Common multiplication and division situations.
- Listed: January 5, 2020 10:10 pm
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Description
Table 2. Common multiplication and division situations.7
| Unknown Product | Group Size Unknown
(“How many in each group?” Division) |
Number of Groups Unknown
(“How many groups?” Division) |
|
| 3 x 6 = ? | 3 x ? = 18, and 18 ¸ 3 = ? | ? x 6 = 18, and 18 ¸ 6 = ? | |
| Equal Groups | There are 3 bags with 6 plums
in each bag. How many plums are there in all? Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether? |
If 18 plums are shared equally
into 3 bags, then how many plums will be in each bag? Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be? |
If 18 plums are to be packed 6
to a bag, then how many bags are needed? Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have? |
| Arrays,4
Area5 |
There are 3 rows of apples
with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle? |
If 18 apples are arranged into 3
equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it? |
If 18 apples are arranged into
equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it? |
| Compare | A blue hat costs $6. A red hat costs 3 times as much as the
blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long? |
A red hat costs $18 and that is
3 times as much as a blue hat costs. How much does a blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first? |
A red hat costs $18 and a blue
hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first? |
| General | a × b = ? | a × ? = p, and p ÷ a = ? | ? × b = p, and p ÷ b = ? |
4The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable.
5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations.
7The first examples in each cell are examples of discrete things. These are easier for students and should be given
before the measurement examples.
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