Add Two-Digit Numbers

Overview

In Lesson 20 of 30 in Building Mathematical Thinking, students add two-digit numbers by separating tens and ones. They connect concrete models, drawings, expanded form, and written equations, beginning with no regrouping before solving problems that require composing a new ten.

Learning intentions

• Students will be able to add two-digit numbers using place value.
• Students will be able to model addition with base-ten blocks, drawings, or expanded form.
• Students will be able to explain when and why regrouping is needed.
• Students will be able to choose a strategy that matches their level of independence.

Success criteria

• I can add tens to tens and ones to ones.
• I can model and solve a two-digit addition problem with no regrouping.
• I can model and solve a problem that requires regrouping.
• I can explain my strategy using words, drawings, or an equation.

Curriculum links

• Adding two-digit numbers using place value, concrete models, drawings, and written methods.
• Fluently adding and subtracting within 100 using place-value strategies.
• Finding 10 more or 10 less mentally and explaining the reasoning.
• Comparing the value of tens and ones in two- and three-digit numbers.

Lesson structure (30 minutes)

1. 0–4 min · Warm-up and hook. Teacher opens with the number-story hook and asks, “How could we find the total without counting by ones?” Students solve 24 + 13 with a partner, share an estimate, and identify the tens and ones in each number.

2. 4–10 min · Model place value. Teacher displays the place-value model slides and models 24 + 13 with color-coded base-ten blocks: 2 tens + 1 ten and 4 ones + 3 ones. Students build or draw the numbers, combine tens and ones, and record 30 + 7 = 37.

3. 10–15 min · Model regrouping. Teacher uses the regrouping example to model 28 + 17, emphasizing that 8 ones + 7 ones makes 15 ones, which can be exchanged for 1 ten and 5 ones. Students represent the exchange with blocks or a drawing and explain, “I regrouped because I had 10 or more ones.”

4. 15–24 min · Guided practice. Teacher distributes the differentiated two-digit addition worksheet and supports students through the first problems, starting with no-regrouping examples and then offering regrouping problems as ready. Students solve using base-ten blocks, aligned templates, grid paper, expanded form, or equations; partners compare strategies using the prompts on the worksheet.

5. 24–27 min · Share and check. Teacher returns to the strategy discussion slides and displays 36 + 25. Students use a quiet think time, then explain whether their answer is 51 or 61 and justify it with a model, expanded form, or place-value explanation.

6. 27–30 min · Exit check. Teacher displays the exit prompt and asks students to complete one independent problem: 47 + 26. Students show a model or equation and finish the sentence, “I regrouped/did not regroup because …”

Resources

• the place-value and strategy slide deck
• the differentiated two-digit addition worksheet
• Base-ten blocks or bundled straws
• Two-color pencils or crayons for tens and ones
• Individual whiteboards and markers
• Grid paper
• Aligned place-value addition templates
• Number cards showing two-digit addends

Assessment

• During modeling, check whether students separate tens and ones and combine like place values.
• During guided practice, ask individual students to explain why regrouping is or is not needed; record whether they use a model, expanded form, or equation accurately.
• Use the exit problem to identify students who can solve independently, students who need continued concrete support, and students ready for mental strategies.

Differentiation

• Support: Begin with no-regrouping problems and use base-ten blocks, aligned templates, and color-coded tens and ones. Keep the addends within a manageable range and provide a worked example beside the first problem.
• Scaffolds: Offer sentence frames such as “I added ___ tens and ___ tens” and “I regrouped because ___.” Read directions aloud, give one step at a time, and allow students to respond orally or by pointing to a model.
• Dyslexia-friendly options: Use a clear sans-serif font, large spacing, minimal decoration, reduced visual load, strong alignment of digits, and consistent colors for tens and ones. Do not require students to read lengthy instructions independently.
• Extension: Students solve selected problems mentally, including examples such as 38 + 27, and justify how they recognized or managed regrouping without drawing every block. They may create a two-digit addition problem whose sum is between 70 and 90 and explain their choices.

Extension

• Solve 46 + 38 mentally in two different ways, such as making a ten or adding tens first.
• Explain why a solution is reasonable by estimating the total before calculating.
• Write a new two-digit addition story problem that requires regrouping and solve it using expanded form.