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: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
problem_activity: Optional activity
In the final phase of the drawing project, students reflect on and revise their work. Students who chose the same paper option confer in small groups to analyze and compare their floor plans. They discuss their decisions, evaluate the accuracy of their drawings, and then revise them as needed.
After revision, students debrief as a class and discuss how the choice of scale, units, and paper affected the drawing process and the floor plans they created.
Launch
Arrange students who use the same type and size of paper into small groups. Give them 8–10 minutes to share and explain their drawings. Display and read aloud questions such as the following. Ask students to use them to guide their discussion.
What scale did you use? How did you decide on the scale?
Do the scaled measurements in each drawing seem accurate? Do they represent actual measurements correctly?
Did the scale seem appropriate for the chosen paper? Why or why not?
What was the first thing you drew in your drawing? Why?
How did you decide on the objects to show in your drawing?
What aspects of your drawings are different?
How could each floor plan be revised to better represent the classroom?
Student Facing
Trade floor plans with another student who used the same paper size as you. Discuss your observations and thinking.
Trade floor plans with another student who used a different paper size than you. Discuss your observations and thinking.
Based on your discussions, record ideas for how your floor plan could be improved.
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
Before debriefing as a class, give students 4–5 minutes of quiet time to reflect. Ask them to write down ideas for revising their floor plan and strategies for creating accurate scale drawings based on their conversation.
Though much of the discussion will take place within the groups, debrief as a class so students can see floor plans created at a variety of scales and on different paper types or sizes. Display a range of scale drawings for all to see and discuss the following questions. (Alternatively, consider posting all students’ work for a gallery walk and ask students to reflect on these questions.)
What are the differences in these drawings?
How did different scales impact the final drawing?
How did the size of paper impact the choice of scale?
What choices were really important when creating the scale drawing?
Would these choices be the same if you were doing a different room in the school? Or some other building?
Representing, Conversing: MLR7 Compare and Connect.
Use this routine to prepare students for the whole-class discussion. Invite students to quietly circulate and read at least 2 other posters or visual displays in the room prior to the whole-class discussion. Give students quiet think time to consider what is the same and what is different about the visual displays of the floor plans created at a variety of scales and on different paper types or sizes. Next, ask students to find a partner to discuss what they noticed. Listen for and amplify observations that include mathematical language and reasoning about how the choice of scale, units, and paper affect the process of creating scaled drawings.
Design Principle(s): Cultivate conversation


correct_option_index: 2