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?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. 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.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Thought: 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.
Answer: B

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
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Thought: This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).
Answer: B

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.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
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?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: 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.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6

fl_problem_001097

7

fl_problem_001392

8
options: Recognize and represent proportional relationships between quantities.

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Activity
When students are finding values to aid in their method, consider allowing them to research typical values online at hardware websites or search for values that would be useful. If these tools are not available, some values are provided here.
Values that may be useful for students:
Typical (modern) shower heads have a flow rate of 1.9 to 2.5 gallons per minute. Older shower heads (pre-1992) could have flow rates up to 5.5 gallons per minute.
Bath tubs hold approximately 120 to 180 gallons of water when completely filled to the top.
The interior of a typical bath tub has an approximate width of 30 to 32 inches, length of 55 to 60 inches, and depth of 18 to 24 inches.
There are approximately 230 cubic inches in 1 gallon of water.
1 liter of water is 1,000 cubic centimeters.
1 liter is approximately 0.26 gallons
1 inch is 2.54 centimeters.
Typical showers last approximately 11 minutes although during a drought, it is recommended to reduce the time to about 5 minutes. During normal circumstances, some people appreciate much longer showers.
After students have made good progress in the activity, tell them to make a display (e.g. poster) to share their method and results.
This activity can take the rest of the class period, if desired.
Launch
Arrange students in groups of 2–4. Tell them either that they should research relative information and provide access to internet enables devices or tell them that they can ask for information they need.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2–3 minutes of work time. Check to make sure students have a valid method for comparing the water usage for a bath and a shower prior to allowing them to research typical values of measurements.
Supports accessibility for: Memory; Organization
Student Facing
Describe a method for comparing the water usage for a bath and a shower.
Find out values for the measurements needed to use the method you described. You may ask your teacher or research them yourself.
Under what conditions does a bath use more water? Under what conditions does a shower use more water?
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
Allow students to share their displays possibly through a gallery walk or ask them to present to the class. After students have had a chance to explore their work, ask them to share ideas they saw that were interesting and any methods they considered but did not use.
Writing, Representing: MLR7 Compare and Connect.
Use this routine when students present their visual displays. Ask students to consider how comparisons were made between water usage of baths and showers. Draw students’ attention to the relationships between quantities in each situation (e.g., How does the rate of water flow from the shower affect water usage? How does tub size affect the comparison?). Emphasize language used to make sense of strategies used to calculate and compare water usage.
Design Principle(s): Maximize meta-awareness; Support sense-making


correct_option_index: 0