standard_description: Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
problem_activity: Narrative
In this activity, students approach 10,000 by counting up in different ways. Each count ends by reaching 10,000. Students count by different amounts and describe patterns and relationships between numbers. The activity is designed to highlight familiar counting patterns as a way to support naming and writing multi-digit numbers. The final questions in the task ask students to consider the magnitude of each number in relation to 10,000.
When students count by large numbers and examine the counted numbers, they observe patterns in how the different digits in the numbers change (MP7).
Representation: Access for Perception.
Provide access to a variety of tools that students may use to approach the task. These might include: a class set of base-ten blocks, colored pencils to color-code place values or highlight the digit that changes, and a visual display reminding students of sketches they can make to represent numbers with thousands and ten-thousands.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Attention
Launch
Groups of 2
“Read the directions for problem 1 and share your understanding of the directions with a partner.”
“What questions do you have before we begin?”
Activity
5 minutes: independent work time
10 minutes: partner work time
As students work,
listen for how students say the numbers and support them in using place value understanding to say the numbers correctly.
look for use of extra digits when writing numbers (for example, students write 90,500 instead of 9,500) and support students with making the revisions by having them say the numbers.
Student Facing
Record each count in the given spaces. The first number has been recorded for you.
Count by 1,000
5,000 , _____________, _____________, _____________, _____________, _____________
Count by 100
9,500 , _____________, _____________, _____________, _____________, _____________
Count by 10
9,950 , _____________, _____________, _____________, _____________, _____________
Count by 1
9,995, _____________, _____________, _____________, _____________, _____________
Complete each statement:
Ten-thousand is 1 more than _____________.
Ten-thousand is 1,000 more than _____________.
Ten-thousand is 10 more than _____________.
Ten-thousand is 100 more than _____________.
Student Response
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Advancing Student Thinking
If students interpret the part a of the last problem to mean “name a number that is 10,000 more than 1,” consider clarifying by asking: “The number 10 is 1 more than what number?” and “The number 100 is 1 more than what number?” Then, restate the sentence in part a: “Ten-thousand is 1 more than what number?”
Activity Synthesis
“How is counting by 100 and 1,000 like counting by 1 and 10?” (When counting by thousands, only the thousands change. This is also the case when counting by ones, tens, and hundreds.)
Have students share their answers for the last problem.
Consider asking: “Who can restate what _____ shared?”
If needed, discuss the placement of the comma in each number.


aligns: no