The purpose of this activity is for students to find the unknown addend in an equation in a way that makes sense to them and to compare their approaches. In the Launch, students are introduced to base-ten blocks and compare them to connecting cubes. Students should be given time to observe the image and touch the connecting cubes and base-ten blocks. Students may find the unknown addend using any approach that makes sense to them.

Monitor and select students with the following approaches to share in the Synthesis:

• Count on to 84 or count back to 41 using connecting cubes or base-ten blocks.
• Combine or separate tens and ones using base-ten blocks.
• Combine or separate tens and ones using a base-ten drawing.

The approaches are sequenced from more concrete to more abstract to help students make sense of and encourage them to use base-ten blocks or drawings in upcoming activities. It also provides opportunities for students to share why they chose a particular tool and how it helped them find the unknown value. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven’t shared recently.

Students have the opportunity in the Activity and the Activity Synthesis to consider the available tools and make a choice that best helps them find the unknown addend (MP5). To support student reflection on the utility of each tool, provide each group with towers of 10 connecting cubes, but not enough to represent the numbers in the equation without needing to create new towers of 10.

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “How are these ways for making the equation true the same? How are they different?” (Some people did the same steps, but they used different tools to show it. Some ways used the same tool, but they are different because one group added tens and ones to find the unknown number, and another group took away tens and ones to find the unknown number.)
• Connect students’ approaches to the learning goal by asking:
  • “What did you notice about the different tools we used?”
  • “What is different about using connecting cubes and using base-ten blocks?”
  • “What is different about using a diagram instead of using blocks?”

The purpose of this activity is for students to find the unknown addend in an equation using addition and subtraction within 100 without composing or decomposing a ten. The Synthesis focuses on which method students prefer and why. Students continue to develop their understanding of the relationship between addition and subtraction as they describe and connect different methods for finding the same unknown number.

• “Which method did you like best? Starting with the total and taking away or starting with the addend you know and adding on?” (I like subtracting because it’s easier for me to see what the unknown number is when I use blocks or drawings. I prefer to add on because the equation shows addition.) 
• “Why did you and your partner find the same number even though one person added and one person subtracted?” (The amount one partner added was the same as what the other partner subtracted. When you subtract, it’s like finding the unknown addend. Addition and subtraction are related.)