2015-2016 Curriculum Blueprint
Grade: 3
Course: Mathematics
Topic 12 – Understand Fractions as Numbers
Flexible Time
Line
9 days
Topic Overview
Students will focus on understanding that fractions are numbers that can represent a portion of a whole or a point on the number line. Students extend
understanding of fair shares to partition shapes and number lines, representing fair shares using fraction notation. Similar to how students view the number 1
as the building block of whole numbers, students learn to view unit fractions as building blocks- understanding that every fraction is a combination of unit
fractions.
Vertical Progression
2nd Grade
 Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.
4th Grade
 Explain, recognize, and generate equivalent fractions.
 Add and subtract fractions with like denominators.
 Multiply fractions by using visual models.
Learning Goal
Essential Question
Students will be able to represent fractions in many different ways.
What are the different ways you can represent a fraction?
Topic 12 Scale
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
*Be selective in choosing problems aligned to the
Step 1: Problem-Based Learning “Solve and Share”
 fraction
standards within the topic. Lessons and problems used for
Problem-Based Learning Lesson Flow Map
 unit fraction
instruction and assessment should be determined through Conceptual understanding is developed when mathematics is
 numerator
collaborative unit planning.
introduced in the context of solving a real problem in which ideas
 denominator
related to the new content are embedded. Conceptual
 line plot
Topic 12: Understand Fractions as Numbers
understanding results because the process of solving a problem
 nearest half inch
Lesson 12-1: Divide Regions into Equal Parts
requires students to connect their prior knowledge with the new
 nearest fourth inch
Lesson 12-2: Fractions and Regions
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Lesson 12-3: Understand the Whole
Lesson 12-4: Number Line: Fractions Less Than 1
Each lesson in the book begins with a Solve and Share. See the links
Lesson 12-5: Number Line: Fractions Greater Than 1
below for additional tasks to be used as needed:
Lesson 12-6: Line Plots and Length
Lesson 12-7: More Line Plots and Length
Math Formative Assessment System (MFAS) Tasks by Standard
Lesson 12-8: Math Practices and Problem Solving: Make
Illustrative Mathematics Tasks by Standard
Sense and Persevere
Step 2: “Visual Learning Bridge”
Enhance student learning by connecting student thinking and
solutions from the Solve and Share to the new ideas of the lesson
through the use of the worked-out problem in the textbook.
Deconstructed Standards
MAFS.3.NF.1.1 (DOK 2) Understand a fraction as 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.
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Recognize a unit fraction such as 1/4 as the quantity formed when the whole is partitioned into 4 equal parts.
Identify a fraction such as 2/3 and explain that the quantity formed is 2 equal parts of the whole partitioned into 3 equal parts (1/3 and 1/3 of the whole 3/3.)
Express a fraction as the number of unit fractions.
Use accumulated unit fractions to represent numbers equal to, less than, and greater than one. (1/3 and 1/3 is 2/3; 1/3, 1/3, 1/3, and 1/3 is 4/3)
MAFS.3.NF.1.2 (DOK 2) Understand a fraction as a number on the number line: represent fractions on a number line diagram.
a) Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that
each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
b) Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its
endpoint locates the number a/b on the number line.
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Define the interval from 0-1 on a number line as the whole.
Divide a whole on a number line into equal parts.
Recognize that the equal parts between 0 and 1 have a fractional representation.
Explain that the end of each equal part is represented by a fraction (1/the number of equal parts.)
Explain that the endpoint of each equal part represents the total number of equal parts.
Represent each equal part on a number line with a fraction.
Define the interval from 0-1 on a number line as the whole.
Divide a whole on a number line into equal parts.
Represent each equal part on a number line with a fraction.
MAFS.3.G.1.2 (DOK 1) Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a
shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
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Know that shapes can be partitioned into equal areas.
Describe the area of each part as a fractional part of the whole.
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole.
MAFS.3.MD.2.4 (DOK 2) Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making
a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
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Define horizontal axis
Identify each plot on the line as data or a number of objects.
Analyze data from a line plot.
Determine appropriate unit of measurement.
Determine appropriate scale for a line plot.
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers, halves, or quarters.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.4.1 Model with mathematics.
Additional Resources & Links
Georgia Unit
Unit 5
 Exploring Fractions
 Candy Crush
 Using Fraction Strips to Explore the Number Line
(Many other lessons in this Georgia unit also pertain to Topic 12)
EngageNY - Module 5
Topic A & Topic D
EngageNY Math Studio Talk: Common Core Instruction for 3.NBT & 3.NF
This video shows strategies for developing an understanding of fractions as
numbers. (11:00 – 13:47)
* YouTube must already be opened on your browser before clicking the link.
www.pearsonrealize.com
Home-School Connection Page
Reteach to Build Understand Pages
Marzano Proficiency Scales Bank
Math Formative Assessment System (MFAS) Tasks by Standard
CPALMS - MFAS includes tasks that teachers can implement with their students,
and rubrics that help the teacher interpret students’ responses.
Higher Order Questions & Writing Connections
Link to Webb’s DOK Guide
* Higher order questions should be utilized to foster a deep, conceptual
understanding of the topic. Encouraging students to express their
mathematical thinking in writing helps them solidify their learning.
 How does a fraction relate to one whole?
 Why is the denominator important in a unit fraction?
 Can all shapes be split into halves, thirds, fourths, sixths and
eighths?
 How are fractions relevant to the real world?
 Explain in your own words what a fraction is.
 Explain the relationship between a numerator and a denominator.
 Describe how you know that fractional parts of a whole are equal.
Draw a model to justify your reasoning.
 What type of graph would you use to represent ___________?
Why?
 Write to explain the data represented.
 Draw conclusions from the data.
 Collect and analyze data. Write up a report to explain the data.
 Write to justify the scale used.
 How is the appropriate unit for measurement determined?
 How can I display fractional parts of data in a graph?
 How can I collect and organize data?
Illustrative Mathematics Tasks by Standard
The site illustrates standards with impeccably crafted tasks, videos, lesson plans,
and curriculum modules.
Common Core Flip Books Provides additional information and sample problems for
every standard
FSA Test Item Specifications
Spiral Review
*Consistent review of previously learned standards allows students multiple opportunities to master and build fluency with mathematical concepts and
procedures.
www.pearsonrealize.com
Daily Review 12-1 through 12-8