options: Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Use properties of operations to generate equivalent expressions.

Represent and solve equations and inequalities graphically.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Multiply and divide within 100.

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

Gain familiarity with factors and multiples.

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

Create equations that describe numbers or relationships

Rewrite rational expressions.

Analyze patterns and relationships.

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

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

Use polynomial identities to solve problems.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Add and subtract within 20.

Interpret the structure of expressions.

Generate and analyze patterns.

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

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Reason about and solve one-variable equations and inequalities.

Write expressions in equivalent forms to solve problems.

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

Work with addition and subtraction equations.

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.

Use the four operations with whole numbers to solve problems.

Solve systems of equations.

Work with radicals and integer exponents.
problem_activity: Narrative
The purpose of this activity is for students to use what they’ve learned about multiplication to solve and represent situations that involve equal groups. Students now have experience with multiple representations and have the opportunity to choose which representation is most helpful to represent multiplication situations.
The launch of the activity is an opportunity for students to share their experiences and ask questions about the objects to ensure each student has access to the context. If it is helpful, display images of the items for students to reference.
MLR8 Discussion Supports.
Synthesis: As students describe their representations of the problems, use gestures to emphasize the number of groups and how many are in each group. For example, trace with your finger around each group, and point to each object in each group to show how many there are.
Advances: Listening, Representing
Representation: Access for Perception
. Provide access to connecting cubes. Ask students to identify correspondences between the concrete and visual representation used.
Supports accessibility for: Conceptual Processing
Launch
Groups of 2
Write the list of objects (“teams, earrings, pencils, pieces of glass, carrots”) on a display for all students to see.
“Take a minute to read this list. When you are done, discuss the objects you know or have questions about.”
3 minutes: partner discussion
Share a few responses.
“Now we’re going to represent and solve more problems with equal groups. Take a couple of minutes to begin working on the problems before you work in partners.”
2–3 minutes: independent work time
Activity
“Work with your partner to solve each problem.”
5–7 minutes: partner work
Identify students who use different representations like drawings of equal groups or tape diagrams as they solve the problems.
Student Facing
Solve each problem. Show your thinking using diagrams, symbols, or other representations.
There are 4 soccer fields. Two teams are on each field. How many teams are there altogether?
There are 7 windows. Each window has 2 pieces of glass. How many pieces of glass are there in the windows?
Jada has 5 bags. Each bag has 10 earrings. How many earrings does Jada have?
Kiran has 4 boxes. Each box has 5 pencils in it. How many pencils does Kiran have?
Andre has 3 bags of carrots. Each bag has 10 carrots. How many carrots does Andre have?
Student Response
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Advancing Student Thinking
If students add or subtract instead of multiply to solve the problems, consider asking:
“Tell me about how you solved this problem.”
“How does the problem involve equal groups?”
Activity Synthesis
For each problem, display different representations, one at a time.
“How does this representation help us see what’s happening in the problem?” (You can see there are 4 groups for the fields and 2 dots in each group for the teams. The diagram is split into 5 parts for the 5 bags, and each section has a 10 in it for the number of earrings.)
“How could each representation help us solve the problem?” (Counting the dots. Counting by 10.)
If needed, “What expression could we write to represent this situation?”


correct_option_index: 2