Guided Lessons

# Regrouping with Base-Ten Blocks

Dive deep into using base-ten blocks to solve two-digit subtraction problems with regrouping. This lesson can be used independently or in conjuction with the lesson Double Trouble: Subtraction Practice.
This lesson can be used as a pre-lesson for the Double Trouble: Subtraction Practice lesson plan.

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This lesson can be used as a pre-lesson for the Double Trouble: Subtraction Practice lesson plan.

Students will be able to subtract two-digit problems with regrouping.

##### Language

Students will be able to describe what it means to regroup using base-ten blocks and a sentence frame.

(8 minutes)
• Write the problem 15 ____ 5 = ____ on the whiteboard. Represent the missing operation and difference with a blank circle or line. Say, "I have a problem and I need help solving it! I made 15 cookies to give to my friends. My dad ate 5 cookies before he knew I was giving the cookies to my friends! I have 10 friends and I really wanted to give each of my friends a cookie. Will I have enough cookies for my friends? How can I solve this problem?"
• Allow a student or two to share out their ideas about how to solve the problem. Guide them as they share out, and discuss whether the problem needs an addition sign or a subtraction sign. Encourage them to explain their reasoning by using some of the following prompts:
• What do you mean by...?
• Can you tell me more about...?
• Can you give me an example of...?
• Clarify that the subtraction sign is the correct choice because when we subtract, we figure out the difference of two numbers. Explain that the difference is the result of subtracting one number from another. The difference is how much two numbers differ from each other in value. Have students repeat after you, "When we subtract, we find the difference." Come up with a movement to support student understanding.
• Record the subtraction sign in the problem so it reads: 15 – 5 = ____. Next, put students into groups of four and provide whiteboards and whiteboard markers, base-ten blocks, number lines, a hundreds chart, and manipulatives (e.g. beads, gems, stones, etc.) to each group of students.
• Tape the large anchor chart labeled "Subtraction Strategies" on the board.
• Discuss the subtraction strategies aloud with the students. For example, say, "One way you can solve this subtraction problem is to draw a picture." Refer to the visuals on the anchor chart to support student understanding.
• Give students 2–3 minutes to solve the subtraction problem as a group. Have students share the strategy they used out loud. Put a tally mark to the left of the anchor chart on the whiteboard to represent the strategy each group used.
• Explain to the students that each group used a strategy, or plan of action, to solve the problem. Explain to the students that there are many different strategies we can use to solve subtraction problems. Say, "Today, we will learn about what it means to regroup and how regrouping with base-ten blocks can support us when we solve two-digit subtraction problems."
(8 minutes)
• Get out base-ten blocks (ones and tens), the Place Value Mat: Two-Digit Numbers worksheet (preferably laminated), and turn on the projector or document camera. On the paper, write 24 – 16, vertically. Make sure place values are aligned. Next, provide a real-life story about what the numbers represent so students can connect with the math problem. Say, "We are going to pretend that these numbers represent spiders. I have 24 spiders total in my yard. You think that's a lot? I love spiders! Unfortunately, I also have a lot of toads. So sometimes the spiders go missing. Did you know some toads eat spiders? I had 24 spiders in my yard. The toads ate 16 spiders. How many spiders do I have left?"
• Ask the students to share if you will need to add or subtract, based on the problem you shared and the symbol in the math problem. Provide the following sentence frame to support students as they share their ideas with an elbow partner:
• I think we need to ____ (add/subtract) because ____.
• Clarify that you will need to subtract. Say, "Who remembers what subtraction is?" Have students turn and talk to a partner, sharing their answer, and encourage them to do the movement that represents subtraction as well.
• Tell the students that you are going to solve the problem using the strategy of base-ten blocks. Ask the students to stand up if they have ever used base-ten blocks. Count out two groups of ten and four ones from the blocks. Make sure you count by ones and touch each block up to 24. Place the blocks in the correct column on the Place Value Mat: Two-Digit Numbers. Next, explain to the students that toads ate 16 of the spiders.
• Ask students if you have enough ones to subtract 16. Show them that you can use one group of ten, but you only have four ones. Say, "Ten and four equals fourteen. Is that enough to make 16?" Have a student share their reasoning. Next, tell the students you must regroup by breaking down a 10 rod into 10 ones. Explain that regrouping in subtraction is when you borrow value from a higher place value.
• Count how many ones are now available. Say, "There are 14 ones, but I need to subtract 16." Continue by saying, "I don't have enough ones, but I can use a group of 10. I'm going to subtract one group of 10. How many ones do I need to subtract?" Reinforce that you need to subtract 6 ones. Encourage a student to help you count the difference of 24 – 16. Write the answer of 24 – 16 = 8 on the board. Say, "I had 24 spiders in my yard. 16 spiders were eaten by toads. Now, I only have 8 spiders left in my yard. The difference between 24 and 16 is 8."
• Explain to the students that now they will try using base-ten blocks to regroup with partners!
(10 minutes)
• Put students into pairs and pass out a set of the Subtraction Flashcards: Two-Digit with Regrouping to each partnership. Give each pair one answer sheet, a Place Value Mat: Two-Digit Numbers worksheet, and enough base-ten blocks to effectively solve the problems.
• Explain to the students that they are going to solve the subtraction problems with their partner, using base-ten blocks.
• Ask students to turn and talk to their partners, explaining the concept of regrouping. Reiterate that in subtraction, regrouping means borrowing value from a higher place value. Today, this means borrowing value from the tens place and giving it to the ones place.
• Encourage a student to explain regrouping in their own words.
• Have one partnership come up to the board to model solving one of the subtraction problems on the flashcards. Guide them as they use the Place Value Mat and the base-ten blocks. Provide ample opportunities for them to share their thinking, guiding them to explain the concept of regrouping. Prompting questions include: "I see you don't have enough ones. What will you do next? How do you know how many ones are in one group of ten? One group of ten is the same as ____?"
• Ask students to go back to their seats and give students ten minutes to solve as many subtraction flashcards as they can. Have them record their answers on the answer sheet.
• Discuss answers aloud and ask students how they solved the problems. Use the following sentence frames to support students in sharing out:
• Solving the problems using base-ten blocks was ____ (easy/okay/hard) because ____.
• Using base-ten blocks helped/didn't help me because ____.
• I used a different strategy. The strategy I used was _____.
(8 minutes)
• Keep the students in partnerships and explain that they are going to make their own (co-craft) two-digit subtraction problems. Explain to the students that the goal is to create a subtraction problem that will involve regrouping.
• Share the simple chant, "If there is more on the floor, go next door," to remind them to make sure the number that is being subtracted (on the bottom) has a bigger digit than the total (number on top) in the ones place. Have students help you come up with a visual to "lock-in the learning" and ask them to repeat the chant again, referring to the visual.
• Pass out one set of subtraction problems to each partnership. Tell the students that they will each create their own problem using the subtraction problems in the bag. Tell the students that the numbers in blue will go on the bottom. These numbers have a larger value in the ones place, although they are still smaller values than the red cards. The red cards represent the total amount, so they will go on top. Show the students an example. Next, ask students to create a two-digit subtraction problem with regrouping using the notecards. After they create their problem with cards, they should write it on their whiteboard. Remind them to write a subtraction sign in their problem, too.
• Have students hold up their whiteboards to check for understanding. Encourage a few students to share out, explaining how they knew that the subtraction problem they created would involve regrouping. Ask students to refer to the chant and visual on the board for support.
• Explain to students that after they create their own subtraction problem, they will solve it using the strategy of base-ten blocks. When they are finished, they will exchange problems and discuss how the strategy of the base-ten blocks worked for them. Encourage them to also share any strategies they used that didn't involve the base-ten blocks. Tell the students that if they get different answers, they should try to rework the problem again using the base-ten blocks.
• Write the following sentence frames on the board to help students with in-depth discussions:
• My partner and I used ____ (the same/different) strategies to solve the problems.
• My partner and I got ____ (the same/different) answers.
• After solving the problem again, I learned ____.
• Have one partnership share their ideas with the class.

Beginning

• Review the concept of subtraction using manipulatives and real-world representations.
• Have students draw a visual representation of the vocabulary words discussed during the lesson. Have them record this in their math journal.
• Allow students to share out one answer during the assessment.
• Provide students with manipulatives to use when explaining regrouping during the assessment.

• Encourage students to verbally share their understanding of regrouping with the rest of the class.
• Have students compare/contrast their strategy with their partner's strategy during group work.
• Rotate around the room as students are solving the problems during group work. Record the names of students who demonstrate understanding of the learning objective and language objective. Observe students who are struggling, and write down what part of the process they are struggling with (e.g. the procedure of regrouping itself, need another lesson on using base-ten blocks, need more support in collaborating, understanding of directions).
• Use observations as a formative assessment to help you plan and design future lessons on two-digit subtraction with regrouping to best meet students' needs.
(3 minutes)
• Write the following sentence frames on the board:
• Regrouping means ____.
• Using base-ten blocks made regrouping ____ (easier/harder).
• Have students do a think-pair-share, answering both questions.
• Refer to the Subtraction Strategies anchor chart and explain that using base-ten blocks is just one way they can solve subtraction problems, including subtraction with regrouping!