# Making Tens: Adding and Subtracting Within 100 A hands-on lesson where second graders build two-digit sums and differences using tens and ones. ![Figure 1: A bright classroom table covered in colorful base-ten blocks, tens rods and ones cubes stacked into small towers, with two children's hands](https://goa-cc-uat-aili-app-001.azurewebsites.net/api/generate/a19ce71e-1054-4a7c-aff3-dfefa4f47e34/asset/1655) ## Learning intentions We are learning to add and subtract two-digit numbers within 100. We are learning to use a strategy, like making a ten, to solve addition and subtraction problems. ## Success criteria I can group ones into a ten to help me add two-digit numbers. I can subtract two-digit numbers using a strategy I choose. I can check my sum or difference using the opposite operation. ## Curriculum alignment - Students investigate addition and subtraction within 100 ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844)). - The order in which more than two numbers are added does not affect the sum([Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29846)). - Guiding question: How can addition and subtraction be interpreted? ([Guiding question](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29843)). - Organizing idea: Number, quantity is measured with numbers that enable counting, labelling, comparing, and operating ([Topic](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29820)). ## Materials - Base ten blocks (tens rods and ones cubes), enough for pairs - Small whiteboards and markers, one per student - A large hundred chart posted at the front - Number lines from 0 to 100, one per student - Exit ticket slips (two problems per slip) ## Lesson sequence ### 1. Hook (5 minutes) Hold up two tens rods and four ones cubes. Ask: "How many blocks am I holding?" Let students call out. Write 24 on the board. Add three more ones cubes. Ask: "Now how many do I have? How do you know?" Say: "Today we are adding and subtracting numbers up to 100. We will use tens and ones to help us." ### 2. Direct instruction (10 minutes) Write 34 + 28 on the board. Say: "Watch how I make a ten to solve this." Model with blocks: "I have 3 tens and 4 ones. I have 2 tens and 8 ones. First, I add my tens: 3 tens plus 2 tens is 5 tens, that's 50." "Now I add my ones: 4 plus 8. I know 4 plus 6 makes a ten, so I split the 8 into 6 and 2. 4 plus 6 is 10. I have 2 ones left over." "50 plus 10 is 60. 60 plus 2 more ones is 62." Write: 34 + 28 = 62. Now model subtraction. Write 56 − 19 on the board. Say: "I can think of a number I know that's close to 19. 20 is close to 19." "56 minus 20 is 36. But I subtracted one too many, so I add 1 back: 36 plus 1 is 37." Write: 56 − 19 = 37. Ask: "Why do addition and subtraction go together?" Guide students to notice that 37 + 19 = 56, so subtraction can be checked with addition ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844)). ### 3. Guided practice (10 minutes) Pair students with base ten blocks and whiteboards. Write on the board: 47 + 26. Say: "Talk with your partner. Build 47 with blocks. Build 26 with blocks. Combine your tens first." Walk the room. Ask pairs: "How many tens do you have now? How many ones?" Write the answer together: 47 + 26 = 73. Next problem: 82 − 35. Say: "This time, build 82. Take away 3 tens first. How many tens are left?" Prompt: "Now you need to take away 5 more ones, but you only have 2 ones. What can you do?" Guide students to trade a tens rod for 10 ones. Confirm together: 82 − 35 = 47. **Checkpoint:** Ask each pair to show their blocks for 82 − 35. Look for correct trading of a tens rod for ones. Reteach the trade on the spot if a pair is stuck. ### 4. Independent practice (10 minutes) Give each student a whiteboard and a number line. Write four problems on the board: - 39 + 17 - 64 − 28 - 55 + 26 - 91 − 43 Say: "Choose your own strategy. You can use blocks, the number line, or make a ten in your head. Show your thinking." Circulate and ask individuals: "How did you solve this one? Can you check it with the opposite operation?" ### 5. Consolidation (5 minutes) Bring the class back together. Ask: "Who used making a ten? Who used a number line?" Invite one student to share their strategy for 55 + 26 on the board. Ask the class: "How can we check that 55 + 26 = 81 is correct?" Guide them to try 81 − 26 = 55 ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844)). Close with: "Tomorrow we will keep using these strategies with even trickier numbers." ## Differentiation **Extension:** Give students three addends to combine, such as 24 + 18 + 12, and ask which two numbers they add first and why. This connects to the understanding that a sum can be composed in multiple ways ([Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29846)). Students who finish early can also try estimating before solving, a strategy used with larger numbers in later grades ([Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29925)). **Support:** For students still building fluency, reduce the numbers to within 20 first, using counting on and counting back strategies from Grade 1 ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29757), [Details](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29759)). Provide a filled-in hundred chart and let students count tens by rows before tackling two-digit trades. ## Assessment **Formative check:** Collect the exit ticket with two problems: 46 + 37 and 73 − 25. Look for: - Correct use of tens and ones (are tens combined before ones, or traded correctly during subtraction). - A written or verbal strategy, not just a final answer. - Whether the student attempts to check their answer with the inverse operation ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844)). Students who make trading errors in subtraction need another guided session with blocks before moving to the standard algorithm. --- *AILI rapid lesson · language en · model claude-sonnet-5 · generated 2026-09-17 · id a19ce71e-1054-4a7c-aff3-dfefa4f47e34* ### Sources - node:n1: Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29733) - node:n2: How can addition and subtraction provide perspectives of number? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29756) - node:n3: Students examine addition and subtraction within 20. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29757) - node:n4: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29759) - node:n5: Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29820) - node:n6: How can addition and subtraction be interpreted? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29843) - node:n7: Students investigate addition and subtraction within 100. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29844) - node:n8: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29846) - node:n9: Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29915) - node:n10: How can processes be established for addition and subtraction? (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29922) - node:n11: Students apply strategies for addition and subtraction within 1000. (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29923) - node:n12: Details (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/29925)