standard_description: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
problem_activity: Warm-up
The purpose of this warm-up is to elicit the idea that an increase in sample size is associated with a decrease in margin of error, which will be useful when students investigate the relationship between margin of error and sample size in a later activity. While students may notice and wonder many things about these images, the relationship between sample size and margin of error is the important discussion point. This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is that the margin of error decreases as the sample size increases.
Launch
Tell students that their job is to think of at least one thing they notice and at least one thing they wonder. Display the table for all to see. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion.
Student Facing
Five students wanted to see how many children’s movies have female lead characters. They each took a sample of children’s movies, found the proportion of movies that had female lead characters, then used their results to simulate 100 additional samples. The table shows some of the findings based on the original sample and the simulations.
What do you notice? What do you wonder?
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "student"}, {"_attributes": {"scope": "col"}, "_value": "number of movies used in the original random sample"}, {"_attributes": {"scope": "col"}, "_value": "estimated proportion"}, {"_attributes": {"scope": "col"}, "_value": "margin of error"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "A"}], "td": [{"_value": "20"}, {"_value": "0.273"}, {"_value": "0.204"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "B"}], "td": [{"_value": "20"}, {"_value": "0.205"}, {"_value": "0.189"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "C"}], "td": [{"_value": "30"}, {"_value": "0.280"}, {"_value": "0.180"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "D"}], "td": [{"_value": "30"}, {"_value": "0.232"}, {"_value": "0.157"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "E"}], "td": [{"_value": "50"}, {"_value": "0.205"}, {"_value": "0.115"}]}]}]}]}
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
The purpose of the discussion is to notice that the margin of error tends to decrease when a greater number of things are used in the sample. Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the table. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clarification or point out contradicting information. If the relationship between the margin of error and sample size does not come up during the conversation, ask students to discuss this idea.


aligns: no