**Introduction**

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

fractions.

**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

explanations.

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

precisely.

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

representations.

**Objectives**

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.

**Materials**

Pattern blocks

Elmo, pattern blocks

Whiteboard, markers

Paper, pencil, crayons

**Instructional Procedure**

**Pre-activity**

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.

Lesson

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

task.

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

needed.

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

child.