• express rates in equivalent forms

If Harvey walks at an average speed of 6 km/hr, how far will he walk in 2.5 hours? How long will it take him to walk 21 km?

Jelly powder was on sale for three packages for $1.68. Make a chart to show the cost of six packages, nine packages, twelve packages.

• represent any number in scientific notation

The number of visitors to Banff National Park in 1989 was 4.032396 x 10⁶, and the number of visitors to Kootenay National park was 1 555 607. Which park had more visitors? How many more? Give your answer in standard notation.

If 5.03 x 10^-5 was incorrectly written as 5.03 x 10⁵, how many times larger is this?

The diameter of a human hair is 0.00007m. Write this number in scientific notation, using metres as the unit of measure. What is the diameter in centimetres?

• express three-term ratios in equivalent forms

A recipe calls for 250 ml of sugar, 500 ml of oatmeal, and 750 ml of flour. Write the amounts of ingredients as a ratio. Write another equivalent ratio. Write the equivalent ratio for doubled and tripled recipes.

• demonstrate and explain the meaning of a negative exponent, using patterns (limit to base 10)

Look for a pattern in both the top and bottom numbers. Continue the patterns.

1000 000, 10 000, 1000, 100, 10, ___, ___, ___, ___
10⁵, 10⁴, 10³, 10², 10¹, ___, ___, ___, ___

What is the connection between the two patterns? Make a rule to explain.