few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Your response:
Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Understand ratio concepts and use ratio reasoning to solve problems.
problem_activity: Activity
This activity continues work done in the previous lesson that connected various representations of proportional relationships including images, equations, and descriptions. In this activity students match diagrams, descriptions, and equations that represent a proportional relationship, involving variables
\(x\)
and
\(y\)
. Students then create their own diagram to represent an equation.
Identify students that create diagrams representing each of the unmatched equations, so they can share their work during the discussion.
Launch
Give students 7–10 minutes of quiet think time on the questions. Follow with whole-class discussion.
Representation: Internalize Comprehension.
Begin the activity with concrete or familiar contexts. For example, display a tape diagram with concrete values for
\(x\)
and
\(y\)
such as 20 and 15 respectively. Ask students “How much did 20 decrease by to get to 15?” Highlight the connections between the concrete and abstract tape diagrams. In the concrete tape diagram, 20 decreased by
\(\frac{1}{4}\)
to get 15. In the abstract tape diagram,
\(x\)
also decreased by
\(\frac{1}{4}\)
to get
\(y\)
.
Supports accessibility for: Conceptual processing; Memory
Student Facing
Match each diagram with a description and an equation.
Diagrams:
[IMG]
Descriptions:
An increase by
\(\frac14\)
An increase by
\(\frac13\)
An increase by
\(\frac23\)
A decrease by
\(\frac15\)
A decrease by
\(\frac14\)
Equations:
\(y=1.\overline{6}x\)
\(y=1.\overline{3}x\)
\(y=0.75x\)
\(y=0.4x\)
\(y=1.25x\)
Draw a diagram for one of the unmatched equations.
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
Ask previously identified students to share their diagrams and explain how they represent the equation they chose. Then, ask students that did not share their diagrams to explain whether
\(x\)
(or
\(y\)
) is increased or decreased by some amount in the discussed equations.
Representing, Writing: MLR3 Clarify, Critique, Correct.
Present an incorrect diagram to represent one of the unused equations that reflects a possible misunderstanding from the class. For example, for the equation
\(y=0.75x\)
, draw a diagram where
\(y\)
is greater than
\(x\)
. Prompt students to identify the error, and then write a correct diagram to represent the equation. This will support students to understand the relationship between equations and diagrams.
Design Principle(s): Maximize meta-awareness


correct_option_index: 0