Lesson 6

The purpose of this Number Talk is to elicit strategies and understandings students have for making a ten when adding a two-digit number to a two-digit number. In the synthesis, the focus is on how knowing number combinations to make ten can support finding the value of each sum. For example: \(28 + 2\) can help students think about \(28 + 12\) as \(28 + 2 + 10\). These understandings help students develop fluency and will be helpful when students need to add 2 three-digit numbers that require composing units when adding by place. As students share their thinking, consider recording on an open number line.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record students’ thinking on an open number line and with equations.
• Keep expressions and work displayed.
• Repeat with each expression.

• “What’s the same about all of the expressions?” (I made a ten to find the value for each of them.)
• “Why are \(28 + 2\) and \(67 + 3\) helpful in finding the value of the other expressions?” (We made ten and then added 1 more ten.)
• “In the next activity, we are going to keep thinking about how knowing sums of 10 can help us.”

The purpose of this activity is for students to add two-digit numbers and three-digit numbers that require composing a ten when adding by place. In this activity, students work in groups of 3 and each find the value of a different set of sums. They may use any method that makes sense to them to add and the number choices in each set encourage them to apply methods they have used when adding within 100, including those based on making a ten, counting on by place, and adding tens to tens and ones to ones. In the synthesis, students share the patterns they notice in the sums and their values. Look for opportunities to highlight the ways students notice that the sum of the ones is 10 in each expression to prepare them for the next activity.

• Groups of 3
• Give students access to base-ten blocks.

• “In your group, each of you will find the value of one set of expressions.”
• Make sure students know which set they will work with.
• “As you work, think about patterns you notice.”
• “If it helps, you may use base-ten blocks.”
• 6 minutes: independent work time
• “Compare with your group members and discuss any patterns you noticed.”
• 4 minutes: partner discussion

If students find a sum other than the sum of the two numbers, consider asking:

• “Can you explain how you found the sum?”
• “How could you use a number line or base-ten blocks to show your thinking?”

• “What patterns did you notice in each set?” (Each time we could make a ten with the ones. The number of hundreds didn't change. The sums went up by 10.)
• Share and record responses.
• “How does knowing \(6 + 4 = 10\) help you think about \(536 + 34\)?” (I can add \(530 + 30 = 560\). Then add 10 because I know \(6 + 4 = 10\).)

The purpose of this activity is for students use what they know about combinations of 10 to identify when a ten will be composed when adding a three-digit number and a two-digit number by place.  Students are given a set of cards with three-digit numbers and two-digit numbers and work with their group to decide which numbers will make a ten with no extra ones when they are added together (a “perfect ten”). After finding all the matches, each group member chooses a pair and finds the value of the sum. In the synthesis, students discuss how they could tell a pair of numbers would make a ten by looking at the digits in the ones place. In upcoming lessons, students will use this understanding to anticipate when they may need to compose units when they add 2 three-digit numbers.

When they match numbers whose ones combine to make ten students look for and identify structure which can be helpful when finding sums (MP7).

• Create a set of cards from the blackline master for each group of 3.

• Groups of 3–4
• Give each group a set of cards and access to base-ten blocks.

• “This set of cards includes three-digit numbers and two-digit numbers. Match each three-digit number to a two-digit number, so that when you add them together they will make a ten with no extra ones. When this happens, we are going to say the two numbers make a ‘perfect ten.’”
• “Work with your partner to justify your choices.”
• As needed, provide an example of two numbers that make a “perfect ten” from the previous activities.
• “After finding all the matches, each group member should choose a different pair of numbers and find their sum.”
• “If there is time, switch cards or pick another pair.”
• 15 minutes: small-group work time
• Monitor for groups who focus on finding combinations of 10 in the ones place and explain their reasoning.
• Monitor for students to share how they add their pair of numbers to share in the lesson synthesis.

• Invite groups to share the matches they made and how they know those cards go together.
• Attend to the language that students use to describe their matches, giving them opportunities to describe how they knew adding the numbers would result in composing a ten with no extra ones more precisely.