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: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
problem_activity: Narrative
The purpose of this activity is for students to interpret a scaled picture graph and write questions that can be asked based on the data represented in a scaled picture graph.
MLR8 Discussion Supports.
Use multimodal examples to show the meaning of a symbol. Use verbal descriptions along with gestures, drawings, or concrete objects to show how each flower on the graph is a symbol that represents five flowers that were seen in the park.
Advances: Listening, Representing
Representation: Internalize Comprehension.
Synthesis
:
Invite students to identify which details were needed to solve the problem. Display the sentence frame, “The next time I read a scaled picture graph I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing
Launch
Groups of 2
Display the graphs for all to see.
“What are some strategies you could use to read the graphs?” (In the Flowers I Saw on the Way Home graph I could count each category by 5 since each picture represents 5 flowers.)
1 minute: quiet think time
Share and record responses.
Activity
“Now, we’re going to answer some questions about the scaled picture graphs. You will also have a chance to write your own question that can be asked based on each graph.”
8–10 minutes: partner work time
If there is time, have groups trade books and answer each other’s questions.
Math Community: As students work, monitor for examples of the “Doing Math” actions.
Student Facing
Andre collected data to see how many of each type of flower he saw on the way home. The data is shown in this picture graph:
[IMG]
How many of each type of flower did Andre see on the way home?
roses _____
tulips _____
daisies _____
violets _____
Write 2 questions that you could ask about the flowers Andre saw on his way home.
A group of students were asked, “What is your favorite type of book?” Their responses are shown in this picture graph:
[IMG]
How many students liked each type of book? How do you know?
Write 2 questions that you could ask about students’ favorite types of books based on the graph.
Student Response
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Advancing Student Thinking
If students answer questions about the graph with numbers that don’t match the graph, consider asking:
“How did you answer the questions about the graph?”
“What does the key tell us about each picture in the graph?”
Activity Synthesis
Have students share responses to the questions they answered and explain their reasoning.
Consider asking:
“How did you use the scale to answer the questions?” (I counted by the number that each picture represented, like by 5 for the flowers and by 2 for the students.)
Share a variety of student written questions.
Consider asking:
“How did you know your question could be answered with the graph?” (The data you needed to answer the question was in the graph.)
If time ask, “What questions cannot be answered by this graph?” (How many students' favorite type of book is graphic novels?)


correct_option_index: 0

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