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.
101+102+103=1
1+107=103+104+1010
105+1=106
102+1010=1+51
Sample Response
False: 101+102 is 103 and another 103 makes 106, which is less than 1010.
True: 1 is equivalent to 1010, so the sum is 1010+107, which is 1017.
False: Adding 105 and 1 gives a number greater than 1, not 106. The sum of 105 and 1010 is 1015 or 1105.
True: 1010 is equivalent to 1 and 102 is equivalent to 51, so the two sides have equal values.
Activity Synthesis (Teacher Notes)
“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.
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Differences of Fractions
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.
101+102+103=1
1+107=103+104+1010
105+1=106
102+1010=1+51
Sample Response
False: 101+102 is 103 and another 103 makes 106, which is less than 1010.
True: 1 is equivalent to 1010, so the sum is 1010+107, which is 1017.
False: Adding 105 and 1 gives a number greater than 1, not 106. The sum of 105 and 1010 is 1015 or 1105.
True: 1010 is equivalent to 1 and 102 is equivalent to 51, so the two sides have equal values.
Activity Synthesis (Teacher Notes)
“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.