Add and Subtract Two-Digit Numbers with Tens

Introduction

This lesson plan will teach your learner how to add and subtract two-digit numbers with tens. This lesson builds on understanding addition and subtraction of multiples of ten and emphasizes recognizing patterns in the tens and ones digits.

Before beginning the lesson, your learner should be able to add and subtract two-digit numbers with ten.

Key Concepts to Add and Subtract Two-Digit Numbers with Tens

• Unitizing: Unitizing involves grouping numbers into units, such as tens, to simplify addition and subtraction. For example, adding 20 + 30 can be seen as 2 tens + 3 tens, which can be solved using the simpler number fact of 2 + 3.
• Number Facts: Number facts refer to basic addition and subtraction within 10, such as 3 + 7 = 10 or 8 - 5 = 3. Fluency in these basic facts is crucial for working efficiently with larger numbers.
• Manipulatives and Visual Aids: Tools like Gattegno charts and base-ten blocks will be used in the lesson plan to help learners see the tens and ones structure, making it easier to recognize patterns and understand the relationship between numbers.
• Transition from Visual to Abstract: The lesson plan starts with adding and subtracting on a number line, a helpful visual tool for grasping concepts. This foundation supports the transition to focusing on equations, number facts, and the place value of digits, which are more abstract concepts.

Teaching Plan

The following activities will help your learner to confidently add and subtract two-digit numbers with multiples ten.

Examples and visuals to support the lesson:

1. Reviewing Addition and Subtraction in Multiples of Ten

Begin by reviewing addition and subtraction in multiples of ten. Emphasize unitizing and using known addition and subtraction facts. Use the following stem sentences to reinforce the concepts:

• "I know that ___ plus ___ is equal to ___."
• "So, ___ tens plus ___ tens is equal to ___ tens."
• "I know that ___ minus ___ is equal to ___."
• "So, ___ tens minus ___ tens is equal to ___ tens."

Skill Check
I can add and subtract multiples of 10.

2. Adding Multiples of Ten to a Two-Digit Number

• Introduce addition of a multiple of ten to a two-digit number (e.g., 45 + 30) using a skip-counting approach. Count on in tens from the two-digit number using a number line, hundred square, or Gattegno chart.
• Ask questions to help them identify patterns: "What do you notice about the tens digits? What do you notice about the ones digits?"
• Next, show them that while skip-counting works, there is a more efficient strategy. First, partition the two-digit number into tens and ones. Then, add the tens using a known addition fact. Finally, recombine the tens and ones to find the sum.
• Use base-ten blocks along with equations to represent each step. For example, to find 45 + 30: Partition 45 into 40 and 5 (45 = 40 + 5 ). Add the tens (40 + 30 = 70). Combine the ones with the tens (70 + 5 = 75). Therefore, 45 + 30 = 75.

Skill Check
I can use math tools to add multiples of ten to a two-digit number.

3. Addition Practice

Work through other addition calculations including missing number problems. Also, provide a variety of problems that reinforce the use of number facts.

• Provide a set where the two-digit number is kept same and vary the multiple of ten. For example: 32 + 10, 32 + 20, 32 + 30. These and be solved using the number facts 3 + 1, 3 + 2, and 3 + 3.
• Then provide a set where the two-digit number varies and the multiple of ten stays the same. For example: 15 + 30, 25 + 30, 35 + 30. These can be solved using the number facts 1 + 3, 2 + 3, and 3 + 3.
• Use the following stem sentence to draw attention to the structure: "__ tens and ___ ones, plus ___ tens, is equal to ___ tens and ___ ones."

Skill Check
I can use what I know about numbers to add multiples of ten to a two-digit number.

4. Subtracting Multiples of Ten from a Two-Digit Number

• Once your learner can confidently add multiples of ten, progress to subtracting of a multiple of ten from a two-digit number. Follow the same sequence of activities that were used with addition.
• Start with the less-efficient method of skip counting back in tens, using a number line, hundred square, or Gattegno chart. Then, demonstrate the more efficient method using base-ten blocks to represent the steps.
• Draw attention to the known number fact being used to subtract the multiples of ten.

Skill Check
I can use math tools to subtract multiples of ten from a two-digit number.

5. Subtraction Practice

Work through other subtraction calculations including missing number problems. Once again, provide a variety of problems that reinforce the use of number facts.

• Provide a set where the two-digit number is kept same and vary the multiple of ten. For example: 97 - 10, 97 - 20, 97 - 30. These and be solved using the number facts 9 - 1, 9 - 2, and 9 - 3.
• Then provide a set where the two-digit number varies and the multiple of ten stays the same. For example: 47 - 30, 57 - 30, 67 - 30. These can be solved using the number facts 4 - 3, 5 - 3, 6 - 3.

Skill Check
I can use what I know about numbers to subtract multiples of ten from a two-digit number.

Summary

By the end of this lesson plan, your learner will confidently add and subtract two-digit numbers and tens. They will understand the patterns in digits and how applying number facts can help simplify calculations. This will give your learner a strong foundation for more advanced arithmetic strategies.

Teaching Plan adapted from NCETM under OGL license v3.