options: Write expressions in equivalent forms to solve problems.

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

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

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

Add and subtract within 20.

Work with radicals and integer exponents.

Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving multiplication and division.

Rewrite rational expressions.

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

Write and interpret numerical expressions.

Analyze patterns and relationships.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Use polynomial identities to solve problems.

Multiply and divide within 100.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving addition and subtraction.

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

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

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

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

Solve systems of equations.

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.
problem_activity: Activity
The large quantities involved in these questions lend themselves to arithmetic with powers of 10, giving students the opportunity to make use of scientific notation before it is formally introduced. This activity was designed so students could practice modeling skills such as identifying essential features of the problem and gathering the required information (MP4). Students use powers of 10 and the number line as tools to make it easier to calculate and interpret results.
Notice the ways in which students use relevant information to answer the questions. Identify students who can explain why they are calculating with one operation rather than another. Speed is not as important as carefully thinking through each problem.
Teacher Notes for IM 6–8 Math Accelerated
Adjust time to 15 minutes. Give students 10 minutes of work time.
Launch
From the warm-up, students have decided what information they need to solve the problem. Invite students to ask for the information they need. Provide students with only the information they request. Display the information for students to see throughout the activity. If students find they need more information later, provide it to the whole class then.
Here is information students might ask for in order to solve the problems:
The mass of an average classroom meter stick is roughly 0.2 kg.
The length of an average classroom meter stick is 1 meter.
The mass of the Moon is approximately
\(7 \boldcdot 10^{22}\)
kg.
The Moon is roughly
\((3.8) \boldcdot 10^8\)
meters away from Earth.
The distances to various astronomical bodies the students might recognize, in light years, as points of reference for their last answer. (Consider researching other distances in advance or, if desired, encouraging interested students to do so.)
Arrange students in groups of 2–4 so they can discuss how to use the information to solve the problem. Give students 15 minutes of work time.
Student Facing
How many meter sticks does it take to equal the mass of the Moon? Explain or show your reasoning.
Label the number line and plot your answer for the number of meter sticks.
[IMG]
If you took all the meter sticks from the last question and lined them up end to end, will they reach the Moon? Will they reach beyond the Moon? If yes, how many times farther will they reach? Explain your reasoning.
One light year is approximately
\(10^{16}\)
meters. How many light years away would the meter sticks reach? Label the number line and plot your answer.
[IMG]
Student Response
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Student Facing
Are you ready for more?
Here is a problem that will take multiple steps to solve. You may not know all the facts you need to solve the problem. That is okay. Take a guess at reasonable answers to anything you don’t know. Your final answer will be an estimate.
If everyone alive on Earth right now stood very close together, how much area would they take up?
Student Response
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Activity Synthesis
Select previously identified students to share how they organized their relevant information and how they planned to use the information to answer the questions. The important idea students should walk away with is that powers of 10 are a great tool to tackle challenging, real-world problems that involve very large numbers.
It might be illuminating to put 35 million light years into some context. It is over a thousand trillion times as far as the distance to the Moon, or about the size of a supercluster of galaxies. The Sun is less than
\(1.6 \times 10^\text{-5}\)
light year away from Earth.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Prior to the whole-class discussion, invite students to share their work with a partner. Display sentence frames to support student conversation such as: “First, I _____ because . . .”, “I noticed _____ so I . . .”, “Why did you . . .?”, “I agree/disagree because . . ..”
Supports accessibility for: Language; Social-emotional skills
Speaking: MLR8 Discussion Supports.
Give students additional time to make sure everyone in their group can explain their response to the first question. Then, vary who is called on to represent the ideas of each group. This routine will prepare students for the role of group representative and to support each other to take on that role.
Design Principle(s): Optimize output (for explanation); Cultivate conversation


correct_option_index: 5