Lesson 2
Relate Counting to Addition
Warmup: Number Talk: 2 or 3 More (10 minutes)
Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for adding 2 or 3 more. These understandings help students develop fluency and will be helpful later in this lesson when students count on to add.
In this activity, students have an opportunity to notice and make use of structure (MP7). They may see patterns in the structure of the expressions by noticing that when an addend changes by one the sum changes by one.
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
Find the value of each expression mentally.
 \(4 + 2\)
 \(5 + 2\)
 \(5 + 3\)
 \(6 + 4\)
Student Response
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Activity Synthesis
 “Did anyone approach the problem in a different way?”
Activity 1: More Shake and Spill (15 minutes)
Narrative
The purpose of this activity is for students to solve Put Together, Total Unknown story problems through a context they are familiar with—the game Shake and Spill. To launch the lesson, the teacher plays a round of the game with students and reminds students to draw a box around the number in the equation that answers the question.
As students find sums, they relate addition to counting on and may apply what they know about the commutative property. Some of the story problems have the smaller addend first to encourage students to consider this property (MP7). Students should make sure that the answer to each question is clear in their representations.
In the activity synthesis, use physical counters as well as students’ representations to compare the two counting on methods.
Advances: Reading, Representing
Required Materials
Materials to Gather
Required Preparation
 Each group of 2 needs 10 twocolor counters.
 Have one cup available to demonstrate Shake and Spill.
Launch
 Groups of 2
 Give students access to 10frames and twocolor counters.
 “Let’s play a round of Shake and Spill together.”
 Demonstrate Shake and Spill.
 “What equation can I write to represent the total number of counters?”
 30 seconds: quiet think time
 Record responses.
 “What number in the equation represents the total number of counters?”
 Draw a box around the total in the equation.
Activity
 Read each problem.
 6 minutes: independent work time
 “Share your thinking with your partner.”
 4 minutes: partner discussion
 Monitor for students who find the sum of 2 and 8 by:
 counting all
 starting at 2 and count on 8
 starting at 8 and count on 2
Student Facing

Priya is playing Shake and Spill.
She spills 7 red counters and 2 yellow counters.
How many counters did she spill in all?
Show your thinking using drawings, numbers, or words.Equation: ________________________________

Tyler spills 5 red counters and 3 yellow counters.
How many counters did he spill in all?
Show your thinking using drawings, numbers, or words.Equation: ________________________________

Clare spills 2 red counters and 8 yellow counters.
How many counters did she spill in all?
Show your thinking using drawings, numbers, or words.Equation: ________________________________

Han spills 3 red counters and 6 yellow counters.
How many counters did he spill in all?
Show your thinking using drawings, numbers, or words.Equation: ________________________________
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Invite previously identified students to share in the sequence above.
 “How are these methods the same? How are they different?” (They are the same because they all add 3 and 6 and get 9. They all counted to get the answer. They are different because they counted different amounts. The first one counted all of the counters. The second counted 6 counters and the third counted 3 counters.)
Activity 2: Are They Both Right? (10 minutes)
Narrative
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to twocolor counters.
Activity
 Read the task statement.
 2 minutes: quiet think time
 3 minutes: partner discussion
Student Facing
Kiran and Clare are finding the value of \(2+ 7\).
Kiran counted on from 2.
\(2 + 7 = \boxed{9}\)
Clare counted on from 7.
\(7 + 2 = \boxed{9}\)
How can both methods be correct?
Show your thinking using drawings, numbers, or words.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
If students show that both equations are true without mentioning the 'add in any order' property, consider asking:
 “How do you know that both methods are correct?”
 “How can we use the same nine counters to move from the first method to the second?”
Activity Synthesis
 Invite 2–3 groups to share their thinking.
 “Kiran and Clare started with different numbers, but they both got the same value. As long as we add the same two numbers, we can add them in either order. This is called the add in any order property.”
 “Which method do you like best? Why?” (I like adding up from the larger number since it is faster than adding up from the smaller number.)
Activity 3: Practice Addition within 10 (10 minutes)
Narrative
The purpose of this activity is for students to find the value of sums within 10. Students may apply what they learned about the commutative property and counting on. They may count on for certain equations, such as \(+1\) or \(+2\) equations as they can keep track easily, but count all for others. In the lesson synthesis, students return to the addition expressions cards they created in a previous lesson.
Supports accessibility for: Organization, Attention
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to 10frames and connecting cubes or twocolor counters.
Activity
 Read the task statement.
 5 minutes: independent work time
 3 minutes: partner discussion
Student Facing
Find the value of each sum.
 \(7 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(3 + 5 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(\boxed{\phantom{\frac{aaai}{aaai}}} = 8 + 2\)
 \(3 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(5 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(\boxed{\phantom{\frac{aaai}{aaai}}} = 4 + 4\)
 \(2 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
 \(\boxed{\phantom{\frac{aaai}{aaai}}} = 1 + 9\)
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Display answers to problems.
Lesson Synthesis
Lesson Synthesis
“Today we saw different ways we can add numbers. Mai is practicing her sums to 10. She has \(7 + 2\) in her ‘got it’ pile and \(2 + 7\) in her ‘not yet’ pile. What would you tell Mai?” (If you know \(7 + 2\), you also know \(2 + 7\).) You can change the order of the numbers and get the same value.
Give students access to their addition cards sorted into ‘got it’ and ‘not yet.’ “Look through your ‘not yet’ cards. If you just know the sum, move it to your ‘got it’ pile. If you still need practice with a sum, keep it in your ‘not yet’ pile.”
Cooldown: How Does it Help? (5 minutes)
CoolDown
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