Warm-up: Number Talk: Numbers that Make 10 (10 minutes)
- 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.
Find the value of each expression mentally.
- \(28 + 2\)
- \(28 + 12\)
- \(67 + 3\)
- \(67 + 23\)
- “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.”
Activity 1: Add Two-digit and Three-digit Numbers (15 minutes)
Materials to Gather
- 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
Find the value of each sum.
\(245 + 15\)
\(134 + 26\)
\(351 + 19\)
\(247 + 23\)
\(133 + 37\)
\(356 + 24\)
\(249 + 31\)
\(138 + 42\)
\(355 + 35\)
- What patterns did you notice?
Advancing Student Thinking
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 \(6 + 4 = 10\).)
Activity 2: Card Sort: Perfect Ten (20 minutes)
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).
Advances: Conversing, Reading
Supports accessibility for: Conceptual Processing
Materials to Gather
Materials to Copy
- Card Sort Perfect 10
- 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.
- Match each three-digit number to a two-digit number. When you add your numbers together they should make a ten with no extra ones.
Pick 1 pair of numbers and find the value of their sum. Show your thinking.
- 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.
“Today you learned that when you add a two-digit number to a three-digit number, knowing sums of 10 can help you tell if you will need to compose a ten.”
Invite previously identified students to share how they found the value of their sums.
Share and record responses.