few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
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.

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

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
problem_activity: Warm-up
This warm-up prompts students to compare four lines. It invites students to explain their reasoning and hold mathematical conversations, and allows you to hear how they use terminology and talk about lines and their properties. To allow all students to access the activity, each figure has one obvious reason it does not belong. Encourage students to move past the obvious reasons (e.g., line
\(t\)
has a different color) and find reasons based on geometric properties (e.g., a slope triangle of line
\(u\)
is not similar to the slope triangles of the other three lines).
So far, we have only considered lines with positive slopes. The purpose of this warm-up is to suggest similarities (same vertical and horizontal lengths of slope triangles) and differences (since they are not parallel, there is something fundamentally different going on here) between lines whose slopes have the same absolute value but opposite signs.
As students share their responses, listen for important ideas and terminology that will be helpful in the work of this lesson. Students may:
Identify lines that have the same slope.
Identify points where lines intersect.
Distinguish between lines with positive and negative values for slope and be able to articulate the difference clearly.
Launch
Arrange students in groups of 2–4 and provide access to geometry toolkits. Display the image of the four lines for all to see. Ask students to indicate when they have noticed one line that does not belong and can explain why. Give students 2 minutes of quiet think time and then time to share their thinking with their group. After everyone has conferred in groups, ask each group to offer at least one reason a particular line doesn’t belong.
Student Facing
Which line doesn’t belong?
[IMG]
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
After students have conferred in groups, invite each group to share one reason why a particular line might not belong. Record and display the responses for all to see. After each response, ask the rest of the class if they agree or disagree. Since there is no single correct answer to the question asking which shape does not belong, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, prompt students to use mathematical terminology (parallel, intersect, slope) correctly. Also, press students on unsubstantiated claims. For example, a student may claim that
\(u\)
does not belong because it has a different slope. Ask how they know for sure that its slope is different from the other lines. Demonstrate drawing a slope triangle and computing slope.
Based on the work done up to this point in the unit, students are likely to assume that the slope of
\(v\)
is
\(\frac13\)
. In the discussion, solicit the idea that there is something fundamentally different about line
\(v\)
compared to the others. You could use informal language like “uphill” and “downhill,” or “tilt direction.” The expressions positive and negative slope do not need to be introduced at this time.


aligns: yes