investigate equivalent fractions - elementary math...investigate equivalent fractions students use...
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ExplorActio
Investigate Equivalent Fractions Students use Cuisenaire" Rods to show equivalent fractions. In this activity,
students will
explore fractions on a number line
recognize equivalent fractions, and
generate equivalent fractions
Common Core State Standard
g 3.NF.A.3b Recognize and
generate simple equivalent
fractions, e.g., 1/2 : = 2/4, 4/6
2/3. Explain why the fractions are Have students explore the following problem
equivalent, e.9., by using a visual Using Cuisenaire Rods, find all equivalent fractions that can be generated for fraction model
1 3 1 2 5
and 6
Help students get started, if necessary. Have them use the dark green rod as a
whole, and ask them to find rods to divide this whole into thirds. Have students Materials
explain their thinking. Elicit that 3 red rods can be used to divide the whole into
Cuisenaire Rods thirds. Then have students use rods to divide the whole into sixths. Confirm that the
Fraction Number Lines students use 6 white rods
(Number 3, the blank line) Have students use the rods to model these relationships on Fraction Number Lines
dry erase markers (Number 3, the blank line) and/or BLM 3 (Number Lines). Ask them to mark and label
BLM 3 (Number Lines) the number line using a dry erase marker (or pencil on BLM 3). Make sure students
2
can identify , and . Make sure they can identify 1 2 3 4
5 and 3
3
6' 6' 6' 6 6
T
0
3
2
4 5
6
6 6
6 6
Confirm that students are on the right track. Have them inspect the relationships tha
can be found between the rods on the number line. For example, you might ask
What can you say about the locations of 2
and? [They are the same.] 3
6
What can you say about the locations of and ? [They are the same.] 2
4
3
6
2 How are and 2
related? How are and related? (In both cases they are equal 4
3
6
6
they are equivalent.]
Have students continue their exploration by generating equivalent fractions for 1 1
3 1 2 5 214 and
Initiate students as follows 4'5'5 6
Work with a partner. Use rods to generate equivalent fractions
Suggest to students that the whole does not always have to be made from a single
rod. For example, to investigate twelfths, the whole can be made using an orange rod with a red rod
Record your findings by drawing the sets of rods you used and the number line models you built,
Be ready to explain why the equivalent fractions that you have found are the same number.
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ha
Have students share with the class which rods they used to generate the
equivalent fractions, Organization of their data might look like this Teacher Talk
Rods Fraction Many students have trouble identifying Equivalent Fractions
equivalent fractions. Consider the xurple/red/white browT pUrH
following dark greer
Equivalent fractions don't "look"
prangeyellow/white the same to students. This is
different from their experience browTred/white
with whole numbers
brown/r Visual fraction models make
equivalent fractions look the inge/red/White
same. By exploring the number
orangefred/whte relationships that make two different
pictures of equivalent fractions look orange
the same, students develop their
number sense relative to fractions
Number line models further reinforce
Note that} and can be expressed as twelfths, as well, In fact, the the idea that two different fractions
number of equivalent fractions that can be built is limited only by the can, in fact, be equal (because
number of rods in the set they are the same point on the
number line) Have students draw some of their number line models on the board, Use
Working with Cuisenaire Rods can prompts such as these to promote class discussion
help greatly. In finding equivalent = Why did some students use different rods than others used to 1
fractions for , for example, students
represent equivalent fractions? will likely star identifying a rod they
can easily divide into whole-number What are two ways that you can verify that two fractions
halves. If they happen to pick a red are equivalent?
rod, they will find that only white rods
What other relationships could you find between two of the equivalent can be used to make halves. Then
fractions you generated? they might reason that the purple rod
being twice the length of the red rod
will generate more fractions. They
discover that two white rods are half
2
of a purple rod and conclude that 4
is equivalent to .They may continue
this reasoning by investigating even
longer rods. Or, if they had started
with longer rods, they might reverse
the reasoning and investigate Look at the ingredients in this recipe
shorter rods
for pickles cup sliced cucumbers
Give students the following scenario: All you cup Vinegar
cup is a -cup
cup sugar measure. How could you use what you know
about equivalent fractions to make this recipe?
Ask students to find, write, and explain their answers. Have students
rewrite the ingredients for this recipe in eighths
Ask the following questions
In eighths, what is the
6
8
equivalent racton
In eighths, what is the equivalent fraction for?
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