options: Represent and solve equations and inequalities graphically.

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

Interpret the structure of expressions.

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

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

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

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

Generate and analyze patterns.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Analyze patterns and relationships.

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

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

Solve systems of equations.

Multiply and divide within 100.

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Understand the relationship between zeros and factors of polynomials.

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

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.
problem_activity: Narrative
The goal of this activity is for students to examine different ways to write the product of a three-digit number and a two-digit number as a sum of partial products. Students match sets of partial products which can be put together to make the full product. Students are provided blank diagrams, familiar from the previous lesson, that they may choose to use to support their reasoning. In the activity synthesis, students relate the expressions and diagrams to equations to prepare them to analyze symbolic notation for partial products in the next activity.
When students relate partial products and diagrams to the product
\(245 \times 35\)
they look for and identify structure (MP7).
MLR8 Discussion Supports.
Display the following sentence frame to support small-group discussion: “I noticed _____ , so I matched . . . .” Encourage students to challenge each other when they disagree.
Advances: Speaking, Conversing
Required Materials
Materials to Copy
Partial Product Expressions
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Display first image from student book.
“What product does this rectangle represent?” (
\(245 \times 35\)
)
“Today, you are going to take turns with your partner picking expressions that can be added together to give the product
\(245 \times 35\)
. You can use the diagrams to explain your reasoning, if they are helpful.”
Activity
10 minutes: partner work time
Monitor for students who:
use the diagram to determine which expressions they will use.
look at the expressions and think about how they could be used to find the full product.
compute the full product in different ways.
Student Facing
[IMG]
[IMG]
[IMG]
Take turns picking out a set of expressions that are equal to
\(245 \times 35\)
when added together. Use the diagrams if they are helpful.
Explain how you know the sum of your expressions is equal to
\(245 \times 35\)
.
What is the value of
\(245 \times 35\)
? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
If students do not choose correct expressions to represent a sum that is equal to
\(245 \times 35\)
, refer to one of the empty boxes in the diagram and ask, “Which multiplication expression represents this partial product?”
Activity Synthesis
Invite previously selected students to share their strategies. As students share, record their reasoning with equations.
Display:
\(245 \times 30 + 245 \times 5  = 245 \times 35\)
“How do you know this equation is true?” (I can put the 30 and 5 together since they are both multiplied by 245. I see that
\(245 \times 30\)
is the top part of the diagram and
\(245 \times 5\)
is the bottom part. Together that’s the whole diagram.)


correct_option_index: 33