few_shots: 
Example 1:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Concept/skill: 
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Answer: 
Yes. This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:70%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "No solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Exactly 1 solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Infinite number of solutions"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9=4x+7}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y=3y+5}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y={x\\over2}}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${3x+6y-9=0}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x=y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${1.25x=1.25y}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9.9=6x+8y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9x=2.5y-8.8}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=1.5}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=2.5}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {}]}]}]}]}
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

Answer: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_000972_pos_0

6

fl_problem_001097_neg_0

7

fl_problem_001392_pos_0

8
standard_description: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
problem_activity: Narrative
The purpose of this activity is for students to learn about the meter as a longer metric unit of length. Students measure longer lengths with a new tool, the meter stick. Students measure strips of tape of different lengths and choose between a centimeter ruler and a meter stick in order to measure each. In the synthesis, students share their measurements of each line and discuss how they chose which tool to use to measure (MP5). Students measure Strips D
–
G in this activity. Students measure the komodo dragon (Strip D) twice to experience measuring the same length with a ruler and a meter stick. They discuss and compare their measurements in the lesson synthesis.
MLR2 Collect and Display.
Direct attention to words collected and displayed from the previous lesson. Add “meter stick” to the collection. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Engagement: Provide Access by Recruiting Interest.
Synthesis: Optimize meaning and value. Invite students to share people they know or specific jobs they recognize that may use the measuring tools they have been exposed to. “When and why might someone use these measuring tools?”
Supports accessibility for: Conceptual Processing
Required Materials
Materials to Gather
Metersticks
Rulers (centimeters)
Launch
Groups of 3–4
Give each group a meter stick.
“We saw that measuring longer lengths with centimeters can be challenging. Luckily, there is a standard unit that is much larger than a centimeter that we can use. It’s called a
meter
.”
Show students a meter stick.
“This is called a meter stick. The length of one end to the other is 1 meter long. Just like we used centimeter cubes at first to measure centimeters. We can use the length of a meter stick to measure length in meters.”
“What do you notice about the meter stick?” (There are lots of little lines; the numbers go up to 100; every tenth number is bold)
30 seconds: quiet think time
Share responses.
“The meter stick makes it easier to measure longer lengths. We can use the meter stick to measure in meters or centimeters.”
“Find 50 cm on the meter stick.”
If time permits, find a few other markings.
Activity
“Now, let’s go back to our job as zookeepers and measure some even larger reptiles.”
“You are going to measure the komodo dragon again and 3 new reptiles."
“You may use any of the measuring tools you have used today. Be prepared to explain why you chose each tool.”
12 minutes: group work time
Monitor for the different ways students measure the ribbon snake and adult alligator including how they record their measurements in meters.
Student Facing
D: komodo dragon
[IMG]
E: adult alligator
[IMG]
F: adult cobra
[IMG]
G: ribbon snake
[IMG]
Measure the length of the komodo dragon in meters.
What is the same or different about your measurements for the komodo dragon from Activity 1 and Activity 2?
Measure each reptile in centimeters or meters. Don’t forget the units.
How long is an adult alligator?
How long is an adult cobra?
How long is a ribbon snake?
Student Response
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Advancing Student Thinking
If students do not measure using the meter stick, or only report their measurements in centimeters, consider asking:
“About how many meters long is the __?”
“What is different about measuring the __ in meters (or meters and centimeters) rather than only centimeters?”
Activity Synthesis
“Which tools did you use to measure Strip G, the ribbon snake? Why did you choose this tool?” (We used the meter stick and took away 10 because it was so close.)
“What did you do when you found that Strip E, the adult alligator, was longer than 3 meters but shorter than 4 meters?” (We saw it was closer to 3 meters so we said it was about 3 meters. We used the meter stick 3 times and then the cm ruler for the rest.)


aligns: no