Ways of Thinking and Properties of Operations

Ways of Thinking and Properties of Operations

Participate in Mathematical Discussions

Opening

Participate in Mathematical Discussions

Listening actively and asking questions during discussions are as important as the presentation.

To create a good math community, you should:

  • Focus on learning, not getting the answer right.
  • Help each other learn.
  • Be responsible for your own learning.

View the Hints during Ways of Thinking to read questions you can ask the presenter. Pick one or ask a your own question.

Discuss:

  • What can you as a listener contribute to improve your classroom math community?

Hint: Here are ways listeners contribute to math discussions:

  • Clarify—Tell the presenter when you do not understand.
    “I did not understand. What do you mean by…?”
  • Critique—Challenge reasoning that is flawed.
    “How do you know that…?”
  • Connect—Explore how different strategies result in the same answer.
    “What you said is like…"
  • Compare—Describe similarities and differences.
    “Is that different from…?”
  • Notice structure—Ask whether a conclusion is always, sometimes, or never true. “Is your conclusion always true for…?"

Properties of Operations as Fruit

Opening

Properties of Operations as Fruit

Discuss:

Which property of operations could this equation represent? How do you know?

Properties of operations as fruit​​​​​​​

Math Mission

Opening

Explain how you know the value of each fruit.

Identify the Value of Each Fruit

Work Time

Identify the Value of Each Fruit

  • Find the whole number from 0 to 9 that each fruit represents to make the equations true.
  • Explain your reasoning.

Ask Yourself:

  • Which properties of operations are useful in identifying the value of each fruit?
  • Does substituting each fruit with a simple symbol make it easier to work through the possible values for the different fruit?
  • Would naming the equations make it easier to explain your reasons for identifying the values of the fruit?

Properties of operations as fruit

Prepare a Presentation

Work Time

Prepare a Presentation

Explain how you identified the value of each fruit.

  • Write the equation(s) that helped you find a value for a fruit and explain why the equation(s) helped.
  • State any properties of operations that you used to find the value of a fruit.
  • Identify any mistakes you made and what you learned from them.
  • Show which equations or symbols were difficult to determine the values.

Challenge Problem

  • Use the fruit to create equations for the other properties of operations.
  • Challenge your partner to find the result and identify the property that you are representing.

Make Connections

Performance Task

Ways of Thinking: Making Connections

Take notes about how your classmates’ strategies for identifying the values of the fruit were similar to and different from yours.

As your classmates present, ask questions such as:

  • Which equation was the most helpful in identifying the value of a fruit?
  • Which was the hardest equation to figure out?
  • Was it helpful to use other symbols in place of the fruit?
  • Which properties did you use to identify the values of the fruit?

Find Unknowns

Formative Assessment

Summary of the Math: Find Unknowns

Read and Discuss

  • One key concept in algebra is the idea of variables. A variable represents an unknown quantity in an equation.
  • In this task, each fruit represents an unknown quantity.
  • Look at this equation. You could express this equation as a = b × a, where a is the apple and b is the coconut.
  • In future lessons, you will work with variables to represent unknown quantities.
  • To solve equations with variables, use the same properties of operations that you use with numeric equations.

Can you:

  • Explain your general strategy for finding the unknown values of the fruit?

Reflect On Your Work

Work Time

Reflection

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

A strategy that I found useful to identify unknown values is…