Question

a teacher asks students to place tiles on the classroom wall to show the alphabet. the tiles will each have one letter or be blank. each letter will have only one tile. the list shows the teachers rules for the arrangement of tiles. think about the lowest multiple of 4 that is the same or greater than the number of letters of the alphabet. 1. they must form a rectangle. 2. the rectangle must have 4 rows. 3. the rectangle must have the least possible number of columns. how many columns of tiles will there be? how many blank tiles will be used? what multiplication fact helped you solve the problem?

Explanation:

Step1: Determine number of letters in alphabet

There are 26 letters in the alphabet.

Step2: Find the lowest multiple of 4 greater than or equal to 26

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28... The lowest multiple of 4 that is the same or greater than 26 is 28.

Step3: Calculate number of columns

Since the rectangle must have 4 rows and the total number of tiles is 28 (to form a rectangle with the least - possible number of columns), and we know that the number of tiles \(N = \text{rows}\times\text{columns}\). Given \(N = 28\) and \(\text{rows}=4\), then \(\text{columns}=\frac{28}{4}=7\).

Step4: Calculate number of blank tiles

The number of letters is 26, and the total number of tiles is 28. So the number of blank tiles is \(28 - 26=2\).

Step5: Identify the multiplication fact

The multiplication fact \(4\times7 = 28\) (or \(7\times4 = 28\)) helped solve the problem.

Answer:

• How many columns of tiles will there be? 7
• How many blank tiles will be used? 2
• What multiplication fact helped you solve the problem? \(4\times7 = 28\) (or \(7\times4 = 28\))