standard_description: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
problem_activity: Narrative
The purpose of this activity is for students to revisit stage 3 of the Shake and Spill center, introduced in kindergarten. In this stage, students see a quantity broken into two parts in different ways. Student write equations to represent each decomposition. Students may write an equation in any way they choose, but the number of counters is presented first to encourage students to write the total before the equal sign. This activity builds toward a future lesson in which students solve Put Together/Take Apart, Addend Unknown story problems and write equations to match them.
During this activity, the teacher collects and displays different equations that students write for the first round. This includes equations where the total is before the equal sign, such as
\(9 = 7 + 2\)
. During the synthesis, students are encouraged to think about how an equation with the total before the equal sign relates back to the context of playing the game (MP2).
Required Materials
Materials to Gather
Cups
Two-color counters
Materials to Copy
Shake and Spill Stage 3 Recording Sheet Grade 1
Required Preparation
Each group of 2 needs 10 two-color counters and a cup (at least 8 oz).
Launch
Groups of 2
Give each group a cup, 10 two-color counters, and recording sheets.
"Today we will revisit a game you played in kindergarten called Shake and Spill. Let's play one round together to make sure everyone remembers how to play."
Display two-color counters and the cup.
“I have some two-color counters. Let’s count them together.”
Place counters in the cup as you count aloud.
“I’m going to write 6 under Total Number of Counters."
Demonstrate shaking and spilling the counters.
"How many red counters are there? How many yellow counters are there?”
30 seconds: quiet think time
Record responses in the table.
“What equation can we write to match the counters?” (
\(4 + 2 = 6\)
,
\(6 = 4 + 2\)
,
\(2 + 4 = 6, 6 = 2 + 4\)
)
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
If needed, play another round.
Activity
“Play the game with your partner. For the first game, you will use 9 counters and record in your book. After the first game, you may choose the number of counters that you want to use, and record on the separate recording sheet.”
10 minutes: partner work time
If needed, ask “Is there another equation you can write to show this round?”
Monitor for and collect 5–6 combinations and equations from round 1.
Student Facing
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[IMG]
Round 1:
{"table": [{"_attributes": {"border": "1", "style": "width:\u201d100%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:27%"}, "_value": "total number of counters"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:15%"}, "br": [{}], "_values": ["red", "counters"]}, {"_attributes": {"scope": "col", "style": "text-align:center; width:15%"}, "br": [{}], "_values": ["yellow", "counters"]}, {"_attributes": {"scope": "col", "style": "text-align:center; width:43%"}, "_value": "equations"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "9"}, {}, {}, {}]}, {"td": [{"_value": "9"}, {}, {}, {}]}, {"td": [{"_value": "9"}, {}, {}, {}]}, {"td": [{"_value": "9"}, {}, {}, {}]}, {"td": [{"_value": "9"}, {}, {}, {}]}, {"td": [{"_value": "9"}, {}, {}, {}]}]}]}]}
Student Response
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Activity Synthesis
Display collected combinations and equations.
“What do you notice about the equations I collected during the first round?” (There are different numbers in the equations. They all equal nine. Sometimes the total is before the equation and sometimes it is after.)
“What does the equation
\(9 = 7 + 2\)
mean?” (The nine counter total is the same amount as seven red counters and two yellow counters or seven yellow and two red.)


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