Author:
Angela Vanderbloom
Subject:
Algebra
Material Type:
Lesson Plan
Level:
Middle School
Grade:
6
Tags:
  • Brackets
  • Numerical Expressions
  • Parentheses
  • Word Problems
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    Text/HTML

    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. 

    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.
    • 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.

    Qualities of Demonstrating Effective Mathematical Thinking

    Lesson Guide

    Explain that during Work Time, students will often illustrate 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 demonstrate clear mathematical thinking:

    • 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 Demonstrating Effective Mathematical Thinking

    During Work Time, you often illustrate their ways of thinking about the mathematics in the lesson.

    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 demonstrate clear mathematical thinking:

    • 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.

    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

    Discuss Mathematical Thinking

    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.

    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?