Lesson 10
Addition and Subtraction with a Ten
Warmup: Number Talk: A Ten and Some Ones (10 minutes)
Narrative
Launch
 Display one expression.
 “Give me a signal when you have an answer and can explain how you got it.”
 1 minute: quiet think time
Activity
 Record answers and strategy.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
 \(10 + 4\)
 \(14  4\)
 \(5 + 10\)
 \(15  5\)
Student Response
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Activity Synthesis
 “How can you use problem one to help you find the difference in problem two?” (If \(10 + 4 = 14\), then I know that \(14  4 = 10\).)
 “Did anyone approach the problem in a different way?”
Activity 1: Story Problems With a Ten (20 minutes)
Narrative
The purpose of this activity is to elicit methods students have for solving story problems involving addition and subtraction with teen numbers. Students are presented with story problem types that are familiar to them to allow for discussion about methods they used to find the answer. Students solve the problems in any way that makes sense to them. They may build values and addon or takeaway, or use what they have learned about the \(10 + n\) structure of teen numbers. Students write equations; they can write many different equations to represent the problem or how they solved it. It is important that students are able to relate their equations to the story problem and explain their work (MP2, MP4).
Advances: Reading, Representing
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to double 10frames and connecting cubes or twocolor counters.
 “Many people have the hobby of collecting things. Do any of you collect something?”
 Share responses.
 “What are some things that you know people collect, or that you might like to collect?” (baseball cards, marbles, rocks)
 30 seconds: quiet think time
 1 minute: partner discussion
 Share responses.
 “Let’s solve some story problems about collections.”
Activity
 Read the task statement.
 “Write two equations to match each of these stories.”
 6 minutes: independent work time
 4 minutes: partner discussion
 Monitor for a student who wrote an addition equation and one who wrote a subtraction equation for the problem about Priya.
Student Facing
 Kiran has a collection of 5 baseball caps.
He gets some more baseball caps for his birthday.
Now he has 15 baseball caps all together.
How many baseball caps did he get?
Show your thinking using drawings, numbers, or words.Equation: ________________________________
Equation: ________________________________

Priya has a comic book collection.
She gets 3 new comic books.
Now she has 13 comic books.
How many comic books did she have to start?
Show your thinking using drawings, numbers, or words.Equation: ________________________________
Equation: ________________________________
Student Response
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Activity Synthesis
 Invite previously identified students to share their equations for Priya’s problem.
 If no student writes a subtraction equation, display \(13  3 =\boxed{\phantom{10}}\).
 “How do the equations match the story problem? How are they related to each other?” (They show that the total number of comic books is 13 and that 3 is one part and 10 is the other part. They all show that 10 is the missing number. The subtraction equations takes 3 away from the 13 to find the other part. The addition equation adds 3 to some number to get 13.)
 “Which equation makes more sense to you? Why?” (Addition, because I know that to get from 3 to 13, I have to add 10. Subtraction, because I know what number to start with and how many to take away. I don't know what numbers to use in the addition equation.)
Activity 2: Related Equations (15 minutes)
Narrative
The purpose of this activity is for students to discuss the relationship between addition and subtraction equations involving teen numbers. Students find the value that makes the addition and subtraction equations true with the unknown in all positions. Students may choose to use objects to represent the problems and find the value that makes the equation true (MP5).
Supports accessibility for: Organization, Attention
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to double 10frames and connecting cubes or twocolor counters.
 Read the problem about Mai.
 30 seconds: quiet think time
 1 minute: partner discussion
 Share responses.
Activity
 Read the task statement.
 4 minutes: independent work time
 4 minutes: partner discussion
Student Facing
Mai is finding the missing number in \(16  10 = \boxed{\phantom{\frac{aaai}{aaai}}}\).
She says, “I can use what I know about 10 and some ones to help.”
What does Mai mean?
Find the number that makes each equation true.
Show your thinking using drawings, numbers, or words.
 \(15  10 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(\boxed{\phantom{\frac{aaai}{aaai}}} = 13  3\)
 \(8 = 18 \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(2 + \boxed{\phantom{\frac{aaai}{aaai}}} = 12\)
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
If students take away using drawings for each equation, consider asking:
 “How did you find the missing value?”
 “How could the double 10frame help you find the missing value?”
Activity Synthesis
 Share solutions for each problem.
 “How are \(\boxed{\phantom3} = 13  3\) and \(2 + \boxed{\phantom 3} = 12\) related?” (One is an addition problem and one is a subtraction problem, but you can use addition or subtraction for either one. For \(\boxed{\phantom 3} = 13  3\) you can subtract or change it to \(3+ \boxed{\phantom3} = 13\). For \(2 + \boxed{\phantom3} = 12\) you can add or change it to \(12  2=\boxed{\phantom3} \). Both have a missing value of 10.)
Lesson Synthesis
Lesson Synthesis
Display 17 on a double 10frame.
Display \(\boxed{\phantom{17}}  10 = 7\). “Today we solved problems and completed equations with 10 and some more. We saw that sometimes we can use addition to help us with subtraction. How can using addition help you find the number that makes this equation true?” (I know that \(7 + 10 = 17\) so the missing number is 17.)
Display \(10 + \boxed{\phantom{3}} = 17\). “How can using subtraction help you find the number that makes this equation true?” (I see on the 10frame that there’s 10 and 7 more. If I take away the 10, there’s 7 left.)
Cooldown: What's Missing? (5 minutes)
CoolDown
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