standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
The purpose of this activity is for students to convert between measurements in milliliters and liters, providing practice multiplying and dividing by 1,000. Students work with numbers in many forms including whole numbers, decimals, fractions, and numbers in exponential form.
Engagement: Internalize Self-Regulation.
Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, provide students with a partially completed chart to compare their answers and talk about the similarities and differences with their partners.
Supports accessibility for: Attention; Memory; Social-Emotional Functioning
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?” (There are different sized water bottles. There are numbers underneath the water bottles. How much more water does the big one hold than the little one? How many milliliters are in a liter?)
Display a table like this one:
{"table": [{"_attributes": {"border": "1", "style": "width:40%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "L"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "mL"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "1,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.1"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "100,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}]}]}]}]}
“What numbers go in the empty boxes in the table?”
30 seconds quiet think time
“Explain your thinking to a partner.”
Fill in the table and leave it displayed for students to refer to during the lesson.
{"table": [{"_attributes": {"border": "1", "style": "width:40%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "L"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "mL"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "1,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "10,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.1"}, {"_attributes": {"style": "text-align:center"}, "_value": "100"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "100"}, {"_attributes": {"style": "text-align:center"}, "_value": "100,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.01"}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}]}]}]}]}
Activity
3–5 minutes: independent work time
1–2 minutes: partner discussion
Monitor for students who:
compare the quantities by converting milliliters to liters
compare by converting liters to milliliters
Student Facing
[IMG]
Complete the table.
{"table": [{"_attributes": {"border": "1", "style": "width:50%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "L"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "mL"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "5"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "6.3"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "0.95"}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(10^2\\)"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "800,000"}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(10^6\\)"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "65"}]}]}]}]}
Decide if the two measurements are equal. If not, choose which one is greater. Explain or show your reasoning.
15 mL and 0.15 L
2,500 mL and 2.5 L
200 mL and
\(\frac{1}{4}\)
L
1 mL and
\(\frac{1}{1,000}\)
L
15,600 mL and 15.5 L
Student Response
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Advancing Student Thinking
If students confuse the operations they need to use to convert milliliters to liters or liters to milliliters, refer to the table from the launch and ask, “What patterns do you notice?”
If necessary, add rows to the table and ask them to explain how many milliliters of water are in 2 liters of water and 3 liters of water, and 0.001 liter of water.
Activity Synthesis
Invite selected students to share how they compared the measurements.
Display: 15,600 mL and 15.5 L
“How many liters are 15,600 milliliters? How do you know?” (15.6 since I divide by 1,000)
“How many milliliters are 15.5 liters? How do you know?” (15,500 since there are 1,000 milliliters in each liter so that’s 15,000 and half of a thousand which is 500.)
“Which is greater? 15,600 milliliters or 15.5 liters? How do you know?” (15,600 mL because I can compare them using either liters or milliliters.)
“When you solved this problem, did you convert from milliliters to liters or from liters to milliliters? Why?” (I converted from liters to milliliters because multiplying by 1,000 is more comfortable than dividing by 1,000.)


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