few_shots: 
Example 1:
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.

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


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:
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).

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


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

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, 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_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
- 10 can be thought of as a bundle of ten ones — called a “ten.”
problem_activity: Narrative
The purpose of this activity is for students to add and subtract multiples of 10 and 100 within 1,000. Students interpret situations with base-ten blocks and base-ten diagrams and use equations to represents sums and differences. In the activity synthesis, students relate the situation, base-ten diagram, and equation and notice, through repeated reasoning, that when adding and subtracting, one can add or subtract hundreds and hundreds and tens and tens (MP7, MP8).
MLR7 Compare and Connect.
Synthesis: Lead a discussion comparing, contrasting, and connecting their different ways of representing the value of Mai and Lin’s blocks together. Ask, “How do these different representations show the same information?” “How are they different?”
Advances: Representing, Conversing
Representation: Access for Perception.
Invite students to act out the scenario of giving and taking hundreds on a number line. Discuss the individual jumps of 100 if a jump of 400 is too much to begin.
Supports accessibility for: Conceptual Processing, Language, Organization
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“These students were using base-ten blocks to find the value of sums and differences.”
“For each problem, represent the student’s value in a way that makes sense to you. You can use base-ten blocks, diagrams, or equations.”
10 minutes: partner work time
For Priya and Jada’s blocks, monitor for students who:
write equations to show the sums and differences.
use base-ten diagrams to show subtraction.
Student Facing
Mai has 2 hundreds, 2 tens, and 3 ones. Lin has 4 hundreds.
Represent their values with base-ten blocks or diagrams.
What is the value of their blocks altogether? Show your thinking.
Andre has 4 hundreds, 2 tens, and 8 ones.
Represent his value with base-ten blocks or diagrams.
Andre gives 2 hundreds to Clare.
What is the value of his blocks now? Show your thinking.
Diego has 6 tens. Tyler has 8 hundreds, 3 tens, and 6 ones.
What is the value of their blocks together? Show your thinking.
Elena has 5 hundreds, 7 tens, and 2 ones. She gives 2 tens to Kiran.
What is the value of her blocks now? Show your thinking.
Priya has 6 hundreds, 5 tens, and 8 ones. Han gives her 3 hundreds.
What is the value of her blocks now? Show your thinking.
Jada has 4 hundreds, 8 tens, and 2 ones. She gives 3 hundreds to Noah.
What is the value of her blocks now? Show your thinking.
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
If students draw diagrams that do not match the situation or write equations that are not true, consider asking:
“Can you explain what you did?”
“Do you notice any patterns when you add or subtract hundreds and hundreds? Tens and tens?”
Activity Synthesis
Invite a student to share their representation and equation for Jada’s blocks. If no students use a base-ten diagram, select a student to share how they use base-ten blocks, and use a base-ten diagram to record their steps.
“How does the base-ten diagram show Jada’s blocks?” (The blocks show how many Jada started with. The lines show the 3 hundreds that were taken away.)
Display
\(482 - 300 = 182\)
“How does the equation show Jada’s blocks?” (482 is what Jada started with and 300 is the 3 hundreds she gave away. 182 is how much she has left.)


aligns: no