 # Standard: MACC.4.NF.1.1 Depth of Knowledge Level 3: Strategic Thinking

```Standard: MACC.4.NF.1.1
Depth of Knowledge
Level 3: Strategic Thinking
Explain why a fraction a/b is equivalent to a fraction
& Complex Reasoning
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.
Explanations and Ideas to Support:
This standard refers to visual fraction models. This
includes area models, linear models (number lines)
or it could be a collection/set models. This
standard extends the work in third grade by using
additional denominators (5, 10, 12, and 100).
Students can use visual models or applets to
generate equivalent fractions.
Students’ initial experience with fractions began in
Grade 3. They used models such as number lines to
locate unit fractions, and fraction bars or strips,
area or length models, and Venn diagrams to
recognize and generate equivalent fractions and
make comparisons of fractions.
Conceptual:
 Students will understand a fractional quantity
can be subdivided into an infinite number of
equal pieces while maintaining the original
fractional quantity, e.g., 1/2 can be subdivided
into 2/4, 4/8 and so on. Those subdivisions are
called equivalent fractions.
 Students will understand the identity property
of multiplication and its relationship to
fractions (1/1, 2/2, 3/3, 4/4,… n/n = 1)
 Students will understand how the identity
property of multiplication is employed to create
equivalent fractions [(n*a)/(n*b) = na/nb]
Procedural:
 Students can identify differences in two
equivalent fractions, with attention to how the
number and size of the parts differ even though
the two fractions themselves are the same size.
 Students can identify how the identity property
of multiplication transforms a fraction into its
fraction.
Representational:
 Students can represent equivalency of fractions
pictorially (a/b is equivalent to (n x a)/(n x b)).
 Students can construct models of equivalent
fractions using manipulatives such as paper,
color tiles, fraction bars, and fraction circles.
 Using a fraction model, students can subdivide
both numerator and denominator by multiplying
with the same factor (a/b is equivalent to (n x
a)/(n x b), because both a and b were changed
by the same factor n), e.g. 1/2 = 2/4 because
(2 x 1)/(2 x 2) = 2/4, or, pictorially.
Aisha, Sara, and Brendan have 20 pencils. Aisha
says 4 of the pencils are hers. Sara says of the
pencils are hers. Brendan says of the pencils
belong to him. Explain how they all could be
right. Use words or drawings.
My mom left ½ of a cake on the counter. The
doorbell rang and one of my friends came over. If
we cut what’s left into equal parts, what fraction
of the whole cake did we each eat? If 3 of my
friends came over and we cut ½ cake that’s left
into equal parts, what fraction of the whole cake
did we each eat? (Ask the child to extend this
reasoning as far as he/she is able.)
Mrs. Caha asked her class to write fractions on their
whiteboards that were equivalent to . Tell if each
student’s fraction is equivalent to Mrs. Caha’s
fraction and show how you know.
Connections:
SMPs to be Emphasized

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Critical Area
 Critical Area 2: Developing an understanding of
MP2- Reason abstractly and quantitatively.
fraction equivalence, addition and subtraction of
MP4- Model with mathematics.
fractions with like denominators and multiplication
MP7- Look for and make use of structure.
of fractions by whole numbers.
MP8- Look for and express regularity in repeated
th
4
Related Standards:
reasoning.
 MACC.4.NF standards
 MA.4.A.2.3, MA.4.A.2.4, MA.4.A.6.3, MA.4.A.6.4,
MA.4.A.6.5
 Use equivalent fractions as a strategy to add and
subtract fractions.
FCAT 2.0 Connections:
Related NGSSS Standard(s)
MA.4.A.6.3- Generate equivalent fractions and
simplify fractions.
Related NGSSS Standard(s)
MA.4.A.6.4- Determine factors and multiples
for specified whole numbers.
FCAT 2.0 Test Item Specification
Benchmark Clarification:
 Students will find equivalent fractions or simplify
fractions to lowest terms.
 Students will rename fractions as mixed numbers
or vice versa.
Content Limits:
 All common factors of the numerator and
denominator must be less than or equal to 10.
 Items will not include graphical representations of
fractions
FCAT 2.0 Test Item Specification
Benchmark Clarification:
 Students will determine factors and/or multiples for
whole numbers.
Content Limits:
 All common factors of the numerator and
denominator must be less than or equal to 10.
 Items will not include graphical representations of
fractions
Common Misconceptions:

Students think that when generating equivalent fractions they need to multiply or divide either the
numerator or denominator, such as, changing 1/2 to sixths. They would multiply the denominator by 3
to get 1/6, instead of multiplying the numerator by 3 also. Their focus is only on the multiple of the
denominator, not the whole fraction. It’s important that students use a fraction in the form of one such
as 3/3 so that the numerator and denominator do not contain the original numerator or denominator.
``` # EXAMPLES To divide by a fraction, multiply by its multiplicative inverse... . 5 . # 9 How do we add and subtract fractions with like denominators? 