, , , , ). The definition of a unit fraction, , is to take one
unit and divide it into n equal parts. One of these smaller parts is the amount represented by the unit fraction. On the
number line, the unit fraction represents the length of a segment when a unit interval on the number line is divided into n
equal segments. The point located to the right of 0 on the number line at a distance from 0 will be .
The fraction can represent the quotient of m and n, or m ÷ n. If the fraction is defined in terms of the unit fraction ,
the fraction means m unit fractions . In terms of distance along the number line, the fraction means the length of m
abutting segments each of length . The point is located to the right of 0 at a distance m × from 0. The numerator of
the fraction tells how many segments. The denominator tells the size of each segment.
Page 6 of 35
A straightforward way to show that fractions represent a solution to a division problem is by using equivalent fractions.
What is 35 ÷ 7? It is 5 because 35 equals 7 × 5. What is 5 ÷ 7? This is more difficult because 5 is not a multiple of 7.
However, 5 = = 5 × × 7 = , and equals 35 unit fractions of . Just as 35 divided by 7 is 5, 35 unit fractions of
divided by 7 is 5 unit fractions of . So 5 ÷ 7 = .
Finding a Fractional Part of a Number
The word of is often used to pose problems involving the multiplication of a whole number by a fraction. At this level,
students have not yet learned to multiply fractions. The problem of finding of 6 can be modeled in terms of a group of 6
objects that has been separated into 3 smaller groups, each of which has 2 objects.
Equivalent Fractions
Two fractions and are equivalent if there exists a number m such that m × × b = . For example, the fact that 2 ×
× 4 = implies that is equivalent to .
Geometrically, this concept can be conveyed in terms of a picture in which there are two ways of representing the same
part of the whole. The fact that is equivalent to can be shown as follows.
Because equivalent fractions represent the same number, they are referred to as equal.
A fraction is in simplest form if the numerators and denominators are as small as possible. A more formal way of stating
this is to say that in a simplest form fraction, the numerator and denominator have no common factors other than 1.
Page 7 of 35
Teaching Tips
Fractions TeachingTip1
Focus on the understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. Develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Also, use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)
Division TeachingTip2
Develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.
What do I Focus On? TeachingTip3
Instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.
Page 8 of 35
Tim really needs to start exercising. So, he plans to run 3/5 of a mile every weekday. If he keeps this schedule,
how far will Tim run in one week? Explain your answer with words, pictures, or mathematical calculations.
Introductory Task Guided Practice Homework Assessment
Focus Questions
Journal Question
Why does a whole number get
smaller when multiplied by a
fraction? Draw a picture to
explain your answer.
Question 1: What happens to a fraction when it is multiplied?
Question 2: How can we compare fractions?
Students will interpret the product (a/b) × q as a parts of a
partition of q into b equal parts; equivalently, as the result of a
sequence of operations a × q ÷ b. MP: Make sense of problems
and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of
structure
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Introductory Task
Lesson 1
Page 9 of 35
1. Isabel had 6 feet of wrapping paper. She used 3/5 of the paper to wrap some presents. How much does
she have left?
2. Kelly had 12 pencils in her pencil case. She lent out 2/3 of them to her friends. How many pencils did
she let her friends borrow?
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 1: Guided Practice
Teachers model with students.
Students will interpret the product (a/b) × q as a parts of a
partition of q into b equal parts; equivalently, as the result of a
sequence of operations a × q ÷ b. MP: Make sense of problems
and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of
structure
Page 10 of 35
3. Manny’s mom gave him $20 to spend on lunch for the week. He used 1/8 of it on Monday. How much
did he have left for the rest of the week?
4. Sarah is reading a 150 page book. She read 4/5 of the books already? How many pages did she read so
far?
5. Nicole baked 24 cupcakes. Her friends came over and ate 5/6 of them. How many does she have left?
Page 12 of 35
1. Isabel had 12 feet of wrapping paper. She used 2/3 of the paper to wrap some presents. How much does
she have left?
2. Kelly had 48 pencils in her pencil case. She lent out 2/3 of them to her friends. How many pencils did
she let her friends borrow?
Introductory Task Guided Practice Homework Assessment
Name____________________________ Date_____________________
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 1: Homework
Students practice skills
at home.
Students will interpret the product (a/b) × q as a parts of a
partition of q into b equal parts; equivalently, as the result of a
sequence of operations a × q ÷ b. MP: Make sense of problems
and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of
structure.
Page 13 of 35
3. Manny’s mom gave him $20 to spend on lunch for the week. He used 1/3 of it on Monday. How
much did he have left for the rest of the week?
4. Sarah is reading a 100 page book. She read 3/5 of the books already? How many pages did she read
so far?
5. Nicole baked 20 cupcakes. Her friends came over and ate 3/4 of them. How many does she have left?
Page 15 of 35
Mr. Oliveira posed a Math question to his class. It stated, “Three-fourths of the class are boys. Two-thirds of
the boys are wearing tennis shoes. What fraction of the class are boys with tennis shoes?” Solve the problem
and provide an explanation that would help a classmate understand your thinking.
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 2
Introductory Task
Students will interpret the product (a/b) × q as a parts of a partition
of q into b equal parts; equivalently, as the result of a sequence of
operations a × q ÷ b. MP: Make sense of problems and persevere
in solving them. Reason abstractly and quantitatively. Model with
mathematics. Use appropriate tools strategically. Attend to
precision. Look for and make use of structure.
Journal Question
In your own words, describe
what happens when you multiply
a fraction by a fraction. Use
pictures to illustrate your point.
Focus Questions
Question 1: Why is the result of a fraction multiplied by
a fraction smaller than the original numbers?
Question 2: What does ½ of ¾ represent?
Page 16 of 35
1. 1/2 of the monkeys in the zoo are female. 1/3 of them are pregnant. What fraction of the monkeys in
the zoo are pregnant?
2. Manny has a board that is 7/8 of a ft. long. He cut it in half. What is the length of the two sections?
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 2: Guided Practice
Teachers model with students.
Students will interpret the product (a/b) × q as a parts of a partition
of q into b equal parts; equivalently, as the result of a sequence of
operations a × q ÷ b. MP: Make sense of problems and persevere
in solving them. Reason abstractly and quantitatively. Model
with mathematics. Use appropriate tools strategically. Attend to
precision. Look for and make use of structure.
Page 17 of 35
3. Kelly has ¼ of a gallon of milk left in her refrigerator. She drank ¼ of it. What fraction of a gallon of
milk is left in the refrigerator?
4. Stewart used 3/6 of a can of oil to fix a squeaky hinge. He used ½ of what was left over to oil his bike.
How much oil does he have left in the can?
5. Nicole baked a lot of cupcakes, but her daughter ate half. Her friends came over and ate 3/4 of what
was left. What fraction of cupcakes does she have left?
Page 18 of 35
6. 3/4 x 1/2 =
7. 7/8 x 4/5 =
8. 1/2 x 1/3 =
9. 4/5 x 7/9 =
10. 7/9 x 1/4 =
11. 2/3 x 7/10 =
Page 19 of 35
Name: ____________________________ Date: _______________________
1. 3/4 of the turtles in the aquarium are female. 1/3 of them are pregnant. What fraction of the turtles in
the aquarium are pregnant?
2. Manny has a board that is 11/12 of a ft. long. He cut it in half. What is the length of the two sections?
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3, 5.MP.4,
5.MP.5, 5.MP.6, 5.MP.7
Lesson 2: Homework
Students practice skills
at home.
Students will interpret the product (a/b) × q as a parts of a partition
of q into b equal parts; equivalently, as the result of a sequence of
operations a × q ÷ b. MP: Make sense of problems and persevere
in solving them. Reason abstractly and quantitatively. Model with
mathematics. Use appropriate tools strategically. Attend to
precision. Look for and make use of structure.
Page 20 of 35
3. Kelly has 1/2 of a gallon of milk left in her refrigerator. She drank 3/4 of it. What fraction of a gallon
of milk is left in the refrigerator?
4. Stewart has a1/2 a bottle of soda. He drank 1/3 of it. What fraction of the bottle of soda does he have
left?
5. Bill has 5/7 of a candy bar. He gave his friend ½ of it. What fraction of the candy bar does he still
have left?
Page 21 of 35
6. 1/4 x 1/2 =
7. 9/11 x 4/5 =
8. 2/5 x 1/3 =
9. 6/7 x 7/9 =
10. 3/4 x 1/4 =
11. 6/7 x 7/10 =
Page 22 of 35
A gardener is going to plant tomatoes and other vegetables in his backyard. The gardener will only use 2/3 of
his backyard for planting and only 1/4 of that area will be for the tomatoes. What fractional part of the
backyard will be used to plant tomatoes?
Introductory Task Guided Practice Homework Assessment
Focus Questions
Journal Question
If the area of a rectangle is
equal to base × height, then
what would the area be for the
following rectangle?
b =2/3 ft. h = 7 ft
Question 1: What does ½ of 7 look like?
Question 2: How can you calculate are if a measurement is a
fraction?
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 3
Introductory Task
Students will find the area of a rectangle with fractional side lengths by
tiling it with unit squares of the appropriate unit fraction side lengths, and
show that the area is the same as would be found by multiplying the side
lengths. Multiply fractional side lengths to find areas of rectangles, and
represent fraction products as rectangular areas.MP: Make sense of
problems and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of structure.
Page 23 of 35
1. 2/3 x 3/5 =
2. 4/5 x 3/7 =
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 3: Guided Practice
Teachers model with
students.
Students will find the area of a rectangle with fractional side lengths by
tiling it with unit squares of the appropriate unit fraction side lengths,
and show that the area is the same as would be found by multiplying the
side lengths. Multiply fractional side lengths to find areas of rectangles,
and represent fraction products as rectangular areas.MP: Make sense of
problems and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of structure.
Use the grid to find the solution.
Page 26 of 35
Name _______________________ Date __________________
1. 2/3 x 4/5 =
2. 3/5 x 2/5 =
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 3: Homework
Students practice skills
at home.
Students will find the area of a rectangle with fractional side lengths by
tiling it with unit squares of the appropriate unit fraction side lengths,
and show that the area is the same as would be found by multiplying the
side lengths. Multiply fractional side lengths to find areas of rectangles,
and represent fraction products as rectangular areas.MP: Make sense of
problems and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of structure.
Page 29 of 35
Joel went to the deli counter of the supermarket and ordered the following:
½ lb of ham
¼ lb of swiss cheese
¼ lb of cheddar cheese
½ lb of turkey
He used exactly 1/3 of each of the ingredients to make sandwiches for his brother and himself. How much of
each item was left after he made the sandwiches?
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 4
Introductory Task
Students will find the area of a rectangle with fractional side lengths by
tiling it with unit squares of the appropriate unit fraction side lengths,
and show that the area is the same as would be found by multiplying
the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.MP:
Make sense of problems and persevere in solving them. Reason
abstractly and quantitatively. Model with mathematics. Use
appropriate tools strategically. Attend to precision. Look for and make
use of structure
Focus Questions
Journal Question
What happens to a fraction that
is multiplied by another
fraction? Explain why.
Question 1: How can multiplication help with division?
Question 2: What does multiplying a fraction really
mean?
Page 30 of 35
Multiply.
1.
1/3 x 2/4 =
2.
2/3 x 5/6 =
3.
2/5 x 3/10 =
4.
6/7 x 1/8 =
5.
2/5 x 2/3 =
6.
6/11 x 3/8 =
Introductory Task Guided Practice Homework Assessment
Lesson 4: Guided Practice
Teachers model with
students.
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Students will find the area of a rectangle with fractional side lengths by
tiling it with unit squares of the appropriate unit fraction side lengths, and
show that the area is the same as would be found by multiplying the side
lengths. Multiply fractional side lengths to find areas of rectangles, and
represent fraction products as rectangular areas.MP: Make sense of
problems and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of structure.
Page 31 of 35
7.
4/5 x 1/6 =
8.
8/9 x 3/10 =
9.
2/3 x 1/3 =
10.
¾ x ¼ =
11.
5/7 x ½ =
12.
1/6 x ¾ =
13.
6/9 x 1/12 =
14.
2/3 x 3/12 =
Page 32 of 35
Name _______________________ Date __________________
1.
1/3 x 2/9 =
2.
2/3 x 5/7 =
3.
2/9 x 3/10 =
4.
6/7 x 1/3 =
5.
4/5 x 2/3 =
6.
6/11 x 3/15 =
Introductory Task Guided Practice Homework Assessment
Lesson 4: Homework
Students practice skills
at home.
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Students will find the area of a rectangle with fractional side lengths by
tiling it with unit squares of the appropriate unit fraction side lengths,
and show that the area is the same as would be found by multiplying the
side lengths. Multiply fractional side lengths to find areas of rectangles,
and represent fraction products as rectangular areas.MP: Make sense of
problems and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools
strategically. Attend to precision. Look for and make use of structure.
Page 33 of 35
7.
4/5 x 1/16 =
8.
8/9 x 3/4 =
9.
1/3 x 1/3 =
10.
¾ x ¾ =
11.
6/7 x ½ =
12.
5/6 x ¾ =
13.
6/10 x 1/12 =
14.
2/7 x 3/12 =
Page 34 of 35
Parent Volunteers Mrs. Smith and Mrs. Jones both volunteer in their children’s classrooms. Mrs. Smith volunteers every 3rd
school day for 1/3 of a day. Mrs. Jones volunteers every 5th day of school for 1/2 of a day. In a given month,
which parent spends more time volunteering?!
Introductory Task Guided Practice Homework Assessment
Numbers and Operation – Fractions 5.NF.3, 5.MP.1, 5.OMP.2, 5.MP.3,
5.MP.4, 5.MP.5, 5.MP.6, 5.MP.7
Lesson 5
Golden Problem
Students will interpret the product (a/b) × q as a parts of a partition of q into b equal
parts; equivalently, as the result of a sequence of operations a × q ÷ b.Students will
find the area of a rectangle with fractional side lengths by tiling it with unit squares
of the appropriate unit fraction side lengths, and show that the area is the same as
would be found by multiplying the side lengths. Multiply fractional side lengths to
find areas of rectangles, and represent fraction products as rectangular areas.MP:
Make sense of problems and persevere in solving them. Reason abstractly and
quantitatively. Model with mathematics. Use appropriate tools strategically. Attend
to precision. Look for and make use of structure.
Focus Questions
Journal Question
Why do fractions play an important
role in our daily lives? Provide at
least three examples of how you use
math outside of school.
Question 1: What strategies can be used to answer a
multiplication problem involving fractions?
Question 2: How do you know an answer is reasonable?
Question 2: What information do we know?
Page 35 of 35
LESSON 5 RUBRIC
GOLDEN PROBLEM
Score Description
3
M T W Th F
x
x
x
x
This student determines that for a given month (assuming a 4 week
month), that both Mrs. Smith (every 3rd
day) and Mrs. Jones (every 5th
day) both work the same amount of time, which is a total of 2 days each.
All work is shown, and the student’s approach and reasoning is
explained. Math representations are labeled, clear and accurate.
2 The student will achieve a correct solution. However, the student’s
approach and reasoning may be incomplete or contain major errors
leading the scorer to make inferences. Math language will be used
throughout, and math representations will be clear and accurate.
1 The student shows some understanding of the task. The student may be
able to determine the number of days each parent worked but then may
not be able to calculate the time. The student may also achieve an
incorrect solution due to a computation mistake. Some math language
will be used, and representations will be attempted.
0 Does not address task, unresponsive, unrelated or inappropriate.
= Every 3rd day. = Every 5th day. x
6 days occur every 3rd day and 4 days occur
every 5th day, therefore….
and