Cross Products

Prior knowledge

Background

This activity uses place value partitioning to solve multiplication problems. It uses the area model. This activity involves whole numbers and decimals in the problems. While the drawings involve using an area model to display the multiplications, (so the size of each box is in some form of proportion to the size of the numbers), it should also be noted that students can do the same problems using a table (or tabular form). In this form area is not considered.

For example: 14 x 51 can be done by using the following table (where all the boxes are the same size).

Comments on the Exercises

Exercise 1
Asks students to solve 2 digit by 1 digit multiplication using the area model to show place value multiplication. It is designed to follow on from a teaching episode in which the strategy is illustrated and used by the students. Once students have convinced themselves that the strategy works with a range of simple numbers they are ready to explore more difficult numbers including decimals.

Exercise 5
Asks students to solve multiplication problems with whole numbers between 10 and 100 for both factors.

Exercise 6
Asks students to solve multiplication problems where one of the factors is a one place decimal and the other factor is a whole number between 10 and 100.

Exercise 7
Asks students to solve multiplication problems where both factors are one decimal place decimals, using numbers less than 10 until the last question which is greater than 10.

Exercise 8
Asks students to find unknowns in problems that involve two decimals to 1dp.

Exercise 9
Asks students to solve word problems. Students may need to be encouraged to use units appropriately.

Exercise 10
Asks students to investigate the use of the strategy for numbers in the 100s

Exercise 11
This exercise introduces x as a length added to both sides of the rectangle and requires students to multiply the algebra and add like terms.