standard_description: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
problem_activity: Narrative
The purpose of this activity is for students to interpret and compare representations that show decomposing a ten to subtract by place. One student shows decomposing a ten by crossing off a ten and drawing 10 ones. The other representation shows a student who begins their drawing with a ten decomposed into 10 ones. Students compare and make connections between the representations and a set of equations that also shows how to find the value of the difference (MP3).
This activity uses
MLR2 Collect and Display
. Advances: conversing, reading, writing
Representation: Internalize Comprehension.
Invite students to identify which details were most useful from each strategy to solve the problem. Display the sentence frame, “The next time I have a subtraction task, I will look for . . . .“ Encourage decomposition, drawing pictures or using manipulatives as the main strategies.
Supports accessibility for: Attention, Memory
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“Diego and Elena drew base-ten diagrams to find the value of
\(82-9\)
.”
“Think about what is the same or different on your own. Then, discuss your ideas with your partner.”
1 minute: quiet think time
2
–
3 minutes: partner discussion
MLR2 Collect and Display
Circulate, listen for, and collect the language students use to describe the diagrams and how the ten is decomposed. Listen for: break apart a ten, decompose, tens, need more ones.
Record students’ words and phrases on a visual display and update it throughout the lesson.
Share responses. Consider asking:
“Did Diego and Elena find the same value for
\(82-9\)
? How do you know?”
“What is the difference between their diagrams?”
“Tyler found the value by using equations. Diego says Tyler’s equations match his diagram. Elena says the equations match her diagram. Who do you agree with?”
2 minutes: independent work time
4 minutes: partner discussion
Monitor for students who agree with Diego, Elena, or both and can explain their reasoning with connections to the diagrams.
Student Facing
Diego and Elena drew base-ten diagrams to find the value of
\(82-9\)
.
Diego
[IMG]
Elena
[IMG]
Compare Deigo’s work to Elena’s.
What is the same?
What is different?
Tyler used equations to show his thinking.
\(82 - 9\)
\(82 = 70 + 12\)
\(12 - 9 = 3\)
\(70 + 3 = 73\)
Diego says Tyler’s work matches his diagram.
Elena says Tyler’s work matches her diagram.
Who do you agree with? Explain.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
Some students may only recognize 82 as 8 tens and 2 ones. Consider asking:
“What was the value of Elena’s blocks before she started subtracting? Explain.”
“How could you make 82 with base-ten blocks if you only had 7 tens?” Allow students to share how they could represent 82 with 7 tens and 12 ones.
Activity Synthesis
Invite previously identified students to share.
“Diego, Elena, and Tyler saw they needed more ones before they could subtract ones from ones. They showed decomposing a ten in different ways.”
Display the list of words and phrases recorded during the activity.
“Here are some of the words we used to describe subtracting by place.”
“Are there any other words or phrases that are important to include on our display?”
As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
Remind students to borrow language from the display as needed.


aligns: no