This Warm-up prompts students to carefully analyze and compare four images of two-color counters in 10-frames. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about a group of objects, including the connections they make between the total amount and the two parts. The Synthesis also invites students to reason about the commutative property.
Launch
Groups of 2
Display image.
“Pick 3 that go together. Be ready to share why they go together.”
"Which 10-frames match ? Which do not? Explain.” (A does because I see 5 counters on top and 3 on the bottom. B does because there’s 5 on top and 3 on the bottom. B does because there are 5 yellow and 3 red. C does not because there are not 8. D does because there are 5 red and 3 yellow.)
“Which 10-frames match ? Which do not? Explain.” (C does not because there are not 8. The rest do because they match . D has 3 yellow first and then 5 red, so I think it matches better than .)
Activity 1
Standards Alignment
Building On
Addressing
Building Toward
1.OA.B.3
Apply properties of operations as strategies to add and subtract.Students need not use formal terms for these properties.Examples: If is known, then is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so . (Associative property of addition.)
The purpose of this activity is for students to revisit Stage 3 of the Shake and Spill center, which was introduced in IM Kindergarten. In this stage, students see a quantity broken into two parts in different ways. Students write expressions to represent each decomposition. This activity helps build common experiences for making sense of Put Together/Take Apart, Addend Unknown problems in the next lesson and serves to continue student conversations about the commutative property and other relationships between addends in expressions that have the same value.
During this activity, the teacher collects and displays different expressions that students write for the first round. When displaying student expressions, consider doing so in a way that encourages them to notice the commutative property (for example, recording and next to each other). Although students may write equations, all students are not expected to do so. Students will have opportunities to practice writing equations to represent Shake and Spill and Put Together/Take Apart, Both Addends Unknown problems in Section D.
Launch
Groups of 2
Give each group a cup, 10 two-color counters, 2 recording sheets, and access to red and yellow crayons.
"Today we will revisit a game you played in Kindergarten called Shake and Spill. Let's play one round together."
Display two-color counters and the cup.
“I have some two-color counters. Let’s count them together.”
Place 6 counters in the cup as you count aloud.
“Now we know how many counters we have. Let's shake them up."
Demonstrate shaking and spilling the counters.
"How many red counters are there? How many yellow counters are there?”
30 seconds: quiet think time
Demonstrate drawing a quick picture on the recording sheet to match the counters.
“What expressions can we write to match the counters?” ( or )
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
If needed, play another round.
Activity Synthesis
Display collected combinations and expressions.
“What do you notice about the expressions I collected during the first round?” (There are different numbers in the expressions. They all equal 9. Some of the numbers are the same, but in different orders. Sometimes the numbers are the same, but they were for different colors.)
Display the equation .
“What does the equation mean?” (The 9 counter total is the same amount as 7 red counters and 2 yellow counters or 7 yellow and 2 red.)
Display the equation .
“What does this equation mean?” (The 9 counter total is the same as 2 red counters and 7 yellow counters or 2 yellow counters and 7 red counters.)
“What is the same about these equations? What is different?” (They have the same total. Everything is the same except the order of the 7 and the 2.)
Activity 2
Standards Alignment
Building On
Addressing
1.OA.A.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 1.
Apply properties of operations as strategies to add and subtract.Students need not use formal terms for these properties.Examples: If is known, then is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so . (Associative property of addition.)
The purpose of this activity is for students to solve Put Together/Take Apart, Both Addends Unknown story problems in the context of the Shake and Spill center. Students generate different combinations of red and yellow counters and compare different expressions that represent these combinations.
Look for the different ways students generate different combinations, including the way they use their emerging understanding of the commutative property or known facts. For example, students may notice that if they know 9 and 1 is a possible combination, they also know 1 and 9 is a possible combination. When students share this thinking, invite them to use the counters to make their reasoning visible to all students.
MLR8 Discussion Supports. Display the following sentence frames to support partner discussion: “I wrote the expression _____ because . . .” and “My picture shows . . .” Advances:Speaking, Conversing
Engagement: Provide Access by Recruiting Interest. Provide choice and autonomy. In addition to two-color counters and connecting cubes, provide access to 10-frames, and red and yellow crayons or colored pencils students can use to represent and solve the story problems. Supports accessibility for: Conceptual Processing, Organization
Launch
Groups of 2
Give students access to 10-frames, two-color counters, and access to red and yellow crayons.
“Let’s solve some story problems about the game we just played.”
Display and read the story about Elena’s counters.
30 seconds: quiet think time
“Tell your partner what this story is about.”
1 minute: partner discussion
Monitor for students who accurately retell the story. Choose at least one student to share with the class.
“We could think of this story as 7 is some red counters and some yellow counters.”
Activity
“Show some ways to make 7 using counters, drawings, numbers, or words.”
“Show as many ways as you can.”
2–3 minutes: independent work time
“Share your thinking with your partner.”
1–2 minutes: partner work time
Invite 3–4 students to share their combinations. As needed, record each combination as an expression.
“Do you think we have found all the way to show 7 as some red and some yellow counters? Why or why not?”
Display and read the story about Tyler’s counters.
“First, write 2 expressions that represent Tyler’s counters. Then show other combinations of red and yellow counters Tyler could spill if he uses the same amount of counters again.”
If needed, explain that a combination is something created by joining or mixing two or more things. In this game, each combination is a number of red counters joined with a number of yellow counters.
3–4 minutes: independent work time
2–3 minutes: partner work time
Monitor for students who:
Use counters to represent the problem and change the color of 1 counter at a time.
Use what they have noticed about the commutative property to generate combinations.
Use what they know about combinations of 10 to generate combinations.
Elena plays Shake and Spill.
She has 7 counters.
What are some ways to show some red and some yellow?
Show your thinking using drawings, numbers, or words.
Tyler plays Shake and Spill.
He spills these counters:
Write 2 expressions to show his counters.
Show other combinations of red and yellow counters that Tyler could spill.
Show your thinking using drawings, numbers, or words.
If you have time, solve the following problems:
What are all the combinations Elena could have?
How do you know?
What are all the combinations Tyler could have?
How do you know?
Activity Synthesis
Invite 1–2 students to share the expressions that represent the image of Tyler’s counters.
Invite 2–3 previously selected students to share some of their combinations and how they generated them.
“What are other combinations of red and yellow counters Tyler might spill?”
Annotate student responses with expressions.
“How are these expressions the same? How are they different?”
Lesson Synthesis
Demonstrate putting 10 counters in a cup.
“When Tyler played Shake and Spill, he used 10 counters. We could think of his game as 10 is something and something:”
Display:
10 is something and something.
“What do the boxes represent?” (The numbers that could make 10. The addends that could make 10.)
As needed, restate as “The boxes represent 2 unknown addends. Both addends are unknown.”
“What are the different combinations of numbers we could put in the boxes?”
Annotate student combinations as equations by writing and writing the numbers students share in the boxes.
Highlight the ways students switch the order of the addends (commutative property) and use known facts.
Standards Alignment
Building On
Addressing
1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., ); decomposing a number leading to a ten (e.g., ); using the relationship between addition and subtraction (e.g., knowing that , one knows ); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent ).
Apply properties of operations as strategies to add and subtract.Students need not use formal terms for these properties.Examples: If is known, then is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so . (Associative property of addition.)
“Play the game with your partner. For the first three rounds, use 9 counters. For the rest of the rounds, you may choose the number of counters.”
10 minutes: partner work time
Consider asking:
“Is there another expression you can write to show this round?”
“What is a way you could count to show me that __ and __ is 9?”
Monitor for and collect 5–6 combinations (number of yellow and number of red) and expressions from the first round.
None
Student Response
None
Advancing Student Thinking
If students discuss expression without connecting them to the total number of counters or only count all to confirm their expression shows the same amount as the total, consider asking:
“How do you know your expression matches 9 counters?”
“Can you show me a way to count without counting each counter 1 by 1?”