Two-Digit Numbers Plus and Minus 1

Introduction

In this lesson plan, your learner will explore two-digit addition on number lines as a strategy for adding two-digit and one-digit numbers. This will help them build a strong understanding of place value and addition concepts.

Before beginning the lesson, your learner should be familiar with number lines up to 100 and be able to add and subtract 1.

Key Concepts for Two-Digit Numbers Plus and Minus 1

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

• One More and One Less: The concepts of "one more" and "one less" help learners understand the relationship between consecutive numbers. For example, 24 is one more than 23, and 23 is one less than 24.
• Using Visual Aids: Number lines and number charts can help learners visualize the relationships between numbers that are one more and one less. For example, one a number line, you can highlight consecutive numbers and show that moving to the right adds 1 and moving to the left subtracts 1.
• Representing with Equations: Once learners grasp "one more" and "one less," they can connect these concepts to addition and subtraction equations. For instance: 23 + 1 = 24 and 24 - 1 = 23. Pay special attention to calculations involving the tens boundary or multiples of ten, such as: 19 + 1 = 20 (reaching 20, a multiple of ten) and 20 - 1 = 19 (subtracting from a multiple of ten).
• Effect on Tens and Ones Digits: During the lesson, focus on how adding or subtracting 1 affects the tens and ones digits in a two-digit number. For example, when adding one to 35, the ones digit increases from 5 to 6, and the tens digit remains 3 (35 + 1 = 36). However, when adding one to 39, the ones digit changes from 9 to 0 while the tens digit increases from 3 to 4 (39 + 1 = 40).

Teaching Plan

The following activities will help your learner become confident with calculating two-digit numbers plus and minus 1. Be sure to work at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Revisiting One More and One Less

• Ensure your learner is confident in counting forwards and backwards in ones to/from 100. They should be familiar with the concept of "one more" and "one less" than a given number up to 10.
• Gradually, extend this knowledge to two-digit numbers. For example, 56 = 55 + 1 because 56 is the number after 55 and 54 = 55 — 1 because 54 is the number before 55.
• Use a number line or Gattegno chart to identify the difference between two adjacent two-digit numbers, emphasizing that the difference is always one ("one more" or "one less").
• For example, ask your learner to identify one more or one less than 54 using the number line. Or on the Gattengo chart, tap on 54 and have them tap on 55 while saying "fifty-five" for one more and tap on 53 while saying "fifty-three" for one less.

Skill Check
I can find one more and one less of a two-digit number.

2. Adding and Subtracting One

• Once your learner is confident with using number lines, move on to representing one more and one less using quantity-value representations such as bead bars, bead strings, or base-ten blocks.
• Show that when adding one, the number of ones increases by one, and when subtracting one, the number of ones decreases by one.
• Use base-ten blocks to represent two adjacent numbers and ask your learner to identify what's the same, what's different, and the addition and subtraction sentences that link the two numbers.
• Explore other representations to deepen your learner's understanding. For example, show the digits on a place-value chart alongside base-ten blocks that represent the same number. Work towards identifying the change of one in the ones digit.
• Demonstrate how to write equations to record what is shown with the visual aids.

Skill Check
I can use different math tools add and subtract one from a two-digit number.

3. Adding Across Tens Boundaries

• Once your learner can add and subtract one without crossing the tens boundary, move on to adding one to a number ending in nine and subtracting one from a multiple of ten.
• Represent these additions and subtractions with both ordinal models (bead bars or number lines) and Dienes blocks. Draw attention to what is the same in each example.
• Show how adding one more to 19 leads to regrouping, changing ten ones into one group of ten.

Skill Check
I can add one to a number ending in 9 and subtract one from multiples of ten.

4. Varied Practice

Provide varied missing number problems and word problems for practice. Here are some examples of word problems in real-life contexts:

• "Saskia bought a chocolate bar for fifty-nine pence and a sweet for one penny. How much did Saskia spend in total?" (Aggregation)
• "Faris bought a bouncy ball that cost forty-nine pence. He gave the shopkeeper fifty pence. How much change did Faris get?" (Partitioning)
• "At first Tiffany had seventy-four marbles; then her friend gave her another marble. How many marbles does Tiffany have now?" (Augmentation)
• "At first the baker had twenty-five cakes; then someone bought one cake. How many cakes does the baker have now?" (Reduction)
• "Ollie built a tower sixty-seven centimetres tall. Sarah’s tower is one centimetre shorter than Ollie’s tower. How tall is Sarah’s tower?" (Difference)

Skill Check
I can solve missing number problems and word problems that have two-digit numbers plus or minus one.

Summary

By the end of this lesson plan, your learner will confidently use "two-digit addition on number lines" and understand "adding two-digit and one-digit numbers" using number lines. They will use practical, pictorial, and abstract representations to solve addition problems, making math both engaging and intuitive.

Teaching Plan adapted from NCETM under OGL license v3.