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Comparing Fractions

This project includes a lesson plan, New York State Learning Standards, lesson objectives,
and instructional protocol for a first grade elementary algebra -helper/math-tutor-southern-california.html">mathematics lesson on comparing

N.Y.S. Mathematics Standards
Standard 1 – Students will use mathematical analysis, scientific inquiry, and engineering
de sign , as appropriate to pose questions, seek answers, and develop solutions .

Standard 2 – Students will access, generate, process, and transfer information using
appropriate technologies.

Standard 3 – Students will understand mathematics and become mathematically confident by
communicating and reasoning mathematically, by applying mathematics in real -world settings,
and by solving problems through the integrated study of number systems , geometry, algebra,
data analysis, probability, and trigonometry .

Performance Indicators

Reasoning and Proof Strand
♦ Students will recognize reasoning and proof as fundamental aspects of mathematics.

o 1.RP.1 Recognize that mathematical ideas need to be supported by evidence.

♦ Students will develop and evaluate mathematical arguments and proofs.

o 1.RP.5 Justify general claims, using manipulatives
o 1.RP.6 Develop and explain an argument verbally or with objects
o 1.RP.7 Listen to and discuss claims other students make

Communication Strand
♦ Students will communicate their mathematical thinking coherently and clearly to
peers, teachers, and others.

o 1.CM.3 Share mathematical ideas through the manipulation of objects,
drawings , pictures, charts, and symbols in both written and verbal

♦ Students will use the language of mathematics to ex press mathematical ideas

o 1.CM.6 Use appropriate mathematical terms, vocabulary, and language.

Representation Strand

♦ Students will create and use representations to organize, record, and communicate
mathematical ideas.

o 1.R.1. Use multiple representations including verbal and written language,
acting out or modeling a situation, drawings, and/or symbols as

Students will work first as a class, then in small groups to compare fractions . Students will
gain practice with vocabulary relating to fractions, and gain practice with making and
defending mathematical statements, problem solving, and counting.

Pattern blocks
Elmo, pattern blocks
Whiteboard, markers
Paper, pencil, crayons

Instructional Procedure

1. Students will be shown a yellow hexagon (on the Elmo) by the instructor and told that
this shape represents the entire class. They will then be asked to stand and move so
that the class is in two equal parts on either side of the classroom. Students will be
encouraged to problem solve about the best way to accomplish this task. Any “extra”
students throughout this activity can stand next to the instructor as an assistant.
The instructor will then ask the students whether the parts are equal and how many
children are in each part? What do we call two equal parts of a whole (halves)?
Instructor will now show the red trapezoid and ask whether this shape could be used
to represent the class as they are now divided (yes).

2. The blue rhombus will be added to the shapes on the Elmo and the instructor will ask
the students how many parts they would have to divide into now (three) and have
them arrange themselves accordingly. Students could be asked which group had more
students in it, when they were in halves or in thirds. Student responses will be
recorded on the white board.

3. The green triangle will now be added to the Elmo and students will be asked how many
parts they have to divide into now (six) and move as needed. Now students can be
asked which group had more students in it, sixths or halves. Thirds or sixths?
Student responses will be added to the white board.

4. Students will return to their tables.


1. Students will be asked to work with others at their tables to create statements
describing the relationship between the blocks, recording their thinking on paper with
pencils, crayons, etc. Example: the yellow hexagon is bigger than the green triangle,
the sixth is smaller than the third, and two-sixths are the same as (equal to) onethird ,
and so on. The instructor will circulate to encourage and assist students as
necessary. A timer could be set to limit the working time and help keep students on

2. Students will be selected from each group to come and share their thinking by putting
their papers on the Elmo and offering verbal explanations as well.

3. The following word problem will be put on the Elmo for students to solve. They will be
encouraged to try it on their first, then to talk with others at their table to explain
their reasoning. The instructor will circulate to encourage and assist students as

Queen Pam wants to divide her kingdom between her three children. She will
give 1/6 to her oldest son, 1/6 to her youngest son, and 2/3 to her daughter.
Will this work? Yes, or no and WHY? Can you tell who the queen’s favorite
child is? Use your blocks to figure it out. Show your thinking on your paper. Be
ready to share with your table and the class.

4. Several students can be selected to come to the Elmo to share their answers and
their thinking with the class.

5. The students will be given the following word problem to do as individual practice. It
could then be collected without being shared with the class and used as an
assessment. The instructor will circulate to encourage and assist as needed.

King Bob wants to divide his kingdom between his three children but he’s not
sure what to do. He wants to give 1/3 to his oldest son, 1/3 to his youngest
son, and 2/3 to his daughter. Will this work? Yes, or no and WHY? Use your
blocks to figure it out. Show your thinking on your paper. Be ready to hand
your work in to the teacher with your name on it.

Extension Activities
Students can go on the internet to gain further practice with fractions.
Stickers, paper models (made from construction paper), stencils and so on can be used to
create a student-made book about fractions or students can use a software program such as
Kids Works to create a computer-generated book. The books could compare fractions, tell a
story with fractions, or simply describe fractions as developmentally appropriate for each

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