NF: Number and Operations - Fractions
Content Area:
Course(s):
Time Period:
Length:
Status:
Mathematics
Mathematics 4
March
N/A
Published
Enduring Understandings
Models can represent equivalent fractions.
For every fraction there is an infinite set of equivalent fractions.
Creating common numerators or denominators help us to compare fractions without a model.
A fraction can be decomposed into unit fractions.
Models can be used to add, subtract, or multiply fractions.
Mixed numbers and improper fractions represent more than one whole.
Common denominators allow you to compare/combine fractions by representing their value using same size
parts of the whole.
Decimal numbers can be ordered and compared by using an understanding of place value.
Essential Questions
How can you use models to show equivalent fractions?
How can we compare fractions if they do not have the same denominator?
How does decomposing fractions help us in computing with fractions?
What is significant about fractions with denominators of 10 or 100?
Content
Learners will:

Extend understanding of fraction equivalence and ordering.

Build fractions from unit fractions by applying and extending previous understandings of operations
on whole numbers.

Understand decimal notation for fractions, and compare decimal fractions.

Decompose fractions into unit fractions.

Add and subtract fractions with like denominators.

Add and subtract mixed numbers with like denominators.

Solve word problems involving addition and subtraction of fractions and mixed numbers.

Multiply a fraction by a whole number.

Solve word problems involving multiplication of fractions by whole numbers.
To show evidence of meeting this standard, students will be able to:

Show how fractions are equivalent through demonstration and modeling.

Compare two fractions with unlike denominators by creating a common denominator.

Compare two fractions with unlike denominators by comparing to a benchmark fraction.

Decompose fractions into unit fractions.

Add and subtract fractions with like denominators.

Add and subtract mixed numbers with like denominators.

Solve word problems involving addition and subtraction of fractions and mixed numbers.

Multiply a fraction by a whole number.

Solve word problems involving multiplication of fractions by whole numbers.

Read the decimal number using the place value name; e.g., .32 and 32/100 are read as thirty-two
hundredths.

Accurately convert from decimal to fraction with denominators of 10 or 100.
Vocabulary:
denominator, fraction, numerator, unit fraction, equivalent fractions, common factor, benchmark
fraction, decompose, compose, mixed numbers, mixed number, whole number, hundredth, place
value, tens, tenth, decimal point
Modifications and Accommodations:

Use models and computation to show equivalent fractions.

Use a number line to identify and write equivalent fractions.

Use benchmark fractions to compare fractions with unlike denominators.

Use common denominators and equivalent fractions to order fractions with unlike denominators.

Use models to add fractions with like denominators.

Use models to subtract fractions with like denominators.

Use the number line to add and subtract fractions with like denominators.

Identify and convert mixed numbers to improper fractions and vice versa.

Use models to add and subtract mixed numbers.

Decompose fractions and represent them as compositions of fractions in a variety of ways.

Use unit fractions and multiplication to describe fractions that are multiples of unit fractions.

Use models to multiply fractions by whole numbers.

Use computational algorithms to add and subtract fractions with the same denominator and multiply fractions by whole
numbers.

Work with a hundredths grid to convert fractions to decimals.
Skills
Topic 8

Use area models to recognize and generate equivalent fractions

use a number line to locate and identify equivalent fractions

use multiplication to find equivalent fractions

use division to find equivalent fractions

use benchmarks, area models, and number lines to compare fractions

use models or rename fractions to compare

construct arguments about fractions
Topic 9

use fraction strips and number lines to add fractions

decompose a fraction or mixed number into a sum of fractions in more than one way

solve problems involving joining parts of the same whole by adding fractions

use tools such as fraction strips, area models, and number lines to subtract fractions

solve problems involving separating parts of the same whole by subtracting fractions

count forward or backward on a number line to add or subtract

use number lines and benchmark fractions to estimate fraction sums and differences

use models and equivalent fractions to add and subtract mixed numbers

use equivalent fractions and properties of operations to add mixed numbers with like denominators

use equivalent fractions, properties of operations, and the relationship between addition and subtraction to
subtract mixed numbers with like denominators

use previously learned concepts and skills to represent and solve problems
Topic 10

Use a model to understand a fraction as a multiple of a unit fraction

use models to multiply fractions by whole numbers

use symbols and equations to multiply a fraction by a whole number

use drawing and equations to represent and solve problems involving multiplying a whole number and a mixed
number

use the four operations to solve problems involving time

use previously-learned concepts and skills to represent and solve problems
Topic 12

relate fractions and decimals with denominators of 10 and 100

locate and describe fractions and decimals on number lines

compare decimals by reasoning about their size

add fractions with denominators of 10 and 100 by using equivalent fractions

use fractions or decimals to solve word problems involving money

use the structure of the place-value system for decimals to solve problems
Resources
Math Program
enVision2.0 Fourth Grade - topics 8, 9, 10, 12
Literature
Fraction Fun by David Adler
Working with Fractions by David Adler
The Lion's Share by Matthew McElligott
Pizza Counting by Christina Dobson
Fractions, Decimals, Percents by David Adler
A Fraction's Goal Parts of a Whole
Fractions in Disguise
Piece=Part=Portion by Scott Gifford
Polar Bear Math by Ann Nagda
Go Fractions by Judith Stamper
Multiplying Menace by Pam Calvert
Fabulous Fractions by Lynette Long
Music Math by Kathleen Collins
The Wishing Club: A Story About Fractions by Donna Jo Napoli
Twizzlers Percentage Book by Jerry Pallotta
Web Sites:
Fraction mosaics: http://www.scholastic.com/teachers/top-teaching/2015/04/practical-differentiation-fractionsmosaics
Eureka Math, grade 4 module 5 http://greatminds.net/maps/main/login
Tenmarks.com
https://www.frontrowed.com/
http://www.insidemathematics.org/common-core-resources/mathematical-content-standards/standards-bygrade/4th-grade (many choices)
https://learnzillion.com/resources/74905-measurement-and-data-4th-grade
http://nextgen.apps.sparcc.org/math/3-5
http://www.mathplayground.com/common_core_state_standards_for_mathematics_grade_4.html
http://www.k-5mathteachingresources.com/support-files/birthday-fractions.pdf
Simplifying activity: http://www.education.com/activity/article/simplest-form/
http://www.scholastic.com/teachers/top-teaching/2015/04/practical-differentiation-fractions-mosaics
Birthday fractions: http://www.k-5mathteachingresources.com/support-files/birthday-fractions.pdf
Fractional me: http://theteachingthief.blogspot.com/2012/04/art-math-fractional-me.html
Place value yahtzee:
https://cdn.shopify.com/s/files/1/0955/2452/files/Place_Value_Yahtzee_Score_Cards.pdf?7660609586503075550
Standards
MA.4.4.NF.C.6
Use decimal notation for fractions with denominators 10 or 100.
MA.K-12.2
Reason abstractly and quantitatively.
MA.K-12.3
Construct viable arguments and critique the reasoning of others.
MA.4.4.NF.C.7
Compare two decimals to hundredths by reasoning about their size. Recognize
that comparisons are valid only when the two decimals refer to the same whole.
Record the results of comparisons with the symbols >, =, or <, and justify the
conclusions, e.g., by using a visual model.
MA.4.4.NF.B.4c
Solve word problems involving multiplication of a fraction by a whole number,
e.g., by using visual fraction models and equations to represent the problem.
MA.K-12.4
Model with mathematics.
MA.4.4.NF.C
Understand decimal notation for fractions, and compare decimal fractions.
MA.K-12.5
Use appropriate tools strategically.
MA.4.4.NF
Number and Operations—Fractions
MA.4.4.NF.A
Extend understanding of fraction equivalence and ordering.
MA.K-12.6
Attend to precision.
MA.K-12.7
Look for and make use of structure.
MA.4.4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ
even though the two fractions themselves are the same size. Use this principle to
recognize and generate equivalent fractions.
MA.4.4.NF.A.2
Compare two fractions with different numerators and different denominators,
e.g., by creating common denominators or numerators, or by comparing to a
benchmark fraction such as 1/2. Recognize that comparisons are valid only when
the two fractions refer to the same whole. Record the results of comparisons with
symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction
model.
MA.4.4.NF.B
Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers.
MA.4.4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
MA.4.4.NF.B.3a
Understand addition and subtraction of fractions as joining and separating parts
referring to the same whole.
MA.4.4.NF.B.3b
Decompose a fraction into a sum of fractions with the same denominator in more
than one way, recording each decomposition by an equation. Justify
decompositions, e.g., by using a visual fraction model.
MA.K-12.8
Look for and express regularity in repeated reasoning.
MA.4.4.NF.B.3c
Add and subtract mixed numbers with like denominators, e.g., by replacing each
mixed number with an equivalent fraction, and/or by using properties of
operations and the relationship between addition and subtraction.
MA.4.4.NF.B.3d
Solve word problems involving addition and subtraction of fractions referring to
the same whole and having like denominators, e.g., by using visual fraction models
and equations to represent the problem.
MA.4.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction
by a whole number.
MA.4.4.NF.B.4a
Understand a fraction a/b as a multiple of 1/b.
MA.4.4.NF.C.5
Express a fraction with denominator 10 as an equivalent fraction with
denominator 100, and use this technique to add two fractions with respective
denominators 10 and 100.
MA.4.4.NF.B.4b
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to
multiply a fraction by a whole number.
MA.K-12.1
Make sense of problems and persevere in solving them.