Add and Subtract Two-Digit Numbers with 10

Introduction

This lesson plan will teach your learner how to add and subtract two-digit numbers with 10. They will start by exploring ten more and ten less using manipulatives and visual aids. Then apply it to adding and subtracting ten. This lesson builds on understanding counting in multiples of ten and emphasizes recognizing patterns in the digits.

Before beginning the lesson, your learner should be able to add and subtract 10 with a multiple of ten.

Key Concepts to Add and Subtract Two-Digit Numbers with 10

Here are a few concepts that are helpful to know for the lesson:

• Exploring Ten More and Ten Less: Using manipulatives like base-ten blocks and visual aids such as number lines, hundred squares, and Gattegno charts to help your learner transition to adding and subtracting ten. In this lesson, we will start with using visual aids to identify ten more and ten less than a two-digit number. Employing visual aids will help your learner navigate the sequence of numbers while reinforcing their understanding of the structure of numbers.
• Transitioning to Addition and Subtraction: Using manipulatives like base-ten blocks and visual aids such as number lines, hundred squares, and Gattegno charts to help your learner transition to adding and subtracting ten. Ultimately the goal is for them to get comfortable solving equations without relying on the visual aids.
• Recognizing Patterns in Digits: Throughout the lesson, your learner's attention will be drawn to recognizing patterns in the digits while adding and subtracting ten. For instance, they will recognize that the tens digit changes while the ones digit remains the same, helpint them to develop fluency in adding and subtracting ten.

Teaching Plan

The following activities will help your learner become confident with adding and subtracting two-digit numbers with ten.

Examples and visuals to support the lesson:

1. Revisiting Counting in Multiples of Ten

• Start by revisiting counting forwards and backwards in multiples of ten.
• Use visual aids like number lines, hundred squares, or Gattegno charts to show numbers that are ten more or ten less.
• Ask questions such as: "What is ten more than forty?" "What is ten less than fifty?"
• Next, explore patterns in the tens and ones digits. Use visual representations, such as a Gattegno chart, to emphasize the underlying mathematical structure.
• Draw attention to what remains the same and what changes: "When we find ten more, the tens digit changes, and the ones digit stays the same." "When we find ten less, the tens digit changes, and the ones digit stays the same."
• Once your learner is comfortable identifying patterns with multiples of ten, extend the generalized statements to all ten more/less relationships between 10 and 99.
• Use chanting and physical tapping on number lines, hundred squares, or Gattegno charts to reinforce patterns: "Fourteen, twenty-four, thirty-four..." "One-ten-four, two-ten-four, three-ten-four..."
• Practice counting using real-life contexts such as money, length, mass, and capacity. Use single pennies for the ones in money contexts to make the quantity value more evident. During counting practice, occasionally stop to ask what number comes next and why.

Skill Check
I can count by tens starting from different numbers.

2. Identifying Ten More/Ten Less

• Next, work on identifying ten more/less than a given number, using number lines, hundred squares, or Gattegno charts. Use the following stem sentences to describe relationships: "Ten more than ___ is ___. ___ is ten more than ___. Ten less than ___ is ___. ___ is ten less than ___."
• You can also incorporate manipulatives. For example, use base-ten blocks to add and remove tens blocks, while describing the process with stem sentences: "We had ___ tens and ___ ones. Ten more gives us ___ tens and ___ one's. We had ___ tens and ___ ones. Ten less gives us ___ tens and ___ ones."
• Whether working with manipulatives or visual aids, draw attention to the fact that the tens digit changes but the ones digit remains the same.
• Provide additional practice finding ten more/less than a given number, completing sequences on a number line, and solving missing number sequences. Initially use representations like number lines, hundred squares, Gattegno charts, or base-ten cubes for support. Then, progress to identifying ten more/less without the support of manipulatives and visual aids.

Skill Check
I can find ten more and ten less than a number.

3. Adding and Subtracting Ten

• Once your learner is confident identifying ten more and ten less, introduce equations alongside the concrete/pictorial representations.
• Mirror a sequence of counting on in tens: "14 + 10 = 24, 24 + 10 = 34, 34 + 10 = 44, 84 + 10 = 94." Then work backwards through the same sequence: "94 - 10 = 84, 84 - 10 = 74, 74 - 10 = 64, 24 - 10 = 14."
• Ensure that your learner understands that there is a count of ten between each highlighted number by counting in ones before moving to addition/subtraction of tens down/up the column.
• Use generalized statements: "When we add ten, the tens digit changes, and the ones digit stays the same. When we subtract ten, the tens digit changes, and the ones digit stays the same."
• Progress to working through sequences of equations without a visual scaffold, drawing on learners' knowledge of number composition and generalized statements.
• Explore the inverse relationship between the addition and subtraction of ten. Find and record ten more than a given number, then record the inverse for ten less. For example: "26 + 10 = 36, 36 - 10 = 26."
• Present addition and subtraction calculations out of sequence until your learner is confident working from any two-digit number. For example: "74 + 10, 53 - 10."

Skill Check
I know that when we add or subtract 10, the tens digit changes but the ones digit stays the same.

4. Incorporating Other Math Concepts

Use this as an opportunity to reinforce other important concepts such as commutativity of addition and using subtraction to find differences.

• Use part-part-whole models to support understanding that addition is commutative.
• Encourage your learner to realize they can use their knowledge of adding ten to find, for example, 10 + 36, rather than thinking of this calculation as finding 36 more than 10.
• Use stem sentences: "One part is ten, the other part is ___, and the whole is ___. This can be recorded as ten plus ___ is equal to __, or as ___ plus ten is equal to ___."
• Next, apply subtraction of ten from two-digit numbers to problems with the difference structure. Use a Dienes ten rod aligned with a number line to demonstrate sliding the rod along to find pairs of numbers with a difference of ten.
• Show pairs of numbers with a difference of ten on the Gattegno chart. Ask learners to identify pairs of numbers that have a difference of ten and explain how they know each pair has a difference of ten.

Skill Check
I can use different math tools to help me add and subtract two-digit numbers with 10.

5. Varied Practice

Provide practice in the form of missing number/symbol and missing part/whole problems. Also, apply addition and subtraction of ten in various real-life contexts. Here are some examples:

• "I have ten blue pens and thirty-six red pens. How many pens do I have altogether?" (aggregation)
• "First the bean sprout was twelve centimeters tall, and then it grew ten centimeters. How tall is the bean sprout now?" (augmentation)
• "I have eighty-three balls. Ten of them are footballs, and the rest are tennis balls. How many tennis balls do I have?" (partitioning)
• "I had forty-nine pence and then I spent ten pence. How much money do I have left?" (reduction)
• "My sunflower is seventy-five centimeters tall, and my friend’s sunflower is sixty-five centimeters tall. How much taller is my plant?" (difference)
• "I scored forty-three points. My friend scored ten more points than me. How many points did my friend score?" (difference)
• "My friend has ten pence more than me. He has eighty-two pence. How much money do I have?" (difference)

Skill Check
I can solve word problems that involve adding and subtracting two-digit numbers with 10.

Summary

By the end of this lesson plan, your learner will be able to confidently add and subtract two-digit numbers with 10. They will understand the patterns in digits and how working with multiples of ten simplifies calculations, laying the foundation for more advanced addition and subtraction strategies like carrying and borrowing.

Teaching Plan adapted from NCETM under OGL license v3.