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* *Reflection: Standards Alignment
Describing Numbers - Section 4: Independent Practice

This can be a difficult lesson for some of my students. During partner practice, I am really pushing kids to deepen their understanding through use of the Standards of Mathematical Practice (SMPs).

When I ask students to explain to me why certain choices are incorrect, they're engaging with a number of mathematical practices. They have to make sense of the problem (**SMP 1)**, in order to eliminate answer choices. In order to translate the scenario into the appropriate integers, students must decontextualize (and then recontextualize) the problem. This sort of reasoning is the heart of **SMP 2** (Reason Abstractly and Quantitatively). By asking students to engage in a conversation with me about which choices are incorrect, I'm asking them to engage with **SMP 3** (Construct a Viable Argument).

It's not a big lift on me or my planning at all to ask students 'how did you know this was wrong/right?' and it is a question I intentionally use daily.

Students engage with **SMP 4** (Model with Mathematics) when they create number line models. A huge part of my course involves creating models to make sense of, understand, prove, etc. I want my students to model all of the time.

The Standards for Mathematical Practice have guided me, in terms of the types of questioning I am using in my lessons (oral and written).

*Supporting Learning with the SMPs*

*Standards Alignment: Supporting Learning with the SMPs*

# Describing Numbers

Lesson 8 of 8

## Objective: SWBAT write, interpret, and explain statements of order for rational numbers in real-world contexts.

#### Think About It

*7 min*

Students work on the Think About It problem in pairs. After 3 minutes of writing time, I have 3-4 students share out the contexts they've written. As they share, I record the contexts on the board (weight, temperature, bank accounts, etc). I'll then ask the rest of the class to share out any other contexts they've written about (without having them read everything they've written), and record those on the running list.

I'll leave the list on the board throughout the lesson, so that students can access it as a resource as they work.

#### Resources

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#### Guided Practice

*20 min*

In this unit, students have learned how to interpret real-world contexts and compare and order rational numbers. In this lesson, students write real-world contexts to describe comparisons provided, as well as match comparison and real-world contexts.

Because there isn't new content in this lesson, I do not facilitate an Intro to New Material section. Instead, I lead students through Guided Examples.

The first example reads -5 is less than 4. I ask students to come up with a real-world situation that can be described by this inequality, by first thinking about a context that could apply to these numbers. Together, we'll write a context. In general, students should follow these steps in the written responses:

- Describe overall context
- Describe integers in context separately
- Include one ending statement that compares both integers within the context

For example, the answer to the first problem might read "The Patriots made two plays in the last quarter. On the first play, the team lost five yards. On the second play, the team gained four yards. The first play yielded fewer yards than the second play.”

#### Resources

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#### Partner Practice

*15 min*

Students work in pairs on the Partner Practice problem set. As they work, I circulate around the room and check in with each group. I am looking for:

- Are students choosing applicable contexts for each inequality?
- Are students using the correct structure to create a context?
- Are students trying each answer choice when matching a context to a comparison?
- Are students describing the comparisons within a context coherently?
- Are students explaining why their real-world application makes sense correctly?

I'm asking:

- Why does that context apply to these numbers?
- Why does your description make sense given the comparison of numbers?

If students are struggling with the context, I will refer them to the list we came up with as a class during the Think About It section.

After 10 minutes of partner practice time, students complete the Check for Understanding problem independently. I'll circulate and check their work.

#### Resources

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#### Independent Practice

*15 min*

Students work on the Independent Practice problem set.

As I circulate, I'll ask students to explain to me why any of the incorrect answers for Problems 1 - 4 are incorrect. I want to give students to justify their choices and talk about math.

I'll also ask students to create me a visual model for a problem as I circulate, so that they get practice using a visual representation as justification.

#### Resources

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#### Closing and Exit Ticket

*10 min*

After independent work time, I have students share their responses to Problem 9 with their partners. They're able to give one another feedback and hear another possible response for this problem.

Students then independently complete the Exit Ticket to close the lesson.

#### Resources

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##### Similar Lessons

###### Pre Test

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*Resources(9)*

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###### Ordering Rational Numbers

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Environment: Urban

- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
- UNIT 7: Expressions
- UNIT 8: Equations
- UNIT 9: Inequalities
- UNIT 10: Area of Two Dimensional Figures
- UNIT 11: Analyzing Data

- LESSON 1: Integers: Number Lines and Absolute Values
- LESSON 2: Integers in the Real World
- LESSON 3: Interpret Integers in Context
- LESSON 4: Comparing and Ordering Integers
- LESSON 5: Identifying Positive Rational Numbers on Number Lines
- LESSON 6: Identifying and Representing Rational Numbers on a Number Line
- LESSON 7: Comparing Rational Numbers
- LESSON 8: Describing Numbers