options: Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
problem_activity: Optional activity
This optional activity gives students another opportunity to use what they have learned about all operations to model and solve a problem in a baking context. Students need to make sense of the problem and persevere in solving it (MP1).
Students may approach the problem in different ways (by drawing diagrams, making computations, reasoning verbally, etc.). Students may also choose different operations to obtain the information they need. For instance, instead of dividing by a fraction, they may perform repeated subtraction. Notice the different methods students use and identify strategies or explanations that should be shared with the class.
Launch
Consider arranging students in new groups of 2. Give students 7–8 minutes of quiet work time and then 1–2 minutes to discuss their response with their partner. Ask students to be prepared to explain their reasoning.
Conversing, Writing: MLR5 Co-craft Questions.
Use this routine to increase students' awareness of the language of mathematical questions. Display the problem about baking cookies, but withhold the final section that includes the question. Give students 2–3 minutes to write down any mathematical questions they have about the situation presented, then to share their questions with a partner. Circulate and listen for questions that involve combining fractional amounts of ingredients. Reveal the actual question and ask students to compare their questions with the original.  Listen for and amplify any questions involving the relationships between the two quantities in this task (number of cups of flour and number of cups of butter).
Design Principle(s): Cultivate conversation; Support sense-making
Student Facing
Mai, Kiran, and Clare are baking cookies together. They need
\(\frac 34\)
cup of flour and
\(\frac 13\)
cup of butter to make a batch of cookies. They each brought the ingredients they had at home.
Mai brought 2 cups of flour and
\(\frac 14\)
cup of butter.
Kiran brought 1 cup of flour and
\(\frac 12\)
cup of butter.
Clare brought
\(1\frac 14\)
cups of flour and
\(\frac34\)
cup of butter.
If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of cookies can they make? Explain your reasoning.
Student Response
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Activity Synthesis
Consider combining every 2–3 groups of 2 students and having students discuss their responses and methods in larger groups of 4–6.
If time permits, reconvene as a class to highlight a couple of strategies and reflect on the effectiveness and efficiency of students’ strategies. For example, if some students performed repeated addition instead of multiplying (or repeated subtraction instead of dividing), ask if repeated addition (or subtraction) is always as efficient as multiplication (or division), or under what circumstances one method might be preferred over the other.


correct_option_index: 1