Free Write 9

What is the recommended progression for teaching exponents?

• Use whole-number exponents to denote powers of 10.

• Write and evaluate numerical expressions with whole-number exponents.

• Apply the order of operations to expressions with exponents.

• Use scientific notation.

• Understand and use square roots and cube roots.

• Apply properties of integer exponents to generate equivalent expressions.

What are “quantity contexts” for teaching positive/negative numbers?

They provide opportunities for students to combine opposites to equal zero.

What are “linear contexts” for teaching positive/negative numbers?

They provide real-world applications for linear concepts, often using the number line. Examples include:

• Temperature

• Altitude

• Timelines

• Football (yard lines)

What visual tools are recommended for positive/negative numbers?

Two-color counters and number lines.

How is absolute value defined?

It is the distance between a number and zero (e.g., ∣n∣).

What are the three meanings of the minus sign with negative numbers?

1. Subtraction

2. Negative number

3. The opposite of a number

What is the primary goal when teaching operations with positive/negative numbers?

To move away from memorizing rules and toward using visual representations connected to symbolic computations.

What are two effective strategies for teaching these operations?

1. Have students create an open number line with illustrations and corresponding equations.

2. Use two-color counters for addition, subtraction, multiplication, and division.

How can teachers help students see relationships among different number types (e.g., irrational, whole)?

By using:

• Visual models/representations

• Contextual connections

• Classification tasks