Add With Place Value

Overview

In this 30-minute lesson, students add whole numbers through 100,000 by aligning place values and combining units. They build on prior work with place-value relationships and regrouping, moving from concrete blocks to a vertical addition algorithm.

Learning intentions

• Students will be able to add numbers to 100,000 using place value.
• Students will be able to line up digits by place before adding.
• Students will be able to regroup when a place has 10 or more units.
• Students will be able to explain how addends combine to make a sum.

Success criteria

• I can line up ones, tens, hundreds, thousands, and ten-thousands.
• I can add from right to left.
• I can regroup when I have 10 or more in a place.
• I can check that my sum is reasonable.

Curriculum links

• Measurement and Data — use the four operations to solve measurement and real-world problems, representing quantities clearly.
• Measurement and Data — express quantities using related units and organized tables or representations.
• Number and Operations in Base Ten — read, represent, compare, and operate with multi-digit whole numbers using the meaning of each digit.
• Mathematical practices — reason quantitatively, use tools strategically, and explain thinking.

Lesson structure (30 minutes)

1. 0–4 min · Hook and review. Teacher opens the place-value hook and review slides and displays 2,300 + 1,200, asking, “How could we combine these numbers without counting by ones?” Students turn and talk, identify the addends, and predict the sum using place-value language.

2. 4–11 min · I do: model. Teacher uses place-value blocks and a large, color-coded vertical algorithm to model 24,105 + 3,002, saying aloud: “I line up the places, start at the ones, add each column, and regroup when needed.” Students watch, name each place, and show with fingers where the digits belong. Emphasize that zeros hold places and must remain aligned.

3. 11–17 min · We do: interactive regrouping. Teacher uses the interactive digit-tile and regrouping slides to present 48,000 + 12,000 and 9 + 8. Invite students to move or direct digit tiles and regrouping cubes on the smartboard. Students solve each problem with a partner, explain what changes when 10 ones become 1 ten, and signal thumbs up when the algorithm matches the model.

4. 17–25 min · You do: guided practice. Teacher distributes the place-value addition practice worksheet and gives each pair a place-value mat, blocks, and digit tiles. Students solve two multi-digit problems, beginning with blocks and then recording the vertical algorithm; partners check alignment and regrouping. Offer an optional calculator check only after students have shown their work.

5. 25–30 min · Exit assessment and close. Teacher displays the independent check and closing slides and asks students to complete the five multiple-choice items on the worksheet independently. Students select an answer and circle or write one place-value step that helped them; review one item aloud and restate the success criteria.

Resources

• the place-value addition slide deck
• the place-value addition practice worksheet
• Place-value blocks or base-ten cubes
• Place-value mats through ten-thousands
• Digit tiles and regrouping cubes
• Smartboard or interactive display
• Pencils and colored pencils
• Optional calculators for checking completed work

Assessment

• During modeling, listen for students’ use of addend, sum, place value, and regroup. Ask, “Why must the digits be aligned?”
• During partner practice, check whether students begin at the ones place, preserve zeros, and record regrouping accurately.
• Use the five-item exit check: 1) 2,300 + 1,200 = 3,500; 2) 24,105 + 3,002 = 27,107; 3) 5,600 + 700 = 6,300; 4) 48,000 + 12,000 = 60,000; 5) 9 + 8 = 17. Items missed identify the place-value or regrouping skill needing reteaching.

Differentiation

• Support students with concrete blocks before symbols, reduced-digit examples, preprinted lined place-value grids, and color-coded columns. Keep one place color consistent across the mat, worksheet, and board.
• Pair students strategically. Give partners roles such as builder, recorder, and checker, then switch roles so each student explains the process.
• Provide dyslexia-friendly options: large, clearly aligned columns; a sans-serif font; high contrast; generous spacing; minimal visual clutter; short oral directions; and directions read aloud and repeated one step at a time.
• Provide sentence frames: “I aligned the ___ place with the ___ place,” “I regrouped because ___,” and “The sum is reasonable because ___.” Challenge ready students to create a number addition problem that requires regrouping in two places and explain its solution.