few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Concept/skill: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
problem_activity: Problem 1
How many?
[IMG]
Problem 2
Determine the value of the unknown in each equation below.
a.
$$a = 7 \times 8$$
b.
$$42 \div b =7$$
c.
$$49 = 7 \times c$$
d.
$$d\div 7 = 9$$
Problem 3
Here is the partially filled-in multiplication table from Lessons 1 and 6.
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text-align:center"}, "_value": "6"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "7"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "8"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "9"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "10"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "2"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "6"}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "12"}, {"_attributes": {"style": "text-align:center"}, "_value": "14"}, {"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "18"}, {"_attributes": {"style": "text-align:center"}, "_value": "20"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "3"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "6"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "9"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "12"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "15"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "18"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "21"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "24"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "27"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "30"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "12"}, {"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "20"}, {"_attributes": {"style": "text-align:center"}, "_value": "24"}, {"_attributes": {"style": "text-align:center"}, "_value": "28"}, {"_attributes": {"style": "text-align:center"}, "_value": "32"}, {"_attributes": {"style": "text-align:center"}, "_value": "36"}, {"_attributes": {"style": "text-align:center"}, "_value": "40"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "5"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "10"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "15"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "20"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "25"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "30"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "35"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "40"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "45"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "50"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "6"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "12"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "18"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "24"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "30"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "36"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "42"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "48"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "54"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "60"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "7"}, {"_attributes": {"style": "text-align:center"}, "_value": "14"}, {"_attributes": {"style": "text-align:center"}, "_value": "21"}, {"_attributes": {"style": "text-align:center"}, "_value": "28"}, {"_attributes": {"style": "text-align:center"}, "_value": "35"}, {"_attributes": {"style": "text-align:center"}, "_value": "42"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "70"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "24"}, {"_attributes": {"style": "text-align:center"}, "_value": "32"}, {"_attributes": {"style": "text-align:center"}, "_value": "40"}, {"_attributes": {"style": "text-align:center"}, "_value": "48"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "80"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "9"}, {"_attributes": {"style": "text-align:center"}, "_value": "18"}, {"_attributes": {"style": "text-align:center"}, "_value": "27"}, {"_attributes": {"style": "text-align:center"}, "_value": "36"}, {"_attributes": {"style": "text-align:center"}, "_value": "45"}, {"_attributes": {"style": "text-align:center"}, "_value": "54"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "90"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "10"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "20"}, {"_attributes": {"style": "text-align:center"}, "_value": "30"}, {"_attributes": {"style": "text-align:center"}, "_value": "40"}, {"_attributes": {"style": "text-align:center"}, "_value": "50"}, {"_attributes": {"style": "text-align:center"}, "_value": "60"}, {"_attributes": {"style": "text-align:center"}, "_value": "70"}, {"_attributes": {"style": "text-align:center"}, "_value": "80"}, {"_attributes": {"style": "text-align:center"}, "_value": "90"}, {"_attributes": {"style": "text-align:center"}, "_value": "100"}]}]}]}]}
Add the new facts you encountered in this lesson to your multiplication table.


aligns: yes