Lesson 1: Addition and Subtraction Review

Getting Started

In this unit, you'll review, practice, and extend your work with whole numbers and decimal numbers. This lesson will help you brush up on your addition and subtraction skills.

Are you already pretty good at doing addition problems like these by hand?
If so, you'll be ready to do addition problems that involve decimal numbers because the algorithm used is very similar to what you already know. (Remember that an algorithm is just a step-by-step way of performing a particular task, often a calculation or problem-solving type of task.) The algorithm for adding two whole numbers might be stated like this:
  1. First, write down the numbers, one on top of the other, being sure the place value digits are lined up (ones with ones, tens with tens, etc.).
  2. Next, add the digits in the ones column. If the sum of those digits is a value greater than 9, write down the "ones" digit of this sum in the ones column under the two numbers, and write a "1" at the top of the tens column. Doing this regroups the 10 ones to the tens column as 1 ten. (Sometimes you'll hear this called "carry the 1.")
  3. Next, add all the digits in the tens column, including the "1" that was regrouped from the addition of the digits in the ones column, and write down this sum in the tens column under the two numbers.
  4. As needed, continue the same process with the hundreds column, the thousands column, and so on.
At this point in your math work, you may not consciously be thinking through the details of this algorithm every time you add two numbers together, but you're still following the steps. Go ahead and solve the three problems shown above and then share your answers with a parent.

Stuff You Need

  • 3-hole drilled card stock (kit)
  • colored pencils
  • construction paper (kit)
  • fine point dry-erase markers (kit)
  • glue or glue stick
  • Interactive Notebook
  • laminated grid (kit)
  • marker
  • scissors

Ideas to Think About

  • How are algorithms used in math?
  • Why are the standard addition and subtraction algorithms useful?

Things to Know

  • An algorithm is a step-by-step way of performing a particular task, often a calculation or problem-solving type of task.
  • Adding and subtracting multi-digit decimal numbers is very similar to adding and subtracting multi-digit whole numbers.


  • Compute fluently with multi-digit numbers
  • Fluently add and subtract multi-digit decimals using the standard algorithm for each operation
  • Solve real-world and mathematical problems involving the four operations with rational numbers

Introducing the Lesson

Unit 1 will allow your child to review, practice, and extend his work with whole and decimal numbers. In this lesson, he will apply the standard multi-digit addition and subtraction algorithm he learned in previous math courses to adding and subtracting multi-digit decimal numbers. In addition to having mastered his basic addition and subtraction facts, your child should also be familiar with the following:
  • Adding and subtracting numbers to the thousands, including addition problems that involve regrouping and subtraction problems that involve borrowing.
  • Decimal numbers and the place value system; specifically the meaning of digits in the different "columns" (e.g., the tenths column, the hundredths column, etc.)
Your child should begin by solving the three addition problems in this section:
  • 57 + 19 = 76
  • 428 + 356 = 784
  • 2,457 + 5,319 = 7,776