Sample Learning Progression Scale (for a chunk of learning): The learning progression scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly
language. The purpose is to articulate distinct levels of knowledge and skills relative to a specific topic and provide a roadmap for designing instruction that reflects a progression of
learning. The sample learning progression scale shown below is just one example for PLCs to use as a springboard when creating their own scales for student-owned progress
monitoring. The learning progression scale should prompt teams to further explore question #2, “How will we know if and when they’ve learned it?” for each of the focus
standards in the unit and make connections to Design Question 1, “Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind
that a 3.0 on the scale indicates proficiency and includes the actual standard. A level 4.0 extends the learning to a higher cognitive level. Like the unit scale, the goal is for all
students to strive for that higher cognitive level, not just the academically advanced. A level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build
towards the standard.
Math Florida Standard(s):
MAFS.5.NF.2.4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. 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. For example, use a
visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
b. 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.
MAFS.5.NF.2.5 - Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole
numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and
relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
MAFS.5.NF.2.6 - Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the
problem.
MAFS.5.MD.2.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems
involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if
the total amount in all the beakers were redistributed equally.
Learning Progression
Sample Tasks
Score
4.0
I can…
 Analyze errors in computation of the multiplication of fractions.
 Create word problems that match equations.
 Describe how you know if a product will be larger or smaller when
multiplying be fractions and mixed numbers.
Mrs. Smith said that the area of the square classroom is 42 square feet. She
measured the length of one wall as 6 ½ feet. Is her computation of the
classroom’s total area correct? Why or why not? Use a visual fraction model to
justify your answer.
Without calculating, place these expressions in order of value from least to
greatest:
4x
This a working document that will continue to be revised and improved taking your feedback into consideration.
3
5
4x
5
3
4x
7
7
4x1
5
6
Pasco County Schools, 2016-2017
Using one of the expressions above, create a word problem that accurately
matches the expression.
3.5
3.0
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
I can…
 Apply and extend previous understandings of multiplication to
multiply a fraction or whole number by a fraction. (MAFS.5.NF.2.3)
 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.
 Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the
basis of the size of the other factor, without performing the
indicated multiplication. (MAFS.5.NF.2.4)
 Explaining why multiplying a given number by a fraction greater than
1 results in a product greater than the given number (recognizing
multiplication by whole numbers greater than 1 as a familiar case);
explaining why multiplying a given number by a fraction less than 1
results in a product smaller than the given number; and relating the
principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of
multiplying a/b by 1. (MAFS.5.NF.2.5)
Create a story context for this equation.
2
3
4
5
× =
A classroom has a length of 4 ½ yards and a width of 3 yards. What is the total
area of the classroom? Use a visual fraction model to represent the problem
and solution.
Without calculating, determine whether your product will be greater than or
less than the original factor.
1
4
x =
3 5
3
2
4
x =
5
4
5
Sammy says that the product of and
3
7
will be less than both factors. Is he
correct? Why or why not?
2.5
2.0
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
I can…
 Solve real world problems involving multiplication of fractions and
mixed numbers, e.g., by using visual fraction models or equations to
represent the problem. (MAFS.5.NF.2.3)
 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.
(MAFS.5.NF.2.4)
 Compare the values of two fractions using greater than, less than or
equal to. (MAFS.5.NF.2.5)
2
3
Use a visual fraction model to show the product of × 4
2
3
4
5
Do the same with × =
A classroom has a length of 4 ½ yards and a width of 3 yards. What is the total
area of the classroom? Use a visual fraction model to represent the problem
and solution.
Compare the fractions listed below using <, >, or =
3
8
☐
4
7
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2016-2017

Calculate the value of a fraction multiplied by whole number or a
fraction by a fraction. (MAFS.5.NF.2.5)
Evaluate the expressions below:
3
The student will recognize or recall specific vocabulary, such as:
 Denominator, numerator, product, quotient, equivalent fraction, unit
fraction, fraction greater than one, simplest form, partition, line plot
8
x
4
7
7x
4
5
I The student will:
 Match fraction models to division of whole numbers leading to answers in the form of fractions.
 Select the proper equation to find the area of a rectangle with fractional length sides.
 Recognize when multiplying fractions will create a larger solution, or a small solution.
1.0
The student will perform basic processes, such as:
 Multiplying a fraction by a whole number
 Use a model to multiply a fraction by a whole number
 Use the identity property of multiplication
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2016-2017