options: Use properties of operations to generate equivalent expressions.

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

Interpret the structure of expressions.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Represent and solve equations and inequalities graphically.

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

Represent and solve problems involving addition and subtraction.

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

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

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

Understand the relationship between zeros and factors of polynomials.

Work with addition and subtraction equations.

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

Analyze patterns and relationships.

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

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

Multiply and divide within 100.

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Gain familiarity with factors and multiples.

Solve systems of equations.

Add and subtract within 20.
problem_activity: Narrative
The purpose of this activity is for students to transition from reasoning about division concretely or visually (using base-ten diagrams) to doing so more abstractly (by writing equations). It also reinforces the connections between multiplication and division.
Students make sense of three different strategies of dividing 78 by 3 and attend to the connections between the visual and numerical representations of the same quotient. As they do so, they practice reasoning quantitatively and abstractly (MP2).
During the synthesis, discuss how place value units play a role in all three strategies.
MLR8 Discussion Supports.
Synthesis: Display Lin, Priya, and Tyler’s strategies. As students share their observations, annotate the display to illustrate connections. For example, annotate where students see the divisor, dividend, and quotient on each diagram.
Advances: Listening, Representing
Launch
Groups of 2
“Take a couple minutes to make sense of Lin, Priya, and Tyler’s work.”
2 minutes: quiet think time
Activity
“Work with your partner to make sense of Lin, Priya, and Tyler’s work and to complete the activity.”
7–8 minutes: partner work time
Monitor for students who:
make connections between the equations and the base-ten diagram
recognize how Tyler’s equations and reasoning are different from Priya’s equations
Identify students who can explain these connections or distinctions to share during the synthesis.
Student Facing
Lin, Priya, and Tyler found the value of
\(78 \div 3\)
. Their work is shown. Make sense of each student’s work.
Lin
[IMG]
Priya
\(\begin{align} 3\times 10&= 30\\ 3\times 10&= 30\\ 3\times \phantom{0}6 &= 18 \\ \overline {\hspace{5mm}3 \times 26} &\overline {\hspace{1mm}=78 \phantom{000}} \end{align}\)
Tyler
\(\begin{align} 3\times 20&= 60\\ 3\times \phantom{0}6 &= 18 \\ \\20 + 6 &= 26 \end{align}\)
How are the three students’ work alike?
How are they different?
Student Response
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Activity Synthesis
Invite students to share how Lin, Priya, and Tyler’s work are alike and how they are different.
Select previously identified students to share additional connections that they noticed.
“Why does it make sense that Priya and Tyler wrote multiplication equations to find the value of a quotient?” (Multiplication and division can represent the same equal-groups situation. To divide 78 by 3 is to find how many are in each of 3 groups or how many groups of 3 there are. We can multiply up to 78 to find the answer.)
Consider asking: “What new ideas about dividing numbers did you learn and would like to try? Talk to a new partner about why you’d like to try them.”


correct_option_index: 6

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