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, in json format:
{
  "explanation": "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: Generate and analyze patterns.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

Work with equal groups of objects to gain foundations for multiplication.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

Rewrite rational expressions.

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

Solve equations and inequalities in one variable.

Interpret the structure of expressions.

Solve systems of equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Analyze patterns and relationships.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the connections between proportional relationships, lines, and linear equations.

Gain familiarity with factors and multiples.

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

Understand properties of multiplication and the relationship between multiplication and division.

Understand the relationship between zeros and factors of polynomials.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand and apply properties of operations and the relationship between addition and subtraction.

Work with radicals and integer exponents.

Add and subtract within 20.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.
problem_activity: Narrative
The purpose of this activity is for students to revisit stage 3 of the Shake and Spill center, introduced in kindergarten. In this stage, students see a quantity broken into two parts in different ways. Student write equations to represent each decomposition. Students may write an equation in any way they choose, but the number of counters is presented first to encourage students to write the total before the equal sign. This activity builds toward a future lesson in which students solve Put Together/Take Apart, Addend Unknown story problems and write equations to match them.
During this activity, the teacher collects and displays different equations that students write for the first round. This includes equations where the total is before the equal sign, such as
\(9 = 7 + 2\)
. During the synthesis, students are encouraged to think about how an equation with the total before the equal sign relates back to the context of playing the game (MP2).
Required Materials
Materials to Gather
Cups
Two-color counters
Materials to Copy
Shake and Spill Stage 3 Recording Sheet Grade 1
Required Preparation
Each group of 2 needs 10 two-color counters and a cup (at least 8 oz).
Launch
Groups of 2
Give each group a cup, 10 two-color counters, and recording sheets.
"Today we will revisit a game you played in kindergarten called Shake and Spill. Let's play one round together to make sure everyone remembers how to play."
Display two-color counters and the cup.
“I have some two-color counters. Let’s count them together.”
Place counters in the cup as you count aloud.
“I’m going to write 6 under Total Number of Counters."
Demonstrate shaking and spilling the counters.
"How many red counters are there? How many yellow counters are there?”
30 seconds: quiet think time
Record responses in the table.
“What equation can we write to match the counters?” (
\(4 + 2 = 6\)
,
\(6 = 4 + 2\)
,
\(2 + 4 = 6, 6 = 2 + 4\)
)
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
If needed, play another round.
Activity
“Play the game with your partner. For the first game, you will use 9 counters and record in your book. After the first game, you may choose the number of counters that you want to use, and record on the separate recording sheet.”
10 minutes: partner work time
If needed, ask “Is there another equation you can write to show this round?”
Monitor for and collect 5–6 combinations and equations from round 1.
Student Facing
| total number of counters | red                   counters | yellow                   counters | equations |
|--------------------------|--------------------------------|-----------------------------------|-----------|
|                          |                                |                                   |           |
|                          |                                |                                   |           |
[IMG]
Round 1:
| total number of counters | red                   counters | yellow                   counters | equations |
|--------------------------|--------------------------------|-----------------------------------|-----------|
|            9             |                                |                                   |           |
|            9             |                                |                                   |           |
|            9             |                                |                                   |           |
|            9             |                                |                                   |           |
|            9             |                                |                                   |           |
|            9             |                                |                                   |           |
Student Response
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Activity Synthesis
Display collected combinations and equations.
“What do you notice about the equations I collected during the first round?” (There are different numbers in the equations. They all equal nine. Sometimes the total is before the equation and sometimes it is after.)
“What does the equation
\(9 = 7 + 2\)
mean?” (The nine counter total is the same amount as seven red counters and two yellow counters or seven yellow and two red.)


correct_option_index: 31