In this activity, students analyze three different ways to subtract. They see that taking away is one way to find the difference, but that you can also count up or use known addition facts. Students further solidify their understanding that addition and subtraction are related, which sets the groundwork for a later activity when students solve subtraction problems within 10.

• Invite previously identified students to share.
• “Who can restate what _____ just showed us?” (Diego subtracted by taking away 6 counters one at a time and saw that there were 4 counters left. Mai subtracted by thinking about addition. She counted up from 6 until she got to 10 and saw she counted up 4. Noah knows his sums of 10. He knows 10 can be made by 6 and 4, so .)
• “Which method do you like best?” (I know my sums to 10 so, I would use that. I like counting up because I like to add more than take away.)

The purpose of this activity is for students to identify patterns when subtracting (MP7). Students have access to connecting cubes and two-color counters to make sense of the problems and explain their thinking (MP1). As students subtract, they continue to develop relational thinking and notice that:

• As the subtrahend, or the number being subtracted, increases, the difference decreases.
• As the subtrahend decreases, the difference increases.

This vocabulary is not necessary to use with students. During the Activity Synthesis, select students who can explain each of the ideas. When students show their thinking using objects and mathematical language to explain why the concept is true, they construct viable arguments (MP3).

This activity uses MLR8 Discussion Supports. Advances: Listening, Representing

• “Can you explain how you found the value of each difference?”
• “How can you use the drawing you made for , to find the value of ?”

• Invite previously identified students to share.
• As students share, record their thinking with diagrams and equations.
• “Just like addition, there are patterns in subtraction. Understanding patterns can help you find differences.”

The purpose of this activity is for students to find the value of differences within 10. Students are encouraged to think about how patterns in subtraction problems and knowing sums within 10 can help them find the value of the differences. Students may use take away or counting up methods.

The problems are written for students to think about different methods for solving. For example, students may find the value of  by taking away 3 to get 7, then see that they can find by knowing the relationship between 3, 7, and 10. Students should work in groups of 2, with a different partner than they had in the previous activity.

• “Were there any expressions that helped you with another expression? How did they help you?” ( and . They are related because . , , and . There is a pattern. Since the number being subtracted gets 1 bigger, the difference gets 1 smaller.)