Author:
Benjamin White
Subject:
Algebra
Material Type:
Lesson Plan
Level:
Middle School
Grade:
6
Provider:
Pearson
Tags:
Brackets, Numerical Expressions, Parentheses, Word Problems
License:
Creative Commons Attribution Non-Commercial Share Alike
Language:
English
Media Formats:
Text/HTML

Education Standards (14)

Matching Numeric Expressions to Descriptions

Matching Numeric Expressions to Descriptions

Overview

Students are introduced to classroom routines and expectations, and complete a full mathematics lesson. The class discusses how to clearly present work to classmates. Partner work is modeled, and partners then work to match numerical expressions to corresponding word descriptions. Students read and discuss a summary of the math in the lesson, and then write a reflection about their thoughts.

Key Concepts

Students match a numerical expression to its corresponding description in words. Students interpret parentheses and brackets in numerical expressions and they construct viable arguments and critique the reasoning of others. Students learn to use the exponent 2 to represent squaring.

Goals and Learning Objectives

  • Describe the classroom routines and expectations.
  • Consider how to present work clearly to classmates.
  • Collaborate with a partner.
  • Critique a partner’s reasoning.
  • Connect a numerical expression to its corresponding word description.
  • Learn to use an exponent of 2 to represent squaring.

Lesson Routines

Lesson Guide

Thank students for their effort during the last lesson.

Tell students that each lesson has a similar structure and follows these classroom routines:

  • Opening sparks your thinking about the math in today’s lesson.
  • Work Time asks you to solve one or more problems on your own and with your partner.
  • Ways of Thinking is a time for you and your classmates to present your mathematical thinking. As a class, you will discuss the different mathematics you and your classmates used to solve the problems.
  • Apply the Learning is a chance for you to work on your own and apply the mathematics you just learned.
  • Summary of the Math has you pull together your ideas about today’s math after the Ways of Thinking discussion.
  • Reflection involves looking back on today’s lesson and looking forward to future lessons to write questions or ideas that you are still wondering about.
  • Exercises gives you an opportunity to work through other problems that build on the mathematics of today’s lesson.

Tell students that they will complete all of their work in their notebook. They should save all their work, because what they record, even mistakes, represents their thinking. Thinking cannot be erased—it can only be revised and improved upon. Explain that students can create a new document to show their revised work.

Opening

Lesson Routines

In each lesson, you have the same routines.

  • Read through the list of routines.
  • Listen as your teacher explains what you will do during each routine.

Classroom Expectations

Lesson Guide

Discuss these classroom expectations:

  • The procedure for gathering materials as students enter the room, including any technology they will be using
  • The routine for submitting exercises, with regard to when and how
  • The procedure for obtaining any additional materials needed for the lesson
  • The procedure and locations for putting away materials at the end of the lesson
  • Any other routines or habits that fit with the classroom norms that the class established and that will help the class run smoothly

Posting this list of classroom expectations for the class will be helpful because many of these expectations are relevant for every lesson. Alternatively, you can ask students to complete a graphic organizer, summarizing the information in their notebooks.

Opening

Classroom Expectations

These are our classroom expectations.

Discuss:

  • As I enter the classroom, I am expected to…
  • I am expected to submit exercises before…
  • To get the tablet and any additional materials, I am expected to…
  • To put away materials at the end of the lesson, I am expected to…
  • I am also expected to…

Qualities of Effective Presentations

Lesson Guide

Explain that during Work Time, students will often prepare a presentation illustrating their ways of thinking about the mathematics in the lesson. Ask students to consider these questions:

  • How do you organize your work to clearly communicate your thinking about a problem?
  • What kinds of visuals are helpful?
  • How can you make sure you explain your strategies and reasoning well?

Have students spend a few minutes thinking about these three questions on their own. Then have students discuss their ideas with their partner.

When students are done, have them share their ideas with the class. As with the classroom norms, when students generate their own ideas, they take ownership of their own learning.

These Hints for students are ideas about how to prepare clear presentations:

  • Understand your own work.
  • Use visuals and gestures to help others know what you are talking about.
  • Say fewer words and choose them carefully.
  • Include diagrams and graphs, when appropriate.
  • Speak clearly and slowly.
  • Stay calm. Remember to breathe.
  • Listen carefully to comments and questions.
  • Pause to think about your response before speaking.

Record these ideas on a class chart as you project them for the class. After all ideas are listed, review each one for clarity. Agreement is not necessary because diversity in presentation styles can be beneficial and this list should grow over the year.

Opening

Qualities of Effective Presentations

During Work Time, you often prepare a presentation.

Discuss:

  • How do you organize your work to clearly communicate your thinking about a problem?
  • What kinds of visuals are helpful?
  • How can you make sure you explain your strategies and reasoning well?

Here are ideas about how to prepare clear presentations:

  • Understand your own work.
  • Use visuals and gestures to help others know what you are talking about.
  • Say fewer words and choose them carefully.
  • Include diagrams and graphs, when appropriate.
  • Speak clearly and slowly.
  • Stay calm. Remember to breathe.
  • Listen carefully to comments and questions.
  • Pause to think about your response before speaking.

Model Partner Work

Lesson Guide

Have students watch as you demonstrate how to complete a card sort with a partner.

Teacher Demonstration

Tell students that they will often work with a partner during class. Today, students will work with a partner to match different forms of an expression.

Model working with a partner by inviting a student to be your partner. Use the Card Match interactive and explain each step as you model it.

  • Find two cards that match.
  • Explain to your partner why the cards match. Have your partner ask questions if she is unclear about your reasoning.
  • Ask your partner to find two cards that match and explain her reasoning to you. Ask questions if she is unclear in her explanation.
  • Once you and your partner agree on the matches, evaluate each expression on your own. Then check with your partner. If you agree, write its value in your Notebook.

Show students how they will write the value in their Notebook but do not have them record it at this time. They will do that during Work Time.

Model the idea that after partners explain their ideas to each other, they should use any time that remains to clarify their work as they prepare their presentation.

Opening

Model Partner Work

Watch your teacher demonstrate how to complete this task with a partner.

  • Take turns matching word cards to numerical expression cards.
  • Explain to your partner how you know the cards match. Challenge your partner to have clear and complete explanations.
  • Evaluate the expression on your own and then check that you agree with your partner.
  • Use any extra time to clarify and improve your work.


INTERACTIVE: Card Match

 

Math Mission

Lesson Guide

Discuss the Math Mission. Students will connect a numerical expression with its meaning in words.

Work Time

Connect a numerical expression with its meaning in words.

Match Expressions and Words

Lesson Guide

Have students work with their partners and take turns matching word cards to numerical expression cards.

ELL: Having students work together allows you to monitor individual student progress by listening to and recording student conversations and peer problem solving. This type of collaborative work gives ELL students the opportunity to use mathematical language and to engage in conversation with their peers.

Interventions

Student does not remember how to use exponents for squaring.

  • What exponent can be used to represent squaring?
  • What does an exponent of 2 mean?

Student is unsure about the effect of parentheses.

  • What is the difference between the expression 82 + 2 and the expression (2 + 8)2?
  • Why are brackets needed in the expression 2[(7 + 8) − 2]?
  • How do you know when you need to have parentheses?

Mathematical Practices

Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.

Students engage in productive partner dialog by presenting their explanations and critiquing each other’s reasoning.

 

Work Time

Match Expressions and Words

Work with your partner.

  • Take turns matching word cards to numerical expression cards.
  • Explain to your partner how you know the cards match. Challenge your partner to have clear and complete explanations.
  • Evaluate the expression on your own and then check that you agree with your partner.
  • Use any extra time to clarify and improve your work.

Hint:

  • What is the difference between an expression, such as 82 + 2 and an expression with similar quantities and operations, such as (2 + 8)2?
  • How do you know when parentheses are needed?
  • Why are brackets needed in the expression 2[( 7 + 8 ) − 2]?

INTERACTIVE: Card Match

Prepare a Presentation

Lesson Guide

Have students prepare a presentation that describes their strategies for matching numerical expressions to word descriptions. Remind students to think about the qualities of an effective presentation. If they would like to, students can refer to the hints in Task 3 about how to prepare a clear presentation.

ELL: When observing students, give students advance notice that they will be presenting their work on a specific problem during the Ways of Thinking discussion. This will give students ample time to prepare.

Preparing for Ways of Thinking

As students work, circulate and listen carefully to their reasoning. Watch for these things:

  • Is the listener asking questions when the speaker is unclear?
  • Do both partners explain their processes, even if they each did something similar?
  • Do students understand how to square a number?
  • Do students follow the order of operations when evaluating expressions?

Challenge Problem

Answers

  • Answers will vary. Possible answer: Multiply the quantity 2,035 plus165.5 by 12.25 and then subtract 1,445: 12.25(2,035 + 165.5) − 1,445.

Work Time

Focus on the meaning of numerical expressions.

  • Describe your strategies for matching the numerical expression cards to word cards.
  • Explain your reasoning and justification.
  • Identify any mistakes you made and what you learned from them.
  • Include any questions your partner asked about your explanation.

INTERACTIVE: Card Match

Challenge Problem

Create your own numerical expressions and matching word descriptions. In your expressions, use numbers with more than four digits, include fractional quantities, and use three different operations.

Make Connections

Lesson Guide

Have several student pairs present one of their card matches and their explanation. Ask students who correctly and incorrectly matched the cards to present, especially students who show the common issues identified in Interventions.

As students present, have their classmates take notes about how their own strategy for solving the problem was similar to and different from the presenters’ strategies. Students should look for new ideas that they might want to try themselves.

Encourage students to ask questions about the presenters’ thinking to better understand the different mathematical ideas. The hints on the student screen help model for students productive questions to ask during Ways of Thinking. You can see these sample questions by opening the hints on the student screen.

Have presenters explain how they know the cards match. Make connections between their different approaches and highlight the variability in the strategies that students used.

Mathematics

Ask students:

  • Why is the order of the words not always the same as the order in the numerical expression? [Answer: Numerical expressions are not evaluated left to right; instead, operations in parentheses are completed before others.]
  • What words helped you know that you needed parentheses? [Answer: Commas and the term “the quantity” identified separation of operations. Operations at the beginning of the word description often need to include parentheses in the numerical expression.]

Ask a few students who completed the Challenge Problem to present their numerical expressions and corresponding word descriptions. Ask students to explain how they knew that the expressions and word descriptions matched.

Have partners share with the class an example of justifying and critiquing each others' reasoning. Partners should either summarize their work for the class or explain their disagreement and how they resolved it.

Performance Task

Ways of Thinking: Make Connections

Take notes about how your own thinking is similar to and different from your classmates' thinking.

  • Are there new ideas that you want to try out?

  • What critiques do you have about your classmates' ways of thinking?

As your classmates present, ask questions such as:

  • Why is the order of the words not always the same as the order in the numeric expression?
  • What words helped you identify that you needed parentheses?
  • Where did you include your strategy and explanation in your presentation?
  • Are there any visuals it would be helpful to add to your presentation?

Describe Expressions

Lesson Guide

Tell students that for most lessons, they will summarize what they learned after Ways of Thinking. During Summary of the Math, students will either individually write a summary of the mathematical concepts of the lesson or read and discuss a summary as a class. Today the class will read and discuss a summary together.

Mathematics

First, have partners read and discuss the summary together for a few minutes. Then ask the class:

  • What role do parentheses and brackets have in an expression?
  • Why are parentheses used?
  • What does the word “quantity” mean?
  • How do you represent squaring in a numerical expression?
  • Are there other things that might be useful to add to this summary?

Invite students to contribute any other points they think are important.

SWD: Some students with disabilities may struggle to explain their mathematical reasoning in words. Provide sentence starters or paragraph frames to support students.

Formative Assessment

Summary of the Math: Describe Expressions

Read and Discuss

  • Parentheses and brackets identify operations that should be performed before other operations.
  • Parentheses are used to group parts of an expression together when you want them to act as a single quantity.
  • You read 82 as "8 squared" which means "8 times 8."

Can you:

  • Write a numerical expression from its description in words?
  • Write in words a description of a numerical expression?
  • Explain why the expression and the words match?
  • Evaluate the numerical expression?

Reflect On Your Work

Lesson Guide

Have each student write a brief reflection before the end of class.

Discuss that reflections are a time for students to write questions or wonderings that have arisen during the lesson. Students should reflect on questions such as these:

  • What are you curious about?
  • What would you like to pursue further in a different way?

Review the reflections to see what things students wonder about the meaning of expressions.

Work Time

Reflection On Your Work

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

Something I wonder about the meaning of expressions is…