options: Generate and analyze patterns.

Perform arithmetic operations on polynomials.

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

Write expressions in equivalent forms to solve problems.

Gain familiarity with factors and multiples.

Multiply and divide within 100.

Work with radicals and integer exponents.

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

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

Represent and analyze quantitative relationships between dependent and independent variables.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

Work with addition and subtraction equations.

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

Represent and solve equations and inequalities graphically.

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

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

Analyze patterns and relationships.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.

Solve systems of equations.

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

Use polynomial identities to solve problems.

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

Represent and solve problems involving addition and subtraction.

Understand the relationship between zeros and factors of polynomials.

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

Rewrite rational expressions.
problem_activity: Narrative
The purpose of this activity is for students to understand that the same division expression can be used to represent both types of division situations. Students are given two situations and asked to match a division expression to one of the situations, but the expression matches both situations given. It is okay if students do not recognize that the expression matches both situations in the activity, because it will be discussed in the activity synthesis. Students learn that the number we are dividing by is called the
divisor
and understand that the divisor can represent the size of the groups or the number of groups. When students explain that a divisor can be interpreted differently based on the situation it represents, they reason abstractly and quantitatively (MP2).
MLR2 Collect and Display.
Circulate and collect the language students use as they consider the two situations. Listen for and clarify any questions about the context. On a visible display, record words and phrases such as: put in groups, split, divide, number of groups, etc. During the synthesis, add “divisor” to the display and highlight connections to any related language.
Advances: Conversing, Reading
Launch
Groups of 2
“Let’s look a bit closer at division expressions. Take a minute to read these two situations.”
1 minute: quiet think time
Activity
“Work with your partner to decide which situation the expression represents.”
2–3 minutes: partner work time
Student Facing
Consider these two situations.
A. Han has 21 toy cars. He puts the same number of cars in each of 3 boxes. How many cars will be in each box?
B. Han has 21 toy cars. He wants to put 3 cars in each box. How many boxes will he need?
Which situation does the expression
\(21 \div 3\)
represent? Explain your reasoning.
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Student Response
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Activity Synthesis
Invite students to share their responses and reasoning.
“How can the same expression represent two different situations?” (Both situations involve the same numbers, 21 and 3. Both situations involve putting 21 objects into equal groups. In one case, the 3 is the number of objects in the group, but in the other, it is the number of groups. Both situations are talking about 21 divided by 3, just in different ways.)
“We noticed that the number that we are dividing by, 3, can have two different meanings. It can mean 3 groups or 3 objects in each group.”
“When we divide, the number we divide by is called the
divisor
. In the expression
\(27 \div 3\)
, the divisor is 3.”


correct_option_index: 22