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Illustrative Mathematics
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Grade 4, Unit 3
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Section B, Lesson 9
Differences of Fractions
Activities
Lesson Check
Practice
Teacher Notes
Warm-up
True or False: Sums of Tenths
10 min
Narrative
This
Warm-up
prompts students to reason about sums of fractions with the same denominator and to apply their understanding of equivalence, especially of whole numbers and fractions. The reasoning here will be helpful as students explore subtraction of fractions later in the lesson.
Launch
Display one statement.
“Give me a signal when you know whether the statement is true and can explain how you know.”
1 minute: quiet think time
Teacher Instructions
Share and record answers and strategies.
Repeat with each statement.
Student Task
Decide if each statement is true or false. Be prepared to explain your reasoning.
1
10
+
2
10
+
3
10
=
1
\frac{1}{10}+\frac{2}{10}+\frac{3}{10}=1
10
1
+
10
2
+
10
3
=
1
1
+
7
10
=
3
10
+
4
10
+
10
10
1+\frac{7}{10}=\frac{3}{10} + \frac{4}{10} + \frac{10}{10}
1
+
10
7
=
10
3
+
10
4
+
10
10
5
10
+
1
=
6
10
\frac{5}{10}+1=\frac{6}{10}
10
5
+
1
=
10
6
2
10
+
10
10
=
1
+
1
5
\frac{2}{10}+\frac{10}{10}= 1 + \frac {1}{5}
10
2
+
10
10
=
1
+
5
1
Sample Response
False:
1
10
+
2
10
\frac{1}{10}+\frac{2}{10}
10
1
+
10
2
is
3
10
\frac{3}{10}
10
3
and another
3
10
\frac{3}{10}
10
3
makes
6
10
\frac{6}{10}
10
6
, which is less than
10
10
\frac{10}{10}
10
10
.
True: 1 is equivalent to
10
10
\frac{10}{10}
10
10
, so the sum is
10
10
+
7
10
\frac{10}{10}+\frac{7}{10}
10
10
+
10
7
, which is
17
10
\frac{17}{10}
10
17
.
False: Adding
5
10
\frac{5}{10}
10
5
and 1 gives a number greater than 1, not
6
10
\frac{6}{10}
10
6
. The sum of
5
10
\frac{5}{10}
10
5
and
10
10
\frac{10}{10}
10
10
is
15
10
\frac{15}{10}
10
15
or
1
5
10
1\frac{5}{10}
1
10
5
.
True:
10
10
\frac{10}{10}
10
10
is equivalent to 1 and
2
10
\frac{2}{10}
10
2
is equivalent to
1
5
\frac{1}{5}
5
1
, so the two sides have equal values.
Synthesis
“How can you explain your answer, without finding the value of each side?”
Consider asking:
“Who can restate ___ ’s reasoning in a different way?”
“Does anyone want to add on to _____ ’s reasoning?”
Standards
Addressing
4.NF.3.a
·
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.a
·
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Activity
Jump to Subtract
20 min
Activity
What’s the Difference?
15 min
Activity
Jump Back
15 min