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Illustrative Mathematics
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Grade 4, Unit 4
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Section A, Lesson 2
Equivalent Decimals
Activities
Lesson Check
Practice
Teacher Notes
Warm-up
True or False: Equivalent Fractions
10 min
Narrative
The purpose of this True or False is to revisit equivalent fractions in tenths and hundredths. The reasoning students do here will be helpful later when students make sense of and identify decimals that are equivalent to given fractions or given decimals.
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 strategy.
Repeat with each statement.
Student Task
Decide whether each statement is true or false. Explain your reasoning.
50
100
=
5
10
\frac{50}{100} = \frac{5}{10}
100
50
=
10
5
20
10
=
20
100
\frac{20}{10} = \frac {20}{100}
10
20
=
100
20
2
=
1
+
90
100
2 = 1 + \frac{90}{100}
2
=
1
+
100
90
3
1
10
=
31
10
3\frac{1}{10} = \frac{31}{10}
3
10
1
=
10
31
Sample Response
Sample responses:
True, because 50 hundredths and 5 tenths are both
1
2
\frac{1}{2}
2
1
.
False, because
20
10
\frac{20}{10}
10
20
is 2 and
20
100
\frac{20}{100}
100
20
is less than 1.
False, because
1
+
90
100
1 + \frac{90}{100}
1
+
100
90
is
1
90
100
1\frac{90}{100}
1
100
90
, which is less than 2.
True, because
3
+
1
10
3 + \frac{1}{10}
3
+
10
1
is
30
10
+
1
10
\frac{30}{10} + \frac{1}{10}
10
30
+
10
1
, which is equal to
31
10
\frac {31}{10}
10
31
.
Synthesis
“What do you know about the relationship between tenths and hundredths that helped you decide whether each statement is true or false?” (One tenth is 10 hundredths and one tenth is 10 times 1 hundredth. There are 10 tenths in 1 whole and 100 hundredths in 1 whole. If we multiply the numerator and denominator of a fraction in tenths by 10, we get an equivalent fraction in hundredths.)
Standards
Addressing
4.NF.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.
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.<span>Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.</span> <span>For example, express <span class="math">\(3/10\)</span> as <span class="math">\(30/100\)</span>, and add <span class="math">\(3/10 + 4/100 = 34/100\)</span>.</span>
Activity
Card Sort: Diagrams of Fractions and Decimals
15 min
Activity
True or Not True?
20 min