This topic is preparation for solving word problems (application problems) based on multiplication and division. Students learn to represent a multiplicative relationship in a grid that is derived in the lessons on this topic.
Students learn to represent repeated multiplication by the same number as a multiplication table, and how the table is related to an array, which has been used to illustrate multiplication in prior lessons. The table has three rows. The bottom row shows a variable factor that is different in each column. The middle row shows the constant factor that is the same in each column, and the top row shows the product.
The purpose of using this table is to use it as the basis for a graphic organizer as support for learning to solve word problems in later lessons. When the design of the table is explained, the middle row is deleted, and the student learns that the value in the top row in the first column tells them the number that goes in every column of the middle row, so that row is no longer needed.
In the problems in this lesson, the student is given a two-row multiplication table with a single value missing. The student must use the information in the table to determine what the constant factor is and use that to determine the missing product or missing factor.
In this lesson, the two-row multiplication from the prior lesson is condensed further. In this lesson, all but two of the columns of the table are removed, resulting in a grid with four boxes – two in each row and two in each column. The numbers in the grid are defined as a multiplication number family.
In a multiplication number family displayed in this grid, the first column tells the multiplicative relationship since the bottom left box is always 1, and the upper left box is the product of 1 and some number. When given these two numbers, it’s possible to determine the missing number in the right column when the other number in that column is given. When both numbers in the right column are given, along with the 1 in the bottom left box (which is always present), the ratio of these two numbers tells the missing number in the upper left cell.
This is the graphic organizer that will be used in solving word problems in later lessons. In the problems in this lesson, students are given a multiplication number family in the grid with one of the three values (other than 1) missing. They use the information in the grid to write a multiplication sentence, with either the product or one of the factors missing.
In this lesson, students extend what the learned in prior lessons to find the missing number in a multiplication number family presented in the graphic organizer used in the last lesson. They are given a number family grid with one of the three numbers missing, as in the last lesson, but in this lesson, they find the missing number without writing a multiplication number sentence and enter the number in the grid.