## Properties of Operations

## Opening

# Discuss:

What do you remember about these properties of operations?

What do you remember about these properties of operations?

When working by yourself, you should:

- Make sense of the problem.
- Use “ask myself” questions to see what you need to understand before starting.
- Persevere through difficulty by using what you do know.

Read the worked problem. Then watch your teacher give an example of how to use “ask myself” questions to understand the problem.

- Are these expressions equivalent?

2(8 + 7) + 5

5(4 + 3)

- Use the properties of operations to show each of the steps taken to determine if the expressions are equivalent or not.

Here are ideas for “ask myself” questions:

- What does
mean?*_**_*__ - What is this problem talking about?
- What kinds of comparisons is the problem looking at?
- What are the numbers in the problem and what do they mean?
- What is the problem asking for?

Here are ideas for what to do if you get stuck:

- Look at similar problems you have solved previously.
- Model the problem using counters or other materials.
- Sketch a diagram or other representation.
- Write what you do know.
- Write down questions to ask later.
- Check other resources.

Justify equivalent expressions by using the properties of operations.

- Are these expressions equivalent?

$\left({2}^{2}\right)\left(4\cdot \frac{1}{4}\right)+2$

3 ⋅ 2

- Use the properties of operations to show each of the steps taken to determine if the expressions are equivalent or not.

Hint:

- What questions did you ask yourself before you worked on this problem?
- Why can you change the order of the numbers for addition and multiplication but not for subtraction and division?
- How did you know when to use parentheses and when you can remove the parentheses?

- Are these expressions equivalent?

58 ⋅ 31

$1,500+240+\frac{1}{2}\left(58\right)$

- Use the properties of operations to show each of the steps taken to determine if the expressions are equivalent or not.

Hint:

- What questions did you ask yourself before you worked on this problem?
- Why can you change the order of the numbers for addition and multiplication but not for subtraction and division?
- How did you know when to use parentheses and when you can remove the parentheses?

- Describe your strategies for identifying the relevant properties of operations.
- State which properties were more difficult to understand.
- Identify any mistakes you made and what you learned from them.
- Include any questions your partner asked about your explanation.

- Write two other expressions that are equivalent to:

$\left({2}^{2}\right)\left(4\cdot \frac{1}{4}\right)+2$

Take notes about how your classmates used the properties of operations in their justifications.

As your classmates present, ask questions such as:

- How are the steps of these two different solutions similar and different?
- Why are these expressions equivalent even though they look different?

A good summary clearly explains the important mathematics of today’s lesson.

- Write a summary about how to justify that two expressions are equivalent.

Hint:

- Check your summary. Do you explain what it means when expressions are equivalent?
- Do you define the properties of operations?
- Do you define
*justify*?

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

**Using properties of operations helps me…**