Exponents: Number Sense Activities

Here is a collection of number sense activities. A calculator could be used to check reasoning. In each activity, there is more than one way to figure out a response without using a calculator.

Approach 1: Whole class activity. Have the class work in pairs or groups and answer to the whole class.

Approach 2: Mathematical Distraction. During individual work (regular class work), or as a homework, invite students to write their solution to a number sense activity on the board. Review responses and reasons at an appropriate time in the class.

Number Sense Activity 1:

Compare the first five powers of 4 with the first ten powers of 2. Explain the pattern.  Choose various values of m and n such that the following equation is true:

    \[2^m=4^n\]

Number Sense Activity 2:

Write three different equations, choosing values for m and n carefully such that the equation

    \[3^m=9^n\]

is true. Check your equations with a calculator.

Number Sense Activity 3:

Which one of the following is true:

    \[\frac{4^6}{5^6}&\geq \frac{4^7}{5^7}\]

    \[\frac{4^6}{5^6}&= \frac{4^7}{5^7}\]

    \[\frac{4^6}{5^6}&\leq \frac{4^7}{5^7}?\]

Number Sense Activity 4:

Which is bigger;

    \[\frac{2^6}{3^7}\]

or

    \[\frac{2^7}{3^6}?\]

Number Sense Activity 5

Put the values in the correct place in the table

    \[ \boxed{\frac{2^3}{3^3};\quad \frac{2^5}{2^{10}}; \quad \frac{10^6}{10^7}; \quad \frac{8}{1.9^3}; \quad \frac{3.2^3}{27} } \]

 

Ball park Value
Between 0 and 0.5
Between 0.5 and 1
More than 1 .

Number Sense Activity 6:

Which is bigger,

1 \times 2 \times 3 \times 4 \times 5 \times 6

or

2^8?


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