Resource Overview Skill or Concept: Use models to write equivalent fractions, especially relationships among halves, fourths, and eights, and thirds and sixths. (QT‐N‐116) Identify combinations of fractions that make one whole. (QT‐N‐540) 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.
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Sample Lesson Plan: Understanding Fractions with Pattern Blocks
Unit of Study
Grade Level
NCTM Standards
Common Core
Standards
Big Idea
IEP Objectives
Lesson Outcomes
Preparation:
Standards and Key Concepts
Fractions: Understanding Fraction Equivalences and Operations
3-4
Compute fluently and make reasonable estimates.
In grades 3-5
x All students 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.
x All students should recognize and generate equivalent forms of
commonly used fractions, decimals and percents.
Number and Operations - Fractions:
Grade 3: Develop an understanding of fractions as numbers.
1. Understand a fraction 1/b as the quantity formed by 1 part when a whole
is partitioned into b equal parts; understand a fraction a/b as the quantity
formed by a parts of size 1/b.
3. Explain equivalence of fractions in special cases, and compare fractions
by reasoning about their size.
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4,
4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a
visual fraction model.
Grade 4 : Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers.
3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Decompose a fraction into a sum of fractions with the same denominator in
more than one way, recording each decomposition by an equation.
A whole can be divided into fractional parts that can be written as a fraction
number.
Given onscreen pattern block models and guided practice, the student will
identify fractional amounts and equivalent fractions for shapes and colored
areas in 4 out of 5 examples on three consecutive sessions.
1. Students will identify fractional parts of a whole and write the fraction
number.
2. Students will identify equivalent fractions for fractional parts of a
whole.
3. Students will write an equation adding each fractional part of the
whole.
1. List the vocabulary words and definitions on the board or chart paper
2. Provide each student with a set of pattern blocks.
3. Review the How to use the Unitizing with Pattern Blocks tool video
at: http://www.conceptuamath.com/fractions.html#PatternBlocks
4. Set up the Unitizing with Pattern Blocks Tool:
Click the Hide/Show fraction button to hide the fraction number.
Select the pie model.
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Sample Lesson Plan: Understanding Fractions with Pattern Blocks
Overview:
In this lesson students will use pattern block manipulatives to identify fractional parts of a whole.
Students write fractions that represent parts of the whole, create addition equations for the various
parts of the whole and recognize equivalence. Prerequisite skills include….
This lesson is designed for use with the Free Tool from Conceptua Math for whole group teacher
facilitated instruction and with the premium tools from Conceptua Math for independent practice and
assessment.
Lesson Implementation
Activating Strategy
Open the Free Unitizing with Pattern Blocks tool and select the large hexagon
Advanced Organizer
from the predesigned patterns. Instruct students to select one large yellow
hexagon from their pattern blocks. Ask them how many of the green
equilateral triangles fit onto or are equal to the hexagon? Discuss that if the
hexagon represents one whole how we can represent that as a fraction?
How would we represent one of the equilateral triangles?
Enter the 1/1 fraction into the grey fraction box and lock the “whole”. Point
out that the hexagon that represents one whole is divided into equal parts in
the shape of the triangle to make determining fractional parts easier. Have
students count with you the parts. Explain that today you will be working to
identify fractional parts of a whole and learning how to write those parts as
fraction numbers. You will explore the different ways one whole can be
divided into fractional parts.
Demonstrate
Model
Teacher Facilitation
Continue on using the same hexagon.
Ask students how many red trapezoids would it take to equal the whole
hexagon? What would the fraction of one of the trapezoids be? Then drag
one trapezoid and three triangles to the shape. Have student do the same
with their pattern blocks.
Have students represent the trapezoid as a fraction and enter it into the red
fraction number box. Do the same for the three triangles.
Ask students what we know about these two fractions (1/2 and 3/6) probe
until students recognize that they are equal and review or introduce the
vocabulary term equivalence.
Now ask students if they can think of a sentence to explain the pattern.
Guide them toward stating a sentence that includes; ½ and 3/6 equals one
whole. You may choose to expand their thinking by writing ½ +3/6 = 1
Be sure to review vocabulary throughout this demonstration.
Vocabulary
Fraction- equal part of the whole
Equivalent- two or more fraction numbers that represent the same amount
Represent- to stand for, in this lesson the fraction that stands for the amount
of a colored area of the whole
hexagon, trapezoid, rhombus, equilateral triangle, parallelogram,
Guided Practice
Repeat the above sequence using a stamped double hexagon grey shaded
area for the whole. Have students use their pattern blocks to create the
shape and explore different ways to cover the block. Have them share with a
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Sample Lesson Plan: Understanding Fractions with Pattern Blocks
peer and together write either sentences or equations that represent their
work. Have some students share their work using the software. Be sure to
note equivalent fractions. Be sure to ask students, why the hexagon is now
½ and not 1 whole. Remember the tessellation button can be used as a
reinforcer and to further your discussion about parts of the whole.
Independent Practice
Assign students one of the pattern block activities to work on independently.
Check for
Understanding
It is important that students be encouraged to discuss what they know about
fractions as they work independently. Ask questions to elicit responses that
require the use of the new vocabulary. 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. Students can also
be required to write down equations that represent their pattern.
Summarizing
Strategy
Closure
Open the Unitizing with Pattern Blocks tool and reproduce one of the patterns
from the independent work activities you assigned. Be sure to select one that
either presented a challenge for students or one in which multiple ideas can
be discussed.
Formative: Provide students with a pattern to create using their pattern
blocks. Have students cover the shape using blocks you assign and write the
fraction numbers.
Summative: Review the Big Idea 4, Topic 2 Student performance data
Assessment
Adaptations
Be sure accessibility features of the student activities are activated for
students who require supports to manipulate the models using alternate
methods. If a student does have difficulty using the number line, allow
him/her to switch to a part/whole model.
Extending and
Refining
The Unitizing Fractions on a Grid tool would be good follow-up as students
can apply the same skills learned in this lesson to colors placed on a grid. Or
you can do the following:
Select the triple hexagon shape from the predesigned patterns and set it
represent one whole. Follow the steps outlined in the Guided Practice
section of this lesson plan. For a real challenge, set the pattern amount to be
½.
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