Transcript Fraction Cards and Decimal Squares



Honor the challenge in this work and set the tone for teachers as
learners
Build conceptual knowledge of fractions, and acknowledge most of
us come with procedural

Become proficient with the work in Investigation 1

Know how and where to highlight the standards for students.
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.
Draw a representation and write a
short story (scenario) to go with it.
It’s easy…
 Multiply the numerators 5x2 =10
 Multiply the denominators 6x3=18
 Now you must reduce 10/18. divide 10 and 18
by 2 and you get 5/9
5/
6
5/
6
+ 2 /3
x
2/
…Solve the problem?
…Draw a
picture/representation?
3
…Write a word problem?
Stolen Opportunity!
What learning did that
take from us?


What do the Common Core State Standards
have to say about HOW students demonstrate
their understanding of fractions?
On your standards, highlight the phrase
“using (a) visual fraction model(s)” everywhere
you see it.
 Halves,
 Thirds
fourths, and eighths
and sixths
 Fractions
of a set
In grade 4,
expectations
are limited to
fractions with
denominators
….?

At your table…
◦ Create 4 DIFFERENET
representations of ¼
of a sandwich. (On
the left side of your
poster).


How do you know
this is ¼?
How could you
PROVE it?

How do you know
these fourths are
equal?

2.G.3. 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., and describe the
whole as two halves, three thirds, four fourths.
RECOGNIZE THAT EQUAL SHARES OF IDENTICAL
WHOLES NEED NOT HAVE THE SAME SHAPE.
“If they don’t look the same,
they aren’t equal”

If the blue is ¼,
then what is the
white?
Build fractions from unit fractions by applying and extending previous understandings of operations on whole
numbers.
4.NF.3. a. Understand addition and subtraction of fractions as joining and separating parts referring to the
same whole.
b. 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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Where is the opportunity to be mindful about
standards 4.NF.3 a and b?

At your table…
◦ Create 4 DIFFERENET
representations of 1/8
of a sandwich.

Using fourths to
find eighths
Chart: Fractions That are Equal
 Look at the bottom of page 34: Discussion- How are
Thirds and Sixths Related? Read to the bottom of page 35.

What is the math focus for discussion?

How is the idea of equivalent fractions introduced?
Chart: Fractions That are Equal
 Look at the bottom of page 34: Discussion- How are
Thirds and Sixths Related? Read to the bottom of page 35.
If you skipped this discussion, what
standard would students miss?
4.NF.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.




I have a crate of 24 oranges. ¼ go to Mr.
Freed. The rest go to Ms. Lee.
What fraction of the oranges will Ms. Lee get?
How many oranges will Mr. Freed get?
How many oranges will Ms. Lee get?


Look at the 3 possible student responses on
page 39. Which student best illustrates this
standard?
Why?
??????
¼ is greater than ½
How could students prove whether the
following equation is true or false?
1
4
+
1
2
+1 +
6
1
12
=1
But I thought students didn’t have to add with
unlike denominators! Read teacher note p.
56

Bring some student examples of SAB 14


Students must find common denominators to
add fractions.
Students in 4th grade only add and subtract
with common denominators.
1/2
Students develop understanding of fraction
equivalence and operations with fractions. They
recognize that two different fractions can be
equal (e.g., 15/9 = 5/3), and they develop
methods for generating and recognizing
equivalent fractions. Students extend previous
understandings about how fractions are built
from unit fractions, composing fractions from
unit fractions, decomposing fractions into unit
fractions, and using the meaning of fractions and
the meaning of multiplication to multiply a
fraction by a whole number.