Formative Assessment Lesson Plan
Grade 4 Mathematics Example
Formative Assessment Lesson Plan - Grade 4 Mathematics Example
The formative assessment planning examples starting on page 4 outline questions teachers might consider as they develop tasks within a math lesson
integrating the principles of formative assessment and support grade-level instruction for all students. Additionally, the template provides space for:
Standards alignment
Key concepts
Connection to previous learning
Connection to future learning
Learning goals
Success criteria
There are multiple examples outlined below, but educators may only need one piece of information for each to ground the formative
assessment task in the grade level content.
NOTE: These tasks would be embedded within a 60-minute Lesson on the Benchmarks listed below.
STANDARDS ALIGNMENT
2007, current, Minnesota Math Standard & Benchmark(s) (NOTE: The highlighted phrases and underlining indicate emphasis of the formative
assessment tasks within the standard statements.)
Standard: 4.1.2 Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand
how decimals represent quantities.
Benchmark: 4.1.2.1 Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number
lines and other manipulatives. Use the models to determine equivalent fractions.
2022, future, Minnesota Math Standard & Benchmark(s)
Standard: 4.3.4 Number Relationships: Describe/interpret and use quantities, relationships between and representations of quantities
and number systems. Describe and relate operations. Use strategies and procedures accurately, efficiently and flexibly. Assess the
reasonableness of the results.
Benchmark: 4.3.5.12 Explain why a fraction
is equivalent to a fraction
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
by using visual models, with attention on how the number
and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate
equivalent fractions. (MP3)
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
2
Common Core State Standards for Mathematics (CCSS-M) NOTE: CCSS statements are the same grain size as MN benchmarks.
Standard: 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to
how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize
and generate equivalent fractions.
Key Concepts
Resources for using the K–12 Mathematics Standards Progression document to connect to prior and future concepts:
Video – Representing fractions with models to identify and explain equivalencies
The purpose of this lesson is for students to generate equivalent fractions using a representation that makes sense to them.
Video – The Progression of Fractions in Minnesota Math Standards (including visual representations)
Connection to Previous Learning
In grade 3, students learned to recognize and generate simple equivalent fractions. In earlier lessons, they reasoned about the size of fractions
and identified some equivalent fractions. Throughout those experiences, they used fraction strips, tape diagrams, number lines, and benchmark
fractions to support their reasoning. The Progression of Fractions in Minnesota Math Standards video shows these connections.
Early Childhood Indicators of Progress (ECIPS):
2–3 year old: (M7.4) Imitates using an object to measure another object.
4–5 year old: (M7.9) Compares and orders more than two items in some way. (M7.10) Uses comparison vocabulary (longer/shorter,
taller/shorter, farthest/closest).
Kindergarten: (K.3.2.1) Use words to compare objects according to length, size, weight and position. (K.3.2.2) Order two or three objects
using measurable attributes, such as length and weight.
1st: 1.3.2.1: Measure the length of an object in terms of multiple copies of another object.
2nd: (Measuring – Benchmark 2.3.2.2): Demonstrate an understanding of the relationship between length and the numbers on a ruler by
using a ruler to measure lengths to the nearest centimeter or inch.
3rd: (Unit Fractions – Benchmarks 3.1.3.1 & 3.1.3.2): (3.1.3.1) Read and write fractions with words and symbols. Recognize that fractions
can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. (3.1.3.2) Understand
that the size of a fractional part is relative to the size of the whole.
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
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Connection to Future Learning
Based on The Progression of Fractions in Minnesota Math Standards video, the following connections were identified:
4th: Benchmark 4.1.2.1 Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips,
number lines and other manipulatives. Use the models to determine equivalent fractions.
5th: Benchmark 5.1.2.3 Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
6th: Benchmark 6.1.3.2 Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and
division to make sense of procedures for multiplying and dividing fractions.
7th: Benchmark 7.1.1.5 Recognize and generate equivalent representations of positive and negative rational numbers, including
equivalent fractions.
8th: Benchmark 8.2.4.6 Represent relationships in various contexts with equations and inequalities involving the absolute value of a
linear expression. Solve such equations and inequalities and graph the solutions on a number line.
9th–11th: Benchmark 9.2.2.6 Sketch the graphs of common non-linear functions such as
,
,
,
and translations of these functions, such as
. Know how to use graphing technology to graph these functions.
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
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Learning Goals
What will students learn by the
end of the lesson? TIP: Use the
Benchmark Achievement Level
Descriptors.
Success Criteria
What will students be able to do
when they meet the learning
goal? TIP: Use the Benchmark
Achievement Level Descriptors.
Eliciting Evidence During Learning
What learning tasks will students engage with to elicit evidence of
learning? How will learning tasks be structured to show student learning
as it develops during the lesson?
Teacher Facing
Generate equivalent
fractions using a
representation that
makes sense to
students.
Student Facing
Let’s find some
equivalent fractions.
Does Not Meet
Identifies fraction strips
representing the same
fractions
Partially Meets
Identifies fraction circles
representing the same
fraction
Meets
Uses fraction models
(such as fraction strips,
fraction circles, other
manipulatives, and
written descriptions) to
determine equivalent
fractions
Uses fully labeled
number lines to plot
equivalent fractions
Exceeds
Interprets fraction
models to identify
multiple equivalent
fractions
Determines equivalent
representation of
fractions plotted on a
number line with
minimal labeling
Source: © CC BY 2021 Illustrative Mathematics®
The purpose of this warm-up is to elicit students’ prior understanding of
equivalence and strategies for comparing fractions. To determine
equivalence, students may rely on familiarity with benchmark fractions,
use fraction strips, or think about the relative sizes of the fractional
parts. They may also use their knowledge about fractions with the same
numerator or denominator. In any case, students have opportunities to
look for and make use of structure (MP7). Display one prompt at a time.
Listen to and record student thinking.
Warm-up: True or False: Equivalence
Decide if each statement is true or false. Be prepared to explain your
reasoning.
Formative Assessment/Teacher-Led Synthesis
If no students refer to a visual representation (a tape diagram or
number line) to explain an equation such as
, ask how one
of these representations could help with their explanation.
“For the pair of fractions that you know are not equal, can you
tell which fraction is greater? How?”
*****
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
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Learning Goals
What will students learn by
the end of the lesson? TIP: Use
the Benchmark Achievement
Level Descriptors
Success Criteria
What will students be able to
do when they meet the
learning goal? TIP: Use the
Benchmark Achievement Level
Descriptors
Eliciting Evidence During Learning
What learning tasks will students engage with to elicit evidence of learning?
How will learning tasks be structured to show student learning as it develops
during the lesson?
The purpose of this activity is to elicit strategies for finding equivalent
fractions when the fractions are represented by tape diagrams or points on
the number line. Students may reason in various ways, but here are two
likely approaches:
partition given fractional parts into smaller equal-size parts and
count the new parts (for instance, partitioning each 1 fourth into 3
parts and then counting the twelfths).
bundle given fractional parts into larger equal-size groups and count
the new groups (for instance, bundling every 2 tenths to make 5
fifths in 1 whole and then counting the fifths).
During this and upcoming activity syntheses, help students recognize
regularity in their moves to find equivalent fractions. In future lessons,
students will connect more explicitly how diagrams of equivalent fractions
relate to a numerical process for generating them. They will relate the
subdividing or grouping of fractional parts to the idea of using multiples and
factors to find equivalent fractions.
Task: Two or More Fractions
1. Each entire diagram represents 1 whole. Write two or more fractions
that the shaded part of each diagram represents. Be prepared to
explain your reasoning.
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
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Learning Goals
What will students learn
by the end of the lesson?
TIP: Use the Benchmark
Achievement Level
Descriptors
Success Criteria
What will students be able to
do when they meet the
learning goal? TIP: Use the
Benchmark Achievement Level
Descriptors
Eliciting Evidence During Learning
What learning tasks will students engage with to elicit evidence of learning? How
will learning tasks be structured to show student learning as it develops during
the lesson?
2. Write two or more fractions that the point on each number line
represents. Be prepared to explain your reasoning.
3. Place a new point on a tick mark on one of the last two number lines (in
part c or d). Then, write two fractions that the point represents.
Formative Assessment/Teacher-Led Synthesis
Advance Student Thinking: Students label number lines using tick marks
alone. For example, if 4 marks are visible (including zero) each line would
be labeled as fourths instead of thirds. If this happens, consider using
the idea of movement from 0 to 1. Ask: “Where is 1 on the number
line?” “If we are moving from 0 toward 1, what does this tick mark
between 0 and 1 mean?” Ask students to review the labels on their
number lines and decide if revisions are needed before continuing to
work on the next activity.
Questions for Synthesis: Select previously identified students to share
how they found multiple equivalent fractions on the two kinds of
representations. Display their work, or display the diagrams in the
activity for them to annotate as they explain.
“How is the process of finding equivalent fractions using diagrams like
the process of using number lines?” (They both involve partitioning
given parts into smaller parts, or bundling the given parts into larger
parts.)
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
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Success Criteria
What will students be able to
do when they meet the
learning goal? TIP: Use the
Benchmark Achievement
Level Descriptors
Eliciting Evidence During Learning
What learning tasks will students engage with to elicit evidence of learning? How
will learning tasks be structured to show student learning as it develops during
the lesson?
“How are they different?” (The length of a diagram usually is 1 whole or
another whole number. A number line doesn’t always show 1 whole, so
we may have to figure out where it is first.)
If time permits: “Can you write other equivalent fractions for diagram
_____?”
“How many fractions do you think you could write for that diagram?”
(This prompts students to begin to realize that there are infinite
equivalent fractions as the whole is partitioned into smaller parts.)
*****
In this activity, students find equivalent fractions for fractions given numerically.
They also work to clearly convey their thinking to a partner, which involves
choosing and using words, numbers, or other representations with care. In doing
so, students practice attending to precision (MP6) as they communicate about
mathematics.
Task: Equivalent for Sure?
For each fraction, find two equivalent fractions.
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
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Success Criteria
What will students be able to
do when they meet the
learning goal? TIP: Use the
Benchmark Achievement
Level Descriptors
Eliciting Evidence During Learning
What learning tasks will students engage with to elicit evidence of learning? How
will learning tasks be structured to show student learning as it develops during
the lesson?
Next, show or explain to your partner how you know that the fractions you
wrote are equivalent to the original. Use any representation that you think is
helpful.
Formative Assessment Task/Teacher-Led Synthesis
FA Task: MLR7 Compare and Connect
“Create a visual display that shows how you found two equivalent
fractions for the second fraction on your list: for Partner A, 10/6, and for
Partner B, 14/10.”
“Include diagrams, notes, and any descriptions that might help others
understand your thinking.”
Synthesis
“Take a few minutes to walk around and look at the work of at least 4
classmates. Make sure to look at the work by both partners, A and B.”
“As you study others’ work, pay attention to how the reasoning is alike
and how it is different.”
“What is the same about the diagrams, words, or explanations that you
saw? What is different?”
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
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Interpreting Evidence Considerations
Based on the content and students’ current knowledge,
what concepts and knowledge will support interpreting
evidence?
Using Evidence During Instruction
What will teachers (and students) do in response to evidence about students’
progress? What instructional strategies might be used to support students’ next
steps in learning?
Use the student response to the teacher-led synthesis
questions to record and represent student thinking for
the class. Use the questions to push all students to give
evidence that meets or exceeds the success criteria.
Meets
Uses fraction models (such as fraction strips,
fraction circles, other manipulatives, and written
descriptions) to determine equivalent fractions
Uses fully labeled number lines to plot equivalent
fractions
Exceeds
Interprets fraction models to identify multiple
equivalent fractions
Determines equivalent representation of fractions
plotted on a number line with minimal labeling
Use Math Language Routine #7 Compare and Connect
In the Compare and Connect routine (MLR 7), students make sense of
mathematical strategies by relating and connecting other approaches to their
own. This routine can be used to support discourse around a problem that can
be approached and solved using multiple strategies or representations.
Display 2 equivalent fractions side by side using tape diagrams and ask
students “What is the same? What is different?” Connect their
observations to strategies for knowing if fractions are equivalent.
Display 2 student representations (one number line and one tape
diagram and/or circle representation) side by side. Ask students what is
the same/different. Ask students to use these representations to
determine if they represent equivalent representations.
Resources:
1. Open Resource Math Curriculum – Illustrative Mathematics at Kendall Hunt’s Site. Grade 4, Unit 2 Lesson 7
2. MN Fraction Progression images for Benchmark 4.1.2.1
3. Benchmark Achievement Level Descriptors
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
10
Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent
quantities. (4.1.2)
Benchmark
Does Not Meet
A typical student at this
level of mathematics
succeeds at few of the
most fundamental
mathematics skills of the
Minnesota Academic
Standards.
Some of the skills
typically demonstrated
may include:
Partially Meets
A typical student at this
level of mathematics
partially meets the
mathematics skills of the
Minnesota Academic
Standards.
Some of the skills
typically demonstrated
may include:
Meets
A typical student at this
level of mathematics
meets the mathematics
skills of the Minnesota
Academic Standards.
Some of the skills
typically demonstrated
may include:
Exceeds
A typical student at this
level of mathematics
exceeds the mathematics
skills of the Minnesota
Academic Standards.
Some of the skills
typically demonstrated
may include:
4.1.2.1
Represent equivalent
fractions using fraction
models such as parts of a
set, fraction circles,
fraction strips, number
lines and other
manipulatives. Use the
models to determine
equivalent fractions.
Identifies fraction strips
representing the same
fractions
Identifies fraction circles
representing the same
fraction
Uses fraction models
(such as fraction strips,
fraction circles, other
manipulatives, and
written descriptions) to
determine equivalent
fractions
Uses fully labeled number
lines to plot equivalent
fractions
Released Examples:
245000, 242042, 244065
Interprets fraction models
to identify multiple
equivalent fractions
Determines equivalent
representation of
fractions plotted on a
number line with minimal
labeling
Released Examples:
43552, 43704, 244715,
245002, 245250, 245252,
245253, 245256, 245503,
245504
Formative Assessment Lesson Plan
Grade 4 Mathematics Exemplar
11
RESOURCES
Illustrative Mathematics (IM) Lesson Use factors to find equivalent fractions
Task Illustrative Mathematics – Explaining Fraction Equivalencies with Pictures
Task Illustrative Mathematics – Fractions and Rectangles
Grade-level Benchmark Achievement Level Descriptors – Benchmark Achievement Level Descriptor
Fractions Progression video – The Progression of Fractions in Minnesota Math Standards
Standards Progressions – K–12 Mathematics Standards Progression