How can we find the volume of a rectangular prism?

What does it mean for one quantity to be double another’s?

What does it mean for one quantity to be double another’s?

The greatest possible volume found so far is 144 cubic units for the rectangular prism with the greater volume and 72 cubic units for the one with the lesser volume. Possible dimensions include:

2 x 8 x 9 for the greater volume and 4 x 3 x 6 for the lesser volume

8 x 6 x 3 for the greater volume and 2 x 4 x 9 for the lesser volume

2 x 8 x 9 for the greater volume and 4 x 3 x 6 for the lesser volume

8 x 6 x 3 for the greater volume and 2 x 4 x 9 for the lesser volume

Source: Joe Schwartz and Robert Kaplinsky

The post Volume of Rectangular Prisms 2 first appeared on Open Middle®.]]>How can dividing by a single digit by a fraction result in a two-digit quotient?

The greatest possible quotient is 72 from either 9 ÷ 1/8 = 72 or 8 ÷ 1/9 = 72.

Source: Robert Kaplinsky

The post Dividing Fractions 4 first appeared on Open Middle®.]]>How can dividing by a single digit by a fraction result in a two-digit quotient?

There are many possible answers including 9 ÷ 1/3 = 27 and 9 ÷ 1/5 = 45.

Source: Robert Kaplinsky

The post Dividing Fractions 3 first appeared on Open Middle®.]]>How can you tell how close your product is to 4/11? How can you tell which of two fractions is closest?

The closest product to 4/11 is 5/7 x 1/2 (or equivalents like 1/2 x 5/7 or 5/7 x 2/4).

Source: Robert Kaplinsky

The post Multiplying Fractions 6 first appeared on Open Middle®.]]>How can there be more than one way to make a product of 2/3?

There are many possible answers including 4/3 x 1/2.

Source: Robert Kaplinsky

The post Multiplying Fractions 5 first appeared on Open Middle®.]]>What two-digit numbers would be too low/high that when multiplied together would not make a three-digit product?

The greatest possible product found so far is 62 x 15 which equals 930 but there may be one even greater. Let us know in the comments what you find.

Source: Robert Kaplinsky

The post Multi-Digit Multiplication 2 first appeared on Open Middle®.]]>What two-digit numbers would be too low/high that when multiplied together would not make a three-digit product?

There are many possible true equations including 32 x 15 = 480 and 52 x 15 – 630.

Source: Robert Kaplinsky

The post Multi-Digit Multiplication 1 first appeared on Open Middle®.]]>How can you have values that are equivalent when rounded to the nearest tenth yet have different whole number values?

There are many possible answers which all round to 2.0 including 1.978 and 2.043.

Source: Robert Kaplinsky

The post Rounding Decimals 3 first appeared on Open Middle®.]]>How can you have values that are equivalent when rounded to the nearest tenth yet have different whole number values?

There are many possible answers including 5.971 and 6.043 which both round to 6.0.

Source: Robert Kaplinsky

The post Rounding Decimals 2 first appeared on Open Middle®.]]>How do the order of operations tell you what you should do first? What possible values can you make on the left/right side of the equals sign? Which side would it be better to start with?

The greatest possible value for both sides of the equal sign is 76 which comes from a few possibilities including 76 ÷ (3 – 2) = 4 + 9 x 8.

Source: Robert Kaplinsky

The post Evaluating Expressions 2 first appeared on Open Middle®.]]>