few_shots: 
Example:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0
standard_description: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this warm-up is to draw students’ attention to the first few multiples of 45, which will be helpful as students continue to work with benchmark angles and use a protractor to measure angles. Students have the skills to perform the multiplication in each equation, but computing each product may be time-consuming. Students can more efficiently tell if the equations are true or false if they consider properties of operations and look for and make use of structure.
Launch
Display one equation.
“Give me a signal when you know whether the equation is true and can explain how you know.”
1 minute: quiet think time
Activity
Share and record answers and strategy.
Repeat with each statement.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
\(2 \times 45 = 6 \times 15\)
\(4 \times 45 = 2 \times 90\)
\(3 \times 45 = 180 - 90\)
\(6 \times 45 = 45 + 90 + 135\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Some students may notice that it is handy to think in terms of
\(2 \times 45\)
because it would mean dealing with multiples of 90 rather than multiples of 45. Highlight their explanations.
If no students decomposed expressions such as
\(3 \times 45\)
,
\(4 \times 45\)
, and
\(6 \times 45\)
into sums of
\(1 \times 45\)
and
\(2 \times 45\)
, discuss how this could be done. (See sample responses.)


aligns: yes