Build a New Ten

Overview

Students use color-coded place-value mats and base-ten blocks to add two-digit numbers with regrouping. The teacher models the place-value rule, then students physically trade ten ones for one ten before explaining their thinking to a partner.

Learning intentions

Students will be able to:

• Add two-digit numbers using place-value strategies and an algorithm.
• Regroup ten ones as one ten when the ones column reaches 10 or more.
• Model addition with base-ten blocks and a place-value mat.
• Explain why regrouping is needed in an addition problem.

Success criteria

• I can line up ones with ones and tens with tens.
• I can add the ones and trade ten ones for one ten when needed.
• I can add the tens after regrouping.
• I can explain, “I regrouped because the ones made 10 or more.”

Curriculum links

• Addition and subtraction within 20: developing accuracy and automaticity with basic facts.
• Adding up to four two-digit numbers using place value, mental strategies, and algorithms.
• Solving one-step addition word problems within 1,000 using place-value strategies.
• Generating and solving a situation represented by an addition number sentence.

Lesson structure (20 minutes)

1. 0–3 min · Hook and connect. Open the hook and place-value slides and show 27 + 15 with a visual of ones cubes filling a ten-frame; ask, “What could we do if we have more than nine ones?” Students turn and talk, then identify the tens and ones in each number.

2. 3–7 min · Explicit model. Display the color-coded tens and ones mat from the regrouping model. Build 27 with two tens rods and seven ones, and 15 with one ten rod and five ones. Students help combine the ones, count 12, and state the rule: “When the ones total is 10 or more, we regroup by trading ten ones for one ten.”

3. 7–11 min · Guided physical practice. Give each student or pair a place-value mat and base-ten blocks. Follow the guided practice directions to solve 34 + 28: students build both numbers, combine the ones, physically trade ten ones for one ten, move the new ten to the tens column, and count the total. Teacher prompts, “How many ones can stay? What did you trade? How many tens now?”

4. 11–14 min · Record the algorithm. Distribute the color-coded regrouping worksheet. Model recording 34 + 28 vertically, matching the worksheet colors: ones in blue, tens in red. Students write 12 in the ones place, record 2 ones and regroup 1 ten, then add the tens to find 62. Emphasize that the regrouped ten is written above the tens column, not added as an extra one.

5. 14–18 min · Partner show and explain. Partners solve one problem from the worksheet, such as 46 + 27, using blocks first and the written method second. Using the visual step cards on the partner show-and-explain slides, Partner A points to each step and explains with a sentence frame: “I regrouped because ___.” Partner B checks the ones, the trade, and the total, then partners switch roles.

6. 18–20 min · Exit check and close. Reveal the exit problem on the exit prompt: 25 + 18. Students solve it on the bottom of the worksheet, draw or circle the regrouped ten, and complete, “I regrouped because the ones made ___.” Collect responses and briefly celebrate accurate explanations.

Resources

• the complete addition regrouping slide deck
• the color-coded regrouping worksheet
• Color-coded place-value mats with tens and ones columns
• Base-ten blocks for each student or pair
• Visual step cards for build, combine, trade, record, and explain
• Pencils and colored crayons or highlighters
• Document camera or interactive display

Assessment

• During modeling and guided practice, check whether students align place values, count the ones accurately, and trade exactly ten ones for one ten.
• Listen for the language “10 or more ones” rather than “I borrowed because I had to,” and ask students to explain the value of the trade.
• Use the exit problem to identify whether students can model or record regrouping and explain why it is necessary.

Differentiation

• Provide a large, uncluttered mat, pre-bundled groups of ten, visual step cards, and one-step teacher prompts for students receiving special education services.
• Use color consistently: red for tens, blue for ones. Allow students to point, draw, build, or verbally explain before writing.
• Offer sentence frames: “I started with ___ ones,” “I traded ___ ones for ___ ten,” and “My answer is ___ because ___.”
• For students ready for more challenge, provide three addends, such as 24 + 18 + 12, and ask them to decide when regrouping is most efficient. Pair multilingual learners with a supportive peer and preview the words tens, ones, combine, trade, and regroup.