Add and subtract within 100

Here you will learn how to add and subtract within 100, including adding and subtracting two-digit numbers using base ten blocks, number lines, the break apart strategy or mental math, and the standard algorithm.

Students will first learn about adding and subtracting within 100 as part of number and operations in base ten in 2 nd grade.

What is adding and subtracting within 100?

Adding and subtracting within \bf{100} is when you add or subtract two-digit numbers using place value strategies and models, such as base ten blocks, or the standard algorithm.

Students will first begin adding within 100 in first grade including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using the strategies shown below.

However, according to the CCSS, they do not begin adding and subtracting 2 -digit numbers as the examples show until second grade.

To add within 100 using base ten blocks:

• Draw the base ten blocks to represent the tens and ones. For addition, combine the tens and combine the ones. Regroup if necessary, then count the total tens and total ones. See the examples below.

To subtract within 100 using base ten blocks:

• Draw the larger number, then cross off the number of tens and ones in the smaller number. Count the remaining tens and ones.
  Note that if there are not enough ones to cross off, you’ll need to exchange 1 ten for 10 ones first. See the examples below.

To add and subtract within 100 using a number line:

• Draw a number line and use it to visually add or subtract. Move forward on the number line for addition and backward for subtraction.

To add and subtract within 100 using mental math or the break apart strategy:

• Split each number into tens and ones. Add or subtract the tens. Add or subtract the ones together. Then combine the remaining tens and ones.

To add within 100 using the standard algorithm:

• Stack the numbers vertically, placing the larger addend on top; be sure to line up the place values correctly. Start by adding the numbers in the smallest place value (the ones place). If the sum is greater than 9, carry over the tens place to the next column. Continue adding each column, regrouping as needed, until all columns are added.

To subtract within 100 using the standard algorithm:

• Stack the numbers vertically, placing the larger addend on top; be sure to line up the place values correctly. Start by subtracting the numbers in the smallest place value (the ones place). If the digit on top is smaller than the one below, borrow from the next higher place value. Continue subtracting each column, borrowing as needed, until all columns are subtracted.

What is adding and subtracting within 100?

Common Core State Standards

How does this relate to 2 nd grade math?

• Grade 2: Number and Operations in Base Ten (2.NBT.B.5)
  Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• Grade 2: Operations and Algebraic Thinking (2.OA.A.1)
  Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

How to add and subtract within 100

In order to add and subtract within 100\text{:}

1. Choose a strategy (Base ten, Number line, Break apart / Mental math, Standard algorithm).
2. Solve.

Add and subtract within 100 examples

Example 1: two-digit addition (base ten blocks)

1. Choose a strategy (Base ten, Number line, Break apart / Mental math, Standard algorithm).

You can use base ten blocks to add. Set up using base ten blocks to represent each number.

2Solve.

Combine the tens and the ones, then counting the total. For this problem, you’ll need to regroup 10 ones into 1 ten before counting the totals.

Example 2: two-digit subtraction (base ten blocks)

Choose a strategy (Base ten, Number line, Break apart / Mental math, Standard algorithm).

You can use base ten blocks to subtract. Set it up by using base ten blocks to represent the larger number only.

Solve.

Solve by removing the number of tens (2) and then the number of ones (4). Count the remaining tens and ones to get the answer.

Example 3: two-digit addition (number line)

Choose a strategy (Base ten, Number line, Break apart / Mental math, Standard algorithm).

Start by drawing a number line and marking the largest number at the front of the number line.

Solve.

Jump forward the number of tens in the second number. Then move forward to add the ones. This could be broken up to get to the next 10, and then add the remaining number of ones.

As an alternative to help with regrouping, you can jump just enough ones to get to a ten first. So in this case, instead of adding 7 ones at once, you add 7 to get to 50, then add 10 to get to 60, then add the remaining 2 ones.

Example 4: two-digit subtraction (number line)

Solve.

Jump backward the number of tens in the second number. Then move backward to subtract the ones. This could be broken down into two jumps.

Example 5: two-digit addition (break apart strategy)

Example 6: two-digit subtraction (break apart strategy)

Example 7: addition word problem (standard algorithm)

A farmer placed 38 red apples and 26 green apples into a basket. How many apples are in the basket altogether?

Choose a strategy (Base ten, Number line, Break apart / Mental math, Standard algorithm).

You can use the standard algorithm to solve this addition word problem.

To set it up, stack the numbers vertically, lining up the place values.

Solve.

To solve, add the digits in the ones column first. Since the sum of these two digits is greater than 10, you need to carry the ten to the next column (the tens column). Then you can add the digits in the tens column (along with the 1 ten that was carried over).

Example 8: subtraction word problem (standard algorithm)

Jack had 74 marbles. He gave 18 marbles to his friend. How many marbles does Jack have now?

Choose a strategy (Base ten, Number line, Break apart / Mental math, Standard algorithm).

You can use the standard algorithm to solve this subtraction word problem.

To set it up, stack the numbers vertically, lining up the place values.

Solve.

To solve, subtract the digits in the ones column first. Since there aren’t enough ones in the number on top, you need to exchange a ten from the next column (the tens column).

Then you can subtract the ones, then the tens.

Teaching tips for adding and subtracting within 100

• Create printable worksheets with mixed addition and subtraction problems within 100 that include an answer key for students to self-assess their work and check for errors. (Start with just addition worksheets and subtraction worksheets before creating mixed worksheets.)

• Make room for math games and flashcards in lesson plans to allow students to continuously practice addition and subtraction facts. This will help prevent calculation errors when adding and subtracting within 100 and boost 1 st grade math skills.

• Use models such as number bonds to help students determine what operation to use when solving word problems.

• Give students completed examples of adding and subtracting using the standard algorithm with missing numbers and ask them to fill in the blanks. This will help them build a stronger understanding of the standard algorithm and prepare them for 3 rd grade math and beyond.

• Encourage students to use number bonds to determine if a word problem is an addition problem or a subtraction problem.

Easy mistakes to make

• Forgetting to regroup or exchange
  Students may forget to regroup or exchange when the sum or difference exceeds 9 in one place value.

• Misaligning digits in the standard algorithm
  When using the standard algorithm, digits must be stacked vertically, aligning the digits that are in the same place value. Not doing so will lead to calculation errors.

Related addition and subtraction lessons

• Addition and subtraction
• Adding and subtracting integers
• Adding and subtracting rational numbers
• Adding and subtracting negative numbers
• Standard algorithm addition

The next lessons are

• Multiplication and division
• Types of numbers
• Rounding numbers

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