Kelsey Butters, Jason Kulinski
November 11, 2013
Section #1
Math Edu. 345 Lesson Plan 3
Planning For Mathematical Understanding: Introduction and Rationale:
For this lesson, we wanted our students to continue working with fraction concepts and
then introduce decimals. During our first lesson, some of the students had a difficult time
understanding equivalency and which fractions are larger than the other. We practiced fraction
equivalency, as well as addition of fractions in our second lesson. We want to continue to work
with fraction concepts this lesson, and then begin to introduce some decimal concepts as well.
This lesson includes portions of the “Math for Parents: Thinking about Fractions, Decimals and
Percents” curriculum. The parents of our students have been invited to participate in this
lesson, so we have planned accordingly and have chose curriculum that involves parents in the
learning process.
Grade Level (s): Fourth Grade
Learning Objectives:
-Students will compare and create decimal strips and fraction strips.
-Students will compare decimal and fraction strips
-Students will determine equivalency of decimals and fractions using fraction and decimal strips.
-Students will determine size of fractions and decimals when comparing.
Core Common State Standards-Mathematics:
CCSS.Math.Content.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.
CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different
denominators, e.g., by creating common denominators or numerators, or by comparing to a
benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two
fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model.
CCSS.Math.Content.4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100.
For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number
line diagram.
CCSS.Math.Content.4.NF.C.7 Compare two decimals to hundredths by reasoning about their
size. Recognize that comparisons are valid only when the two decimals refer to the same whole.
Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g.,
by using a visual model.
Process Standards:
The NCTM Process Standards that are present in this lesson include Numbers and
Operations, Problem Solving, Reasoning and Proof, Communication, Connections, and
Representation.
Numbers and Operations
In this lesson, students use their understanding of numbers, as well as how to represent
numbers and number relationships. Students in these grades should “develop understanding of
fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as
divisions of whole numbers.” They should also “recognize and generate equivalent forms of
commonly used fractions, decimals, and percents.” Finally, students should be able to “develop
and use strategies to estimate computations involving fractions and decimals in situations
relevant to students’ experiences.
(NCTM 148)
Problem Solving
Students will build new mathematical knowledge through problem solving. In this
lesson, students can “apply and adapt a variety of appropriate strategies to solve problems,” as
stated in the NCTM text. The types of problems that are present in this lesson require and build
upon problem solving skills.
(NCTM 182)
Reasoning and Proof
Students can use reasoning and proof to “make and investigate mathematical
conjectures” as stated in the text. There are a number of fraction and decimal problems that we
included that involve students using their reasoning skills to determine the answer.
(NCTM 188)
Communication
In this lesson, students need to “communicate their mathematical thinking coherently
and clearly to peers, parents, teachers, and others.” We encourage students to communicate
their reasoning and methods for solving problems in this lesson. There is a possibility that
parents of students will be present, so communication between practicum students, students,
and parents will be important. Students also need to “organize and consolidate their
mathematical thinking through communication.”
(NCTM 194)
Connections
Students in grades 3-5 should be able to “understand how mathematical ideas
interconnect and build on one another to produce a coherent whole.” This lesson involves
fractions which interconnect to decimals and percents. It is important for students to make
connections and build on their prior knowledge.
(NCTM 200)
Representation
Students participating in this lesson will have to “use representations to model and
interpret physical, social, and mathematical phenomena.” There are a couple problems in this
lesson that involve using representations, and students are always encouraged to show models
to explain how they came to a solution.
(NCTM 206)
Materials:
-Paper
-Pencil
-Markers
-Decimal strips
-Fraction strips
-Resources from “Math for Parents”
-”Fractions, Decimals and Percents Domino Game”
Lesson:
Connecting Fractions to Decimals:
1. Give students and parents two strips from the Decimal Strip template.
2. Explain to the students and parents that they will be filling in the blanks on the strips in
fraction measures of tenths on one strip, and decimals (0.1, 0.2, etc.)
3. Allow students and parents time to work through the decimal strip.
4. Ask students and parents to discuss their strategies for making the strips. Participants should
be encouraged to share alternative approaches.
5. Once the group has finished their decimal and fraction strips, students and parents can PairShare to discuss any similarities or differences they notice between the two strips.
-Create a T-Chart of the similarities and differences
6. Ask students them share their observations with the rest of the group.
7. Fraction Families will be brought up in this discussion. The purpose of Fraction Families is to
determine equivalency.
-We will ask students how fraction families relate and how those families relate to
decimals.
Which is Larger?
Students and parents will complete questions on a worksheet from the “Math for Parents”
curriculum that requires participants to determine which decimal is larger. The use of the
decimal strip will be encouraged as students and parents can use the decimal strip to assist
them in solving these problems.
Decimal/Fraction Maze:
1. After discussing the relationship between fractions and decimals, students and parents will
complete a fun maze to connect fractions and decimals.
2. Provide students with the maze sheet and colored markers.
3. Students will use their markers to connect different paths from 0, which is the starting
number.
4. There are a variety of different solutions, so once all students and parents have found at least
one solution, we will share as a group.
Extension(s):
Fraction, Decimal, and Percent Dominoes
If time permits and students are not being challenged by the activities, we will play this fun
game. It involves using domino cards and looking for relationships between fractions, decimals,
and percents. Incorporating percents would add a challenge to our lesson as we have only
focused on decimals and percents in previous lessons.
Anticipated Difficulties:
We anticipate the students to understand the relationship between a fraction and a
decimal. The students should be able to turn a fraction into a decimal using long division. If
they are unable to do so, we will work with the students and also allow the use of a calculator.
We will encourage mental math for the easier fractions. The students may not understand how
to classify the fractions into fraction families. We will take the time to work with the students on
fraction families and allow time for questions.
Differentiation:
Differentiation for this lesson can be achieved by adjusting any of the fractions or
decimals to make the problems either easy or more difficult. If the students seem to be
struggling with an activity, adjustments can be made to relate the activity to their prior
knowledge. When students demonstrate understanding, the instructors can then move on to
more difficult types of problems. If the students are excelling, the fractions and decimals can be
changed so the problems become more complex. This lesson can be easily modified to meet
the needs of a variety of learners. One of our extension options is a “domino” game that
involves fractions, decimals, and percents. Incorporating the topic of percents could be a
challenge.
Identifying and Supporting Language Demands:
The vocabulary in this lesson is comprehensive, but a list could be provided to meet the
learning needs of a student if necessary.
Assessment:
The students will hand in their decimal “mazes” to the instructor. Throughout the lesson,
the students will be asked the following questions about their reasoning.
-Why did you put the decimals where you did?
-What are the similarities between fractions and decimals?
-What are the differences between fractions and decimals?
-How are fractions and decimals related?
-Why did you choose the path you chose?
Source(s):
Math for Parents: Thinking About Fractions, Decimals, and Percents.
Fraction Percentage Decimal Dominoes by Dana Weld is licensed under a Creative Commons
Attribution-NonCommercial-NoDerivs 3.0 United States License.