Resource Overview Use benchmark numbers (zero, one‐half, one) and models to compare and order fractions. Skill or Concept: (QT‐N‐115) Use models to write equivalent fractions, especially relationships among halves, fourths, and eighths, and thirds and sixths. (QT‐N‐116) Excerpted from: Conceptua Math 625 Second Street, #205, Petaluma, CA 94952 www.conceptuamath.com © Conceptua Math, LLC This resource may be available in other Quantile utilities. For full access to these free utilities, visit www.quantiles.com/tools.aspx.
The Quantile® Framework for Mathematics, developed by educational measurement and research organization MetaMetrics®, comprises more than 500 skills and concepts (called QTaxons) taught from kindergarten through high school. The Quantile Framework depicts the developmental nature of mathematics and the connections between mathematics content across the strands. By matching a student’s Quantile measure with the Quantile measure of a mathematical skill or concept, you can determine if the student is ready to learn that skill, needs to learn supporting concepts first, or has already learned it. For more information and to use free Quantile utilities, visit www.Quantiles.com. 1000 Park Forty Plaza Drive, Suite 120, Durham, North Carolina 27713 METAMETRICS®, the METAMETRICS® logo and tagline, QUANTILE®, QUANTILE FRAMEWORK® and the QUANTILE® logo are trademarks of MetaMetrics, Inc., and are
registered in the United States and abroad. The names of other companies and products mentioned herein may be the trademarks of their respective owners.
Sample Lesson Plan: Order Fractions on a Number Line
Unit of Study
Grade Level
NCTM Standards
Big Idea
IEP Objectives
Lesson Outcomes
Preparation:
Standards and Key Concepts
Fractions: Introducing Strategies for Ordering Fractions on a Number Line
3-6
Understand numbers, ways of representing numbers, relationships among
numbers, and number systems.
Grades 3-7
x 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.
x Use models, benchmarks, and equivalent forms to judge the size of
fractions
x Explore numbers less than 0 by extending the number line and
through familiar applications;
Grades 6-8
x Compare and order fractions, decimals, and percents efficiently and
find their approximate locations on a number line
Fractions are numbers that can be compared and ordered
Given a number line and 3-5 numerical representations of proper fractions
and teacher modeling, the student will drag each fraction to the correct
location and explain his reasoning with 100% accuracy for 3 consecutive
sessions.
1. Students will demonstrate how partitioning can assist them in placing
and ordering numbers on a number line.
2. Students will use part/whole models to order fractions and transfer
the order to placement on a number line.
3. Students will explain how they can show two or more fractions being
equivalent and explain the definition of equivalency using a number
line.
List the vocabulary words and definitions on the board or chart paper
Prepare paper number line strips, acquire fraction manipulatives such as
fraction strips
Review the How to Use the Order Fractions on a Number Line tool video at
http://www.conceptuamath.com/fractions.html#OrderingFractions
Set up the Order Fractions on a Number Line Tool:
Create 5 fractions and lock them ½, ¼, 1/8, 2/8, 3/8
Overview:
This lesson presents two strategies to help students determine the size of a fraction and to order
fractions on a number line. It is important to reinforce concepts such as fractions are numbers,
partitioning using the denominator, and equivalent fractions are two or more numbers that name the
same amount and therefore that represent the same point on a number line. Although this lesson is
designed for students in intermediate grades, we have found it to be an important part of instruction in
middle school classes, as many students have not acquired mastery of this concept.
www.conceptuamath.com
Copyright Conceptua™ Math
1
Sample Lesson Plan: Order Fractions on a Number Line
Activating Strategy
Advance Organizer
Lesson Implementation
Display the free Order Numbers on a Number Line Tool from Conceptua
Math set up according the description in the Preparation area above.
Discuss the Big Idea—Fractions are numbers that can be compared and
ordered. Point out that there are many ways to think of fractions, parts of a
whole, parts of a set, parts of a region or area, as measurement. We also
use fractions in money and time. Today we will discuss using a
measurement model.
Ask students to provide examples of when they would use fractions in
measurement.
Tell them that in order to be more accurate when thinking about fractions you
are going to show them two strategies or determining size and ordering of
fractions using a number line.
Review vocabulary that will be important for the lesson
Demonstrate
Model
Teacher Facilitation
www.conceptuamath.com
1. Ask students how they might determine the location of the fractions on
the number line given that there are no tick marks to assist them. If
they struggle, ask them which fraction would be best to begin with.
Discuss/review how the denominator tells the number of partitions or
equal parts.
2. Guide students into placing the ½ on the number line.
3. Guide students in selecting the ¼ fraction and review that if there are
4/4 in the whole, that 2/4 would be the same point as ½. Guide them
to see that you would then partition the ½ line segment into 2 parts
and the 1/4th would be ½ of that. If using an interactive white board,
have students drag the fraction to the correct location.
4. Repeat the process in step 3 using the 1/8 and 3/8 fractions.
5. Review Strategy one, which is partitioning using the denominator,
using the fractions with larger denominators to assist in determining
the size of fractions with smaller denominators.
6. Reset the screen and place the same fractions out on the number
line.
7. This time introduce how the use of visual models and visualizing can
help students place the numbers on the number line. Ask students
which models would be most helpful. After discussion, select the
vertical bars. Have students assist you in lining up the fraction
representations (vertical bars) from smallest to largest above the
number line. Once they are accurate, discuss how this representation
relates to the number line (the bars visually show the number and size
of the partitions). Place the fractions and check work. Have students
justify their answers.
Copyright Conceptua™ Math
2
Sample Lesson Plan: Order Fractions on a Number Line
Vocabulary
Guided Practice
Numerator- top number of the fraction symbol. Represents the number of
parts selected
Denominator- The bottom number of the fraction symbol It is the unit or
number of equal parts in the whole
Partition- something that divides or splits up a space
Greater than- to be larger
Less than - to be smaller
1. Provide students with number line strips and fraction strips
2. Continue with 2 or 3 more sets of fractions using the Free Order
Fractions on a Number Line tool. Have students independently select
a strategy and either fold (partition) their paper number lines and
place the set of fractions or order the fraction strip models.
3. Drag the numbers to the number line using one of the strategies.
Compare and discuss answers.
Independent Practice
Assign students Theme 1 Topic 4 or Theme 5 topic 2 if you choose to focus
on equivalent fractions Activities to work on independently
Check for
Understanding
Question students as they work independently. Have them identify their
choice of strategy and justify their thinking. Be sure to question how the size
of the denominator can assist them in determining the location of the fraction
on the number line. Asking how do you know and why questions can
facilitate thinking more critically about fractions as they work independently in
the Conceptua Math student activities.
Present students with a set of 5 fractions. Have students draw a number line
partition the line according the denominators of the fractions and place the
fractions on the number line. Then ask students to draw representations of
each fraction using a part/whole model such as the vertical bar. Have them
write an explanation justifying the placement of the fractions.
Formative: The summarizer can be used to determine the level of each
students understanding.
Summative: Review the Student performance data in the Conceptua Math
premium student activities.
Summarizing
Strategy
Closure
Assessment
Adaptations
Extending and
Refining
www.conceptuamath.com
Be sure accessibility features of the student activities are activated for
students who require supports to manipulate the models using alternate
methods.
Students who have difficulty partitioning the number line can be given number
lines with tick marks for 1/2 and fourths. Students may find the use of a ruler
to be more concrete.
Students with visual motor difficulties can be given magnetic manipulatives.
The free Estimating with Benchmark Fractions tool can be used in a follow-up
lesson. This would present the use of benchmarks such as 0,1 and ½ to
determine size of a fraction when using a measurement model.
Copyright Conceptua™ Math
3