Operation Track

Operation Track

Operational tracks are found in all four modules of the Corrective Mathematics Series. These tracks consist of teaching problem-solving routines that allow students to work with a wide variety of computational problems. These routines include all subtypes of problems that students might encounter while working with maths for academic purposes and in their everyday lives, such as borrowing from zero in subtraction and multiplying a number by zero in a ones column.

Each module teaches problem-solving routines in different stages. For example, the Subtraction module introduces pre-skills for borrowing, which subsequently assist students in applying the skills in the Multiplication and Division operations and problems.

The module-wise description of the stages in which students are taught problem-solving routines in the operations tracks are:

Addition:  

• Adding columns of single-digit numbers.  
• Adding columns of multi-digit numbers without carrying.  
• Writing only the number being carried in a box of tens column numbers, with the sums for the ones column provided.  
• Adding numbers carrying from tens to hundreds, without a box or sum provided.  

Subtraction: 

• Subtracting the bottom numbers from the top numbers in one column number.
• Pre-skills for borrowing are taught. These skills include teaching students how to borrow, when to borrow, which column to borrow from, rewriting numbers after borrowing and subtracting numbers after borrowing. 
• Work with four types of problems: borrowing from one column, zero, consecutive columns, and as many as three consecutive columns.

Multiplication:  

• Non-carrying column problems and horizontal problems with counters.  
• Introducing carrying and writing carrying numbers in a box.  
• Multiplying 2-digit numbers. 

Division: 

• Single-digit divisor problems. Students learn to underline the part of the dividend that is at least as big as the divisor, resulting in up to 3-digit answers, answers with zero in the middle, and the final digit. 
• Work with underlined problems to find the remainder.  
• Round off the divisor and underline part of the problem to the nearest tens number when working with 2-digit divisors.  

Exercise 6 from Lesson 18 on page 54 of the Series Guide is an example in which the students learn all the steps required in a borrowing problem with one column, while showcasing the previously learned pre-skills at work.